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Generalized Geometric Mean Decomposition and DFE Transceiver Design—Part I: Design and Complexity

Liu, Chih-Hao and Vaidyanathan, Palghat P. (2012) Generalized Geometric Mean Decomposition and DFE Transceiver Design—Part I: Design and Complexity. IEEE Transactions on Signal Processing, 60 (6). pp. 3112-3123. ISSN 1053-587X. doi:10.1109/TSP.2012.2189855.

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This paper considers a new matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The inner most triangular matrix has its diagonal elements equal to the geometric mean of the singular values of the target complex matrix. The complexity (defined in terms of the number of floating point operations) of the new decomposition, generalized geometric mean decomposition (GGMD), depends on its parameters, but is always less than or equal to that of geometric mean decomposition (GMD). The optimal parameters which yield the minimal complexity are derived. The paper also shows how to use GGMD to design an optimal decision feedback equalizer (DFE) transceiver for multiple-input multiple-output (MIMO) channels without zero-forcing constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_(2)(K) times complexity advantage over the GMD transceiver, where is the number of data symbols per data block and is a power of 2. In a companion paper, performance analyses of the proposed GGMD transceiver in terms of arithmetic mean square error (MSE), symbol error rate (SER) and Gaussian mutual information are performed, and comparisons with well-known transceivers are made. The results show that the proposed transceiver reaches the same optimality that a GMD MMSE transceiver can possibly achieve.

Item Type:Article
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URLURL TypeDescription
Vaidyanathan, Palghat P.0000-0003-3003-7042
Additional Information:© 2012 IEEE. Manuscript received April 26, 2011; revised October 31, 2011; accepted February 20, 2012. Date of publication March 05, 2012; date of current version May 11, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Martin Haardt. This work is supported in parts by the ONR Grant N00014-11-1-0676 and the California Institute of Technology. The authors are grateful to P. Pal and C.-C. Weng for their valuable feedback and useful comments regarding the paper.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1-0676
Subject Keywords:Cyclic prefix systems; generalized geometric mean decomposition; geometric mean decomposition; transceivers
Issue or Number:6
Record Number:CaltechAUTHORS:20120620-094432896
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Official Citation:Chih-Hao Liu; Vaidyanathan, P.P.; , "Generalized Geometric Mean Decomposition and DFE Transceiver Design—Part I: Design and Complexity," Signal Processing, IEEE Transactions on , vol.60, no.6, pp.3112-3123, June 2012 doi: 10.1109/TSP.2012.2189855
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31975
Deposited By: Jason Perez
Deposited On:20 Jun 2012 20:54
Last Modified:09 Nov 2021 20:02

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