Signal Processing Techniques for Software Radio

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1 Signal Processing Techniques for Software Radio Behrouz Farhang-Boroujeny Department of Electrical and Computer Engineering University of Utah c 2007, Behrouz Farhang-Boroujeny, ECE Department, University of Utah, USA

3 1 Introduction 1 2 Fourier Analysis and Linear Time-Invariant Systems Fourier Series Fourier Transform Linear Time-Invariant Systems Convolution integral Transfer function Energy and Power Spectral Density Energy-type signals Power-type signals Random signals Passing a signal through an LTI system Digital Transmission Systems Pulse Amplitude Modulation Pulse-Shape Designs for Band-Limited Communications Raised-cosine filter Matched filtering and square-root raised-cosine filter Causality Modulation Techniques Carrier-amplitude modulation Quadrature amplitude modulation Carrier-phase modulation Binary to Symbol Mapping Differential Encoding and Decoding Baseband Equivalent of a Passband Channel i

4 ii Contents 4 Sampling and Discrete Time Systems Sampling Reconstruction of x(t) from the samples x(nt s ) Aliasing Antialiasing filter Nyquist criterion for intersymbol interference free communication Sampling in the Frequency Domain Numerical Computation of the Fourier Transform: Discrete Fourier Transform (DFT) Derivation of DFT Properties of DFT Fast Fourier transform (FFT) Time and frequency scales Improving the frequency resolution of the spectrum via zero padding Discrete-Time Signals and Systems The z-transform and Fourier transform of discrete-time signals Energy and power spectral density Passing a signal through an LTI system Precautionary notes Digital Filters Filter specifications Filter design using windowing method Equiripple filters Nyquist (M) and square-root Nyquist (M) filters Multirate Signal Processing M-fold Decimator and L-fold Expander M-fold decimator L-fold expander Rate Conversion L-fold interpolation M-fold decimation L/M-fold rate change Commutative Rules The Polyphase Representations Efficient Structures for Decimation and Interpolation Filters Polyphase structure for decimator filterss Polyphase structure for interpolator filters

5 iii Commutator Models L/M-fold resampling The polyphase identity Multistage Implementation Interpolated FIR (IFIR) technique Multistage realization of decimation and interpolation filters Cascaded Integrator-Comb Filters M-fold CIC interpolator M-fold CIC decimator Application Examples Timing recovery All digital modulator All digital demodulator Parallel polyphase filtering for very fast sampling rates An Overview of Transceiver Systems Building Blocks MATLAB Simulation of Digital Transmission Systems Baseband PAM transceiver Eye Patterns in PAM Systems QAM Transceiver Eye Patterns in QAM Systems The Impact of Frequency Offset on the Baseband Equivalent of Passband Channels Adaptive Systems Wiener Filter The real-valued case Principle of orthogonality Extension to the complex-valued case The LMS Algorithm Range of µ, stability and misadjustment The normalized LMS algorithm The Method of Least-Squares Formulation of the Least-Squares Estimation The standard recursive least-squares algorithm Sampling with Automatic Gain Control Phase-Locked Loop Continuous-Time PLL Linear model of PLL and its analysis

6 iv Contents 8.2 Discrete-Time PLL Linear model of PLL and its analysis Designing discrete-time PLL from continuous-time PLL Maximum Likelihood Phase Detection Cost function and the optimum phase The LMS algorithm for phase detection: a derivation of PLL Alternative stochastic gradient A note on the step-size parameter µ Higher order PLLs A PLL with Extended Lock Range Carrier Acquisition and Tracking Non-Data Aided Carrier Recovery Methods Binary PSK with a rectangular pulse-shape Binary PSK with a band-limited pulse-shape Quadrature Amplitude Modulation Non-Data Aided Carrier Acquisition and Tracking Algorithms Coarse carrier acquisition Fine carrier acquisition and tracking Costas Loop Pilot Aided Carrier Acquisition Method Data Aided Carrier Tracking Method Timing Recovery Non-Data Aided Timing Recovery Methods Fundamental results The timing recovery cost function The optimum timing phase Improving the cost function Non-Data Aided Timing Recovery Algorithms Early-late gate timing recovery Gradient-based algorithm Tone extraction algorithm Data Aided Timing Recovery Methods Muller and Muller s method Decision directed method Channel Equalization Continuous-Time Channel Model Discrete-Time Channel Model Symbol-spaced equalizer Fractionally-spaced equalizer

7 v Symbol-spaced vesus fractionally-spaced equalizer Performance Study of Equalizers Wiener-Hopf equations Numerical examples Adaptation Algorithms Cyclic Equalization

Digital Signal Processing

Digital Signal Processing Fourth Edition John G. Proakis Department of Electrical and Computer Engineering Northeastern University Boston, Massachusetts Dimitris G. Manolakis MIT Lincoln Laboratory Lexington,