DSP Techniques for Software Radio

DSP Front End Processing

Dr. Jamil Ahmad

2

The DSP Front End

DSP Front End for Software Radio Analog-to-Digital Conversion

Techniques Direct Digital Synthesis

3

Up Conversion and Multiplex

The DSP Front End

DSP Front End Processing Digital Channel Selection Digital Multiplexing

RF Front End

IF Down ConversionAnd Digitization

Frequency Band Channelization

Direct Digital Synthesis

ADC

DAC

DDC

DDS

RF In

terfa

ce DUC

Channelizer

Channelizer

(Base Station)

4

Data Conversion

Sampling

Reconstruction Voltage Mapping

AnalogDomain

Continuous-Time Continuous Valued

Signals

ADC

Discrete TimeContinuous

ValuedSignals

Quantization

0 1 0 0 1 0, 0 1 1 0 0 1, …

DigitalDomain

Discrete-TimeDiscrete Valued

Signals

DAC

Continuous TimeDiscrete Valued

Signals

5

Sampling and Aliasing

Why Filter Before Sampling

10KHz

0 40KHz 80KHz-40KHz -20KHz 20KHz 60KHz

6

Sampling and Aliasing

0 10KHz-10KHz

0-10KHz 10KHz

40KHz 80KHz-40KHz 0 20KHz 60KHz-20KHz

Applying Anti-Aliasing Filter

7

Sampling Bandpass Signals

Direct Sampling of BP Signals

What should be the Sampling Rate? Images in Bandpass Sampling

Fc-Fc 0f

8

Bandpass Sampling

Nyquist Second theorem

fL fHB

fc

21

1

2

1

2

L Ls

H

H

H

f fF B M

M B B

fB

M B

ffB

Minimum Sampling Rate is Twice the Bandwidth

largest integer smaller than

e.g., 47.78 47

x x

Nyquist rate achievable only at integer multiples of highest frequency and the Bandwidth of the BP Signal

9

Bandpass Sampling

/ HB f

10

Bandpass Sampling

Consider the case where ( an Odd Integer)Hf LB L

L = 5 for this case

L is Odd here

Whenever fH = LB, We can choose Fs = 2B to perfectly “interweave” the shifted spectral images

11

Bandpass Sampling

Advantages of BP Sampling

Bandpass Sampling

ADC

( )x t

cos(2 )cf t

BasebandSampling

ADCLPF

( )x t

A BP-Sampling ADCWorks like a Mixer andA Baseband-Sampling ADC

12

Hilbert Transformer (HT)

What is Hilbert Transform? 90o Phase Shifter All Pass Magnitude Characteristics

22 sin ( / 2)0

( )

0 0d

nn

h n nn

13

Hilbert Transformer

-10 -5 0 5 10-1.5

-1

-0.5

0

0.5

1

1.5

2 ( )dh n

-1/7 -1/5-1/3

-1

1

1/31/5

1/7

14

Hilbert Transform

I/Q Conversion1

2

ND

( )x n

z -D

hd(n)

Discrete Hilbert Transform

( ) ( ) ( )i qz m x m jx m

15

Digital Conversion

Practical System

AAF SamplingQuantiza-

tion

Sampling Clock

AnalogSignal

Bandlimited Analog Signal

Coder)(~ tx )(tx )(nx )(ˆ nx

SampledSignal

QuantizedSignal

Bit Stream

16

Digital Conversion

Quantization Signal level divided into discrete steps Samples rounded to the nearest step

value Introduces errors in the signal which is

treated as ‘Quantization Noise’ or ‘Quantization Error’

Quantization Error depends upon the quantization step size

17

Digital Conversion - Quantization

x̂

x

Step Size

Quantization error = )(ˆ)()( nxnxne

Quantization Noise = 12

22 qN

Signal-to-Quantization Noise = BSQNR 02.6

B = Number of Bits

18

Digital Conversion

Binary Coding

x̂

Two’s Complement Code

Offset Binary Code

Fraction Value

011 111 3/4

010 110 1/2

001 101 1/4

000 100 0

111 011 -1/4

110 010 -1/2

101 001 -3/4

100 000 -1

19

Digital Conversion - Quantization

20

Data Conversion

Dynamic Range SDR utilizes wide band ADCs Critical for SDR Design to

accommodate all type of analog input signals

Full-Scale Range Utilization

10

% 6.02 20log

100

FSRDynamic Range B

21

Data Conversion Quantifying Dynamic Performance

Harmonic Distortion Total Harmonic Distortion (THD) Thermal Noise Signal-to-Noise and Distortion Ratio (SINAD) Effective Number of Bits (ENOB) Signal-to-Noise Ratio Spurious-Free Dynamic Range (SFDR) Intermodulation Distortion (Two Tone and

Multi-Tone)

22

Data Conversion

Total Harmonic Distortion (THD)

Signal-to-Noise and Distortion Ratio (SINAD)

110

0

10log dBi

i

PTHD

P

010

1

10log dB

ii

PSINAD

N P

23

Data Conversion

Thermal Noise

Effective Number of Bits (ENOB)

T eP kT B Te = Effective Noise Temperature

k = 1.38 ×10-23 J/K

B = Signal Bandwidth

( 1.763) / 6.02ENOB SINAD

24

Data ConvertersAD9220 12Bit 10MBPS ADC SINAD and ENOB

at Different Input Signal Level

25

Data Conversion

Spurious-Free Dynamic Range (SFDR)

01010log dB

max( )i

PSFDR

P

26

Data Converters

Improvement Techniques Dithering

Out of Band Subtractive

Automatic Gain Control (AGC) Response Time

27

Direct Digital Synthesis (DDS)

The DSP Front-End

28

Direct Digital Synthesis (DDS)

What is DDS? Digital Waveform Generator Flexibility in Control and Precision Fundamental Block in SDR No Manual Tuning

29

Direct Digital Synthesis

DDS Approaches ROM Lookup Table

LookupTable

Delay

FrequencyWord

Accumulator

DAC

30

DDS Approaches

ROM Lookup

To generate 1100Hz tone withSampling Rate of 8KHz and 0.5Hz Resolution, Calculate

i) Number of Points in LUTii) Input Frequency Word Value

31

DDS Approaches

ROM Lookup ApproachDesign Solution:

0.5

28000

f

f

Fs

In the Phase Wheel 2

N

2 216000

8000

N

Required Frequency Resolution

Frequency Word Value

11002 2 0.86393

8000

f

Fs

32

DDS Approaches

Issues with ROM LUT Method ROM Size directly proportional to Fs ROM Size Inversely Proportional to

Frequency Resolution Memory Problem Phase Noise

33

DDS Approaches

Taylor Series Approximation

For small

3 5 71 1 1sin( )

3! 5! 7!

Its true when

0Fs f

34

DDS Approaches

Digital Oscillator Widely used in

DTMF Tone Generation

Issues with Higher Frequencies

)2()1(cos2)(

2,0)1(

sin)2(

0

00

0

nynyny

F

fy

Ay

s

Z-1

Z-1

-1

a1

( )y n