Globally Optimal Linear Precoders for Finite Alphabet Signals Over Complex Vector Gaussian Channels

We study the design optimization of linear precoders for maximizing the mutual information between finite alphabet input and the corresponding output over complex-valued vector channels. This mutual information is a nonlinear and non-concave function of the precoder parameters, posing a major obstac...

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Vydané v:IEEE transactions on signal processing Ročník 59; číslo 7; s. 3301 - 3314
Hlavní autori: Chengshan Xiao, Zheng, Yahong Rosa, Zhi Ding
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY IEEE 01.07.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Alphabets
Applied sciences
Channels
Coding, codes
Design optimization
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Finite alphabet input
Information, signal and communications theory
Iterative algorithms
Iterative methods
linear precoding
Materials
Mathematical analysis
Mathematical models
MIMO
Mutual information
Optimization
Resource management
Signal and communications theory
Signal processing algorithms
Signal, noise
Studies
Telecommunications and information theory
vector Gaussian noise channel
Vectors
Vectors (mathematics)
Alphabet
Channel capacity
Bit error rate
Gaussian channel
Maximum mutual information
Finite alphabet input
Iterative method
Algorithm
Power allocation
Channel coding
Optimization
Complex variable method
linear precoding
Gaussian noise
Signal processing
Numerical simulation
Pretreatment
Mutual information
vector Gaussian noise channel
Quadratic function
ISSN:1053-587X, 1941-0476
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Popis
Shrnutí:We study the design optimization of linear precoders for maximizing the mutual information between finite alphabet input and the corresponding output over complex-valued vector channels. This mutual information is a nonlinear and non-concave function of the precoder parameters, posing a major obstacle to precoder design optimization. Our work presents three main contributions: First, we prove that the mutual information is a concave function of a matrix which itself is a quadratic function of the precoder matrix. Second, we propose a parameterized iterative algorithm for finding optimal linear precoders to achieve the global maximum of the mutual information. The proposed iterative algorithm is numerically robust, computationally efficient, and globally convergent. Third, we demonstrate that maximizing the mutual information between a discrete constellation input and the corresponding output of a vector channel not only provides the highest practically achievable rate but also serves as an excellent criterion for minimizing the coded bit error rate. Our numerical examples show that the proposed algorithm achieves mutual information very close to the channel capacity for channel coding rate under 0.75, and also exhibits a large gain over existing linear precoding and/or power allocation algorithms. Moreover, our examples show that certain existing methods are susceptible to being trapped at locally optimal precoders.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2140112