Signal Processing and Optimization for Transceiver Systems 1st Edition by P P Vaidyanathan, See May Phoong, Yuan Pei Lin ISBN 1139042742 9781139042741

Signal Processing and Optimization for Transceiver Systems 1st Edition by P P Vaidyanathan, See May Phoong, Yuan Pei Lin – Ebook PDF Instant Download/Delivery: 1139042742, 9781139042741
Full download Signal Processing and Optimization for Transceiver Systems 1st Edition after payment

Product details:

ISBN 10: 1139042742 
ISBN 13: 9781139042741
Author: P P Vaidyanathan, See May Phoong, Yuan Pei Lin

Signal Processing and Optimization for Transceiver Systems 1st Table of contents:

Part 1: Communication fundamentals
1 Introduction
1.1 Introduction
1.2 Communications systems
1.3 Digitial communication systems
1.3.1 Discrete-time equivalent
1.4 MIMO channels
1.5 Scope and outline
Part 1: Communication fundamentals
Part 2: Transceiver optimization
Part 3: Mathematical background
Part 4: Appendices
1.6 Commonly used notations
2 Review of basic ideas from digital communication
2.1 Introduction
2.1.1 Chapter overview
2.2 Signal constellations
2.2.1 Average energy in a PAM constellation
2.2.2 Average energy in a QAM constellation
2.3 Error probability
2.3.1 Error probability for PAM signals
2.3.1.A Case of Gaussian noise
2.3.2 Error probability for QAM signals
2.3.3 Gray codes
2.4 Carrier-frequency modulation
2.4.1 Generation of single side band signals
2.4.2 Extracting baseband PAM from modulated versions
2.4.3 Modulating the QAM symbol
2.4.4 Extracting the complex QAM signal from the real version
2.5 Matched filtering
2.5.1 Case of white noise
Remarks
2.5.2 The chirp or LFM signal
2.5.2.A Finite-duration chirp
2.5.2.B Fourier transform of finite-duration chirp
2.5.2.C Autocorrelation of finite-duration chirp
2.5.3 SNR Improvement due to matched filtering
2.5.4 Matched filtering and detector performance
2.5.5 Other sources of errors in detection
2.6 Practical considerations in matched filtering
2.7 Concluding remarks
2.A The baseband signal and the passband signal
2.A.1 Baseband channel model for QAM
2.A.2 Baseband channel model for PAM
2.A.2.A PAM/SSB case
Problems
3 Digital communication systems and filter banks
3.1 Introduction
3.2 Multirate building blocks
3.2.1 Polyphase decomposition
3.2.2 Transform domain formulas
3.2.2.A Frequency-domain viewpoint
3.2.2.B Notations for decimation and expansion
3.2.3 Multirate identities
3.2.4 Alias-free decimation
3.2.5 Decimation of multiband signals
3.2.5.A Alias-free(M) regions
3.3 Decimation filters
3.4 Interpolation filters
3.4.1 Time-domain view of interpolation filter
3.4.2 The Nyquist(M) property
3.4.3 Interpolation filters in communications
3.5 Blocking and unblocking
3.6 Parsing a scalar signal into a vector signal
3.7 Decimation and interpolation in polyphase form
3.7.1 Decimation and interpolation filters
3.7.2 Transmitting filter banks or synthesis filter banks
3.7.3 Receiving filter banks or analysis filter banks
3.8 The transmultiplexer system
3.8.1 The multiplexing operation
3.8.2 Redundancy in transmultiplexers
3.8.3 Types of distortion in transmultiplexers
3.9 Analysis of the transmultiplexer system
3.9.1 Blocked version of the transceiver system
3.9.2 The pseudocirculant channel matrix
3.9.3 Perfect symbol recovery
3.10 Concluding remarks
Problems
4 Discrete-time representations
4.1 Introduction
4.2 Conversion between continuous and discrete time
4.2.1 The sampling identity
4.3 Discrete-time representations of channels
4.3.1 Digital communication over a SISO channel
4.3.1.A Minimum bandwidth versus excess bandwidth
4.3.1.B The digital transceiver
4.3.2 Digital communication over a MIMO channel
4.3.2.A The digital MIMO transceiver
4.4 The raised-cosine function
4.4.1 Nyquist property of the raised cosine
4.4.2 Generalizations
4.5 MIMO systems and multiuser systems
4.6 Digital equalization
4.7 Oversampling the received signal
