Software Defined Radio Engineering course sampler

04/12/2023 John Reyland, PhD

04/12/2023 John Reyland, PhD 2

Software Defined Radio EngineeringDay 1:

• SDR Introduction • SDR Approaches:

• Software Communications Architecture (SCA)• NASA STRS• GNU Radio and Simulink

• SDR Advantage/Disadvantage• Digital Modulation for SDR

Day 2:

Day 3:

• RF Channels• Channel Equalization• Multiple Access Techniques• Source and Channel Coding

• Analog Signal Processing• Digital Signal Processing Stop me

and ask!!!!


Software Defined Radio EngineeringBasic High Level Structure of a Software Defined Radio:


Software Defined Radio EngineeringThe SDR Challenge:


Software Defined Radio EngineeringEconomical approach to getting started in SDR

Not shown: GPP feeds back setup commands to reconfigure the radio


Software Defined Radio EngineeringWhat can you make from these?

• Software defined radio?

• A radio that has a well defined configuration file system that can be setup for any signal within the limits of available hardware. The key concept is that hardware and configuration files are flexible enough to be used in the future for signals and were not anticipated when the radio was first built.

• Switch defined radio?

• A radio that requires the user to choose between a set of explicitly provided signal functionality. Also called a multimode radio.

• Software designed radio?

• A radio that depends on programed components to process a predefined signal. A pager or Gen 2 cell phone is an example.

Space Telecommunications Radio System (STRS)


Goal: A single architecture capable of supplying the range of NASA mission classes

NASA requirements range from a small highly optimized radio with severe size, weight and power constraints to complex radios with multiple operating frequencies and high data rates. From [S13]:

“The STRS standard provides a common, consistent framework to develop, qualify, operate and maintain complex reconfigurable and reprogrammable radio systems. ...

The standard focuses on the key architecture components and subsystems by describing their functionality and interfaces for both the hardware and the software including waveform applications. “

7

Space Telecommunications Radio System (STRS)


Software Communications Architecture (SCA)

A personal computer is based on an architectural infrastructure that establishes an set of common practices and interfaces for writing applications.


Can a radio be designed like this?

The US Government seems convinced!

Software Communications Architecture (SCA)

A goal of SCA is, from [S2]:

“Provide for the portability of applications between different SCA compliant implementations.”

SCA seeks to save time and money by enabling deployment of SCA compliant waveform applications on radio hardware manufactured by various companies.


GNU Radio and Simulink


Simulink and GNU Radio comparison:

Simulink runs sample by sample (or frame by frame) simulation steps. Time steps are locked to the fastest sample rate (however, not all blocks need to change state at this rate). For each time step, a simulation state is updated. Subtle but important: simulation states are updated as fast as the CPU can run, but they still match how the state progression in a hardware sampling clock implementation such as an FPGA.

GNU Radio block diagrams achieve high speed simulation by generating the largest possible batch of output samples when the scheduler determines the input samples are available. GNU Radio block processing is event driven, an event (i.e. output data ready) in an upstream block triggers processing in a downstream block. Items can have metadata time tags, however this is an add-on that slows down processing..

Both Simulink and GNU Radio are developed in BDEs running on a PC. However, Simulink seems to have been able to take over a large part of the FPGA development market.

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SDR Advantages


SDR Makes Possible Adaptive Coding and Modulation (ACM):

20

1 sPC WLogWN

W = Channel bandwidth limit (Hz)C = Input data rate, not including coding (bits/second)Ps = Signal power (watts)N0 = Noise power spectral density (watts/Hz) R = Actual channel data rateR<C for arbitrarily low error rate

“Given a discrete memoryless channel [i.e. each signal symbol is perturbed by Gaussian noise independently of the noise effects on all other symbols] with capacity C bits per second, and an information source with rate R bits per second, where R<C, there exists a code such that the output of the source can be transmitted over the channel with an arbitrarily small probability of error.”

