Standard APCO25 Physical Layer of the Radio Transmission Chain691654/FULLTEXT01.pdf · Standard...

Standard APCO25Physical Layer of the

Radio Transmission Chain

MATHIEU SIMON

Master’s Degree Project

Stockholm, Sweden

XR-EE-KT 2014:001

Master ThesisSupervised by Christophe M.

Examined by Lars Kildehøj Rasmussen

January 25, 2014

The reproduction, distribution and use of this document as well as thecommunication of its contents to others without explicit authorization isprohibited. Offenders will be held liable for the payment of damages. All

rights reserved in the event of the grant of a patent, utility model ordesign.

II

Acknowledgments

Firstly, I would like to thank Philippe M. manager of the DSP SW department at Cassidian,for having proposed this internship, in accordance to my field of studies as well as particularlychallenging and therefore, very interesting.

Special thank to my supervisor at Cassidian, Christophe M. for his insightful guidance, constanthelp and encouragement that helped me conduct this project during those six months. Thankto Laurent M. for his numerous and crystal clear explanations along with his patience. Thanksto my colleagues Mickael M. and Jimmy S. for their professional insights and daily upliftinghumor. Big thanks to all the other members of the DSP Software team, Olivier, Lynda andValentin for having kindly integrated me within their team.

I would also like to thank all the teachers and classmates that helped me understand the differentaspects of digital communications, through courses or fruitful discussions.Special thank to Lars Rasmussen for having accepted to examine my thesis and for his courseat KTH, particularly helpful during my thesis.

Finally, I would like to warmly thank my parents and sister, to whom I dedicate this thesis, fortheir constant support in my studies.

This document and its content are the property of CASSIDIAN and should not be copied orcirculated without prior permission. All use outside the pre-defined scope is forbidden.

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CONTENTS CONTENTS

Contents

1 Abstract XI

2 Sammanfattning XII

3 Company presentation 13.1 Airbus Group - EADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Airbus Defence and Space - Cassidian . . . . . . . . . . . . . . . . . . . . . . . . 13.3 DSP SW team . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

4 Introduction 24.1 Professional Mobile Radio - PMR . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.2 Specificity of PMR networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.3 Project P25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34.4 Thesis objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5 P25 Phase 1 frames format 55.1 Header frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55.2 Voice frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55.3 Link Data Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65.4 Superframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

6 P25 Phase 2 frames format 86.1 Time slot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86.2 Superframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7 Modulation - Demodulation 107.1 Phase 1 modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7.1.1 C4FM modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107.1.2 CQPSK modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7.2 Phase 2 modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187.2.1 DQPSK modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187.2.2 D8PSK modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207.2.3 HCPM modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7.3 Phase 1 demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247.4 Phase 2 demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8 Encoders - Decoders 278.1 Hamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278.2 Shortened cyclic code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288.3 Golay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308.4 Reed-Solomon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318.5 BCH code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348.6 Trellis code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348.7 Simulation acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34


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CONTENTS CONTENTS

9 Synchronization 369.1 Rough temporal synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . 369.2 Fine-tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10 Performances 3810.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3810.2 Modem - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

10.2.1 Static Reference Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 3910.2.2 Faded Reference Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 3910.2.3 Adjacent Channel Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . 4210.2.4 Co-channel Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4210.2.5 Delay spread resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

10.3 Modem - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4410.3.1 Static Reference Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 4410.3.2 Faded Reference Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 4410.3.3 Adjacent Channel Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . 4610.3.4 Co-channel Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710.3.5 Delay spread resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

10.4 Encoders/Decoders tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810.5 Graphical user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

11 Integration on a USRP device 5211.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5211.2 Matlab Spectrum Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5211.3 Intermediate frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5411.4 Detection of synchronization frames . . . . . . . . . . . . . . . . . . . . . . . . . 55

12 Conclusion 57

13 Further studies 57

Appendices 58

A Propagation models 58

B Theta’s pdf derivation 61


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LIST OF FIGURES LIST OF FIGURES

List of Figures

4-1 Working principle of a P25 network . . . . . . . . . . . . . . . . . . . . . . . . . . 34-2 Cassidian mobile terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44-3 Cassidian TETRA base station . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45-1 Diagram of Header Code Word Construction . . . . . . . . . . . . . . . . . . . . 65-2 Diagram of Voice Code Word Construction . . . . . . . . . . . . . . . . . . . . . 75-3 Logical Data Unit 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75-4 Phase 1 superframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76-1 Phase 2 TDMA Slot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86-2 Phase 2 superframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97-1 C4FM modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107-2 C4FM constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117-3 C4FM eye-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117-4 C4FM transmission filter impulse response . . . . . . . . . . . . . . . . . . . . . . 127-5 PSD of C4FM transmitted baseband signal . . . . . . . . . . . . . . . . . . . . . 127-6 Θ1 and Θ2 joint probability density function . . . . . . . . . . . . . . . . . . . . . 157-7 Freq probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . . 167-8 Theoretical BER as a function of Eb

N0. . . . . . . . . . . . . . . . . . . . . . . . . 17

7-9 CQPSK modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177-10 CQPSK constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187-11 CQPSK eye-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187-12 CQPSK transmission filter impulse response . . . . . . . . . . . . . . . . . . . . . 187-13 PSD of CQPSK transmitted baseband signal . . . . . . . . . . . . . . . . . . . . 187-14 DQPSK constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197-15 DQPSK eye-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197-16 DQPSK transmission filter impulse response . . . . . . . . . . . . . . . . . . . . . 207-17 PSD of DQPSK transmitted baseband signal . . . . . . . . . . . . . . . . . . . . 207-18 D8PSK constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217-19 D8PSK eye-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217-20 D8PSK transmission filter impulse response . . . . . . . . . . . . . . . . . . . . . 217-21 PSD of D8PSK transmitted baseband signal . . . . . . . . . . . . . . . . . . . . . 217-22 HCPM constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237-23 HCPM eye-diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237-24 HCPM transmission filter impulse response . . . . . . . . . . . . . . . . . . . . . 237-25 PSD of HCPM transmitted baseband signal . . . . . . . . . . . . . . . . . . . . . 237-26 C4FM and CQPSK demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 247-27 H-CPM non-coherent demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . 257-28 Performances of H-CPM non-coherent demodulation depending on equalizers . . 268-1 Syndrome decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2910-1 Static Reference Sensitivity - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . 3910-2 TU 8 sensitivity - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4010-3 TU 100 sensitivity - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4010-4 HT 100 sensitivity - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4110-5 Adjacent Channel Rejection - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . 4210-6 Co-channel Rejection - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42


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LIST OF FIGURES LIST OF FIGURES

10-7 Delay spread resistance - Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4310-8 Static Reference Sensitivity - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . 4410-9 TU 8 sensitivity - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510-10TU 100 sensitivity - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510-11HT 100 sensitivity - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4610-12Adjacent Channel Rejection - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . 4610-13Co-channel Rejection - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710-14Delay spread resistance - Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710-15Results Visualization GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4911-1 USRP R© E100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5211-2 USRP R© N210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5211-3 Matlab GUI used to get ”real-time” information about the signal . . . . . . . . . 5311-4 Motorola terminal XTS 5000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5311-5 Correction of the frequency shift, observed with a waterfall . . . . . . . . . . . . 5411-6 Constellation obtained without any intermediate frequency . . . . . . . . . . . . 5411-7 Constellation obtained with an intermediate frequency . . . . . . . . . . . . . . . 5411-8 Visualization of the demodulated signal on a spectrum analyzer . . . . . . . . . . 5511-9 Inter-correlation between received signal and reference . . . . . . . . . . . . . . . 5611-10Reconstructed sound signal after transmission over the air . . . . . . . . . . . . . 56A-1 Propagation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58A-2 TU channel impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A-3 HT channel impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60B-1 Problem diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61B-2 Θ probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62


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LIST OF TABLES LIST OF TABLES

List of Tables

1 C4FM mapping table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Theoretical sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 CQPSK mapping table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 D8PSK mapping table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Logarithm table in GF(26) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Exponential table in GF(26) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 States Transitions for Trellis code 1/2 . . . . . . . . . . . . . . . . . . . . . . . . 348 States Transitions for Trellis code 3/4 . . . . . . . . . . . . . . . . . . . . . . . . 359 Simulation time gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3510 Results summary and comparison to standard requirements - Phase 1 . . . . . . 4311 Results summary and comparison to standard requirements - Phase 2 . . . . . . 4812 TU propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5813 HT propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59


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LIST OF TABLES LIST OF TABLES

Acronyms

ALGID Algorithm IDAPCO25 Association of Public Safety Communications Officials’ Project 25AWGN Additive White Gaussian NoiseBER Bit Error RateC4FM Continuous Four Level Frequency ModulationCASA Construcciones Aeronauticas Sociedad AnonimaCPM Continuous Phase ModulationCQPSK Compatible Quadrature Phase Shift KeyingD8PSK π/8 Differential Shift Keyed ModulationDASA Daimler Chrysler Aerospace AGDFE-MSE Decision Feedback Minimum Square Error EqualizerDFE-ZF Decision Feedback Zero-Forcing equalizerEADS European Aeronautic Defence and SpaceFDMA Frequency Division Multiple AccessFIR Finite Impulse ResponseGF Galois FieldH-CPM Harmonized Continuous Phase ModulationH-DQPSK Harmonized Differential Quadrature Phase Shift Keyed ModulationHT Hilly TerrainISI InterSymbol InterferenceKID Key IDentifierLSB Least Significant BitLTE Long Term EvolutionL-MSE Linear Minimum Square Error EqualizerL-ZF Linear Zero-Forcing equalizerMFID Manufacturer’s IDentifierMI Message IndicatorMLSE Maximum Likelihood Sequence EqualizerMSB Most Significant BitP25 Project 25pdf probability density functionPMR Private/Professional Mobile RadioPSD Power Spectral DensityRS Reed-SolomonSNR Signal to Noise RatioTDMA Time Division Multiple AccessTETRA TErrestrial Trunked RAdioTGID Talk-group IDTIA Telecommunications Industry AssociationTos Sampling timeTs Symbol timeTU Typical UrbanUDP User Datagram ProtocolUSRP Universal Software Radio Peripheral


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1 ABSTRACT

1 Abstract

Professional Mobile Radio (PMR) also known as Private Mobile Radio or Land Mobile Radio(LMR) are radio systems conceived for public safety or professional event organizers. They aredesigned to provide a reliable and robust communication system independent from conventionalpublic networks.In France, for instance, the national police is equipped with a PMR network, namely ACROPOL,that blankets the entire country and allows both voice and low data rate services.The object of this thesis is the North-American standard Project P25. It is a standard definedby the Telecommunications Industry Association (TIA) and is currently used by many radiocommunication systems in North-America.This report presents the results of a Matlab/C simulation designed to provide performancesinformation on P25 physical layer. This knowledge is exploited to verify that the standardrequirements are met. The final purpose of this thesis is the integration of Project 25 Layer 1on a real radio platform. Thus, this report gauges the performances of all the modulators definedin the TIA standard for both Project 25 phase 1 and phase 2. Several tests are presented, theywere realized in different conditions, that is with different channel models, propagation modelsas well as with or without any fading, in static and dynamic conditions.From this simulation, the Bit Error Rates vs Eb

N0results have been extracted and are presented.

The complete Forward Error Correction part has also been implemented and the correctioncapability of all the encoders and decoders has been verified, yielding the BER vs Eb

N0plots. The

resistance to an interferer has been evaluated, in several cases, with an interferer in the samechannel or in an adjacent channel.The second part of this report presents the integration of the physical layer on a radio device.This was done to validate that both physical and MAC layers were compliant to the standard.This has been realized by interfacing the radio platform with Matlab via an Ethernet link andusing UDP protocol. Furthermore, at the end of the thesis some conclusions are drawn andfuture possible studies are detailed.


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2 SAMMANFATTNING

2 Sammanfattning

Privat mobil radio (PMR) ar ett radiosystem som anvands for offentlig sakerhet eller av pro-fessionella arrangorer. PMR ar utformad att ge en robust och palitlig tradlos kommunikation-ssystem som ar oberoende av offentliga natverk.I Frankrike till exempel ar polisen utrustad med ett PMR-natverk som kallas ACROPOL.Natverket tacker hela landet och mojliggor bade rost- och datakommunikationer.amnet i detta exjobb ar det Nordamerikanska standard projektet P25 vilket etablerades avTelecommunication Industry Association (TIA). De flesta radiosystem dar denna standard an-vands finns for narvarande i Nordamerika. Denna rapport visar resultatet av en Matlab ochC-simulering utformad att ge prestandainformation av P25:s fysiska skikt. Informationen somfas av simuleringen anvands for att kontrollera att standardkraven uppfylls. Det primara syftetav denna tes ar integrationen av P25 i en radioplattform. Rapporten uppskattar alla modulatorsbeteenden som specificeras i TIA-standarden i fas ett och tva.Testerna som redovisas har genomforts pa olika satt, antingen med olika kanalmodeller ellermed olika spridningsmodeller i statistiska och dynamiska forhallanden.Felrattande koder har implementeras i simuleringen och aven korrektionsformagan har kon-trollerats for alla kodare och avkodare.Den andra delen av denna rapport handlar om integreringen av systemet i en radioapparat foratt kontrollera att bade det fysiska skiktet och datalanken fungerar felfritt. Radioapparaten varansluten till Matlab for att simuleringen skulle kunna anvandas och testet genomfordes med enMotorola-apparat som redan slappts ut pa marknaden. I slutet av rapporten dras slutsatserkring resultaten och mojliga framtida studier diskuteras.


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3 COMPANY PRESENTATION

3 Company presentation

3.1 Airbus Group - EADS

The European Aeronautic Defence and Space Company (EADS) is an aerospace and defensecompany. EADS was created in July 2000 as the merger of three European aeronautic anddefense companies: the french company Aerospatiale-Matra SA, the German Daimler ChryslerAerospace AG (DASA) and the Spanish Construcciones Aeronauticas Sociedad Anonima (CASA).EADS is therefore a global leader in aerospace and defense, and provides civil and military air-craft, space rockets, satellites, missiles and communication systems with revenues of 43 billioneuros and counts 133 000 employees (2012). Its CEO is currently Thomas Enders.In 2013, it was announced that EADS was planning to change its name to Airbus Group inJanuary 2014.

3.2 Airbus Defence and Space - Cassidian

Cassidian is the main division of EADS defense security services. It counts around 28,000employees and is present in more than 80 countries throughout the world. Its field of activitiesencompasses radio communication systems, unmanned aerial systems and radar technology.Along with EADS change of name to Airbus Group, Cassidian will merge with Astrium andAirbus Military to form Airbus Defence and Space in 2014.

3.3 DSP SW team

My internship took place in the DSP Software Engineering Department. The team I worked infocuses on :

• DSP Software functions development (signal processing and real-time processing) for LTE,TETRA, TETRAPOL, and APCO25

• System architecture studies:

– New PMR standards performances and implementation costs, LTE for instance

– Antenna processing

– Digital communications, signal processing and audio analysis

The team counts around twenty people composed of engineers, service providers and trainees.The department is divided between France and Finland. The team is focused on the developmentof PMR standards TETRA and particularly of the future LTE standard. The work is carried outin cooperation with other teams in Elancourt, especially with hardware engineers who developthe radio boards. Some projects are also led together with research laboratories, for instancewith the CNAM institute in Paris.


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4 INTRODUCTION

4 Introduction

4.1 Professional Mobile Radio - PMR

The first analog PMRs were developed in the 20s in the USA. PMRs are commonly narrow bandsystems using a Frequency Modulation or an Amplitude Modulation. Frequency Modulationis widely exploited for the constant envelope signal it creates, which does not require a linearPower Amplifier before being transmitted over the air.PMRs are radio communication systems dedicated to public safety professional or events orga-nizers such as firemen, policemen or Olympic Games organizers for instance. Their robustnessand reliability is crucial since they should keep working even in case of a natural catastrophe,such as a hurricane, a flood... They shall work even when the conventional networks are out oforder.

PMRs usually provide voice and low data rate services, such as text messages. Nevertheless, thedevelopment of broadband LTE may pave the way to Private Mobile Network able to conveylarge data such as images or even videos.This feature would be particularly helpful to firemen or policemen, who could have access tomaps or get visual information about an ongoing event.

4.2 Specificity of PMR networks

• Trunking

It is a technique allowing the network resources to be shared, a channel is allocated forthe duration of a voice or data transmission. At the end, it is released and available forother terminals. A user does not have a dedicated channel, instead a channel among apool will be allocated by the site controller.

• Conventional mode/Direct Mode

If some terminals are out of the coverage area of the network, they can communicatewith one another without control channel. They communicate on a dedicated channelhard-coded into the terminal. They can also communicate through a simple repeater thatre-transmits the signal at higher power to cover a longer distance.

• Group call

Several users may be registered in a common talk-group. If the Group ID contained inthe signal corresponds to their talk-group, they listen to this signal.

• End-to-end encryption

PMRs allow end-to-end encryption, that is an uninterrupted encryption of data froman emitter to a receiver. It ensures confidentiality of the communication as well as itsintegrity.

• Air interface encryption

Unlike the end-to-end encryption, this mode encrypts and decrypts the data at eachextremity of a communication link. Solely the transmission over the air is encrypted, andthird parties may have access to plain data.



4.3 Project P25 4 INTRODUCTION

• Simulcast

It is the broadcasting of the same information by several sites. It can consequently improvethe network coverage. The synchronization of the different sites is a crucial condition.Simulcast performances of Project 25 are further discussed in this report.

4.3 Project P25

Project 25 (P25) is the standard for the design and manufacture of interoperable digital two-way wireless communications products. Developed in North America with state, local and fed-eral representatives and Telecommunications Industry Association governance, P25 has gainedworldwide acceptance for public safety, security, public service, and commercial applications.The published P25 standards suite is administered by the Telecommunications Industry As-sociation. Radio equipment that demonstrates compliance with P25 is able to meet a set ofminimum requirements to fit the needs of public safety. The P25 standard was created by, andis intended for, public safety professionals.[3]

Figure 4-1: Working principle of a P25 network



4.4 Thesis objective 4 INTRODUCTION

In a normal mode, where all the resources are available, a communication is done using thetrunked mode. If a user with Terminal 1 wants to call the user with Terminal 2; Terminal 1sends a request to the base station on a dedicated signaling channel. The request is transmittedto the site controller which allocates a channel for the upcoming communication. The base sta-tion sends this information to terminals 1 and 2 which can start communicating on this channelthrough the base station.

If a failover happens and the trunked radio system can no longer communicate with the sitecontroller, the system is put in a failsoft mode. In this case, all the base stations work in theconventional mode, that is, they act as simple repeaters. The users must then switch to con-ventional mode to support the failsoft mode. The terminal is programmed to use a dedicatedchannel hard-coded in its memory. Users can then communicate directly to another user orthrough a base station which acts as a bare repeater.

In both cases, the communications are half-duplex, this means that users talk in turn and notsimultaneously. A push-to-talk button is used to start communicating and released to free theresource for the other user.Details about Project 25 can be found on the official website [3].

Figure 4-2: Cassidian mobile terminal Figure 4-3: Cassidian TETRA base station

Figs.4-2 and 4-3 show two products developed by Cassidian, a TETRA mobile terminal and aTETRA base station. Cassidian also proposes some products concerning the APCO25 standard,but solely for the core network and not for the access network.

4.4 Thesis objective

The thesis objective is to implement the entire Physical Layer of this standard, as well as a partof the Media Access Layer. Some choices have to be made to reach the best performances thatcan be achieved for this standard. The final purpose is the validation of the implementation byexploiting a radio platform to communicate with a terminal that is known to be compliant tothe standard.



5 P25 PHASE 1 FRAMES FORMAT

5 P25 Phase 1 frames format

Note: Part of the following information is directly extracted from TIA Recommended CommonAir Interface [11].P25 Phase 1 uses a FDMA access method, it works in a 12.5 kHz bandwidth at rate 4800 baud,with two bits per symbol, it can operate in both an analog or digital mode, however this studytreats only of the digital mode.

In Phase 1 :

• 45 % of the bits are used to encode the voice information

• 30 % are required for Forward Error Correction

• 25 % are exploited for signaling

5.1 Header frame

The header word includes the following information fields :

• Message Indicator (MI) 72 bitsThis is the initialization vector for the choice of an encryption algorithm.

• Manufacturer’s ID (MFID)8 bitsThis is asserted when non-standard features are included in the voice message by themanufacturer. This field has a standard value when all of the other information fieldsconform to the definitions of the Common Air Interface. It is a minimum requirementfor a standard radio to be able to transmit or receive messages using the standard fielddefinitions of the Common Air Interface, with the standard value for the MFID field. Theminimum requirement for standard receivers is to ignore messages which do not containthe standard value for the MFID field.

• Algorithm ID (ALGID) 8 bitsThis identifies the encryption algorithm in systems with multiple algorithms.

• Key ID (KID) 16 bitsThis identifies the encryption key for systems with multiple encryption keys.

• Talk-group ID (TGID) 16 bitsThis identifies the talk-group for the message. These information fields are concatenatedtogether into 120 bits. They are then separated into 20 symbols of 6 bits each. Eachsymbol is called a hex bit. These are encoded with a (36,20,17) Reed-Solomon code toyield 36 hex bits. These 36 hex bits are then in turn encoded.

5.2 Voice frame

The vocoder produces 8 information vectors of decreasing importance, the pitch is for examplecoded in the first vector denoted u0. A voice frame is encoded into a binary vector of 144 bits.The vectors are protected using two different codes, a Golay and a Hamming code. Four Golay



5.3 Link Data Unit 5 P25 PHASE 1 FRAMES FORMAT

Figure 5-1: Diagram of Header Code Word Construction

codewords are used to protect the four first vectors (u0 7→ u3), adding 44 bits to the 48 bits ofinformation.The next 3 information vectors (u4 7→ u6) are protected using a (15,11,3) Hamming code, adding12 parity bits to the 33 information bits.The last 7 least significant bits are not protected.A pseudo-noise sequence (PN sequence) is constructed from u0 and is XOR-ed to the remainingprotected vectors. This sequence is defined as follows:

p0 = 16u0

pn = [173pn−1 + 13849] mod 65536 ∀n ∈ [1, 114].Let pn[15] denote the 15th bit of pn, then the PN sequence is (pn[15])n∈[1,114]

Finally, the vectors are concatenated as described in Fig.5-2 and interleaved. This yields a codeword more robust with respect to burst errors, that is more resistant to fading. The interleavingtable is provided in [11]. A voice frame is transmitted in about 20ms.

5.3 Link Data Unit

Before being transmitted over the channel, the voice frames are concatenated into a data unit,either called Logical Link Data Unit 1 or Link Data Unit 2. A LDU1 is described in Fig.5-3and consists of 9 voice frames. A LDU2 has a similar structure, the position of the voice framesis similar, but the other frames differ from a LDU1 frame.

5.4 Superframe

A superframe consists of a LDU1 followed by a LDU2. At the beginning of a voice communi-cation, a header is sent over the channel followed by several superframes, the communicationis terminated with a Terminator Data Unit not described here. A superframe constitutes thebasic block of a voice communication in phase 1.



5.4 Superframe 5 P25 PHASE 1 FRAMES FORMAT

Figure 5-2: Diagram of Voice Code Word Construction

Figure 5-3: Logical Data Unit 1

This superframe is depicted Fig. 5-4.

Figure 5-4: Phase 1 superframe



6 P25 PHASE 2 FRAMES FORMAT

6 P25 Phase 2 frames format

It has been decided that P25 phase 2 would use a two-slot TDMA access scheme, that is one12.5 kHz channel can convey two individual voice calls. This allows a re-use of P25 Phase 1technologies and does not involve any changes in the licensing requirements.The data transmission speed is increased compared to Phase 1, two different schemes are usedto transmit the 12 kbit/s data stream.H-CPM is used for uplink, that is in the mobile terminals so that non-linear power amplifiers canbe used. H-DQPSK is used for downlink, that is in the base stations, since many were alreadyequipped with linear power amplifiers, and this modulator increases the simulcast performances.

In Phase 2 :

• 40 % of the bits are used to encode the voice information

• 20 % are required for Forward Error Correction

• 40 % are exploited for signaling

6.1 Time slot

Figure 6-1: Phase 2 TDMA Slot

Since a TDMA scheme is used, 6 symbols are used at the beginning and at the end of a frameto smoothly increase and decrease the power and consequently prevent inter-frame interference.Four pilot symbols are available at the beginning and anew four at the end of a frame to estimatethe channel.Those symbols are particularly interesting when a H-CPM modulation scheme is used as it isdescribed section 7.4. In a voice communication, every TDMA slot conveys up to 4 voice frames.



6.2 Superframe 6 P25 PHASE 2 FRAMES FORMAT

6.2 Superframe

By analogy to phase 1, there also exists a superframe in the second phase of the standard. Thisframe also lasts 360 ms with 6 slots reserved for the inbound channel (downlink) and 6 reservedfor the outbound channel (uplink). The repartition of these slots is given by Fig.6-2.

Figure 6-2: Phase 2 superframe

Further details about the Media Access Layer for phase 2 can be read in [13].