4.8 Fractionally spaced equalizers
4.8.1 FSE structure in polyphase form
4.8.2 Comparing SSE and FSE with examples
4.8.2.A Solving for the FIR FSE
4.8.2.B Channel with zeros outside the unit circle
4.8.2.C Scatter diagrams
4.8.3 The zero-forcing property of the equalizer
4.8.4 Non-uniqueness of FSE
4.8.5 Need for excess BW
4.9 Noble identities and digital design of filters
4.10 MMSE equalization
4.10.1 MMSE equalizers based on Wiener filtering
4.10.1.A Memoryless case
4.10.2 Uncorrelated noise
4.10.2.A Special case of white signal and white noise
4.11 Concluding remarks
Problems
5 Classical transceiver techniques
5.1 Introduction
5.2 Matched filtering and reconstructibility
5.2.1 Reconstructibility of y(t)
Pulse matching is not sufficient
5.2.2 Reconstructibility of s(n)
5.2.3 Relation to linear independence
5.2.4 Generality of matched filtering
More examples of information lossless receiver filters
5.3 The sampled-noise whitening receiver filter
5.4 Vector space interpretation of matched filtering
5.5 Optimal estimates of symbols and sequences
5.5.1 Estimates of a symbol based on the received sample
5.5.2 Symbol estimate based on a sequence of received samples
5.5.3 MAP or ML estimates and error probabilities
5.5.4 The ML estimate in the Gaussian case
5.6 Viterbi algorithm for channel equalization
5.6.1 The trellis diagram
Showing the noise-free outputs
5.6.2 Finding the closest path
5.6.3 The Viterbi algorithm
5.6.4 Viterbi algorithm and maximum likelihood estimates
Discussions
5.7 Decision feedback equalizers
5.8 Precoders for pre-equalization of channels
5.9 Controlled ISI and partial-response signals
5.10 Concluding remarks
5.A General form of receiver filter
Problems
6 Channel capacity
6.1 Introduction
6.2 Ideal lowpass channel
6.3 SNR gap for PAM signals
6.4 Capacity of frequency-dependent channel
6.5 Splitting the channel into subbands
6.6 Circularly symmetric complex random vectors
6.6.1 Properties of circularly symmetric random vectors
6.6.2 Circularly symmetric variables with specific covariances
6.6.3 Gaussian circularly symmetric random vectors
6.6.4 Entropy of Gaussian random vectors
6.6.5 Relation to other definitions
6.6.5.A Zero mean not implied by Definition 1
6.6.5.B Restriction on shifts
6.7 Capacity for MIMO and complex channels
6.7.1 Mutual information
6.7.2 Solution to the maximum mutual information problem
Discussion
6.7.3 Arbitrary noise covariance
6.8 Concluding remarks
Problems
7 Channel equalization with transmitter redundancy
7.1 Introduction
7.2 Zero padding
7.2.1 Elimination of interblock interference
7.2.2 Equalization at the zero-prefix receiver
7.2.2.A Effect of zeros of the channel
7.2.2.B Summary (zero padding)
7.2.3 Generalization of the precoder matrix
7.3 Introduction of the cyclic prefix
7.3.1 Working principle of the cyclic-prefix system
7.3.2 The cyclic-prefix receiver
7.4 The circulant matrix representation
From pseudocirculants to circulants
Summary (cyclic-prefix systems)
7.5 Variations of the cyclic-prefix system
Remarks
7.6 The discrete multitone system
7.7 Concluding remarks
Historical remarks
Problems
8 The lazy precoder with a zero-forcing equalizer
8.1 Introduction
8.2 Noise amplification and Frobenius norm
8.3 Frobenius norm of left inverse as A grows taller
8.4 Application in equalization
8.5 The autocorrelation property
8.6 Effect of increasing the block size
8.7 Concluding remarks
8.A Monotonicity of noise gain
Problems
Part 2: Transceiver optimization
9 History and outline
9.1 Introduction
9.2 A brief history of transceiver optimization
9.2.1 General remarks on early work on equalization
9.2.2 Joint optimization of continuous-time filters
9.2.3 Optimization with zero forcing, for TV signals
9.2.4 Joint optimization of filters for discrete-time symbol streams
9.2.5 Turning the hybrid system into an all-discrete system
9.2.6 MIMO channels
9.3 Outline for Part 2