12

SDR Advantages


Adaptive Coding and Modulation (ACM):

ACM attempts to take advantage of the extra BW efficiency available when link conditions improve

100

10 2 1C

WbE WLog

N C

0

signalb

noise

P CE

N P W

Shannon limit graph is based on equations from [A19], page 388

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SDR Advantages


Adaptive Coding and Modulation:

Given a current and slowly changing set of channel conditions, select a combination of modulation and channel coding for best throughput. Practical ACM has two basic requirements:

1. Current channel conditions must be accurately known and must be slowly changing. This works best where the receiver can report performance back to the transmitter over a return channel. Open loop approaches, based on weather conditions or link distance computed from GPS, may also be possible. In any case long reporting delays make the system less stable. Note also that ACM is probably restricted to slow fading channels

2. The radio must support multiple waveforms at multiple data rates.

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SDR Modulation Types

A standard GMSK transmitter design, let’s discuss each block separately


04/12/2023 © John Reyland, PhD

Here is the output spectrum showing orthogonal channels spaced 1/12TS apart

Note that sampling is faster than the original symbol rate: fsample = 4/3Ts

0 2

SMT16

sampleS

fMT

2

SMT

8

SMT

8

SMT

16sample

S

fMT

16



We take advantage of the cyclic nature of the IFFT output by adding a block of endsamples to the beginning of each block shifted out.

This prefix has no useful data, however it’s starting phase will be discontinuous withthe phase of the previous block. This discontinuity results in a transient that the receiver can ignore due to the prefix.

Consider that each block has M user symbol streams on M orthogonal channels.This means that each symbol in each channel has it’s own prefix, thus multipath echos occurring during the prefix can be ignored by the receiver

17



Here is how the OFDM circuit is changed to add the cyclic prefix

18

RF Propagation Channels


Diversity combining not difficult to implement on uplink:

What about down link from tower to handset? Handset cannot have multiple receive antennas spaced about ½ wavelength apart, about 16.6 cm at 900 MHz

19



Space-time coding [R12]:

Two base station antennas transmit the same symbols but with different coding. Receiver has only one antenna. Performance is equivalent to two receive antenna diversity combining using maximum ratio combining. This is using in LTE [R10] and wireless LANs [R11].

In this example, transmit signal is:

Symbol Time: Symbols ready to transmit

Transmit antenna 0 Transmit antenna 1

0 s(0), s(1) s(0) s(1)

1 -s(1)* s(0)*

2 s(2), s(3) s(2) s(3)

3 -s(3)* s(2)*

… …. … …

0 1( ) ,s t s s

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* *0 1

* *1 0

(0) (0) (1)

(1) (0) (1)

s h r h r

s h r h r

Time: Symbols ready to transmit

Transmit antenna 0

Transmit antenna 1

0 s(0), s(1) s(0) s(1)

1 -s(1)* s(0)*

2 s(2), s(3) s(2) s(3)

3 -s(3)* s(2)*

… …. … …

0 1

* *0 1

(0) (0) (1)

(1) (1) (0)

r h s h s

r h s h s

Signal at receive antenna during the first two symbol times

Receive decoder has already estimated the channels and forms these signals

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.( )t

( )v t

( ) ( ) cos ( )rv t v t t

Fixed inertial reference frame

Doppler frequency shift andtime dilation affect RF channelswhere receiver and/or transmitter are moving relative to each other


Some Definitions:

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c Speed of light, 3e8 meters/second

cf Carrier frequency (Hz)( )t Angle between receiver’s forward velocity and

line of sight between transmitter and receiver

( ) ( ) cos ( )rv t v t t Velocity of receiver relative to transmitter

( )df t Doppler carrier frequency shift at receiver

( )tT t Transmit symbol time

( )rT t Receive symbol time


Example 1:

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cf 1 GHz = 1e+9 Hz

( )v t v 350 meters/second (constant, approx. Mach 1)