7 MODULATION - DEMODULATION

7 Modulation - Demodulation

7.1 Phase 1 modulation

In Project P25 phase 1, two kinds of modulators are defined and according to the standard, bothshould be demodulated using the same receiving chain. A non-coherent approach was chosen forits low complexity and the good results it provides. This section describes C4FM and CQPSKmodulators. Some theoretical results have been derived in order to provide a reference for thedemodulator performances. Since all modulation schemes carry the information in their phaseor frequency, the derivation intends to show the impact of an additive white noise on the signalphase and on its derivative.

7.1.1 C4FM modulator

The C4FM is a constant envelope frequency modulation.The modulation sends 4800 symbols/s with each symbol conveying 2 bits of information. Theinformation bit stream is first mapped to symbols as defined in Table 1.The signal is then over-sampled to form a Dirac comb weighted by those symbols. It is shapedwith a Raised-cosine filter defined in eq.(2) to obtain a signal without intersymbol interference.This filter is cascaded with a shaping filter defined in eq.(1). The resulting signal is thenintegrated and sent over the channel as the phase of a complex exponential.A summary of the transmission chain is shown on Fig.7-1.

Information Bits Symbols Deviation

01 +3 +1800Hz

00 +1 +600Hz

10 −1 −600Hz

11 −3 −1800Hz

Table 1: C4FM mapping table

Figure 7-1: C4FM modulator

|P (f)| = magnitude of the Tx Shaping Filter

|P (f)| =πf4800

sin( πf4800)

for |f | < 2880Hz

|P (f)| = 0 for |f | > 2880Hz

(1)

|H(f)| = magnitude of the Raised Cosine Filter

|H(f)| = Tos2Ts

for |f | < 1920Hz

|H(f)| = Tos2Ts

(12

(1 + cos

(2πf1920

)))for 1920Hz < |f | < 2880Hz

|H(f)| = 0 for |f | > 2880Hz

(2)



7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

where :

• Tos : Sample time

• Ts : Symbol time, Ts ' 208µs

The time expression of H can be found in [4].

The baseband signal, s, can be written as:

s(t) = exp(iφ(t)) (3)

With : {φ(t) = 2πh

∑akq(t− kTs)

q(t) =∫ t−∞ p(u)du

(4)

1. p is the convolution of the Raised-Cosine defined in eq.(2) with the shaping filter definedin eq.(1).

2. h is the modulation index equals to 14 for a C4FM modulation scheme.

3. (ak) are the symbols, with values in set {−3,−1, 3, 1}.

This signal has a continuous phase, its frequency varies roughly in the range [−1800Hz, 1800Hz].

−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Inphase

Quad

rature

Figure 7-2: C4FM constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120−8

−6

−4

−2

0

2

4

6

8

Time (µs)

Figure 7-3: C4FM eye-diagram

Figures 7-2 to 7-5 show different representations of the modulated baseband signal. The con-stellation shows a perfect circle since the modulation has a constant envelope. The transmissionfilter described previously is also plotted in Fig.7-4, although it is a FIR, it lasts 24 symbols toimprove its spectral efficiency. The signal PSD is shown Fig.7-5, its wide shape is characteristicof a CPM modulation.




−2,500 −2,000 −1,500 −1,000 −500 0 500 1,000 1,500 2,000 2,500−2

−1

0

1

2

3

4

5

6·10−2

Time (µs)

Am

plitu

de

Transmission filter impulse response

Figure 7-4: C4FM transmission filter im-pulse response

−25 −20 −15 −10 −5 0 5 10 15 20 25−140

−120

−100

−80

−60

−40

−20

0

Frequency (kHz)

Pow

erSpectralDen

sity

(dB)

Figure 7-5: PSD of C4FM transmittedbaseband signal

Theoretical derivation

Project P25 defines a standard static sensitivity, as the level of EbN0

reached when standard BERis achieved (standard BER being 5%). This measure is done when the signal is sent over anAWGN channel without any fading. The theoretical sensitivity of the C4FM modulation schemeis determined as follows :

Let s(t) = exp(jφ(t)) be the baseband signal sent over the channel.Let N(t) be the additive complex white Gaussian noise with variance N0.

The signal received after transmission over the channel and filtered by the Low-pass filter isdenoted y.After being received, y is sampled at rate 1

Tos.

Let t = t0 = k0Tos be a sample time. To simplify the calculation, φ(t0) will be considered asequal to zero without loss of generality, the result for any other angle can be found by a simpleshift.

From this point, all the calculations are done using discrete time signals.The random variables are written with capital letters unlike the deterministic signals.The energy per sample is arbitrarily unitary, thus given a level of Eb

N0in decibels, the noise

variance can be deduced as :

N0 = 10−EbN0

+10 log10(2)−10 log10( TsTos )

10 (5)

The frequency response of the Low-pass filter is defined as :{H(ν) = 1 for |ν| < fcTos = ν0

H(ν) = 0 otherwise(6)

where ν represents the reduced frequency, that is ν = fTos.The corresponding time filter is thus :

h[k] = 2ν0sinc(2ν0k) (7)




The received signal Y [k] is :

Y [k] = A[k] exp(jΘ[k]) = (s[k] +N [k]) ? h[k] (8)

where ? represents the convolution of two discrete time signals.Let Θ1 denote the random variable Θ(t0) and Θ2 be the random variable Θ(t0 + Tos).

The Low-pass filter h is unitary, and wider than the useful signal bandwidth, therefore s canbe considered as non-altered by h.Hence,

Y [k] = A[k] exp(jΘ[k]) = s[k] + (N [k] ? h[k]) = s[k] +W [k] (9)

W [k] = Wx[k] + iWy[k] (10)

This equation can be re-written at sampling time as :

Y [k0] = A[k0] exp(jΘ[k0]) = 1 +W [k0] (11)

W is still Gaussian (as a linear combination of Gaussians), however it has been colored by thefiltering.

Let rh be the auto-correlation function of h, and rw be the auto-correlation function of W :

rW [k] = rh[k]N0

rWx [k] = rh[k]N0

2

rWy [k] = rh[k]N0

2

(12)

Let ρ denote the Pearson product-moment correlation coefficient of Wx[k0] and Wx[k0 + 1](Wy[k0] and Wy[k0 + 1])

ρ =rh[1]

rh[0](13)

In addition,

var[Wx[k0]] = var[Wx[k0]] = var[Wx[k0]] = var[Wx[k0]] = rh[0]N0

2(14)

Where var denote the variance of a random variable.The joint probability density function of Wx[k0] and Wx[k0 + 1] can be deduced :

fWx0 ,Wx1(x1, x2) =

1

πN0

√1− ρ2

exp

(− 1

N0(1− ρ2)

(x2

1 − 2ρx1x2 + x22

))(15)

The joint probability density function of Wy[k0] and Wy[k0 + 1] is the same. Furthermore, thesets of random variables (Wx[k0],Wx[k0 + 1]) and (Wy[k0],Wy[k0 + 1]) are independent.Hence, the joint pdf of these 4 random variables is the product of the joint pdfs of the two sets,that is :




fWx0 ,Wx1 ,Wy0 ,Wy1(x1, x2, y1, y2) =

1

π2N20 (1− ρ2)

exp

(− 1

N0(1− ρ2)

(x2

1 + y21 − 2ρ(x1x2 + y1y2) + x2

2 + y22

))(16)

From this expression, a polar coordinate change can be used to express the joint pdf of Θ1 andΘ2 defined above.This pdf is :

fΘ1,Θ2(θ1, θ2) =∫ +∞

0

∫ +∞

0

1

π2N20 (1− ρ2)

exp

(−g(r1, r2, θ1, θ2)

N0(1− ρ2)

)r1r2dr1dr2

(17)

with :

g(r1, r2, θ1, θ2) =

(r1 cos θ1 − 1)2 + (r1 sin θ1)2 − 2ρ((r1 cos θ1 − 1)(r2 cos θ2)

+ (r1 sin θ1)(r2 sin θ2)) + r22

(18)

Since this integral is not easily evaluated, a Matlab script was written to get a numerical solution.An example is given Fig.7-6.The parameters used for this example are:

• Modulation rate : 4800 baud.

• Sampling frequency : 14400 Hz

• low-pass filter cut-off frequency : 9600 Hz

• EbN0

= 0 dB.

Note on Fig.7-6 that the maximum is obtained for θ1 = θ2 = 0 which is logical. Furthermore,Θ1 and Θ2 are correlated, since the highest probabilities are obtained along the diagonal, thatis when θ1 = θ2.Since the information is not carried by the phase but by the signal frequency at the samplingtime, this frequency is derived as the derivative of the phase divided by 2π. The signal beingdiscrete, the frequency freq(t) is derived as :

freq(t) =θ(t+ Tos)− θ(t)

2πTos(19)

Hence, the pdf of Freq, a random variable defined by Freq = Θ2−Θ12πTos

can be deduced from Θ1

and Θ2’s joint pdf. The pdf of Θ1 is not sufficient to give a conclusion because Θ1 and Θ2 arecorrelated. They are even more correlated as the oversampling increases. Freq’s pdf, fFreq(f),can be calculated as the ”inner” autocorrelation of the joint pdf, that is :




−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4−4

−3

−2

−1

0

1

2

3

4

θ1 (rad)

θ 2(rad)

Logarithm of Θ1 and Θ2 joint pdf

−8

−7

−6

−5

−4

−3

−2

−1

0

Figure 7-6: Θ1 and Θ2 joint probability density function

fFreq(f) =

∫ +∞

−∞fΘ1,Θ2 (θ − 2πfTos, θ)dθ (20)

The probability density function fFreq is shown in Fig.7-7.From this distribution, the error probability can be derived, assuming that no more than onebit is erroneous when a symbol is erroneous. This assumption holds at relatively high SNR, thatis at SNR around the static sensitivity, since a Gray coding is used in this modulation scheme.It follows that the bit error probability is roughly half the symbol error probability.The symbol error probability is finally deduced as :

Pesymb = 2Pebit =1

2P (Freq ∈ [−600Hz, 600Hz]) +

1

4P (Freq ∈ [−∞, 600Hz])+

1

4P (Freq ∈ [−600Hz,+∞])

(21)

A Matlab script was written to plot the theoretical BER as a function of EbN0

, which is shown inFig.7-8.The horizontal line represents the standard BER, that is 5% of error. The interested reader canfind a derivation of Θ’s exact pdf in Annex B.One can notice that the BERs plotted on Fig.7-8 give a sensitivity lower, and even much lowerthan the one obtained with the simulation. Table 2 summarizes those values. This can beexplained by the assumption made previously, the useful signal has been supposed unaltered bythe channel filter. However, a C4FM modulation uses a Frequency Modulation whose PSD isnon-zero even for high frequencies, thus the signal is always altered.Nevertheless, the higher the cut-off frequency, the more the assumption holds. There exists a




−4,000 −3,000 −2,000 −1,000 0 1,000 2,000 3,000 4,000−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

·10−3

Frequency (Hz)

Frequency pdf

Figure 7-7: Freq probability density function

trade-off between noise rejection and signal deterioration that gives the best sensitivity, but thistrade-off problem is non-trivial.

fc 7200 Hz 8000 Hz 8800 Hz

Sensitivity (BER = 5%) 1.6 dB 2.7 dB 4 dB

Table 2: Theoretical sensitivity

7.1.2 CQPSK modulator

The CQPSK modulation is an Inphase and Quadrature modulation. The modulation sends 4800symbols/sec with each symbol conveying 2 bits of information. The information bit stream isfirst mapped to symbols Ik as defined in Table 3. The transmission chain is summarized inFig.7-9.

Information Bits Symbols (Ik) Phase change (rad)

01 +3 +3π4

00 +1 +π4

10 −1 −π4

11 −3 −3π4

Table 3: CQPSK mapping table

The baseband formula for a CQPSK signal is:




−4 −2 0 2 4 6 8 10 12 1410−5

10−4

10−3

10−2

10−1

100

Eb/N0 (dB)

BE

R

Comparison of BER plots with different channels low-pass filters

fc = 7200 Hzfc = 8000 Hzfc = 8800 Hz

Figure 7-8: Theoretical BER as a function of EbN0

s(t) =

∫ √EsTs

exp(jφ(u, I))h(t− u)du (22)

φ(t, I) =π

4

∑Ik (23)

where :

• Es : Energy per symbol


h(t) defines a filter applied to the Inphase and Quadrature signals, thus it constraints thespectral spread of the baseband modulated signal s(t). It is defined as a Raised-Cosine with a

roll-off coefficient α = 0.2 and a bandwidth of (1+α)Ts

= 5760Hz.

