Digital Modems Lecture 1 Fall 2008. Course “mechanics”
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Transcript of Digital Modems Lecture 1 Fall 2008. Course “mechanics”
Digital Modems
Lecture 1Fall 2008
Course “mechanics”
Schedule & names for this semester
Every Tuesday, 12 pm-2:15 pm Lecturers
Andreas Polydoros Costas Aidinis Stelios Stefanatos
{polydoros}, {caidinis}, {sstefanatos}@phys.uoa.gr
Offices: Building V, Second floor.
Course Outline Fundamentals of detection theory
Detection problem formulation Cost functions Likelihood ratio Optimal detection rules (Bayes/Neyman-Pearosn) Handling of nuisance parameters
Discrete representation of stochastic processes Signal space/basis Orthonormal/Karhunen-Loeve expansion Likelihood functionals
Application in communications Binary/M-ary systems Coherent/Non-coherent detection in AWGN Error probability
Recommended Reading
Course text-book
H. L. Van Trees, Detection, Estimation, and modulation theory
Additional references
J. G. Proakis, Digital Communications S. M. Kay, Fundamentals of statistical signal processing:
Detection theory
A Systems View
ISO-OSI Protocol stack
Application Layer
Network Layer
Link Layer
Physical Layer
Transport Layer
Web, FTP, VoIP
TCP, UDP
IP, routing
MAC
Capacity, bits, noise, waveforms
TerminologyThe 'Open Systems Interconnection Basic Reference Model' (OSI Reference Model or OSI Model) is an abstract description for layered communications and computer network protocol design. It was developed as part of the Open Systems Interconnection (OSI) initiative[1]. In its most basic form, it divides network architecture into seven layers which, from top to bottom, are the Application, Presentation, Session, Transport, Network, Data-Link, and Physical Layers. It is therefore often referred to as the OSI Seven Layer Model.
The Physical Layer defines the electrical and physical specifications for devices. In particular, it defines the relationship between a device and a physical medium.
To understand the function of the Physical Layer in contrast to the functions of the Data Link Layer, think of the Physical Layer as concerned primarily with the interaction of a single device with a medium, where the Data Link Layer is concerned more with the interactions of multiple devices (i.e., at least two) with a shared medium. The Physical Layer will tell one device how to transmit to the medium, and another device how to receive from it (in most cases it does not tell the device how to connect to the medium). Obsolescent Physical Layer standards such as RS-232 do use physical wires to control access to the medium.The major functions and services performed by the Physical Layer are:Establishment and termination of a connection to a communications medium. Participation in the process whereby the communication resources are effectively shared among multiple users. For example, contention resolution and flow control. Modulation, or conversion between the representation of digital data in user equipment and the corresponding signals transmitted over a communications channel. These are signals operating over the physical cabling (such as copper and optical fiber) or over a radio link.
Source: http://en.wikipedia.org/wiki/OSI_model
Three-part PHY-layer system model
Tx: Transmitter Rx: Receiver Channel: Models the physical distortion Noise: Thermal noise, interference, …
Tx Channel Rx
noise
Block-Diagram Functions of Tx
Source Discrete or analog
Source coding Redundancy removal (entropy coding) Data compression (introducing distortion)
Channel coding Introduces redundancy to compensate for channel/noise
Data format Mapping bits to symbols, create packets, frames, e.t.c.