( )t 0 (constant, worst case for Doppler shift)

rv v Velocity of receiver relative to transmitter

350 10(350)( ) 1 9 1167

3 8 3d d c

vf t f f e Hz

c e

Doppler carrier frequency shift at receiver

1( ) 1 6

1 6t tT t T ee

Transmit symbol time

350( ) (1 6) 1 (1 6)(1.000001167)

3 8t

r r t

vTT t T T e e

c e

Receive symbol time

This means receive symbol time increases by 0.0001167%. - called time dilation

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RF Propagation Channelsd = distance between transmitter and receiver at leading edge of transmit pulsed+vTt = distance between transmitter and receiver at trailing edge of transmit pulse

Transmit Pulse, duration = Tt

Received Pulse, duration = Tr

d

c

td vT

c

Propagation time at leading edge of transmit pulse

Propagation time at trailing edge of transmit pulse

t td vT vTd

c c c

Additional time duration of pulse at the receiver

1tt t

vT vT T

c c

Dilated time duration of pulse at the receiver

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Multiple Access Techniques

Transmitter applies spreading chip sequence:

Receiver applies known transmitter chip sequence to remove spreading:

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Transmitter applies spreading chip sequence:

Receiver applies INCORRECT transmitter chip sequence, customer data is still spread:

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Multiple Access TechniquesDe-Spreading results in 10Log(4) = 6dB noise reduction, called Processing Gain:

I

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I

Spread Spectrum is used for Multiple Access:

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Source and Channel CodingOverview: A real world example - an IS-95 cell phone handset voice channel

Long Code Generator

Long Code Mask

Symbol Repetition

BlockInterleaver

Speech Samples Walsh

Code Modulator

Data Burst Randomizer

To

Offs

et Q

PS

K M

odu

lato

r

1200 bps2400 bps4800 bps9600 bps

3600 bps7200 bps14400 bps28800 bps

28800 bps 28800 bps 307200 cps

1.22

88 M

cps

1.22

88 M

cps

8420

I-Chan Chips

1.2288 Mcps

Q-Chan Chips

1.2288 Mcps

Variable Rate

Vocoder

Convolutional Encoder

Rate 1/3, k=9

64000 bps

Source Coding

Removes Redundancy

Channel Coding

Adds Redundancy

Interleaving Isolates Errors

Spectrum Spreading

for processing

gain

We will discuss each block in detail …

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Source and Channel CodingStep 7: Traceback from largest final PM

© John Reyland, PhD

Note traceback bit sequence: 1 1 1 0 1, reversed = 1 0 1 1 1 = transmit bit sequence

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Channel Equalization Techniques

04/12/2023John Reyland, PhD

Raised cosine pulses have an extremely important attribute: at the ideal sampling points, they don’t interfere with each other

Over an ideal channel, delayed transmit signal will be observed at the receiver.

Ideal channel: ( ) ( )received transmits t s t

Channel Equalization TechniquesIntersymbol Interference (ISI) comes about due to imperfect channels:


( ) 0.5 1 0.5 1receivey n x n x n x n

Green = postcursor, occurs prior to the main sampleBlue = main sample in this illustrationYellow = precursor, occurs after the main sample

Channel Equalization TechniquesFor this simple channel, we can calculate the effect of ISI:


x(n-1) x(n) x(n+1) Received signal, no ISI Received signal, ISI

-1 -1 -1 -1 -2 = -0.5-1-0.5

-1 -1 1 -1 -1 = -0.5-1+0.5

-1 1 -1 1 0 = -0.5+1-0.5

-1 1 1 1 1 = -0.5+1+0.5

1 -1 -1 -1 -1 = 0.5-1-0.5

1 -1 1 -1 0 = 0.5-1+0.5

1 1 -1 1 1 = 0.5+1-0.5

1 1 1 1 2 = +0.5+1+0.5

Primary effect of ISI is to degrade the BER . Simple BER calculations are no longer valid:

