Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication

• Published in: IEEE transactions on wireless communications Vol. 7; no. 8; pp. 2957 - 2963
• Main Authors: Zhifei Fan, Scharf, L.L., Gubner, J.A.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.08.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Analog precoder; Applied sciences; Bit error rate; canonical coordinates; Channels; Communication channels; Coordinate measuring machines; Data communication; Data transmission; Decomposition; Design engineering; Detection, estimation, filtering, equalization, prediction; equalizer; Equalizers; Exact sciences and technology; Frequency; Gaussian noise; Geometry; Information, signal and communications theory; Mathematical models; Mean square error methods; Mean square errors; Modulation, demodulation; multichannel communication; Mutual information; Signal and communications theory; Signal, noise; Subspaces; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Wireless communication; Additive noise; Design criterion; Parameter estimation; Multichannel transmission; Bit error rate; Gaussian channel; Two channel system; Transmission channel; Information rate; Subspace method; Data transmission; Equalizer; Information transmission; Mean square error; Frequency selection; Gaussian noise; Channel estimation; Modulation; multichannel communication; Analog precoder; geometry; canonical coordinates; Multiple channel; Mutual information
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2008.060666

This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L 2 (R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual two- channel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel.