Low Complexity User Selection Algorithms for Multiuser MIMO Systems with

Block Diagonalization

Zukang Shen, Runhua Chen, Jeff Andrews,

Robert Heath, and Brian Evans

The University of Texas at Austin

Nov. 1, 2005

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Multi-Antenna Systems Exploit the spatial dimension with multiple antennas Improve transmission reliability – diversity

Combat channel fading [Jakes, 1974]

Combat co-channel interference [Winters, 1984]

Increase spectral efficiency – multiplexing Multiple parallel spatial channels created with multiple antennas at

the transmitter and receiver [Winters, 1987] [Foschini et al., 1998] Theoretical results on point-to-point MIMO channel capacity

[Telatar, 1999]

Tradeoff between diversity and multiplexing A theoretical treatment [zheng et al., 2003]

Switching between diversity and multiplexing [Heath et al. 2005]

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Point-to-Point MIMO SystemsNarrowband system modelMIMO channel matrix

Rayleigh model, i.i.d. complex GaussianRay-tracing models [Yu et al., 2002]

Space-Time

Transmitter

Space-Time

Receiver

User Data User Data

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Downlink Multiuser MIMO SystemsDownlink: a centralized basetation communicates to

multiple users simultaneouslyBoth the basestation and users are equipped with

multiple antennasQuestions: how to utilize the spatial dimension? What

is the capacity limit?

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Capacity of MIMO Gaussian Broadcast Channels

Duality between MIMO Gaussian broadcast and multiple access channels [Vishwanath et al., 2003] [Viswanath et al., 2003]

Dirty paper coding [Costa 1983]

Sum capacity achieved with DPC [Vishwanath et al., 2003]

Iterative water-filling [Yu et al., 2004] [Jindal et al., 2005]

Capacity region of MIMO Gaussian broadcast channels [Weingarten et al., 2004]

Practical coding schemes approaching the DPC sum capacity [Zamir et al., 2002] [Airy et al., 2004] [Stojnic et al., 2004]

Too complicated for cost-effective implementations

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Block DiagonalizationBD is a Linear precoding technique

BD enforces zero inter-user interference [Spence et al., 2004] [Choi et al., 2004] [Wong et al., 2003] [Pan et al., 2004]

Effective point-to-point MIMO system

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Number of Simultaneously Supportable Users with BD

AssumptionsNumber of transmit antennasNumber of receive antennasActive users utilize all receive antennasUser channel information is known at Tx

Zero inter-user interference requires in the null space of

Dimension of :Maximum # of simultaneous users:

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The Need for Low Complexity User Selection Algorithms

Select a subset of users to maximize the total throughput when

Exhaustive searchOptimal for total throughputComputationally prohibitive

Two suboptimal user selection algorithms Linear complexity in the number of usersTotal throughput close to the optimal

Related workSemi-orthogonal user set construction [Yoo et al., 2005]

Antenna selection [Gharavi-Alkhansari et al., 2004]

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Greedy User Selection Algorithms

, apply BD to calculate the total channel energy

Apply the C-algorithm to

users selected

YesNo

Capacity Based(C-algorithm)

Channel FrobeniusNorm Based(N-algorithm)

, apply BD to calculate the sum capacity

users selected or sum capacity decreases

Yes No

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Computational Complexity

Critical matrix operations Frobenius norm Gram-Schmidt

orthogonalization Water-filling algorithm Singular value

decomposition

Proposed algorithms have complexity

Average CPU run time(Pentium M 1.6G Hz PC)

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Monte Carlo Results

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Summary

Block diagonalization is a realizable linear precoding technique for downlink multiuser MIMO systems

User selection is necessary to exploit the multiuser diversity

Near-optimal low complexity user selection algorithms are desirable for implementations