Chapter 10: Optimal SISO transceivers
Chapter 11: Optimal transceivers for diagonal channels
Chapter 12: MMSE transceivers with zero-forcing equalizers
Chapter 13: MMSE transceivers without zero-forcing equalizers
Chapter 14: Bit allocation and power minimization
Chapter 15: Transceivers with orthonormal precoders
Chapter 16: Minimization of error probability in transceivers
Chapter 17: Optimization of cyclic-prefix transceivers
Chapter 18: Optimization of zero-padded transceivers
Chapter 19: Optimization of DFE transceivers
Optimization summary
10 Single-input single-output transceiver optimization
10.1 Introduction
10.2 Optimization of the SISO communication system
10.2.1 Minimizing MSE under the product constraint
Remarks
10.2.2 Optimal choice of the product filter
10.2.2.A Formulating the optimization problem
10.2.3 Optimum compaction filters
10.3 The all-discrete SISO channel
10.3.1 MMSE transceiver without zero forcing (pure MMSE)
10.3.2 MMSE transceiver with zero forcing (ZF-MMSE)
Summary
Discussion
10.4 General forms of optimal filters
10.4.1 The receiver filter G
Proof of Lemma 10.2. Observe first that
10.4.1. More general noise power spectrum
Remarks
10.4.2 Form of the optimal prefilter
10.4.2.A Introducing the alias-free prefilter Fa(jomega)
10.4.2.B Choice of the alias-free(T) prefilter Fa(jomega)
10.4.3 The all-digital equivalent
10.5 Excess bandwidth and oversampling
10.6 Optimal pulse shape in single-pulse case
10.6.1 Optimum receiver filter
10.6.2 Optimum pulse
Discussions
10.6.2.A MIMO radar
10.7 Concluding remarks
Problems
11 Optimal transceivers for diagonal channels
11.1 Introduction
Chapter outline
11.2 Minimizing MSE under the ZF constraint
11.2.1 Solving for the optimal multipliers
11.3 Minimizing MSE without ZF constraint
11.4 Maximizing channel capacity
11.5 Minimizing the symbol error rate
11.5.1 Introducing the unitary matrix U
11.5.2 Expression for minimized error rate
11.5.2.A How large should the SNR be?
11.6 Examples of optimal diagonal transceivers
Example 11.2
Example 11.3: Improvement due to BER optimization
11.6.1. Lazy precoder versus optimal precoder
Example 11.4: Lazy precoder versus optimal precoder
11.7 Concluding remarks
Problems
12 MMSE transceivers with zero-forcing equalizers
12.1 Introduction
Scope and outline
12.2 Assumptions on noise and signal statistics
12.2.1 Noise covariance matrix
12.2.2 Signal covariance matrix
12.3 Problem formulation
12.3.1 Simplification using the ZF constraint
12.3.2 General form of F
12.3.3 Stationarity condition for optimality
12.4 Solution to the ZF-MMSE problem
12.4.1 Optimal ordering of diagonal elements
12.4.2 Finding the optimal Uf
12.4.3 Finding the optimal Sf
12.4.4 Expressing the solution using the channel SVD
12.5 Optimizing the noise-to-signal ratio
12.6 Concluding remarks
12.A Generality of minimum-norm inverse
12.B Diagonalization approach to optimization
12.B.1 Diagonalizing the problem
12.B.2 ZF-MMSE solution for the diagonal channel
12.B.3 Conversion to a majorization problem
12.B.4 Optimal choice of Uf
12.C Rectangular channel
Problems
13 MMSE transceivers without zero forcing
13.1 Introduction
Chapter outline
13.2 Formulation of the problem
13.3 MMSE equalizer for fixed precoder
13.4 Formulating the optimal precoder problem
13.4.1 Rewriting the error covariance
13.4.2 Rewriting the error covariance
13.5 Solution to the optimal precoder problem
13.5.1 Identification of the constants K and D
13.5.2 Expression for minimized mean square error
13.6 Structure of the MMSE transceiver
Remarks
13.7 Concluding remarks
13.A A result on traces
Problems
14 Bit allocation and power minimization
14.1 Introduction
14.2 Error probabilities, bit rates, and power
14.3 Minimization of transmitted power with bit allocation
14.4 Optimizing the precoder and equalizer
14.4.1 Eliminating the precoder matrix F using the ZF constraint
14.4.2 Finding the optimal equalizer G
