Multiuser%20Resource%20Allocation%20in%20Multichannel%20Wireless%20Communication%20Systems

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Multiuser Resource Allocation in Multichannel
Wireless Communication Systems

• Zukang Shen
• Ph.D. Defense
• Committee Members
• Prof. Jeffrey G. Andrews (co-advisor)
• Prof. Melba M. Crawford
• Prof. Gustavo de Veciana
• Prof. Brian L. Evans (co-advisor)
• Prof. Robert W. Heath, Jr.
• Prof. Edward J. Powers
• Communications, Networks, and Systems Area
• Dept. of Electrical and Computer Engineering
• The University of Texas at Austin
• Jan. 19, 2006 (updated slides)

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Outline
Contribution Multichannel Objective New Constraints Low Complexity Algorithm
1 Multiuser orthogonal frequency division multiplexing Frequency domain Sum capacity Proportional user data rates Decouple subchannel and power allocation
2 Multiuser multi-antenna systems with block diagonalization Spatial domain Sum capacity Joint precoding and post-processing Receive antenna selection
3 User selection in multi-antenna systems with block diagonalization Spatial domain Sum capacity Systems with a large number of users Greedy capacity and channel norm based algorithms
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Resource Allocation in Wireless Systems

• High data rate transmission
• Wireless local area networks (WLAN) 54 -- 108
  Mbps
• Metropolitan area networks (WiMAX) 10 -- 100
  Mbps
• Cellular systems (3GPP) 1 -- 4 Mbps
• Limited resources shared by multiple users
• Transmit power
• Frequency bandwidth
• Transmission time
• Code resource
• Spatial antennas
• Resource allocation impacts
• Power consumption
• User throughput
• System latency

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Multiuser Diversity

• Multiuser wireless communication systems
• Independent fading channels
• Multiuser diversity

Resource Allocation Resource Allocation
Static Adaptive
Users transmission order Pre-determined Smartly scheduled
Channel state information Not exploited Wellexploited
SystemPerformance Poor Good
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Downlink Multiuser Multichannel Systems

• Downlink systems
• Centralized basestation transmits to multiple
  users simultaneously
• Limited resources at basestation
• Multiple channels created in
• Frequency orthogonal frequency division
  multiplexing (OFDM)
• Space multiple transmit and receive antennas
• Adaptive resource allocation
• Goal Optimize system throughput subject to
  constraints
• Method Formulate resource allocation as
  optimization problem
• Optimal solution typically computationally
  prohibitive to find
• Low complexity resource scheduling algorithms
  desired
• Assumption Perfect channel state information of
  all users known at basestation

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Outline

• Introduction
• Contribution 1 Adaptive resource allocation in
  multiuser OFDM systems with proportional rate
  constraints
• Optimization framework balancing throughput and
  fairness
• Decoupling subchannel and power allocation
• Allocating power optimally for a given subchannel
  allocation
• Contribution 2 Sum capacity of downlink
  multiuser MIMO systems with block diagonalization
  
• Contribution 3 Low complexity user selection
  algorithms in multiuser MIMO systems with block
  diagonalization
• Conclusion

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Multiuser OFDM (MU-OFDM)

• Orthogonal frequency division multiplexing
• Zero inter-symbol interference
• Parallel frequency subchannels
• Multiple access technology
• Downlink multiuser OFDM
• Users share subchannels and basestation transmit
  power
• Users only decode their own data
• Resource allocation methods
• Static TDMA, FDMA
• Dynamic multiuser diversity
• Users feedback channelinformation to basestation
• Basestation determinesresource allocation

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MU-OFDM Adaptive Resource Allocation
Objective Advantage Disadvantage
Max sum capacity Jang et al., 2003 Best sum capacity No data rate fairness among users
Max minimum users capacity Rhee et al., 2000 Equal user data rates Inflexible user data rates distribution
Max weightedsum capacity Cendrillon et al., 2004 Data rate fairness adjustable by varying weights No guarantee for required proportional user data rates
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MU-OFDM with Proportional Rates
Contribution 1

• Objective Sum capacity
• Constraints
• Total transmit power
• No subchannel shared by multiple users
• Proportional rate constraints
• Advantages
• In theory, fill gap of max sum capacity max-min
  capacity
• In practice, allow different service privileges
  and different pricing

B Transmission bandwidth
K of users
N of subchannels
pk,n power in user ks subchannel n
hk,n channel gain of user ks subchannel n
N0 AWGN power density
Rk User ks capacity
System parameter for proportional rates
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Subchannel Allocation
Contribution 1

• Modified method of Rhee et al., 2000, but we
  keep the assumption of equal power distribution
  on subchannels
• Initialization (Enforce zero initial
  conditions)Set , for
  . Let
• For to (Allocate best
  subchannel for each user)
• Find satisfying
  for all
• Let ,
  and update
• While (Then iteratively give
  lowest rate user first choice)
• Find satisfying
  for all
• For the found , find satisfying
  for all
• For the found and , Let
  , and update

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Power Allocation for a Single User
Contribution 1

• Optimal power distribution for user
• Order
• Water-filling algorithm
• How to find for

K of users
N of subchannels
pk,n power in user ks nth assigned subchannel
Hk,n Channel-to-noise ratio in user ks nth assigned subchannel
Nk of subchannels allocated to user k
Pk,tot Total power allocated to user k
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Power Allocation among Many Users
Contribution 1

• Use proportional rate and total power constraints
• Solve nonlinear system of K equations
  /iteration
• Two special cases
• Linear case
  , closed-form solution
• High channel-to-noise ratio and

where
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Comparison with Optimal Solution
Contribution 1
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Comparison with Max-Min Capacity
Contribution 1
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Comparison with Max Sum Capacity
Contribution 1
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Summary of Contribution 1