Figure 7-9: CQPSK modulator




−2 −1.8−1.6−1.4−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Inphase

Quadrature

Figure 7-10: CQPSK constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120−8

−6

−4

−2

0

2

4

6

8

Time (µs)

Figure 7-11: CQPSK eye-diagram

−1,000 −800 −600 −400 −200 0 200 400 600 800 1,000−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (µs)

Am

plitu

de


Figure 7-12: CQPSK transmission filterimpulse response

−50 −40 −30 −20 −10 0 10 20 30 40 50−100

−90

−80

−70

−60

−50

−40

−30

−20

−10

0

Frequency (kHz)

Pow

erSpectral

Den

sity

(dB)

Figure 7-13: PSD of CQPSK transmittedbaseband signal

The CQPSK eye-diagram Fig.7-11 is much wider than for a C4FM modulation scheme, thereforeit should be more resistant to multipath. However, as it can be observed in Fig.7-10, thesignal can get close to zero. If the noise variance is high enough, the inphase and quadraturecomponents can quickly change their sign. In a non-coherent demodulation, this creates aconsiderable amount of errors. The PSD in Fig.7-13 shows a narrow signal, typical of anamplitude modulation scheme. The finite impulse response Fig.7-12 is shorter than the C4FMone, but is sufficiently long to give an excellent spectral efficiency. As it is seen section 7.3, bothmodulators can be demodulated using the same receiving chain in a non-coherent approach.

7.2 Phase 2 modulation

7.2.1 DQPSK modulator

DQPSK or H-DQPSK stands for Harmonized differential quadrature phase shift keyed. Thebaseband formula for a DQPSK signal is:

s(t) =

∫ √EsTs


where :




φ(t, I) =π

4

∑Ik (25)

where :



h(t) defines a filter applied to the Inphase and Quadrature signals, thus it constraints thespectral spread of the baseband modulated signal s(t). It is defined as a Raised-Cosine with aroll-off coefficient α = 1 and a bandwidth of 3.6 kHz.

H(f) =

{12

(1 + cos

(πffh

))for |f | ∈ [0, fh]

0 otherwise(26)

where :

• fh = 7.2kHz

As it can be seen on Fig. 7-15, the eye-diagram shows that the transmission filter is not aNyquist filter, however, there is solely small inter-symbol interference, so no equalization is usedto demodulate the signal.

−2 −1.8−1.6−1.4−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Inphase

Quad

rature

Figure 7-14: DQPSK constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120−8

−6

−4

−2

0

2

4

6

8

Time (µs)

Figure 7-15: DQPSK eye-diagram

Compared to the CQPSK modulation scheme which is also an amplitude modulation, it canbe observed on the eye-diagram Fig.7-15 is relatively wider than for a CQPSK, however thesymbol time is reduced, therefore it may not be more resistant to delay spread. If the eye-diagram is wide, this also means that the level transitions are very short, and therefore thespectrum efficiency compared to a CQPSK modulator, is reduced. It can be observed that thesignal PSD Fig.7-17 is wider.




−800 −700 −600 −500 −400 −300 −200 −100 0 100 200 300 400 500 600 700 800−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (µs)

Am

plitu

de


Figure 7-16: DQPSK transmission filterimpulse response

−30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30−100

−90

−80

−70

−60

−50

−40

−30

−20

−10

0

Frequency (kHz)

Pow

erSpectralDen

sity

(dB)

Figure 7-17: PSD of DQPSK transmittedbaseband signal

7.2.2 D8PSK modulator

D8PSK stands for π8 differential phase shift keyed modulation. The baseband formula for a

D8PSK signal is:

s(t) =

∫ √EsTs


where :

φ(t, I) =π

8

∑Ik (28)

where :


• Ts : Symbol time, Ts = 250µs

• {Ik} are the symbols defined in table 4

h(t) defines a filter applied to the Inphase and Quadrature signals, thus it defines the spectralspread of the baseband modulated signal s(t). It is defined as a Raised-Cosine with a roll-offcoefficient α = 1 and a bandwidth of 2.5 kHz.

H(f) =

{12

(1 + cos

(πffh

))for |f | ∈ [0, fh]

0 otherwise(29)

where :

• fh = 5kHz

As it can be seen on Fig. 7-19, the eye-diagram shows that the transmission filter is not aNyquist filter, however, there is solely small inter-symbol interference, so no equalization is usedto demodulate the signal.




Information Bits Symbols

010 +7

011 +5

001 +3

000 +1

100 −1

101 −3

111 −5

110 −7

Table 4: D8PSK mapping table

−2 −1.8−1.6−1.4−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Inphase

Quad

rature

Figure 7-18: D8PSK constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120−8

−6

−4

−2

0

2

4

6

8

Time (µs)

Figure 7-19: D8PSK eye-diagram

−1,000 −800 −600 −400 −200 0 200 400 600 800 1,000−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (µs)

Am

plitu

de


Figure 7-20: D8PSK transmission filter im-pulse response

−20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20−120

−100

−80

−60

−40

−20

0

Frequency (kHz)

Pow

erSpectral

Den

sity

(dB)

Figure 7-21: PSD of D8PSK transmittedbaseband signal

The constellation Fig.7-18 shows some transitions that get really close to zero, and thereforeare prone to errors in the case of a non-coherent demodulator. On the other hand, the reducedsymbol rate, as well as the short level transitions Fig.7-19 yield an open eye-diagram. This kindof modulation should offer a better resistance to delay spread than the other modulations.




7.2.3 HCPM modulator

H-CPM stands for Harmonized Continuous Phase modulation and is a form of Continuous PhaseModulation (CPM) operating at 12 kbit/s. The baseband formula for a CPM signal is:

s(t) =

√EsTs

exp(jφ(t, I)) (30)

where :



The information is carried by the signal phase φ(t, I), I being the sequence of symbols sent,I = {Ik}∀k ∈ Z, Ik ∈ {−3,−1, 1, 3}. This phase can be expressed as :

φ(t, I) = 2πh∑k∈Z

Ikq(t− kTs) (31)

where :

• h : Modulation index

• q : Phase response of H-CPM, given by the following formula :

q(t) =

{0 for t < 012 for t > LTs

(32)

• L = pulse response length in symbols.

q(t) is more precisely defined as the integral of a frequency impulse response g(t) defined asfollows :

q(t) =

∫ t

0g(v)dv (33)

g(t) =

{1G

[sinc

(λTs

(t− LTs

2

))cos2

(πLTs

(t− LTs

2

))]for t ∈ [0, LTs]

0 otherwise(34)

H-CPM modulation is defined with parameters : G = 4.345510−4, λ = 34 , h = 1

3 and L = 4.




−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Inphase

Quad

rature

Figure 7-22: HCPM constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120−8

−6

−4

−2

0

2

4

6

8

Time (µs)

Figure 7-23: HCPM eye-diagram

−800 −700 −600 −500 −400 −300 −200 −100 0 100 200 300 400 500 600 700 800−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4·10−2

Time (µs)

Am

plitu

de


Figure 7-24: HCPM transmission filter im-pulse response

−30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30−140

−120

−100

−80

−60

−40

−20

0

Frequency (kHz)

Pow

erSpectral

Den

sity

(dB)

Figure 7-25: PSD of HCPM transmittedbaseband signal

As it can be seen in Fig.7-23, the eye-diagram obtained with the discriminator receiver showsthat the transmission filter is not a Nyquist filter, inter-symbol interference at sampling time isconsiderable and an equalizer is required to eliminate, or at least reduce, those interference.Similarly to a C4FM modulation, the baseband signal PSD is wide and will therefore be alteredby the channel filter. As expected the constellation shows a perfect circle as the signal has aconstant envelope. The transmission filter length is defined by the standard and lasts L = 4symbols.



7.3 Phase 1 demodulation 7 MODULATION - DEMODULATION

7.3 Phase 1 demodulation

Let y(t) be the baseband signal received after transmission over the channel. This signal isfiltered by a Low-Pass filter to reject a maximum of noise and keep the useful signal. Thenthis signal is normalized to yield a constant envelope signal, this is necessary before using adiscriminator method.If there is no fading or noise, y(t) = s(t) where s(t) is the baseband signal before transmissionover the channel.The discriminator method consists in computing :

1

2πTosiy(t)(y(t+ Tos)− y(t)) (35)

When developed it yields :

1

2πTosiy(t)(y(t+ Tos)− y(t)) =

eiθ(t+Tos) − eiθ(t)

2πTosieiθ(t)

' φ(t+ Tos)− φ(t)

2πTos' 1

2π

dφ(t)

dt=h∑akp(t− kTs)Tos

(36)

After filtering by the receiving filter, the obtained signal does not have ISI and thus at samplingtime the signal value is :

Chak0Tos

(37)

Where C is a constant depending on the transmitting filter, thus C is known and ak can be found.

In order to yield the best results, the demodulator should not be the same for a C4FM modu-lator and a CQPSK modulator.In the first case, the signal after discriminator should be filtered by the inverse shaping filter1/P (f).In the second case, the signal should be filtered by an averaging filter, with length equal to thenumber of samples per symbol.

However, the inverse shaping filter 1/P (f) is a truncated sinc function, thus its Fourier Trans-form is the averaging filter defined above, convolved with a sinc function.The assumption that this sinc function is a Dirac is made. It deteriorates the C4FM modulationperformances, but gives the best performances for a CQPSK modulator.

Figure 7-26: C4FM and CQPSK demodulator




7.4 Phase 2 demodulation

DQPSK and D8PSK :

In P25 Phase 2, all the modulators face ISI. However, as it can be seen in Fig.7-15 and Fig.7-19,for both DQPSK and D8PSK modulators, the eye-diagram is not closed and since they bothare QPSK modulations, they can be demodulated using the non-coherent approach described inthe previous section. This is the method that was exploited in the simulation, it yields decentresults for a low-complexity demodulator.

Figure 7-27: H-CPM non-coherent demodulator

H-CPM :

Concerning the H-CPM modulator, the eye-diagram is completely closed as shown in Fig.7-23,therefore an equalizer is required to remove or at least attenuate ISI. Five different equalizershave been implemented and benchmarked to find the best trade-off between low-complexity andsatisfying results.Those equalizers are listed below :

• Linear Zero-Forcing equalizer (L-ZF)

• Linear Minimum Square Error Equalizer (L-MSE)

• Decision Feedback Zero-Forcing equalizer (DFE-ZF)

• Decision Feedback Minimum Square Error Equalizer (DFE-MSE)

• Maximum Likelihood Sequence Equalizer (MLSE)

As described in section 6, 4 symbols are present at the beginning of a frame, and 4 at the end.They may be used by some equalizers.

• Zero-forcing

The Zero-Forcing equalizers use an a priori model of the channel, therefore they do notuse the knowledge of those symbols.

• MSE

Both MSE equalizers need an estimate of the channel autocorrelation matrix, a trainingsequence is used to define the filter which is then used whichever the conditions. Thatmeans that the channel is never corrected by the MSE equalizers. The knowledge of the 4symbols could be exploited but a rapid test proved that the MSE method did not convergeby solely using those symbols as a training sequence.




• MLSE

The MLSE equalizer uses the symbols to open and close the trellis, it helps staying on thecorrect path while demodulating. Nevertheless, the channel is not estimated either withthis method.

Details about those different equalizers can be found in [6]. The BER vs EbN0

results in staticcondition with AWGN are shown in Fig.7-28 for the different equalizers.At high SNRs, MSE and Zero-forcing equalizers should behave equally which is not what isobserved. This is explained by the fact that the MSE takes into account the channel filtereffect unlike the zero-forcing equalizer which uses the hard-coded transmission filter responseunaltered by the channel filter.

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1510−4

10−3

10−2

10−1

100

EbNo (dB)

BER

BERs as a function of EbNo (dB)

HCPM static, speed 0, enc RAW, eq ZFHCPM static, speed 0, enc RAW, eq DFEZFHCPM static, speed 0, enc RAW, eq MSEHCPM static, speed 0, enc RAW, eq DFEMSEHCPM static, speed 0, enc RAW, eq MLSE

Figure 7-28: Performances of H-CPM non-coherent demodulation depending on equalizers

The results for the H-CPM modulation scheme presented in this report were done using aMLSE equalizer, since it gives significantly better results than the other equalizers. Its highercomplexity does not considerably slow down the simulation, however it should be improved toyield better results as it does not meet every single standard requirements as pointed further inthis report.



8 ENCODERS - DECODERS

8 Encoders - Decoders

Note: For all codes with codewords length less than 32 bits, the processing has been doneusing a decimal representation to accelerate the computations. The simulation has been devel-oped on a 32 bit computer, thus the codes with codewords shorter than 32 bits can be storedin the registers of the computer processor. Since the encoding and decoding require a lot ofcircular shifts for most of the codes, having the codewords stored on a shift register considerablyspeeds up the computations. Furthermore, the memory used to encode a bit-stream sequenceis low.

In this part, the following notations are used:

• k length of an information word, that is before encoding

• n length of a codeword, that if after encoding

• d minimal distance of a code

• t correction capability of a code

The parameters are given in the following order (n, k, d).For Reed-Solomon codes, the parameters are given in hex-bits rather than in bits.

The following encoders are defined in the Common Air Interface [11] for phase 1 and in theMedia Access Control Layer for Phase 2. Nevertheless, the way of decoding is not standardizedand may differ with vendors. The description of the decoders hereafter described may not bethe optimal decoding whether regarding speed or correction capability. For each code, a shortdescription of its use in the standard is stated.

8.1 Hamming

Two Hamming codes are used in P25 phase 1, a standard code, and a shortened code. Theyare defined by their generator matrices given below.

Hamming standard

The standard code protects the voice frames as described in section 5.Generator Matrix for Hamming (15, 11, 3) is given by :

Gham std =

1 0 0 0 0 0 0 0 0 0 0 1 1 1 10 1 0 0 0 0 0 0 0 0 0 1 1 1 00 0 1 0 0 0 0 0 0 0 0 1 1 0 10 0 0 1 0 0 0 0 0 0 0 1 1 0 00 0 0 0 1 0 0 0 0 0 0 1 0 1 10 0 0 0 0 1 0 0 0 0 0 1 0 1 00 0 0 0 0 0 1 0 0 0 0 1 0 0 10 0 0 0 0 0 0 1 0 0 0 0 1 1 10 0 0 0 0 0 0 0 1 0 0 0 1 1 00 0 0 0 0 0 0 0 0 1 0 0 1 0 10 0 0 0 0 0 0 0 0 0 1 0 0 1 1

(38)



8.2 Shortened cyclic code 8 ENCODERS - DECODERS

Hamming short

The shortened code is used to protect the Encryption Sync Word that conveys synchronizationand identification information for a system encrypted with multiple keys.Generator Matrix for Hamming (10, 6, 3) is given by :

Gham sht =

1 0 0 0 0 0 1 1 1 00 1 0 0 0 0 1 1 0 10 0 1 0 0 0 1 0 1 10 0 0 1 0 0 0 1 1 10 0 0 0 1 0 0 0 1 10 0 0 0 0 1 1 1 0 0

(39)

EncodingThe input bit-stream is separated into row vectors of length k, those vectors are successivelymultiplied by the generator matrix to yield the codewords.

c = vinputGham (40)

DecodingSince the code is systematic, the parity matrix can be easily computed. The minimal Hammingdistance of this code being d = 3, only one error can be corrected. A method with syndrome isused in the simulation and is defined as follows :

1. The syndrome is computed from the received word, using the parity matrix.

2. If the syndrome is equal to zero, the received word is considered to be correct.

3. If the syndrome is a column of the parity matrix, then the column gives the position ofthe error, this error is added to the received word and yields the correct codeword.

4. If the syndrome does not correspond to a column of the parity matrix, the received wordcannot be corrected since the code can correct up to t = 1 error.

The procedure is summarized in Fig.8-1.All possible syndromes are pre-computed and stored in a static table, the corresponding errorvector is also hard-coded in a table.The table containing the syndromes is sorted to make the search of the received syndrome moreefficient, this search is done using a Binary Search Algorithm.

8.2 Shortened cyclic code

This code is only used in phase 1, it protects the Low Speed Data Word which use is not definedin the CAI. This word can therefore be used for custom application, for instance GPS locationdata, information about the network and some other relevant information.

EncodingThe (16, 8, 5) shortened cyclic code is deduced from the (17, 9, 5) cyclic code by keeping thecodewords with MSB equal to 0 and erasing this bit.NB : (16, 8, 5) shortened cyclic code is NOT cyclic.



8.2 Shortened cyclic code 8 ENCODERS - DECODERS

Figure 8-1: Syndrome decoding

A systematic cyclic code is constructed with a generator polynomial g(X). In this case thegenerator polynomial is :

g(X) = X8 +X5 +X4 +X3 + 1 (41)

A message to be sent is represented by a polynomial M(X) of degree < k with coefficients inGF (2).The corresponding codeword C(X) is thus :

C(X) = M(X)Xn−k + remainder

(M(X)Xn−k

g(X)

)(42)

In the simulation, the codewords are generated in this way, the complexity being lower than amatrix/vector multiplication.First, the remainder of the euclidean division of M(X)Xn−k by g(X) is computed. The sys-tematic part, that is M(X)Xn−k, is added afterwards.It is noticeable that every codeword is a multiple of the generator polynomial. The converse isalso true, every multiple of the generator polynomial is a codeword.

DecodingSince the code has a minimal distance of d = 5, up to t = 2 erroneous bits by received word canbe corrected.The cyclic properties of the original code are exploited to perform the decoding.For a given codeword, a cyclic (right or left) shift of its components yields another codeword.Hence, all the syndromes corresponding to received words with 1 and 2 errors do not need tobe computed. One can indeed shift the received word to come down to a case where the shiftedreceived word has an error in the first bit. It suffices to compute all the syndromes correspond-ing to 1 and 2 errors, including one in the first bit.



8.3 Golay 8 ENCODERS - DECODERS

The procedure used to decode a word is the following :

1. A zero is appended to the received word to be able to exploit the cyclic properties.

2. The syndrome is computed by taking the remainder of the received polynomial by g(X)

3. If the syndrome is equal to zero, the received word is correct. If it is not, a table look-upis performed to check if the syndrome corresponds to an error vector.

4. If it does, the received word is corrected by adding the error vector corresponding to thissyndrome. If it does not, the received word is cyclically shifted and the same procedureis applied to the new polynomial.

5. After all the shifts, if no syndrome was found, then the received word had more than t = 2errors and cannot be corrected. Otherwise, the word has been corrected.

NB : The cyclicity of the code reduces the number of syndromes to compute, and thus thetable look-up is less time consuming. In total there are

(n1

)syndromes corresponding to one

error, and(n2

)corresponding to two errors. Now, with one static error in first bit, there are only

1 syndrome corresponding to one error, and(n−1

1

)corresponding to two.

The gain in the general case is :

G =

∑tk=1

(nt

)∑tk=1

(n−1t−1

) (43)

In this case, t = 2 n = 16, the gain in G = 13616 = 8.5.

8.3 Golay

Two Golay codes are used in P25 phase 1, a standard code, and a shortened code formed froman extended Golay code.

Golay standard

EncodingThe standard (23, 12, 8) Golay code is a cyclic code. The procedure to encode such codes hasbeen described in the previous section. It is exploited to protect the Most Important Bits of avoice frame, for instance the pitch information as described in section 5.DecodingThe decoding is also the same as previously described. However, the Golay code can correct upto 3 errors. Thus, the numbers of syndromes to compute is higher and the gain defined witheq.(43) is equal to G = 2047

254 = 8.06

Shortened Golay

EncodingThe shortened (18, 6, 8) Golay code is not a cyclic code. It ensures the protection of the headercodeword described in section 5. This code is constructed from the extended (24, 12, 8) Golay



8.4 Reed-Solomon 8 ENCODERS - DECODERS

code which is not cyclic either. The extended code is formed from the standard (23, 12, 8)code by appending another parity bit at the end of the codeword. The shortened Golay code isformed by deleting the left most 6 bits of the extended code. That is keeping all the codewordswith 6 MSBs equal to zero and deleting this part. In the simulation, the generator matrix ishard-coded and the codewords are computed with a matrix/vector multiplication in GF (2).

DecodingThe LSB of the received word is ignored and 6 bits are appended as MSBs so that the cyclicalproperties can be used. The decoding is then similar to the procedure used for the standardGolay. Moreover, it also has a minimal distance of 8 and can thus correct up to 3 errors. Thegain defined with eq.(43) is also G = 2047

254 = 8.06

8.4 Reed-Solomon

The Reed-Solomon codes are used in both phases of Project 25.

In phase 1:

• A (24,12,13) code is used to protect the Link Control word, that contains data about thecommunication. This may the source identifier, the talk-group identifier or other kind ofinformation.

• A (24,16,9) code protects the Encryption Sync Word together with the shortened Hammingcode previously described.

• A (36,20,17) code protects the header frame together with a Golay code previously defined.

In phase 2:

• A (46, 26, 21) code is used to protect an IEMI frame.

• A (45, 26, 20) code protects a S-OEMI frame.

• A (52, 30, 23) code ensures the transmission of an I-OEMI frame

• A (44, 16, 29) code protects the Encryption Sync Signal

IEMI, S-OEMI and I-OEMI frames are not detailed in this report, they are used to transmitvarious kind of data in different conditions.

EncodingThe Reed-Solomon encoder requires the use of a different algebra and the concept of GaloisField with order p, GF(2p), that is a special finite dividing ring with 2p elements.Details about Reed-Solomon codes can be found in [1], [7] and [2].AdditionIn this ring addition is a bit-to-bit XOR.

MultiplicationThe multiplication is defined from a primitive characteristic polynomial with coefficient inGF (2)(F (α) = α6 +α+ 1 in this case). The successive powers of α (α0, α1, α2...) are divided by F (α).




The remainder of this division yields a polynomial of degree < deg(F ) = p. This polynomialhas coefficients in GF (2) and thus can be seen as a binary vector of length p.The decimal values corresponding to these vectors (and thus to the successive powers of α) arestored in a table exp.Multiplying a0 and a1 with (a0 = αe0 , a1 = αe1) ∈ GF (2p)2, results in a0a1 = α(e0+e1)[2p−1]).The values e0 and e1 are also stored in a table, namely log.

For this particular Galois Field :

b 0 1 2 3 4 5 6 7 . . .

log(b) NaN 0 1 6 2 12 7 26 . . .

Table 5: Logarithm table in GF(26)

e 0 1 2 3 4 5 6 7 . . .

exp(e) 2 4 8 16 32 3 6 12 . . .

Table 6: Exponential table in GF(26)

The Reed-Solomon code being cyclic, the encoding of a message M(X) is the same as the onedescribed for the cyclic code. However, the euclidean division must now be computed in GF (2p).DecodingDecoding a (n, k, d) Reed-Solomon code is a daunting task since it can correct many errors.Although it is a cyclic code, a syndrome decoding method would be too time-consuming, be-cause the size of the look-up table would be too considerable. The chosen procedure, based onPeterson-Gorenstein-Zierler algorithm, is described below :

A generator polynomial of a Reed-Solomon code is given by :

g(X) =n−k∏i=1

(X + αi) (44)

Let R(X) be a received word.If R(X) is erroneous, it can be written as the sum of a correct codeword polynomial C(X) andan error polynomial E(X).

R(X) = C(X) + E(X) (45)

Since C(X) is a multiple of the generator polynomial g(X), the roots of g are also roots of C,the syndromes are denoted Sj , and are defined as:

Sj = R(α(j+1)) = E(α(j+1)) =w∑k=1

eikα(j+1)ik ∀j = 0 . . . n− k − 1 (46)




Where w is the number of errors in E(X) (R(X) can be corrected iff w ≤ t).

Let λ(X) =∏wk=1(1 +Xαik) = 1 +

∑wk=1 λkX

k be the locator polynomial. The errors locationscan easily be deduced from λ’s roots.One can prove that :

λwS0 + λw−1S1 + · · ·+ λ0Sw = 0λwS1 + λw−1S2 + · · ·+ λ0Sw = 0...

...λwSn−k−w−1 + λw−1Sn−k−w + · · ·+ λ0Sn−k−1 = 0

(47)

This system can be re-written as :

S0 S1 . . . SwS1 S2 . . . Sw+1...

Sn−k−w−1 Sn−k−w . . . Sn−k−2

λwλw+1

...λ1

=

SwSw+1

...Sn−k−1

(48)

The number of errors w is unknown. However, it is required to both define and solve the linearsystem. The method used in the simulation to find w is to define the matrix Smat:

Smat =

S0 S1 . . . Sn−k

2−1

S1 S2 . . . Sn−k2

...Sn−k

2−1 Sn−k

2. . . Sn−k−2

(49)

The matrix rank corresponds to the number of errors w (there are w linearly independent rowsin Smat). The rank is computed using the Gauss-Jordan reduction on Smat in the Galois FieldGF (2p). Then, the linear system (48) is solved, using Gauss-Jordan reduction again. Thatyields the coefficients of polynomial λ. Since the roots of λ are elements of GF (2p), whichis a finite field of 2p elements, it is easy to determine the roots of lambda by computing λ(a)∀a ∈ GF (2p). In practice, only n values of GF (2p) are used, since the errors can only be locatedin the codeword! Thus, the script computes :

λ(α−ik) ∀ik = (1, . . . , n) (50)

The set of ik for which λ(α−ik) = 0 gives the errors locations.Let Xk = αik and Yk = eik ∀k ∈ (1, . . . , w). Then eq.(46) can be re-written as :

X1 X2 . . . Xw

X21 X2

2 . . . X2w

...Xw

1 Xw2 . . . Xw

w

Y1

Y2...Yw

=

S1

S2...Sw

(51)

The Gauss-Jordan reduction algorithm is anew used to solve eq.(51) in GF (2p). Hence, theerror values Yk are known and the received word can be corrected.



