Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication
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 th...
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| Vydáno v: | IEEE transactions on wireless communications Ročník 7; číslo 8; s. 2957 - 2963 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Piscataway, NJ
IEEE
01.08.2008
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 1536-1276, 1558-2248 |
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| Abstract | 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. |
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| AbstractList | 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 super(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. 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@@u2@(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. 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. 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. |
| Author | Zhifei Fan Gubner, J.A. Scharf, L.L. |
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| Keywords | 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 |
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| References | ref35 ref13 ref34 ref15 ref14 ref31 ref30 ref33 ref32 ref2 ref1 ref18 marshall (ref17) 1979 fan (ref7) 2004 gubner (ref12) 2003 ref24 ref23 ref26 ref20 ref22 gallager (ref10) 1968 ref21 loeve (ref16) 1977 ref28 ref27 grochenig (ref11) 2001 ref29 ref9 fan (ref8) 2004 ref3 john (ref19) 2000 ref5 fan (ref6) 2006 scharf (ref25) 1990 daubechies (ref4) 1991; 22 |
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| Snippet | This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective... 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. This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency- selective... |
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| SubjectTerms | 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 |
| Title | Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication |
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