0

2(bit error) bEP Q

N

For the non-ISI case becomes much more complicated with ISI

Analog Signal Processing


Continuing on, we can calculate the receiver noise at the ADC input

RXnoisedBm NdBm RXdB RXdBP P NF G

Composite Noise Figure up to the VGA output:

31 2 410 0

0 0 1 0 1 2 0 1 2 3

11 1 110RxdB

FF F FNF Log F

G G G G GG G GG G

Composite Gain (max AGC gain): 10 0 1 2 3 410RXdBG Log G GG G G

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Composite ADC noise floor consists of receiver noise plus ADC noise:

310

5 10RXnoisedBmP

RXnoise ADCV G R

Start by converting receiver noise at the ADC input to a voltage:

/20, 10 SNR

ADCnoise FS RMSV V

Given the ADC data sheet SNR rating, calculate the ADC generated input noise voltage:

G5 = 2 = transformer turns ratio. RADC = ADC input resistance

2 2NoiseFloorADC ADCnoise RXnoiseV V V

We assume these two are normally distributed random variables, therefore we sum the variance and take the square root to get back to a composite ADC noise floor voltage

Typically < 0.5 milliVolt. Note that both voltages are measured across RADC

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ADC dynamic range details for one in-band signal:

10max

20log 8FS

ADC

VdB

V

Minimum SNR required by the modulation type:

Signal power must be backed off by peak to average power ratio (PAPR). For OFDM:

min1020log ADC

MinNoiseFloorADC

VSNR

V

Note: ADC driver amplifier must also have sufficient dynamic range

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Digital Signal Processing


Packet payloads generally use more complicated bandwidth efficient modulationA simple example where the packet data length is based on the interleaver size:


We will organize the SDR DSP discussion around the receiver architecture below:


This setup is suitable for many linear modulations in common use today:

• Nonlinear demodulation would replace equalizer with phase discriminator and also probably not have carrier tracking

• CDMA would required additional code synchronization circuits• OFDM would require an FFT to separate subcarriers



Intermediate center frequency Fif = 44.2368 MHz. Does this mean sampling frequency Fs > 88.4736 MHz ?

No, we can bandpass sample, by making Fs = (4/3) Fif = 58.9824 MHz. This has advantages:

• Lower sample rate => smaller sample buffers and fewer FPGA timing problems• Fif can be higher for the same sample rate, this may make frequency planning easier

Disadvantage is that noise in the range [Fs/2 Fs] is folded back into [0 Fs/2]



Complex basebanding process in the frequency domain, ends with subsampled Fs = 29.491 MHz



Halfband Filter response

Typical Matlab code:

1 2 3 4 5 6 7 8 9 10 11-0.2

0

0.2

0.4

0.6HalfBand filter Impulse Response, Order=11

0 3.6864 7.3728 11.0592 14.7456 18.432 22.1184 25.8048 29.4912-40

-30

-20

-10

0

Frequency (MHz)

Re

sp

, d

B

0 3.6864 7.3728 11.0592 14.7456 18.432 22.1184 25.8048 29.49120

0.5

1

Frequency (MHz)

Re

sp

, lin

ea

r

Fss = 58.9824e6;

% Setup halfband filter for input subsamplingPassBandEdge = 1/2-1/8;StopBandRipple = 0.1;b=firhalfband('minorder', … PassBandEdge, … StopBandRipple, … 'kaiser');

% Check frequency response[hb,wb] = freqz(b,1,2048);plot(wb,10*log10(abs(hb)));set(gca,'XLim',[0 pi]);set(gca,'XTick',0:pi/8:pi);set(gca,'XTickLabel',(0:(Fss/16):(Fss/2))/1e6);

Digital Signal Processing DSP Circuits for IF to Complex BB process


Inphase Halfband Filter

HI(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6

Quadrature Halfband Filter

HQ(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6

Fs/4 Local Oscillator

I(n) + jQ(n) = [1+j0,0+j1,-1+j0,0-j1,1+j0, ...]