Modulator Convert the discrete-time input to the continuous-time
transmitted waveform
source coding
channel coding
data format
modulatorsource
Transmitted waveform
Receiver performs the inverse operations
Tx-Rx diagram for different AI’s
- BPSK (m=1)- QPSK (m=2)- 16-QAM (m=4)- 64-QAM (m=6) m=log2(Μ)
2log ( )b
W
RR
r M
/bR rbRBitSource
Encoding Interleaving
Modulation
SymbolMapping
IFFTSerial/Parallel
CPInsertion
Spreading Scrabling
Rx
Tx
Channel
Equalization/demodulation
FFTEqualization -Parallel/Serial
CPRemoval
Despreading/Equalization
Descrabling
Channel estimation /Synchronization
Decoding DeinterleavingSymbol
Demapping
WR W CR R
1) Single Carrier2) CDMA3) Multi-carrier
(1)
(2)
(3)
(2)
(1)
(3)
0
bE
N 0
CbE
N
Scrambler Puncturing InterleaverReed-
SolomonConvolutional
Encoder
Turbo Encoder Puncturing
Constellation Encoder
Pilot Generator
Pilot & Data Multiplexer
ST Encoder (TSD)
Mapping
Mapping
IFFT
IFFT
Cyclic Prefix Insertion
PAPR Scaling
Output Logic
Adaptivity Control
From
RxPreambles Generator
Output Logic
PAPR Scaling
Cyclic Prefix Insertion
Input LogicData
Command
A modern Tx: MIMO/OFDM
A modern Rx: MIMO/OFDM
Input Logic
Input Logic
PAPR Scaling
PAPR Scaling
Synchronization
Frame Acquisition
Symbol Offset Estimation
Frequency Offset Estimation
Frame Acquisition
Symbol Offset Estimation
Frequency Offset Estimation
Joint Sym
bol Synch
Joint Frequency O
ffset Synch
Sync Preamble Extraction
Cyclic Prefix Extraction
Cyclic Prefix Extraction
FFT
FFTSync
Preamble Extraction
Demapper / DC Extraction
Demapper / DC Extraction
Channel Acquisition
ST Decoder (TSD)
Maximum Ratio Combiner
Phase TrackingPhase
Correction
Soft Decision Constellation
Decoder
LLR Constellation
Decoder
De-PuncturingDe-Interleaver Reed-Solomon
Convolutional Decoder (Viterbi)
Output Logic
Turbo DecoderDe-Puncturing Noise variance / SNR estimation
Adaptive Metric Calculation
Preambles
Data RxPilots
Data Preambles
Data Rx
Theory
Physical Channel
Distortion-less (LOS) channel:
Two-ray channel:
2j fh t A t H f Ae F
A
: channel gain: delay
21 j fh t t A t H f Ae F
Tx
Rx H f
f1
21
2
Physical Channel
The two-ray channel is the simplest example of a multipath fading channel
Question: Under what circumstances is the two-ray channel distortion-less
Answer: It depends on the pulse shape If the channel is (approximately) distortion-
less If the channel inevitably introduces severe distortion
2T2T
x t
F
sin 2
2
fTX f
fT
1 T
2 1 2 ( )T T T
Inference in general
Inference is the task of learning (e.g., making estimations/decisions) based on given data
Examples of inference: Estimate the path loss introduced by a fading channel Estimate the range of an enemy aircraft Predict the stock market’s gain/loss Decide on which product is best Decide on which model best fits the observations
In this course we concentrate on a single sub-topic of inference theory: Hypothesis testing (Detection theory)
Emphasis will be given on how the theory is applied to design optimal receiver structures
Decision criteria
A cost function must be defined in order to obtain a detection rule
This function quantifies the cost of taking erroneous decisions What is the cost of “detecting” an aircraft when it is
actually not there? What is the cost of missing the presence of the aircraft?
After construction of the cost function an optimal decision rule can be obtained that results in minimum cost
The appropriate cost function depends upon the context of the specific problem and is not unique
Hypothesis testing @ Rx side
Problem formulation: We are given a set of data (observations)
This set could have been generated as the outcome of one of M possible hypothesis
Given the data, and any other statistical information, we want to decide on the correct hypothesis
Examples: Decide if the data provided by a radar indicate the
presence of an aircraft From a noisy received signal, decide on the transmitted
digital sequence
1.
0
M
m m
H
Rx Problem formulation
Radar example:
Binary transmission example:
1
2
:
:
r t s t w t
r t w t
H
H
r t
s t
w t
: observed signal: signal generated by the aircraft (if present): AWGN of power 0 2N
1
2
:
:
r t s t w t
r t s t w t
H
H
Rx Problem formulation
In this class, only distortion-less channels will be considered, including AWGN
The observed signals are of the form:
In case the observation is discrete we have
; ; , 0,1, , 1mr t s t w t t m M H T
T : Observation interval
; 0,1, , 1m m M r s w
where now we use vectors instead of continuous-time functions