• Adaptive resource allocation in multiuser OFDM
  systems
• Maximize sum capacity
• Enforce proportional user data rates
• Low complexity near-optimal resource allocation
  algorithm
• Subchannel allocation assuming equal power on all
  subchannels
• Optimal power distribution for a single user
• Optimal power distribution among many users with
  proportionality
• Advantages
• Evaluate tradeoff between sum capacity and user
  data rate fairness
• Fill the gap of max sum capacity and max-min
  capacity
• Achieve flexible data rate distribution among
  users
• Allow different service privileges and pricing

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Outline

• Introduction
• Contribution 1 Adaptive resource allocation in
  multiuser OFDM systems with proportional rate
  constraints
• Contribution 2 Sum capacity of downlink
  multiuser MIMO systems with block diagonalization
  
• Block diagonalization with receive antenna
  selection
• Sum capacity of BD vs. DPC for given channels
• Upper bound on the ratio of DPC and BD sum
  capacity in Rayleigh fading channels
• Contribution 3 Low complexity user selection
  algorithms in multiuser MIMO systems with block
  diagonalization
• Conclusion

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Multi-Antenna Systems

• Exploit 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 transmitter and receiver
  Winters, 1987 Foschini et al., 1998
• Theoretical results on point-to-point multi-input
  multi-output (MIMO) channel capacity Telatar,
  1999
• Tradeoff between diversity and multiplexing
• Theoretical treatment Zheng et al., 2003
• Switching between diversity and multiplexing
  Heath et al., 2005

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MIMO Gaussian Broadcast Channels

• Duality with multiple access channels Vishwanath
  et al., 2003
• Dirty paper coding (DPC) Costa, 1983
• Sum capacity achieved with DPC Vishwanath et
  al., 2003
• Iterative water-filling algorithm Yu et al.,
  2004 Jindal et al., 2005
• Capacity region Weingarten et al., 2004
• Coding schemes approaching DPC sum
  capacityZamir et al., 2002 Airy et al., 2004
  Stojnic et al., 2004
• Too complicated for cost-effective implementations

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Block Diagonalization (BD)

• Linear precoding technique
• Zero inter-user interference Spencer et al.,
  2004
• in the null space of
• Advantages Simple transceiver design
• Effective point-to-point MIMO channel
• Disadvantages Suboptimal for sum capacity
• Channel energy wasted for orthogonalizing user
  channels
• Transmit signal covariance matrices not optimal

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BD with Receive Antenna Selection
Contribution 2

• Why joint processing?
• Confine to be selection matrix, e.g.
  
• Lower system overhead for conveying
• BD with receive antenna selection
• Exhaustive search for optimal selection matrices

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BD vs. DPC Given Channels
Contribution 2

• Theorem The ratio of DPC sum capacity over BD is
  bounded by
• Ratio of DPC sum capacity over TDMA bounded by
  Jindal et al., 2005
• TDMA only serves one user at a time
• BD supports multiple users
• Valid for any SNR, , , and
• Lemma If user channels are orthogonal, then
• Lemma If and user channelsare in
  same vector space

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BD vs. DPC Rayleigh Fading Channels
Contribution 2

• Lower bound on BD ergodic sum capacity
• Fix a subset of users to serve
• Each users effective channel still Rayleigh
• Equal power allocated for every MIMO eigenmode
• Upper bound on DPC ergodic sum capacity
• Allow user cooperation (effectively
  point-to-point channel)
• Cooperative channel
• Space-time water-filling for effective
  cooperative MIMO channel
• Upper bound on ratio of DPC and BD ergodic sum
  capacity
• Easy evaluation with numerical integrations
• Bound is tight for
• Medium to high SNR, or

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Simulation Results
Contribution 2
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Simulation Results
Contribution 2
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Summary of Contribution 2

• Sum capacity in downlink multiuser MIMO systems
  with block diagonalization
• Formulated joint transmitter precoding and
  receiver post-processing (shown in dissertation)
• Combined block diagonalization with receive
  antenna selection
• Block diagonalization vs. dirty paper coding
• Sum capacity for given channels
• Ergodic sum capacity in Rayleigh fading channel
• Block diagonalization achieves a significant part
  of the optimal sum capacity

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Outline

• Introduction
• Contribution 1 Adaptive resource allocation in
  multiuser OFDM systems with proportional rate
  constraints
• Contribution 2 Sum capacity of downlink
  multiuser MIMO systems with block diagonalization
  
• Contribution 3 Low complexity user selection
  algorithms in multiuser MIMO systems with block
  diagonalization
• Capacity based user selection
• Channel Frobenius norm based user selection
• Conclusion

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Need of User Selection for BD

• Zero inter-user interference requires in
  null space of
• Dimension of
• Maximum number of simultaneous users
• Assuming active users utilize all receive
  antennas
• Select subset of users to maximize total
  throughput
• Exhaustive search
• Optimal for total throughput
• Computationally prohibitive
• 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
Contribution 3
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Computational Complexity
Contribution 3
(m x n) complex matrix operation Flop counts
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
Contribution 3
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Summary of Contributions

• Adaptive resource allocation in multiuser OFDM
• Balanced throughput and proportional user data
  rates
• Derived optimal power allocation given subchannel
  allocation
• Sum capacity of downlink multiuser MIMO systems
• Combined block diagonalization with receive
  antenna selection
• Analyzed sum capacity of BD vs. DPC for given
  channels
• Derived upper bound on ratio of DPC and BD sum
  capacity in Rayleigh fading channels
• Low complexity user selection algorithms in
  multiuser MIMO systems with block diagonalization
• Proposed two algorithms with linear complexity in
  no. of total users
• Achieved near-optimal sum capacity