Low Complexity User Selection Algorithms for Multiuser MIMO Systems with Block Diagonalization

1
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 Systems

• Narrowband system model
• MIMO channel matrix
• Rayleigh model, i.i.d. complex Gaussian
• Ray-tracing models Yu et al., 2002

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Downlink Multiuser MIMO Systems

• Downlink a centralized basetation communicates
  to multiple users simultaneously
• Both the basestation and users are equipped with
  multiple antennas
• Questions 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 Diagonalization

• BD 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

• Assumptions
• Number of transmit antennas
• Number of receive antennas
• Active users utilize all receive antennas
• User 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 search
• Optimal for total throughput
• Computationally prohibitive
• Two suboptimal user selection algorithms
• Linear complexity in the number of users
• Total throughput close to the optimal
• Related work
• Semi-orthogonal user set construction Yoo et
  al., 2005
• Antenna selection Gharavi-Alkhansari et al.,
  2004

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Greedy User Selection Algorithms
Capacity Based (C-algorithm)
Channel Frobenius Norm Based (N-algorithm)
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Computational Complexity

• Critical matrix operations
• Frobenius norm
• Gram-Schmidt orthogonalization
• Water-filling algorithm
• Singular value decomposition
• Proposed algorithms have complexity

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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