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Published January 2012 | public
Journal Article

The Role of GTD in Optimizing Perfect Reconstruction Filter Banks

Abstract

Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we propose GTD (generalized triangular decomposition) filter banks as a subband coder for optimizing the theoretical coding gain. We focus on perfect reconstruction orthonormal GTD filter banks and biorthogonal GTD filter banks. We show that in both cases there are two fundamental properties in the optimal solutions, namely, total decorrelation and spectrum equalization. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can, with no loss of optimality, be used in the optimal biorthogonal GTD coders, which solves the granularity problem in the conventional optimum bit loading formula. We then extend the use of GTD filter banks to wireless communication systems, where linear precoding and zero-forcing decision feedback equalization is used in frequency selective channels. We consider the quality of service (QoS) problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints. Optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent GTD of the channel frequency response.

Additional Information

© 2011 IEEE. Manuscript received February 20, 2011; received June 23, 2011 and September 03, 2011; accepted September 05, 2011. Date of publication September 22, 2011; date of current version December 16, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiqi Gao. This work was supported in part by the ONR Grant N00014-11-1-0676, and Caltech. Part of this paper was presented at the IEEE Conference on Signals, Systems, and Computers, Monterey, CA, November 2010, and IEEE ICASSP, Praque, Czech Republic, May 2011.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023