MIMO Multi-Base-Station Beamforming Design in an Interference Channel Model

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MIMO Multi-Base-StationBeamforming Design in
anInterference Channel Model
Hayssam Dahrouj Connections 2006 Supervisor
Prof. Wei Yu ECE Dept., University of Toronto,
Spring 2006

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Problem Statement

• Study the minimal-power beamforming design
  problem for Multi-Base-Station scenarios between
  several transmitters and several receivers
• Idea generated from multi-user cellular networks

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Main challenges

• Investigate the scenario of designing the optimal
  beamformers for muti-base-station with Fixed
  receivers
• Examine the problem of jointly optimizing the
  MIMO receivers and the transmit beamformers
• Repeat the two problems above with channel
  estimation error

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I. Motivation

• Practical problem e.g. multiuser cellular
  network for partial base-stations coordination
• Important for Cell-edge users

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I. Motivation(continued)

• It still offers all the advantages of MIMO
  systems
• Increasing individual data rates
• Increasing the number of users
• Conventional networks TDMA, FDMA and CDMA
• MIMO introduces spatial dimension that increases
  the number of users when added to existing
  technologies.
• Increasing reliability
• Ensuring multiple copies through diversity
• Better interference suppression and fading
  combating through beamforming design

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II. New Results

• Multiuser Multi-Base-Station cellular network

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II.A.Fixed receivers system model
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II.A. Fixed receivers (Continued)

• Problem Minimize the transmitted power subject
  to signal and interference plus noise ratio
  contraints (SINR)
• Transform the problem into second order cone
  programming (SOCP) problem which has linear
  objective function, linear constraints and
  generalized inequality constraints
• Any SOCP problem can be formulated as a
  semidefinite program (SDP) which has linear
  objective function, linear constraints and
  semidefiniteness constraints
• SDP problems have efficient solvers SEDUMI!

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II.B. Joint optimization of Tx/Rx

• The idea is to build the build the optimal MMSE
  receivers subject to input power constraints
• Hard to maximize individual rates for
  none-Toeplitz structures
• In case of ISI channel, matrices have Toeplitz
  structures
• Minimize a weighted sum of the traces of MSEs
  subject to power constraint
• Re-formulate the problem in the frequency domain
• Using Lagrangian theory, 2 simultaneous equations
  of degree 4 were derived!!
• Efficient solution
• Derive the dual problem and an iterative
  algorithm rather than brute force approach

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II.C. Beamforming problem with imperfect CSI

• Problem How to design beamformers with imperfect
  CSI
• Now the channel matrices are varying with some
  random error matrices each with known
  distribution
• Idea
• Use Robust optimization techniques
• Challenge
• What is the model for a robust semidefinite
  programming ?
• Open up a wide research area!!

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III. Conclusion

• Addressed the problem of minimum-power
  beamforming problem for multi-base station
• Formulated the problem as a SDP in case of fixed
  receiver
• Investigated the problems of joint Tx/Rx design
  and imperfect of CSI

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Thank you!

• Questions?