Software Defined Radio Engineering course sampler

Software Defined Radio Engineering
Day 1:
• SDR Introduction
• SDR Approaches:
•
•
•

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

• SDR Advantage/Disadvantage
• Digital Modulation for SDR

Day 2:
•
•
•
•

RF Channels
Channel Equalization
Multiple Access Techniques
Source and Channel Coding

Day 3:
• Analog Signal Processing
• Digital Signal Processing
2/6/2014

John Reyland, PhD

Stop me
and ask!!!!

2

Basic High Level Structure of a Software Defined Radio:

2/6/2014

John Reyland, PhD

3

The SDR Challenge:

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John Reyland, PhD

4

Economical approach to getting started in SDR

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

2/6/2014

John Reyland, PhD

5

What 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.
2/6/2014

John Reyland, PhD

6

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. “

2/6/2014

John Reyland, PhD

7

Space Telecommunications Radio System (STRS)

2/6/2014

John Reyland, PhD

8

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!

2/6/2014

John Reyland, PhD

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.

2/6/2014

John Reyland, PhD

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.

2/6/2014

John Reyland, PhD

11

SDR Advantages
SDR Makes Possible Adaptive Coding and Modulation (ACM):
C WLog2 1

Ps
WN 0

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 rate
R<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.”
2/6/2014

John Reyland, PhD

12

SDR Advantages
Adaptive Coding and Modulation (ACM):
ACM attempts to take advantage of
the extra BW efficiency available
when link conditions improve

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

Eb
N0

Eb
N0
2/6/2014

John Reyland, PhD

C

10 Log10

W
2W
C

1

Psignal C
Pnoise W
13

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.

2/6/2014

John Reyland, PhD

14

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

2/6/2014

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

f sample

16
MTS

8
MTS

2
MTS

0

2
MTS

8
MTS

f sample

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

2/6/2014

© John Reyland, PhD

16

16
MTS

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

This prefix has no useful data, however it’s starting phase will be discontinuous with
the 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
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17

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

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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

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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: s(t )

s0 , s1

Symbol Time:

Symbols ready to
transmit

Transmit antenna 0

Transmit antenna 1

0

s(0), s(1)

s(0)

s(1)

-s(1)*

s(0)*

s(2)

s(3)

-s(3)*

s(2)*

…

…

1
2

s(2), s(3)

3
…
2/6/2014

….


20

Time:

Symbols
ready to
transmit

Transmit
antenna 0

Transmit
antenna 1

0

s(0), s(1)

s(0)

s(1)

-s(1)*

s(0)*

s(2)

s(3)

-s(3)*

s(2)*

…

…

1
2

s(2), s(3)

3
…

r (0)
r (1)

h0 s(0) h1s(1)
h0 s(1)* h1s (0)*


s (0)

*
h0 r (0) h1r * (1)


s (1)

h1*r (0) h0 r * (1)

2/6/2014

….

Signal at receive antenna during the
first two symbol times

Receive decoder has already estimated the channels
and forms these signals


21

Doppler frequency shift and
time dilation affect RF channels
where receiver and/or
transmitter are moving relative
to each other

(t )

vr (t ) v(t )cos (t )

Fixed inertial reference frame

2/6/2014

.

v(t )

Some Definitions:
c

Speed of light, 3e8 meters/second

fc

Carrier frequency (Hz)

(t )

Angle between receiver’s forward velocity and
line of sight between transmitter and receiver

vr (t ) v(t )cos

(t )

Velocity of receiver relative to transmitter

f d (t )

Doppler carrier frequency shift at receiver

Tt (t )

Transmit symbol time

Tr (t )

Receive symbol time

2/6/2014

Example 1:
1 GHz = 1e+9 Hz

fc

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

v(t ) v

(t )
vr

0 (constant, worst case for Doppler shift)

v

f d (t )

Velocity of receiver relative to transmitter
fd

Tt (t ) Tt

Tr (t ) Tr

v
c

fc

1e9

1
1e 6

Tt

vTt
c

350
3e8

1e 6

10(350)
1167 Hz
3

Doppler carrier frequency shift at receiver

Transmit symbol time

(1e 6) 1

350
3e8

(1e 6)(1.000001167)

Receive symbol time

This means receive symbol time increases by 0.0001167%. - called time dilation
2/6/2014

d = distance between transmitter and receiver at leading edge of transmit pulse
d+vTt = distance between transmitter and receiver at trailing edge of transmit pulse
d
c

Propagation time at leading edge of transmit pulse

Received Pulse, duration = Tr

d vTt
c

Propagation time at trailing edge of transmit pulse

Transmit Pulse, duration = Tt

d vTt
c

Tt

vTt
c
2/6/2014

d
c

vTt
c

Tt 1

v
c

Additional time duration of pulse at the receiver

Dilated time duration of pulse at the receiver

Transmitter applies spreading chip sequence:

Receiver applies known transmitter chip sequence to remove spreading:

2/6/2014

Transmitter applies spreading chip sequence:

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

2/6/2014

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

I

2/6/2014

Spread Spectrum is used for Multiple Access:

I

2/6/2014

Overview: A real world example - an IS-95 cell phone handset voice channel

Long Code Mask

64000 bps

1200 bps
2400 bps
4800 bps
9600 bps

Convolutional
Encoder
Rate 1/3, k=9
3600 bps
7200 bps
14400 bps
28800 bps

Symbol
Repetition
8
4
2
0

Block
Interleaver

28800 bps

28800 bps

Walsh
Code
Modulator

I-Chan Chips
1.2288 Mcps

Data Burst
Randomizer

307200 cps

Q-Chan Chips
1.2288 Mcps

We will discuss each block in detail …

2/6/2014

To Offset QPSK Modulator

Variable
Rate
Vocoder

Interleaving
Isolates
Errors

1.2288 Mcps

Speech
Samples

Channel
Coding
Adds
Redundancy

1.2288 Mcps

Source
Coding
Removes
Redundancy

Long Code
Generator

Spectrum
Spreading
for
processing
gain

Step 7: Traceback from largest final PM

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

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31

Channel Equalization Techniques
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:

sreceived (t )

stransmit (t

)

John Reyland, PhD
2/6/2014

Intersymbol Interference (ISI) comes about due to imperfect channels:

yreceive (n) 0.5x n 1

x n

0.5x n 1

Green = postcursor, occurs prior to the main sample
Blue = main sample in this illustration
Yellow = precursor, occurs after the main sample
John Reyland, PhD
2/6/2014

For 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:
P(bit error) Q

2 Eb
N0

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

John Reyland, PhD
2/6/2014

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

Composite Noise Figure up to the VGA output:

NFRxdB

10 Log10 F0

Composite Gain (max AGC gain):

PRXnoisedBm
2/6/2014

F1 1 F2 1 F3 1
G0
G0G1 G0G1G2

F4 1
G0G1G2G3

GRXdB 10Log10 G0G1G2G3G4

PNdBm

NFRXdB GRXdB


35

Composite ADC noise floor consists of receiver noise plus ADC noise:
Start by converting receiver noise at the ADC input to a voltage:

VRXnoise

G5 RADC 10

PRXnoisedBm
3
10

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

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

VADCnoise

VFS , RMS 10

SNR /20

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

VNoiseFloorADC
2/6/2014

2
2
VADCnoise VRXnoise


Typically < 0.5 milliVolt.
Note that both voltages
are measured across RADC
36

ADC dynamic range details for one in-band signal:
Signal power must be
backed off by peak to
average power ratio (PAPR).
For OFDM:
20 log10

VFS
VADC max

8dB

Minimum SNR required
by the modulation type:
SNRMin
Note: ADC driver amplifier must also
have sufficient dynamic range

2/6/2014


20log10

VADC min
VNoiseFloorADC

37

Digital Signal Processing
Packet payloads generally use more complicated bandwidth efficient modulation
A simple example where the packet data length is based on the interleaver size:

2/6/2014

John Reyland, PhD

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

2/6/2014

John Reyland, PhD


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]
2/6/2014

John Reyland, PhD

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

2/6/2014

John Reyland, PhD

Halfband Filter response

HalfBand filter Impulse Response, Order=11
0.6
0.4

Typical Matlab code:

0.2
0
-0.2

Fss = 58.9824e6;
1

2

3

4

5

6

7

8

9

10

11

Resp, dB

0
-10
-20
-30
-40

0

3.6864

7.3728

11.0592 14.7456 18.432
Frequency (MHz)

22.1184 25.8048 29.4912

% 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);