14.5 Optimal transceiver in terms of channel SVD
14.5.1 Other equivalent forms of the optimal transceiver
14.6 Further properties of the optimal solutions
14.6.1 Diagonal interpretation
14.6.2 Some invariants of the optimal solutions
14.6.2.A Invariance of [GG?]kk[F?F]14.6.2.B Invariance of bit allocation
14.6.3 Remarks on power allocation
14.6.3.A Power allocated to eigenmodes of the channel
14.6.3.B User power allocation
14.6.4 Comparison with MMSE transceivers
14.7 Coding gain due to bit allocation
14.8 Concluding remarks
14.A Which right inverse is the best?
Problems
15 Transceivers with orthonormal precoders
15.1 Introduction
Assumptions and reminders
15.2 Orthonormal precoders restricted to be square
15.2.1 ZF-MMSE transceivers
15.2.1.A Comparison with general nonunitary precoder
15.2.2 Pure-MMSE transceivers
15.2.2.A Comparison with general non-unitary precoder
15.3 Rectangular orthonormal precoder matrices
15.3.1 ZF-MMSE transceivers
15.3.2 Pure-MMSE transceivers
15.4 Concluding remarks
Problems
16 Minimization of error probability in transceivers
16.1 Introduction
16.2 Minimizing error probability in ZF-transceivers
16.2.1 Introducing the unitary matrix U
16.2.2 Minimizing error probability by optimizing U
16.2.3 ZF transceiver with minimum error probability
16.3 Bias in the reconstruction error
16.3.1 Bias removal
16.3.2 Error probability after bias removal from an MMSE estimate
16.3.3 Optimality of bias-removed MMSE estimate
16.3.4 SINR, SER, and error probability
16.4 Minimizing error probability without ZF
16.5 Bias-removed MMSE versus ZF-MMSE
16.5.1 Diagonal channels
16.5.2 Non-diagonal channels
16.6 Concluding remarks
16.A Bias-removed MMSE estimates
16.A.1 Bias-removed estimates
16.A.2 Optimum unbiased estimate
16.A.3 Signal-to-error (SER) ratios
16.B Convexity proof
16.B.1 Special case of QPSK
16.C Pure MMSE with bias removal vs ZF-MMSE
16.D SISO channel: ZF-MMSE vs bias removal
Problems
17 Optimization of cyclic prefix transceivers
17.1 Introduction
17.2 Optimal cyclic-prefix systems: preliminaries
17.2.1 Optimal unitary matrices in the cyclic-prefix case
17.2.2 SVD of a circulant channel
17.3 Cyclic-prefix systems optimized for MSE: details
17.3.1 ZF-MMSE transceiver
17.3.2 Pure-MMSE transceiver
17.4 CP systems with minimum error probability
17.4.1 unitary matrix UChoiceofthe
17.4.2 Circulant form of minimum-BER cyclic prefix transceivers
17.5 DMT systems optimized for power
17.6 The cyclic-prefix system with unitary precoder
17.6.1 Single-carrier and multicarrier cyclic-prefix systems
17.6.2 Error covariances
17.6.3 Minimum-error-probability property of SC-CP systems
17.7 Cyclic-prefix optimization examples
Example 17.1.
Example 17.2
17.8 Increasing the block-size in cyclic-prefix systems
17.9 Power minimization using bit allocation
Example 17.3: Channel with deep nulls
Example 17.4: Channel with deeper nulls
17.10 Concluding remarks
17.A Error probability versus channel-output SNR
Problems
18 Optimization of zero-padded systems
18.1 Introduction
18.2 Zero-padded optimal transceivers
Example 18.1:
Example 18.2:
Example 18.3: Zero padding versus cyclic prefixing
18.3 Effect of increasing M in zero-padded systems
18.4 Concluding remarks
Problems
19 Transceivers with decision feedback equalizers
19.1 Introduction
19.2 Fundamentals of decision feedback equalizers
19.2.1 Decision feedback within a block
19.2.2 Equivalent structure under no error propagation
19.3 The optimal DFE system with zero forcing
19.3.1 Optimal feedforward matrix G for fixed F and B
19.3.2 Lower bound on the MSE
19.3.3 Proof of Eq. (19.25)
19.3.4 Achieving the lower bound (19.25)
19.3.4. Summary: Optimal DFE transceiver with zero forcing
19.4 Optimal DFE system without zero forcing
19.4.1 Optimal feedforward matrix G for fixed F and B
19.4.2 Error covariance
19.4.3 Bound on the error
19.4.4 Minimizing the bound (19.88)
