signal processing technques for software radio

liyuanliu

Signal Processing Techniques
for Software Radio
Author:
Behrouz Farhang-Boroujeny
Department of Electrical and Computer Engineering
University of Utah
c 2007, Behrouz Farhang-Boroujeny, ECE Department, University of Utah,
USA
Contents
Contents
1 Introduction 1
2 Fourier Analysis and
Linear Time-Invariant Systems 3
2.1 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Linear Time-Invariant Systems . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Convolution integral . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 Transfer function . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Energy and Power Spectral Density . . . . . . . . . . . . . . . . . . . 15
2.4.1 Energy-type signals . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Power-type signals . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.3 Random signals . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.4 Passing a signal through an LTI system . . . . . . . . . . . . 19
3 Digital Transmission Systems 21
3.1 Pulse Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Pulse-Shape Designs for Band-Limited
Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Raised-cosine filter . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 Matched filtering and square-root raised-cosine filter . . . . . 27
3.2.3 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Modulation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.1 Carrier-amplitude modulation . . . . . . . . . . . . . . . . . . 32
3.3.2 Quadrature amplitude modulation . . . . . . . . . . . . . . . 35
3.3.3 Carrier-phase modulation . . . . . . . . . . . . . . . . . . . . 39
3.4 Binary to Symbol Mapping . . . . . . . . . . . . . . . . . . . . . . . 42
3.5 Differential Encoding and Decoding . . . . . . . . . . . . . . . . . . 43
3.6 Baseband Equivalent of a Passband Channel . . . . . . . . . . . . . 43
i
ii Contents
4 Sampling and Discrete Time Systems 53
4.1 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1.1 Reconstruction of x(t) from the samples x(nTs) . . . . . . . . 54
4.1.2 Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.3 Antialiasing filter . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.4 Nyquist criterion for intersymbol interference free
communication . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.5 Sampling in the Frequency Domain . . . . . . . . . . . . . . . 56
4.2 Numerical Computation of the Fourier Transform: Discrete Fourier
Transform (DFT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.1 Derivation of DFT . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 Properties of DFT . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.3 Fast Fourier transform (FFT) . . . . . . . . . . . . . . . . . . 62
4.2.4 Time and frequency scales . . . . . . . . . . . . . . . . . . . . 62
4.2.5 Improving the frequency resolution of the spectrum via zero
padding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Discrete-Time Signals and Systems . . . . . . . . . . . . . . . . . . . 63
4.3.1 The z-transform and Fourier transform of discrete-time
signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.2 Energy and power spectral density . . . . . . . . . . . . . . . 67
4.3.3 Passing a signal through an LTI system . . . . . . . . . . . . 70
4.3.4 Precautionary notes . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 Digital Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4.1 Filter specifications . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.2 Filter design using windowing method . . . . . . . . . . . . . 73
4.4.3 Equiripple filters . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4.4 Nyquist (M) and square-root Nyquist (M) filters . . . . . . . 83
5 Multirate Signal Processing 97
5.1 M-fold Decimator and L-fold Expander . . . . . . . . . . . . . . . . 97
5.1.1 M-fold decimator . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.2 L-fold expander . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2 Rate Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2.1 L-fold interpolation . . . . . . . . . . . . . . . . . . . . . . . 103
5.2.2 M-fold decimation . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.3 L/M-fold rate change . . . . . . . . . . . . . . . . . . . . . . 105
5.3 Commutative Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.4 The Polyphase Representations . . . . . . . . . . . . . . . . . . . . . 111
5.5 Efficient Structures for Decimation and
Interpolation Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.5.1 Polyphase structure for decimator filterss . . . . . . . . . . . 113
5.5.2 Polyphase structure for interpolator filters . . . . . . . . . . . 116
Contents iii
5.5.3 Commutator Models . . . . . . . . . . . . . . . . . . . . . . . 117
5.5.4 L/M-fold resampling . . . . . . . . . . . . . . . . . . . . . . . 118
5.5.5 The polyphase identity . . . . . . . . . . . . . . . . . . . . . . 121
5.6 Multistage Implementation . . . . . . . . . . . . . . . . . . . . . . . 122
5.6.1 Interpolated FIR (IFIR) technique . . . . . . . . . . . . . . . 122
5.6.2 Multistage realization of decimation and interpolation filters 127
5.7 Cascaded Integrator-Comb Filters . . . . . . . . . . . . . . . . . . . 128
5.7.1 M-fold CIC interpolator . . . . . . . . . . . . . . . . . . . . . 128
5.7.2 M-fold CIC decimator . . . . . . . . . . . . . . . . . . . . . . 132