Resp, linear

1

0.5

0

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

0

3.6864

2/6/2014

7.3728

11.0592 14.7456 18.432
Frequency (MHz)

22.1184 25.8048 29.4912

John Reyland, PhD

DSP Circuits for IF to Complex BB process
Fs/4 Local Oscillator
Inphase Halfband Filter
I(n) + jQ(n) = [1+j0,0+j1,-1+j0,0-j1,1+j0, ...]
HI(z) = h0 + z-2h2 + z-3h3 + z-4h4 + z-6h6

Ib(n)
x(n)

Z-1

h0

Z-1

Z-1

Z-1

Z-1

Z-1

0

h2

h3

h4

0

h6
Ihb(n)
2

Qb(n)

Z-1

h0

Z-1

Z-1

Z-1

Z-1

Z-1

0

h2

h3

h4

0

h6
Qhb(n)
2

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

2/6/2014

John Reyland, PhD

Input
Samp.
Index @
Fs

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

Mixer Output

Quadrature Halfband Filter Tap Signals

x(n)
x(0)
x(1)
x(2)
x(3)
x(4)
x(5)
x(6)
x(7)

I(n)
1
0
-1
0
1
0
-1
0

Q(n)
0
1
0
-1
0
1
0
-1

Ib(n)
x(0)
0
-x(2)
0
x(4)
0
-x(6)
0

Qb(n)
0
x(1)
0
-x(3)
0
x(5)
0
-x(7)

h0
0
x(1)
0
-x(3)
0
x(5)
0
-x(7)

0
0
0
x(1)
0
-x(3)
0
x(5)
0

h2
0
0
0
x(1)
0
-x(3)
0
x(5)

h3
0
0
0
0
x(1)
0
-x(3)
0

h4
0
0
0
0
0
x(1)
0
-x(3)

0
0
0
0
0
0
0
x(1)
0

h6
0
0
0
0
0
0
0
x(1)

x(8)
x(9)

1
0

0
1

x(8)
0

0
x(9)

0
x(9)

-x(7)
0

0
-x(7)

x(5)
0

0
x(5)

-x(3)
0

0
-x(3)

x(10)
x(11)

-1
0

0
-1

-x(10)
0

0
-x(11)

0
-x(11)

x(9)
0

0
x(9)

-x(7)
0

0
-x(7)

x(5)
0

0
x(5)

x(12)
x(13)

1
0

0
1

x(12)
0

0
x(13)

0
x(13)

-x(11)
0

0
-x(11)

x(9)
0

0
x(9)

-x(7)
0

0
-x(7)

x(14)
x(15)

-1
0

0
-1

-x(14)
0

0
-x(15)

0
-x(15)

x(13)
0

0
x(13)

-x(11)
0

0
-x(11)

x(9)
0

0
x(9)

2/6/2014

John Reyland, PhD

Quadrature Half Band Output
@ sample rate = Fs/2

0
x(1)*h0
0
-x(3)*h0 + x(1)*h2
x(1)*h3
x(5)*h0 - x(3)*h2 + x(1)*h4
-x(3)*h3
-x(7)*h0 + x(5)*h2 - x(3)*h4 +
x(1)*h6
x(5)*h3
x(9)*h0 - x(7)*h2 + x(5)*h4 x(3)*h6
-x(7)*h3
-x(11)*h0 + x(9)*h2 - x(7)*h4 +
x(5)*h6
x(9)*h3
x(13)*h0 - x(11)*h2 + x(9)*h4 x(7)*h6
-x(11)*h3
-x(15)*h0 + x(13)*h2 - x(11)*h4
+ x(9)*h6

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

2/6/2014

John Reyland, PhD

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
2/6/2014

John Reyland, PhD

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

u( z )
x( z )

1 z
1 z

1 z
1 z

2/6/2014

1

1

1 z

4
1

1 z

1 z

1 z
1

2

1

1

jz

1 z1
jz 1 1 jz

2

1

1

1

jz

1

1

John Reyland, PhD

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

2/6/2014

John Reyland, PhD

Downsample by 4 shown as 2
downsamples by 2.

Two CIC problems:
• Spectral droop applied to desired
signal (blue)
• Aliasing into desired signal
bandwidth

2/6/2014

John Reyland, PhD

Software Defined Radio Engineering course sampler

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