8.5 BCH code 8 ENCODERS - DECODERS

There exists more efficient algorithm, for example the Berlekamp-Massey method that has alsobeen implemented in the simulation but is not described in this report.

8.5 BCH code

The original BCH code is the a (63, 16, 23) code. An additive parity bit is added as the XORbetween the two LSBs of the input vector. It is used to protect the Network IDentifier alongwith the Data Unit ID which specifies which type of data is sent, for instance a LDU1, LDU2...EncodingThe encoding is completely similar to the encoding of a cyclic code as described in a previoussection. The only difference is the additive parity bit appended at the end of the codewordobtained with the (63, 16, 23) BCH code.DecodingThe decoding is similar to the Reed-Solomon procedure. In the simulation, the last parity bitis ignored.The generator polynomial of the BCH code is given by :

g(X) =

2t∏i=1

(X + αi) (52)

With t being the error correction capacity. (Note : For a Reed-Solomon code n− k = 2t).The rest of the decoding is completely similar to the procedure described in the previous section.

8.6 Trellis code

EncodingTwo trellis codes are used, a rate 1

2 code and a rate 34 code. There are both exploited to protect

data frames in the data communication mode, that is when no voice frames are transmitted.

Input0 1 2 3

State

0 2 12 1 151 14 0 13 32 9 7 10 43 5 11 6 8

Table 7: States Transitions for Trellis code 1/2

It takes FSM state as row entry and input dibit as column entry.DecodingA Viterbi method with hard-input/hard-output is used to decode the trellis code.

8.7 Simulation acceleration

In order to obtain consistent results for the simulation, using many different conditions, partof the simulation was coded in C using mex-files. The processing was considerably accelerated,



8.7 Simulation acceleration 8 ENCODERS - DECODERS

Input0 1 2 3 4 5 6 7

State

0 2 13 14 1 7 8 11 41 14 1 7 8 11 4 2 132 10 5 6 9 15 0 3 122 6 9 15 0 3 12 10 52 15 0 3 12 10 5 6 92 3 12 10 5 6 9 15 02 7 8 11 4 2 13 14 13 11 4 2 13 14 1 7 8

Table 8: States Transitions for Trellis code 3/4

particularly for the channel coding part. Time measures were done for each of the decoders,first using the Matlab implementation and then mex-files. The results are presented in table 9.

Decoders Matlab implementation Mex-files Gain

Hamming Standard 20 µs/bit 50 ns/bit 400

Hamming Short 25 µs/bit 20 ns/bit 1250

Golay Standard 360 µs/bit 240 ns/bit 1500

Golay Short 650 µs/bit 400 ns/bit 1625

Cyclic Short 330 µs/bit 200 ns/bit 1650

Reed-Solomon Header 370 µs/bit 730 ns/bit 500

Reed-Solomon Link Control 310 µs/bit 950 ns/bit 325

Reed-Solomon Encryption 160 µs/bit 700 ns/bit 230

BCH 4750 µs/bit 5400 ns/bit 880

Trellis - Rate 1/2 220 µs/bit 920 ns/bit 240

Trellis - Rate 3/4 340 µs/bit 1190 ns/bit 290

Table 9: Simulation time gains



9 SYNCHRONIZATION

9 Synchronization

In order to sample at the right time, the system needs to be synchronized. During this thesis,the synchronization algorithm has solely been implemented for P25 phase 1. It consists of twosteps described thereafter:

9.1 Rough temporal synchronization

This synchronization is done by using a signal which is not sampled at a high frequency ratecompared to the symbol rate. A sampling rate 10 to 20 times higher than the symbol ratesuffices to get a satisfying rough synchronization. In P25 phase 1, a synchronization frameis sent at the beginning of the header and at the beginning of every LDU frame. That is atleast every 180 ms. This frame consists of a deterministic sequence of 48 bits, let ref[k] be themodulated signal of this frame sampled at fos. Let N be the length of this signal and s[k] be thereceived base-band signal. The purpose of this algorithm is to find where the synchronizationframe is within the signal.The inter-correlation between s and ref is therefore computed:

inter[n] = |N−1∑k=0

s[k + n]ref[k]∗|2 (53)

It is normalized by the power of the received signal:

pow[n] =N−1∑k=0

|s[k + n]|2 (54)

Thus, the ratio of those two expressions is computed and the index of the maximum yields theposition of the synchronization frame:

corr[n] =inter[n]

pow[n](55)

Let n0 be the index of corr’s maximum.

9.2 Fine-tuning

The perfect sampling time is unlikely to be exactly situated at a time t0 = k0Tos, a bias δt canexist, and be equal up to Tos/2 if the rough synchronization has been well done. The fine-tuningconsists in defining a signal :

refδt [k] = ref(kTos + δt) (56)

When δt is small, the following assumption holds:

refδt [k] = ref[k] + δtdref[k]

dt(57)

Let Γ = corr diff[n0]corr[n0]



9.2 Fine-tuning 9 SYNCHRONIZATION

corr diff[n0] =N−1∑k=0

s[n0 + k]dref[k]

dt

∗(58)

corr[n0] =N−1∑k=0

s[n0 + k]ref[k]∗ (59)

Furthermore,

Γ =K∗1 + δtK2

K0 + δtK1(60)

where :

K0 =N−1∑k=0

|ref[k]|2 (61)

K1 =N−1∑k=0

dref[k]

dtref[k]∗ (62)

K2 =

N−1∑k=0

|dref[k]

dt|2 (63)

Therefore, for δt small, the following assumption holds:

δt = real

(K∗1 −K0Γ

K1Γ−K2

)(64)

With this method, the optimal sampling time can be determined in two steps. The only choicethat has to be made, is the original sampling time Tos.



10 PERFORMANCES

10 Performances

10.1 Definitions

Numerous specifications are defined in Project 25 standard, some are easily achievable whilesome require a considerable work. In any case, the system should be optimized to obtain thebest performances.A static sensitivity lower than the one required implies that the user will be able to use thesystem, therefore to communicate in bad conditions thanks to a more robust radio system.In this part, several results are shown in different conditions, without fading, with fading at 8km/h, at 100 km/h, in a single path or multipath environment...The speed in the following results denotes the relative speed between the emitter and thereceiver.

• Static Reference Sensitivity: It is defined as the level of receiver input signal at a specifiedfrequency with specified modulation which will result in the standard BER (5%) at thereceiver detector.

• Faded Reference Sensitivity: It is defined as the level of receiver input signal at a spec-ified frequency with specified modulation which, when applied through a faded channelsimulator, will result in the standard BER at the receiver detector.

• Adjacent Channel Rejection: It is the ratio of the level of an unwanted input signal locatedin an adjacent channel that causes the BER produced by a wanted signal 3 dB in excess ofthe reference sensitivity to be reduced to the standard BER, to the reference sensitivity.For the measure, an interferer using the same modulation scheme has been set in anadjacent channel and has been randomly delayed to provide a more realistic statistics.

• Co-channel Rejection:

The co-channel rejection is the ratio of the level of an unwanted input signal located in thechannel that causes the BER produced by a wanted signal 3 dB in excess of the referencesensitivity to be reduced to the standard BER, to the reference sensitivity.

• Delay spread resistance:

The delay spread resistance is a measure made when a two paths mode is used and therelative speed between the transmitter and the receiver is 100 km/h. It is the delay fromwhich an unwanted signal causes the BER produced by a wanted signal 31 dB in excess ofthe reference sensitivity to be reduced to the standard BER, to the reference sensitivity.This test is realized in a simulcast mode with two paths, both having the same powerlevel.

Relation between received Power and EbN0

The standard specifications define performances in regards to the power level received by theterminal or base station.Let :

• F be the noise figure of the radio equipment (in dB).



10.2 Modem - Phase 1 10 PERFORMANCES

• W be the useful bandwidth (that is the channel filter bandwidth, in Hz).

• kB the Boltzmann constant

• T the room temperature (in Kelvin)

Then the noise N in (dB) at the receiver is :

N = 10 log10(kBTW ) + F (in dBW) (65)

At T = 290K, for a bandwidth of W = 7 kHz and a noise figure of F = 6 dB :

N = −129.55 dBm

10.2 Modem - Phase 1

10.2.1 Static Reference Sensitivity

For a base station, the standard requires a maximum RF input level of −116 dBm for referencesensitivity. This corresponds to an equivalent level of Es

N0of 13.5 dB, and thus an Eb

N0of 10.5 dB.

The relative speed between the emitter and the receiver induces a Doppler Shift that alters thesignal. This Doppler shift creates a slow-fading channel.

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1510−4

10−3

10−2

10−1

100

EbNo (dB)

BER


CQPSK static, speed 0, enc RAW, eqC4FM static, speed 0, enc RAW, eq

Figure 10-1: Static Reference Sensitivity - Phase 1

The static results are slightly better for the CQPSK modulation than for the C4FM modulation.This result was expected since the demodulation used is designed for a CQPSK modulation. Itstill yields acceptable results for a C4FM scheme.

10.2.2 Faded Reference Sensitivity

For a base station, the standard requires a maximum RF input level of −108 dBm for the fadedreference sensitivity. This corresponds to an equivalent level of Eb

N0of 18.5 dB.




Typical Urban, 8 km/h (TU8)

0 2 4 6 8 10 12 14 16 18 20 22 24 2610−3

10−2

10−1

100

EbNo (dB)

BER


CQPSK TU, speed 8, enc RAW, eqC4FM TU, speed 8, enc RAW, eq

Figure 10-2: TU 8 sensitivity - Phase 1


0 2 4 6 8 10 12 14 16 18 20 22 24 2610−3

10−2

10−1

100

EbNo (dB)

BER




The performance differences between Fig.10-2 and Fig.10-3 modes is not pronounced at lowSNR (EBN0

< 14 dB). This means that the Doppler shift does not have a strong influence. Thisis understandable, since the coherence time is much higher than the symbol time, this meansthat the channel variations are not palpable on a symbol scale, therefore demodulation is notclearly affected by the speed. Nevertheless, for a long period of time, deep fades can occur andtherefore cause errors.At high speed, the fades last for a longer time but occur more rarely, therefore the speed hasan effect on the performances, but its value is not such an important matter. However, the use




of a coherent demodulator would yield much better results at low speed than at high speed.Neverthless, it can be observed that at high SNR (EBN0

> 14 dB), the performances are consider-ably degraded at 100 km/h. This is explained by looking at the eye-diagram which is verticallyshifted because of the Doppler effect. Therefore, at high SNR, there will be more errors at highspeed than at low speed.

Hilly Terrain, 100 km/h (HT100)

0 2 4 6 8 10 12 14 16 18 20 22 24 2610−3

10−2

10−1

100

EbNo (dB)

BER


CQPSK HT, speed 100, enc RAW, eqC4FM HT, speed 100, enc RAW, eq

Figure 10-4: HT 100 sensitivity - Phase 1

The difference between HT and TU propagation models is not significant, as it is pointed out inAppendix A, both models present flat responses in a 12.5 kHz bandwidth. Solely the attenuationdiffers, and appear to worsen the performances in the Hilly Terrain propagation mode. This isprobably due to the strong path delayed by 15 µs which makes the demodulator prone to errors.




10.2.3 Adjacent Channel Rejection

−80 −78 −76 −74 −72 −70 −68 −66 −64 −62 −60 −58 −56 −54 −52 −50 −48 −46 −44 −42 −4010−2

10−1

100

CI (dB)

BER

BERs as a function of CI (dB)


Figure 10-5: Adjacent Channel Rejection - Phase 1

The channel rejection is much better for the CQPSK modulator than for the C4FM modulator.This is due to the poor spectrum efficiency of the constant phase modulation as observed Fig.7-5. The required rejection of 60 dB is not reached by this modulation with the chosen receiver.However, this receiver is optimal for the CQPSK modulator but not for the C4FM. A rejectionof 62 dB was attained with the perfect receiver.

10.2.4 Co-channel Rejection

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1510−2

10−1

100

CI (dB)

BER



Figure 10-6: Co-channel Rejection - Phase 1

It is difficult to give a conclusion on the co-channel rejection which is almost intrinsic to themodulation scheme used. Both modulations are conformed to the standard requirements whichsets a maximal co-channel rejection of 9 dB.




10.2.5 Delay spread resistance

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 12010−4

10−3

10−2

10−1

100

Delay (µs)

BER

BERs as a function of Delay (µs)


Figure 10-7: Delay spread resistance - Phase 1

Both modulations behave almost equally to the delay spread test. By looking at the eye-diagrams Figs.7-3 and 7-11, the wider, that is CQPSK, is likely to be the most resistant to sucha test. On another hand, an amplitude modulation is not as resistant as a constant envelopemodulation, so again it is difficult to conclude on this basis. An optimal receiver for the C4FMwould have given slightly better results for this modulation scheme.

The standard gives the power level standard requirements in dBm. For the conversion to SNRs,An arbitrary noise factor of 6 dB was chosen, this is easily achievable for a base station. Thebest radio equipment can reach a noise factor of down to 3 dB.

Co- Superior Inferior DelayStatic TU8 TU100 HT100 channel adjacent adjacent spread(dB) (dB) (dB) (dB) (dB) channel channel (µs)

(dB) (dB)

C4FM 5.8 11.8 12.2 12.6 7.6 −58.6 −58.6 68

CQPSK 5.3 11.2 11.2 11.4 6.7 −68.6 −68.6 75

standardrequirement < 10.5 < 18.5 < 18.5 < 18.5 < 9 < −60 < −60 > 50BER = 5%

Table 10: Results summary and comparison to standard requirements - Phase 1

Table 10 summarizes the modulators performances for phase 1. On the whole, CQPSK obtainsbetter results that the C4FM. However, in a real radio platform, an amplitude modulationpresents more problems. For instance, the power amplifier in a terminal or a base stationhas to be linear on a larger range. For a given amplifier, a constant envelope signal can be




sent with a higher average power than an amplitude modulated signal. Such modulationsencounter problems of saturation and in consequence, clipping; the signal and therefore thesystem performances are degraded. This problem is well known and there exists methods toreduce the Peak to Average Ratio of a signal and limit the degradation.The table also shows that a single standard requirement is not met, the adjacent rejection forthe C4FM modulation scheme. A test with its perfect non-coherent receiver yielded a rejectionover 60 dB but this causes another problem. The standard indeed requires the use of the samedemodulator regardless of the modulation used by the emitter. Using the optimal receiverfor the C4FM scheme causes a substantial degradation of the CQPSK performances. Furtherstudies should be done to fix this issue.Details about the measurement procedures can be found in [9].

10.3 Modem - Phase 2

10.3.1 Static Reference Sensitivity

.−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

10−5

10−4

10−3

10−2

10−1

100

EbNo (dB)

BER


HCPM static, speed 0, enc RAW, eq MLSEDQPSK static, speed 0, enc RAW, eqD8PSK static, speed 0, enc RAW, eq

Figure 10-8: Static Reference Sensitivity - Phase 2

The same remarks as in phase 1 can be done. An exception is the D8PSK modulation whichuses a reduced symbol rate but a greater number of bits per symbol to reach the same bitrateof 12 kbit/s. The reduced minimal distance between symbols causes poor BERs performancescompared to the two other schemes defined in phase 2.

10.3.2 Faded Reference Sensitivity





0 2 4 6 8 10 12 14 16 18 20 22 24 2610−5

10−4

10−3

10−2

10−1

100

EbNo (dB)

BER


HCPM TU, speed 8, enc RAW, eq MLSEDQPSK TU, speed 8, enc RAW, eqD8PSK TU, speed 8, enc RAW, eq



0 2 4 6 8 10 12 14 16 18 20 22 24 2610−3

10−2

10−1

100

EbNo (dB)

BER




As it can be observe in Fig.10-9 and 10-10, the speed influence is also limited in phase 2 whichwas expected. The symbol time is reduced compared to phase 1 and therefore reduces theinfluence of the Doppler shift on the signal.

Hilly Terrain, 100 km/h (HT100)




0 2 4 6 8 10 12 14 16 18 20 22 24 2610−3

10−2

10−1

100

EbNo (dB)

BER


HCPM HT, speed 100, enc RAW, eq MLSEDQPSK HT, speed 100, enc RAW, eqD8PSK HT, speed 100, enc RAW, eq

Figure 10-11: HT 100 sensitivity - Phase 2

Concerning the influence of a multipath propagation, the conclusions given for phase 1 alsoapply to phase 2.

10.3.3 Adjacent Channel Rejection

−80 −78 −76 −74 −72 −70 −68 −66 −64 −62 −60 −58 −56 −54 −52 −50 −48 −46 −44 −42 −4010−2

10−1

100

CI (dB)

BER



Figure 10-12: Adjacent Channel Rejection - Phase 2

Both amplitude modulations are well rejected and meet the standard requirements. However,the continuous phase modulation is anew not sufficiently rejected. Improvements have to berealized on the MLSE equalizer as well as on the channel filter. No change can be done on thetransmission chain since it is defined in the standard and therefore cannot be modified.




10.3.4 Co-channel Rejection

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1510−2

10−1

100

CI (dB)

BER



Figure 10-13: Co-channel Rejection - Phase 2

Same conclusions as in phase 1 apply for the co-channel rejection. The D8PSK standard re-quirement is not defined but the modulation seems to present a particularly low rejection.

10.3.5 Delay spread resistance

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 12010−4

10−3

10−2

10−1

100

Delay (µs)

BER

BERs as a function of Delay (µs)


Figure 10-14: Delay spread resistance - Phase 2

Both D8PSK and DQPSK modulators have a wide eye-diagram, and especially the D8PSKmodulation since the defined symbol time is higher than for the other modulations, thereforeit was expected to yield best results for this test. This conclusion does not hold in practice,excepted for high delays between the two paths. This is explained by the poor performancesthat this modulation presents in a fading mode. Fig.10-14 shows that the Bit Error is much



10.4 Encoders/Decoders tests 10 PERFORMANCES

higher for the D8PSK than for the DQPSK when there is only a single path, that is when thedelay between the two paths is zero.Both DQPSK and HCPM schemes meet the standard requirements for this test.

Superior Inferior DelayStatic TU8 TU100 HT100 Co-channel adjacent adjacent spread(dB) (dB) (dB) (dB) (dB) channel channel (µs)

(dB) (dB)

H-CPM 6.8 12.8 12.6 12.9 8.6 −50.2 −50.5 55

standard < 10.5 < 18.5 < 18.5 < 18.5 < 9 < −60 < −60 > 35requirement

H-DQPSK 5.6 11.2 11.7 11.6 7 −63.5 −64 76

standard < 10.5 < 18.5 < 18.5 < 18.5 < 9 < −60 < −60 > 65requirement

D8PSK 11.5 16.8 17.8 17.9 11.6 −64 −64.5 61

standard - - - - - - - -requirement

Table 11: Results summary and comparison to standard requirements - Phase 2

Table 11 summarizes the modulators performances for phase 2, all the SNRs are those obtainedor required for a BER of 5%. A single requirement is not met in phase 2, the adjacent rejectionfor the H-CPM modulator, improvements have to be done on the receiving chain to reachit. The D8PSK scheme, which is currently studied by the TIA does not seem to bring anyimprovements compared to the DQPSK. Its reduced symbol rate was expected to help it resistlarge delays between paths in a multipath propagation model. This should have made thisscheme particularly appropriate for a simulcast communication. Nevertheless, its particularlypoor results in both static and dynamic conditions impact strongly its resistance to delay spread.No standard requirements have been defined so far for this scheme, therefore it is difficult toget an idea of what the TIA expects of this modulation.

10.4 Encoders/Decoders tests

The perfect encoding/decoding without any error additions has been performed for the shortestencoders by constructing all possible inputs, encoding them and decoding them. For the largestcodes, many random inputs have been encoded and then decoded.The perfect decoding of all corrigible errors has been performed for the simplest decoders. Thishas been done by constructing all error words with up to t ones, t being the error correctioncapability of the code. Those error words have then been fed into the decoder, the decoded code-words have been checked to be zero codewords. Since the perfect encoding/decoding withoutany errors had been previously checked, the linearity of the codes ensures the perfect decodingwhen a codeword has up to t errors.



10.5 Graphical user interface 10 PERFORMANCES

Figure 10-15: Results Visualization GUI

10.5 Graphical user interface

In order to present the results in a clear fashion, a GUI was created using Matlab guide, pro-viding the interface presented Fig.10-15.

The different menus are :

1. Choice of p25 phase

Make the modulators of either P25 phase available to the user for performances visualiza-tion.

2. Choice of modulators

For phase 1 :

• C4FM

• CQPSK

For phase 2 :

• DQPSK




• D8PSK

• H-CPM

3. Equalizer (available for H-CPM modulator only)

Possible choices :

• Linear Zero-Forcing (L-ZF)

• Decision Feedback Zero-Forcing (DFE-ZF)

• Linear Minimum Square Error (L-MSE)

• Decision Feedback MSE (DFE-MSE)

• Maximum Likelihood Sequence Estimator (MLSE)

4. Type of results

Possible choices :

• BER vs EbN0

results

• BER vs CI results (Interferer)

• BER vs delay spread results

• Eye-diagram of the received baseband signal

• Constellation of the baseband modulated signal

• Impulse response of the transmission filter

• Power Spectral Density of the baseband modulated signal

5. Interferer (available for CI results only)

Possible choices :

• Interferer in the superior adjacent channel

• Interferer in the inferior adjacent channel

• Interferer in the co-channel

6. Data Type

This menu allows to see the BER performances when using a certain encoder, or when aparticular type of data is sent over the channel.

Possible choices :

• RAW - Random bit-stream

• HEADER - Header frame

• LDU1 - Voice frame

• CYCLIC - data encoded using the shortened cyclic code

• HAMMING-STD - data encoded using the standard Hamming code

• HAMMING-SHT - data encoded using the shortened Hamming code

• GOLAY-STD - data encoded using the standard Golay code




• GOLAY-SHT - data encoded using the shortened Golay code

• RS-HDR - data encoded using the shortened Reed-Solomon code used for the header

• RS-LC - data encoded using the shortened Reed-Solomon code used for the LinkControl

• RS-ES - data encoded using the shortened Reed-Solomon code used for the Encryp-tion

• BCH - data encoded using the shortened BCH code

• TRELLIS2 - data encoded using the rate 2/4 trellis code

• TRELLIS3 - data encoded using the rate 3/4 trellis code

7. Propagation and speed

Allows to see the performances in different propagation mode, and at different speed.

Possible choices :

• static, static condition, no multipath, no Doppler effect

• TU 8, Typical Urban condition, 8 km/h. (multipath and Doppler effect)

• TU 100, Typical Urban condition, 100 km/h. (multipath and Doppler effect)

• HT 100, Hilly Terrain condition, 100 km/h. (multipath and Doppler effect)



11 INTEGRATION ON A USRP DEVICE

11 Integration on a USRP device

11.1 Introduction

The second part of this internship was focused on integrating P25 physical layer on a radiodevice. This was achieved by using two Universal Software Radio Peripherals (USRPs), devicesdesigned by Ettus Research. Two different versions of URSPs were used:

• USRP E100

The letter E stands for embedded, the device indeed runs a full distribution of Linux. It isalso equipped with an OMAP3 processor along with a FPGA. The motherboard was usedtogether with a radio daughter-board capable of emitting and receiving a radio signal in thefrequency range [400 MHz, 4400 MHz]. The maximum transmission power is 20 dBm andthe daughter-board allows a full-duplex communication. The Linux distribution is barelyused, since the IQ samples have been directly sent to a computer using the UDP protocolon the 100 Mbit/s Ethernet link. Reception of IQ samples is done through a Matlabmex-file, to avoid missing packets. A missing packet involves a lost of the synchronizationand thus lost of the communication until the next synchronization is performed. All theprocessing is done with Matlab on a separate computer.

• USRP N210

The letter N stands for network, unlike the E100, it does not run a Linux distribution. Itcan be interfaced with Matlab, the samples being sent on the Gigabit Ethernet link. Itwas used with a radio daughter-board capable of emitting and receiving a radio signal inthe frequency range [70 MHz, 2200 MHz]. This board is only half-duplex.

The purpose of this integration was to validate the physical layer, as well as the MAC layer.That is the ability to decode a voice frame, a header frame as described section 5.

Figure 11-1: USRP R© E100 Figure 11-2: USRP R© N210

11.2 Matlab Spectrum Analyzer

A virtual spectrum analyzer was developed to get information about the received signal. TheGUI developed with Matlab can be seen in Fig.11-3. It is able to demodulate all the modulationschemes present in P25 phase 1 & 2. The eye-diagram is plotted as well as the constellation, inFig.11-3, it is a C4FM modulation scheme received from a Motorola terminal, namely XTS 5000Fig.11-4, with carrier at 806 MHz. The signal Power Spectral Density is also plotted and its sizecan be chosen in the range [256, 16384]. It is also visible in the waterfall, each line representing



11.2 Matlab Spectrum Analyzer 11 INTEGRATION ON A USRP DEVICE

the PSD at a given time, this feature is useful to track the behavior of the signal frequency intime.