5.8 Application Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.8.1 Timing recovery . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.8.2 All digital modulator . . . . . . . . . . . . . . . . . . . . . . . 137
5.8.3 All digital demodulator . . . . . . . . . . . . . . . . . . . . . 141
5.8.4 Parallel polyphase filtering for very fast sampling rates . . . . 143
6 An Overview of Transceiver Systems 151
6.1 Building Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.2 MATLAB Simulation of Digital Transmission
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.3 Baseband PAM transceiver . . . . . . . . . . . . . . . . . . . . . . . 154
6.4 Eye Patterns in PAM Systems . . . . . . . . . . . . . . . . . . . . . 156
6.5 QAM Transceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.6 Eye Patterns in QAM Systems . . . . . . . . . . . . . . . . . . . . . 159
6.7 The Impact of Frequency Offset on the Baseband Equivalent of Passband
Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7 Adaptive Systems 171
7.1 Wiener Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.1.1 The real-valued case . . . . . . . . . . . . . . . . . . . . . . . 173
7.1.2 Principle of orthogonality . . . . . . . . . . . . . . . . . . . . 178
7.1.3 Extension to the complex-valued case . . . . . . . . . . . . . 180
7.2 The LMS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.2.1 Range of μ, stability and misadjustment . . . . . . . . . . . . 185
7.2.2 The normalized LMS algorithm . . . . . . . . . . . . . . . . . 188
7.3 The Method of Least-Squares . . . . . . . . . . . . . . . . . . . . . . 188
7.3.1 Formulation of the Least-Squares Estimation . . . . . . . . . 189
7.3.2 The standard recursive least-squares algorithm . . . . . . . . 191
7.4 Sampling with Automatic Gain Control . . . . . . . . . . . . . . . . 198
8 Phase-Locked Loop 201
8.1 Continuous-Time PLL . . . . . . . . . . . . . . . . . . . . . . . . . . 202
8.1.1 Linear model of PLL and its analysis . . . . . . . . . . . . . . 203
iv Contents
8.2 Discrete-Time PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.2.1 Linear model of PLL and its analysis . . . . . . . . . . . . . . 213
8.2.2 Designing discrete-time PLL from continuous-time PLL . . . 217
8.3 Maximum Likelihood Phase Detection . . . . . . . . . . . . . . . . . 219
8.3.1 Cost function and the optimum phase . . . . . . . . . . . . . 219
8.3.2 The LMS algorithm for phase detection: a derivation of PLL 220
8.3.3 Alternative stochastic gradient . . . . . . . . . . . . . . . . . 222
8.3.4 A note on the step-size parameter μ . . . . . . . . . . . . . . 222
8.3.5 Higher order PLLs . . . . . . . . . . . . . . . . . . . . . . . . 224
8.4 A PLL with Extended Lock Range . . . . . . . . . . . . . . . . . . . 225
9 Carrier Acquisition and Tracking 231
9.1 Non-Data Aided Carrier Recovery Methods . . . . . . . . . . . . . . 232
9.1.1 Binary PSK with a rectangular pulse-shape . . . . . . . . . . 232
9.1.2 Binary PSK with a band-limited pulse-shape . . . . . . . . . 233
9.1.3 Quadrature Amplitude Modulation . . . . . . . . . . . . . . . 234
9.2 Non-Data Aided Carrier Acquisition and Tracking Algorithms . . . 240
9.2.1 Coarse carrier acquisition . . . . . . . . . . . . . . . . . . . . 240
9.2.2 Fine carrier acquisition and tracking . . . . . . . . . . . . . . 241
9.2.3 Costas Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
9.3 Pilot Aided Carrier Acquisition Method . . . . . . . . . . . . . . . . 255
9.4 Data Aided Carrier Tracking Method . . . . . . . . . . . . . . . . . . 257
10 Timing Recovery 271
10.1 Non-Data Aided Timing Recovery Methods . . . . . . . . . . . . . . 272
10.1.1 Fundamental results . . . . . . . . . . . . . . . . . . . . . . . 272
10.1.2 The timing recovery cost function . . . . . . . . . . . . . . . 274
10.1.3 The optimum timing phase . . . . . . . . . . . . . . . . . . . 274
10.1.4 Improving the cost function . . . . . . . . . . . . . . . . . . . 278
10.2 Non-Data Aided Timing Recovery Algorithms . . . . . . . . . . . . . 279
10.2.1 Early-late gate timing recovery . . . . . . . . . . . . . . . . . 280
10.2.2 Gradient-based algorithm . . . . . . . . . . . . . . . . . . . . 284
10.2.3 Tone extraction algorithm . . . . . . . . . . . . . . . . . . . . 285
10.3 Data Aided Timing Recovery Methods . . . . . . . . . . . . . . . . . 288
10.3.1 Muller and Muller’s method . . . . . . . . . . . . . . . . . . . 290
10.3.2 Decision directed method . . . . . . . . . . . . . . . . . . . . 292
11 Channel Equalization 301
11.1 Continuous-Time Channel Model . . . . . . . . . . . . . . . . . . . . 301
11.2 Discrete-Time Channel Model . . . . . . . . . . . . . . . . . . . . . . 303
11.2.1 Symbol-spaced equalizer . . . . . . . . . . . . . . . . . . . . . 303
11.2.2 Fractionally-spaced equalizer . . . . . . . . . . . . . . . . . . 303
Contents v
11.2.3 Symbol-spaced vesus fractionally-spaced equalizer . . . . . . 304
11.3 Performance Study of Equalizers . . . . . . . . . . . . . . . . . . . . 305
11.3.1 Wiener-Hopf equations . . . . . . . . . . . . . . . . . . . . . . 305
11.3.2 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . 311
11.4 Adaptation Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 311
11.5 Cyclic Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

liyuanliu

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  PART 1

liyuanliu

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PART 2

Kangxi

Useful information

Kangxi

Useful, thanks.

stormwood

thanks!

zlhrsy

tks a lot!!!!!!!!!!!!!!!!!!

zlhrsy

tks a lot again!!!!!!!!!!!!!!!!!!!!!!

liuwei_0613

难得的好书，谢谢楼主共享！同步部分讲得非常详细。

wxmcumtb

多谢。。。。。。。。。。。。。。