Complex-Valued Matrix Derivatives: With Applications in Signal Processing and Communications

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Cambridge University Press, Feb 24, 2011 - Technology & Engineering
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In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.
 

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Contents

1 Introduction
1
2 Background Material
6
3 Theory of ComplexValued Matrix Derivatives
43
4 Development of ComplexValued Derivative Formulas
70
5 Complex Hessian Matrices for Scalar Vector and Matrix Functions
95
6 Generalized ComplexValued Matrix Derivatives
133
7 Applications in Signal Processing and Communications
201
References
231
Index
237
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About the author (2011)

Are Hjørungnes is a Professor in the Faculty of Mathematics and Natural Sciences at the University of Oslo, Norway. He is an Editor of the IEEE Transactions on Wireless Communications and has served as a Guest Editor of the IEEE Journal of Selected Topics in Signal Processing and the IEEE Journal on Selected Areas in Communications.

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