DSP Techniques for Software Radio by 78zq4k7

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```									DSP Techniques for Software
Radio

DSP Front End Processing

Dr. Jamil Ahmad
The DSP Front End

   DSP Front End for Software Radio
   Analog-to-Digital Conversion
Techniques
   Direct Digital Synthesis

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The DSP Front End
   DSP Front End Processing
    Digital Channel Selection
    Digital Multiplexing

ADC     DDC
RF Interface

Channelizer
Frequency Band
Channelization

DAC                       DDS   DUC
Channelizer

Up Conversion and Multiplex
(Base Station)
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Data Conversion
ADC

Discrete Time
Continuous Valued
Sampling          Signals                  Quantization

Analog                                                                   Digital
Domain                                                                   Domain
Discrete-Time
Discrete Valued
Continuous-Time                                          Signals
Continuous Valued
Signals                                                   0 1 0 0 1 0, 0 1 1 0 0 1, …

Continuous Time
Reconstruction         Discrete Valued
Signals                    Voltage Mapping

DAC
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Sampling and Aliasing
Why Filter Before Sampling

10KHz

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

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Sampling and Aliasing
Applying Anti-Aliasing Filter

-10KHz 0   10KHz

-10KHz   0    10KHz

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

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Sampling Bandpass Signals
   Direct Sampling of BP Signals

f
-Fc      0        Fc

   What should be the Sampling Rate?
   Images in Bandpass Sampling
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Bandpass Sampling
    Nyquist Second theorem                            fc
Minimum Sampling Rate is
Twice the Bandwidth

2        f        f 
Fs         1 L  B M   L                         fL
M 1       B        B                                B fH
2  fH 
           B             x   largest integer smaller than x
 
M 1  B 
e.g.,  47.78  47
      
2 fH
                        Nyquist rate achievable only at integer
 fH                  multiples of highest frequency and the
B
                     Bandwidth of the BP Signal
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Bandpass Sampling

B / fH

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Bandpass Sampling
Consider the case where   f H  LB (L an Odd Integer)

L = 5 for this case

L is Odd here

Whenever fH = LB, We can choose Fs = 2B to perfectly “interweave” the
shifted spectral images
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Bandpass Sampling
   Advantages of BP Sampling
Bandpass
x(t )                 Sampling
ADC
A BP-Sampling ADC
Works like a Mixer and
A Baseband-Sampling ADC
x(t )                       Baseband
LPF    Sampling
ADC

cos(2 f c t )
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Hilbert Transformer (HT)
   What is Hilbert Transform?
   90o Phase Shifter
   All Pass Magnitude Characteristics

 2 sin 2 ( n / 2)
                     n0
hd (n)           n
 0                   n0


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Hilbert Transformer

1.5
                   1
1                  2 hd ( n )
1/3
0.5                                             1/5
1/7
0

-0.5     -1/7 -1/5
-1/3
-1
-1
-1.5
-10        -5                   0             5           10

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Hilbert Transform
   I/Q Conversion
N 1
D
2

z -D

x(n)
z (m)  xi (m)  jxq (m)
hd(n)

Discrete Hilbert Transform

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Digital Conversion
      Practical System

~ (t )
x                  x(t )                 x(n)                ˆ
Quantiza- x(n)
AAF               Sampling                                  Coder
tion

Analog            Bandlimited            Sampled            Quantized           Bit Stream
Signal            Analog Signal          Signal             Signal

Sampling Clock

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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

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Digital Conversion -
Quantization
ˆ
x
3D
2D
D

D  Step Size                                       D   x
2D
Quantization error = e(n)  x(n)  x(n)
ˆ               3D
4D
D2
Quantization Noise =    Nq   2 
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Signal-to-Quantization Noise = SQNR  6.02B

B = Number of Bits

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Digital Conversion
   Binary Coding
Two’s   Offset   Fraction
ˆ
x          Comple
ment
Binary
Code
Value

Code

3D          011      111       3/4
2D          010      110       1/2
D           001      101       1/4
000      100        0
D     111      011       -1/4
2D    110      010       -1/2
3D    101      001       -3/4
4D    100      000        -1

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Digital Conversion -
Quantization

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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

 % FSR 
Dynamic Range  6.02 B  20 log10        
  100 

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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)

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Data Conversion
   Total Harmonic Distortion (THD)
  
  Pi 
THD  10 log10  i 1    dB
 P0 
      
      
   Signal-to-Noise and Distortion Ratio
(SINAD)
        
  P0    
SINAD  10 log10     
 dB
N P


 i
i 1 

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Data Conversion
   Thermal Noise
k = 1.38 ×10-23 J/K
P  kTe B
T                 Te = Effective Noise Temperature
B = Signal Bandwidth

   Effective Number of Bits (ENOB)

ENOB  (SINAD  1.763) / 6.02

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Data Converters
AD9220 12Bit 10MBPS ADC SINAD and ENOB
at Different Input Signal Level

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Data Conversion
   Spurious-Free Dynamic Range (SFDR)

 P0 
SFDR  10log10             dB
 max( Pi ) 

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Data Converters
   Improvement Techniques
   Dithering
   Out of Band
   Subtractive
   Automatic Gain Control (AGC)
   Response Time

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The DSP Front-End

Direct Digital Synthesis (DDS)

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Direct Digital Synthesis (DDS)
   What is DDS?
   Digital Waveform Generator
   Flexibility in Control and Precision
   Fundamental Block in SDR
   No Manual Tuning

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Direct Digital Synthesis
   DDS Approaches
   ROM Lookup Table

Accumulator
Frequency                        Lookup
Table   DAC
Word

Delay

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DDS Approaches
   ROM Lookup

To generate 1100Hz tone with
Sampling Rate of 8KHz and 0.5Hz
Resolution, Calculate
i) Number of Points in LUT
ii) Input Frequency Word Value

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DDS Approaches
   ROM Lookup Approach
Design Solution:
Required Frequency Resolution      Df  0.5
Df   
D  2       
Fs 8000
In the Phase Wheel                       2
D 
N
2      2
N             16000
D      
Frequency Word Value                                  8000
f      1100
  2     2       0.86393
Fs      8000             31
DDS Approaches
   Issues with ROM LUT Method
   ROM Size directly proportional to Fs
   ROM Size Inversely Proportional to
Frequency Resolution
   Memory Problem
   Phase Noise

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DDS Approaches
   Taylor Series Approximation
For small 

1 3 1 5 1 7
sin( )              
3!    5!  7!
Its true when
Fs      f0

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DDS Approaches
   Digital Oscillator
y(n)
   Widely used in
DTMF Tone                                a1        Z-1

Generation                                         Z-1
   Issues with Higher                       -1

Frequencies
y (2)   A sin  0
f0
y (1)  0,  0  2
Fs
y (n)  2 cos 0  y (n  1)  y (n  2)

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