Figure 11-3: Matlab GUI used to get ”real-time” information about the signal

Figure 11-4: Motorola terminal XTS 5000

A typical example can be seen in Fig.11-5. At the beginning of the transmission, there is adifference between the terminal carrier frequency and the receiver carrier frequency. Therefore,the PSD maximum is not located at the center of the waterfall. The carrier frequency is trackedby the receiver and a gradient method corrects the receiver frequency. Observe this drift towardthe emitter frequency. This correction can be observed by looking at the PSD peak movingtowards the center of the waterfall.



11.3 Intermediate frequency 11 INTEGRATION ON A USRP DEVICE

R:/Dossier_personnels/Mathieu_Simon/p25_simu_Matlab_doc/images/waterfall-1.png

−100 −80 −60 −40 −20 0 20 40 60 80 100

5

10

15

20

25

30

35

40

45

50

Frequency (kHz)

Tim

e(nounit)

0

5

10

15

20

25

30

35

40

45

50

55

60

Figure 11-5: Correction of the frequency shift, observed with a waterfall

11.3 Intermediate frequency

A problem was encountered with the received baseband signal. Instead of having a perfect circle,one could observe a constellation as the one depicted in Fig.11-6. There exist a slow varyingcomponent in the baseband signal which makes the center of the constellation move. Therefore,it creates this distorted constellation, this has an effect on the system performances. A solutionconsists in using an intermediate frequency. Instead of multiplying the passband signal by anexponential at the carrier frequency fc, it is multiplied by an exponential slightly shifted atfrequency fc + δf . This signal is then filtered to remove any DC component and numericallyshifted to yield the baseband signal. Since the channel bandwidth for a P25 system is 12.5 kHz,the intermediate frequency used was 20 kHz and the filter width 15 kHz. The constellation ofthis final signal is diagrammed in Fig.11-7.

−0.1 −8 · 10−2−6 · 10−2−4 · 10−2−2 · 10−2 0 2 · 10−2 4 · 10−2 6 · 10−2 8 · 10−2 0.1

−8

−6

−4

−2

0

2

4

6

8

·10−2

Inphase

Quad

rature

Constellation without using an Intermediate Frequency

Figure 11-6: Constellation obtained with-out any intermediate frequency

−8 −6 −4 −2 0 2 4 6 8

·10−2

−6

−4

−2

0

2

4

6

·10−2

Inphase

Quadrature

Figure 11-7: Constellation obtained withan intermediate frequency

Both USRPs have been tested in transmission thanks to a spectrum analyzer. Since this instru-ment can demodulate both P25 phase 1 schemes, it measures several parameters that allowsto evaluate the modulation conformity. Those parameters have been checked before trying to



11.4 Detection of synchronization frames 11 INTEGRATION ON A USRP DEVICE

establish a communication with a P25 terminal available on the market. A screenshot of thespectrum analyzer is shown in Fig.11-8.

Figure 11-8: Visualization of the demodulated signal on a spectrum analyzer

11.4 Detection of synchronization frames

As described in section 9, an algorithm tracks the synchronization frames to get the perfectsampling time. Fig.11-9 is extracted from a communication established by a terminal. Itrepresents the inter-correlation function between the received signal and the reference signal.Each synchronization frame creates a peak in the inter-correlation signal, depicted here witha red circle. At the beginning of the frame, from 0 s to ' 0.15 s, the transmission has notstarted yet. The power ramp-up can be observed from ' 0.15 s to ' 0.18 s, then the firstsynchronization frame is detected. The first frame is always a header frame, it lasts 82.5 ms, soit is shorter than a LDU frame which lasts 180 ms. This is why a narrower gap can be observedbetween the first and the second peak than between the followings.



11.4 Detection of synchronization frames 11 INTEGRATION ON A USRP DEVICE

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time (s)

Intercorrelation

amplitude

Intercorrelation between received signal and reference synchronization frame

Figure 11-9: Inter-correlation between received signal and reference

Once the synchronization is obtained, the different pieces of information are extracted. It hasbeen checked that no errors were detected by the different Forward Error Correction codes. Soit can be considered that the physical layer is compliant to the standard. In a second step, thevoice frames have been de-vocoded and the voice signal played through the computer speakersto check that it is audible and understandable.An example of such a signal is shown in Fig.11-10. Details about the vocoder defined in thestandard can be found in [8].

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Sou

ndsign

alamplitude

De-vocoded received signal after its transmission over the air

Figure 11-10: Reconstructed sound signal after transmission over the air



13 FURTHER STUDIES

12 Conclusion

This thesis is split into two main parts, the evaluation of P25 physical layer performances,followed by its integration on a real radio platform.The first part was implemented with Matlab with help of Mex files to speed up the simulation.The results that were extracted are momentous in the scope of a product development. Theygive a clear comprehension of what can be achieved by the system when the radio problemsare not taken into account. Many BER plots are present in this report, they were realized indifferent conditions. The first basic test is the determination of the static sensitivity which isan indicator of the optimal performances. Others conditions have also been modeled to makesure that the system reaches the standard requirements defined by the TIA. Some of theserequirements are easily reached, while some others, like the spectrum efficiency require moreeffort. Moreover, the Forward Error Correction codes have been implemented in accordanceto the standard. A substantial effort has been made on the decoding part, to improve bothrobustness and rapidity. This latter plays a considerable role when the decoding has to be doneon-the-fly, which is the ultimate purpose. Together with the FEC codes, the MAC structurehas been set up for P25 phase 1. This means respecting the frame formats, as well as allthe operations required to construct them. This includes bit interleaving, randomization andsplitting of codewords.The second part of this thesis was focused on validating the compliancy to the standard. TwoUSRPs have been used to this purpose, they were both interfaced with Matlab to exploit the P25simulation already developed. The capacity to transmit and receive a modulated signal has beensuccessfully tested with both devices, thanks to a spectrum analyzer. Communications betweenthe two USRPs have also been realized and validated. Finally, a voice signal transmitted overthe air by a Motorola terminal and received by a USRP has been re-played through a computerspeakers; validating the implemented system.

13 Further studies

At the end of this thesis, several tasks have to be carried out to get to a final product. The workthat has been done so far can be pursued in the scope of demonstrating the ability to achievea P25 communication. The Forward Error Correction part can be improved by using thereceived soft-symbols instead of the hard-symbols as it presently done. A better equalizer shallbe implemented for the H-CPM modulation scheme to achieve the standard requirements. Acoherent receiver could be implemented and the trade-off between complexity and performancesevaluated, in comparison to the non-coherent approach. A real-time repeater is achievable withina few months for the first phase of the standard. Since the symbol rates are very low, it canprobably even be accomplished with Matlab. However, if a commercial repeater has to bedeveloped, the entire hardware part has to be designed, the USRPs give indeed too poor radioperformances in both reception and emission.



A PROPAGATION MODELS

Appendices

A Propagation models

Figure A-1: Propagation models

In the simulation, different channel propagation models are used to evaluate the P25 layer 1performances. Multipath is simulated, each path being delayed and attenuated. Their amplitudeis Rayleigh distributed, the variance are deduced using the parameters given in table 12 for theTypical Urban mode and in table 13 for the Hilly Terrain mode. The Doppler shift is alsosimulated, the frequency shift is computed using the classic Doppler power spectral densityfunction ’bowl-shaped’. In this simulation, the frequency carrier is fc = 800 MHz, and themaximum speed that can be reached by a user (policeman, fireman...) is around 200 km/h,thus the maximum Doppler shift is ' 148 Hz.Three models are used :

• Static model

Solely one path and no Doppler effect.

• TU (Typical Urban) model

Six paths are modeled, delayed and attenuated as follows :

Parameters used in TU (Typical Urban) propagation mode

Path Relative delay (µs) Average mean power (dB)

1 0 -3

2 0.2 0

3 0.5 -2

4 1.6 -6

5 2.3 -8

6 5 -10

Table 12: TU propagation




Channel impulse and frequency responses are diagrammed in Fig.A-2.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

Time (µs)

Amplitude(dB)

Impulse response of TU channel

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−5

0

5

10

Frequency (MHz)

Pow

er(dB)

Frequency response of TU channel

Figure A-2: TU channel impulse response

• HT (Hilly Terrain) model

Six paths are modeled, delayed and attenuated as follows :

Parameters used in HT (Hilly Terrain) propagation mode

Path Relative delay (µs) Average mean power (dB)

1 0 0

2 0.1 -1.5

3 0.3 -4.5

4 0.5 -7.5

5 15 -8

6 17.2 -17.7

Table 13: HT propagation

Channel impulse and frequency responses are diagrammed in Fig.A-3.




0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Time (µs)

Amplitude(dB)

Impulse response of HT channel

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

Frequency (MHz)

Pow

er(dB)

Frequency response of HT channel

Figure A-3: HT channel impulse response

For both models, the frequency response of the channel has been plotted in the frequencyrange [0, 1 MHz]. It is noticeable that the frequency response can be considered as flat ina 12.5 kHz bandwidth which is the channel bandwidth in P25 phase 1. This was expected,since the coherence bandwidth is much larger than the useful bandwidth.Thus, the symbol time is much larger than the delay spread, and there is limited intersymbol interference.

The Doppler Power Spectral Density function formula is given by:

S(f) =

1πfd

1√1−(ffd

)2 for |f | < fd

0 otherwise(66)

fd is the maximum Doppler shift defined as :

fd =vmax

cfc (67)

where fc is the carrier frequency, vmax the maximum speed difference between the receiverand transmitter and c is the light speed.



B THETA’S PDF DERIVATION

B Theta’s pdf derivation

Let Θ be the random variable defined as :Θ = angle(1 + N) where N is an additive complex Gaussian noise with mean 0 and varianceN0.The derivation of Θ’s pdf can be useful to measure the impact of an additive noise on the phaseof a constant envelope baseband signal.

Figure B-1: Problem diagram

In Fig.B-1, the circle represents the area in which 1 + N will be with a certain probability. Theinteresting parameter here is the angle θ as depicted on the figure.The probability to be found is :

P (Θ ∈ [θ, θ + dθ]) = fΘ(θ)dθ; (68)

Since N is complex Gaussian, its real and imaginary components are also Gaussian with varianceN0/2. The real and imaginary part of 1 + N are also Gaussian and it is easy to write theprobability of 1 +N being in a rectangle. A polar change (r cosφ, r sinφ) gives :

fΘ(θ)dθ =

∫ θ+dθ

θ

∫ +∞

0

1

πN0exp

(− 1

N0

(r2 − 2r cosφ+ 1

))rdrdφ (69)

Moreover,

fΘ(θ)dθ =

∫ θ+dθ

θfΘ(φ)dφ (70)

Thus,

fΘ(θ) =

∫ +∞

0

1

πN0exp

(− 1

N0

(r2 − 2r cos θ + 1

))rdr (71)

Using variable change r = r−cos θ√N02

, this integral can be calculated. The results gives :



B THETA’S PDF DERIVATION

∀θ ∈ [−π, π] :

fΘ(θ) =1

2πe− 1N0

1 +

√π

N0cos θQ

− cos θ√N02

ecos2 θN0

(72)

The probability density function fΘ for a given N0 is diagrammed Fig.B-2.Note 1 : If φ(t0) 6= 0 the function would be the same, solely centred around φ(t0).Note 2 : The interested reader can check that the limit of Θ when N0 approaches infinity is auniform random variable in [−π, π].

Figure B-2: Θ probability density function



REFERENCES REFERENCES

References

[1] Marie-Claude Dumas. Codes correcteurs d’erreurs. 2002.

[2] J. Bibb Cain George C. Clark Jr. Error-Correction Coding for digital communications.Plenum Press, 1988.

[3] http://www.project25.org/. Project 25 technology interest group website.

[4] L. Husson P. Leray A. Wautier J-C Dany, J-L Guyzwiller. Signal et communication. 2011.

[5] John G. Proakis. Digital Communications - Third Edition. McGraw-Hill, 1995.

[6] Lars K. Rasmussen. Advanced Digital Communications. Kungliga Tekniska Høgskolan,January 2013.

[7] Daniel J. Costellor Jr Shu Lin. Error Control Coding: Fundamentals and Applications.Prenctise-Hal, 1983.

[8] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 Vocoder De-scription, is102.baba edition, july 1993.

[9] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 DigitalC4FM/CQPSK Transceiver Measurement Methods, tsb102.caaa edition, april 1994.

[10] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 DigitalC4FM/CQPSK Transceiver Performance Recommendations, tsb102.caab edition, august1994.

[11] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 Recom-mended Common Air Interface, tsb102.baaa edition, april 1994.

[12] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 Common AirInterface Conformance Test, tsb102.baab-a edition, august 1995.

[13] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 Phase 2Two-Slot Time Division Multiple Access Physical Layer Protocol Specification, tia-102.bbabedition, July 2009.

[14] TELECOMMUNICATIONS INDUSTRY ASSOCIATION. APCO Project 25 Phase 2Two- Slot TDMA Media Access Control Layer Description, tia-102.bbac edition, December2010.



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