x(n)

Ib(n)

Qb(n)

Z-1

0h0

Z-1

h6

Z-1

0

Z-1

h4

Z-1

h3

Z-1

h2

2

Z-1

0h0

Z-1

h6

Z-1

0

Z-1

h4

Z-1

h3

Z-1

h2

2

Ihb(n)

Qhb(n)



Input Samp. Index @ Fs

Local Oscillator:I(n) + jQ(n) =

Mixer Output Quadrature Halfband Filter Tap Signals Quadrature Half Band Output @ sample rate = Fs/2

x(n) I(n) Q(n) Ib(n) Qb(n) h0 0 h2 h3 h4 0 h6 x(0) 1 0 x(0) 0 0 0 0 0 0 0 0 0x(1) 0 1 0 x(1) x(1) 0 0 0 0 0 0 x(1)*h0x(2) -1 0 -x(2) 0 0 x(1) 0 0 0 0 0 0x(3) 0 -1 0 -x(3) -x(3) 0 x(1) 0 0 0 0 -x(3)*h0 + x(1)*h2x(4) 1 0 x(4) 0 0 -x(3) 0 x(1) 0 0 0 x(1)*h3x(5) 0 1 0 x(5) x(5) 0 -x(3) 0 x(1) 0 0 x(5)*h0 - x(3)*h2 + x(1)*h4x(6) -1 0 -x(6) 0 0 x(5) 0 -x(3) 0 x(1) 0 -x(3)*h3x(7) 0 -1 0 -x(7) -x(7) 0 x(5) 0 -x(3) 0 x(1) -x(7)*h0 + x(5)*h2 - x(3)*h4 +

x(1)*h6

x(8) 1 0 x(8) 0 0 -x(7) 0 x(5) 0 -x(3) 0 x(5)*h3x(9) 0 1 0 x(9) x(9) 0 -x(7) 0 x(5) 0 -x(3) x(9)*h0 - x(7)*h2 + x(5)*h4 -

x(3)*h6

x(10) -1 0 -x(10) 0 0 x(9) 0 -x(7) 0 x(5) 0 -x(7)*h3x(11) 0 -1 0 -x(11) -x(11) 0 x(9) 0 -x(7) 0 x(5) -x(11)*h0 + x(9)*h2 - x(7)*h4 +

x(5)*h6

x(12) 1 0 x(12) 0 0 -x(11) 0 x(9) 0 -x(7) 0 x(9)*h3x(13) 0 1 0 x(13) x(13) 0 -x(11) 0 x(9) 0 -x(7) x(13)*h0 - x(11)*h2 + x(9)*h4 -

x(7)*h6

x(14) -1 0 -x(14) 0 0 x(13) 0 -x(11) 0 x(9) 0 -x(11)*h3x(15) 0 -1 0 -x(15) -x(15) 0 x(13) 0 -x(11) 0 x(9) -x(15)*h0 + x(13)*h2 - x(11)*h4

+ x(9)*h6

Digital Signal Processing Final Design: Fs/4 downconvert, halfband filter and subsample by 2



After subsampling to Fs = 29.491 MHz, we can filter with an arbitrary low pass filter to reject as much noise as possible:


We can also subsample further to reduce processing load

Digital Signal Processing A popular filter and decimate circuit is the cascaded integrator comb (CIC) filter


2 24

1 1

1 1 1 1

1

1 1 1

1 1( ) 1

( ) 1 1

1 1 1 1

1

1 1 1

z zu z z

x z z z

z z jz jz

z

z jz jz


This CIC filter has the same frequency response as a 4 tap boxcar filter, see [D2]



Downsample by 4 shown as 2 downsamples by 2.

Two CIC problems: • Spectral droop applied to desired

signal (blue)• Aliasing into desired signal

bandwidth


Software Defined Radio Engineering course sampler

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