19.4.5 Achieving the minimized bound (19.98)
19.4.5.A Summary: Optimal DFE transceiver without zero forcing
19.5 Minimizing error probability in DFE transceivers
19.6 Examples of optimal transceivers with DFE
Example 19.1: DFE gain
Example 19.2: Symbol error probability with DFE (zero-padded systems)
Example 19.3: Symbol error probability with DFE (cyclic-prefix systems)
Example 19.4: Effect of increasing the block size
19.7 DFE optimization and mutual information
Discussions
19.8 Other algorithms related to decision feedback
19.8.1 DFE based on QR decomposition of the channel
Discussions
19.8.2 The VBLAST algorithm
Discussions
19.9 Concluding remarks
19.A Matrix triangularization results
19.A.1 The QR decomposition
19.A.2 The QRS decomposition
19.B Proof of the GMD or QRS decomposition
19.B.1 Case of two-by-two diagonal matrices
19.B.2 Diagonal matrices of arbitrary size
Construction of Eq. (19.165)
Details of the proof
19.B.3 Case of arbitrary matrices
19.C Derivation of Eq. (19.72)
19.D Bias-removed MMSE is better than ZF MMSE
Problems
Part 3: Mathematical background
20 Matrix differentiation
20.1 Introduction
20.2 Real matrices and functions
Example 20.1.
20.2.1 Product rule
Example 20.2.
Example 20.3.
Example 20.4.
20.2.2 Scalar functions of vectors
20.2.3 Differentiating the trace of a matrix
Example 20.5.
Example 20.6.
Example 20.7.
Example 20.8.
20.3 Complex gradient operators
20.3.1 Definitions
20.3.2 Functions of real and imaginary parts
20.3.3 Cauchy-Riemann equations
20.3.4 Extension to the case of vector and matrix variables
20.3.5 Stationary points and optimization
20.4 Complex matrices and derivatives
Example 20.9.
Example 20.10.
Example 20.11.
Example 20.12. Symmetric and Hermitian matrices
20.4.1 Differentiating matrix functions with traces in them
Example 20.13.
Example 20.14.
20.4.2 Differentiating matrix functions with inverses in them
Example 20.15.
20.4.3 Differentiating traces of inverses of complex matrices
20.5 Optimization examples
Example 20.16. Beamforming
Example 20.17. Rayleigh-Ritz principle
Example 20.18. A problem with a diagonal solution
Example 20.19. Optimum noise canceller
20.6 Being careful with interpretations …
20.7 Summary and conclusions
Problems
21 Convexity, Schur convexity, and majorization theory
21.1 Introduction
21.2 Review of convex functions
21.2.1 Testing convexity
21.2.2 Examples
21.2.3 The complementary error function
21.2.4 Convex and concave functions of two variables
21.2.5 Composite functions
21.2.6 Jensen?s inequality
21.2.7 Further properties
21.3 Schur-convex functions
Relation to convex functions
21.4 Examples of Schur-convex functions
21.4.1 More examples
A typo
21.4.2 Schur convexity of compositions of functions
21.4.3 Permutation invariance
21.5 Relation to matrix theory
21.5.1 Hermitian matrices and majorization
21.5.1.A Example of a maximizing unitary matrix
21.5.1.B Example of a minimizing unitary matrix
21.5.2 Doubly stochastic matrices, and majorization
21.6 Multiplicative majorization
21.7 Summary and conclusions
22 Optimization with equality and inequality constraints
22.1 Introduction
22.2 Setting up the problem
22.2.1 Definitions and conventions
22.2.2 Karush?Kuhn?Tucker (KKT) conditions
22.2.3 Non-negative variables
22.3 Maximizing channel capacity
22.4 MMSE transceiver
22.4.1 Final form of the solution
22.4.2 Choice of K
22.4.2.A Optimality of K
22.4.3 How does power in a channel depend on noise?
22.5 KKT conditions are only necessary conditions
22.5.1 Capacity is maximized
22.5.2 MSE is minimized
22.6 Concluding remarks

People also search for Signal Processing and Optimization for Transceiver Systems 1st:

signal processing and optimization for transceiver
    
signal processing and optimization for transceiver systems
    
why is signal processing important
    
what is signal processing
    
signal processing and optimization for transceiver systems pdf