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Design of Multiple Antenna Coding Schemes with Channel Feedback

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1 Design of Multiple Antenna Coding Schemes with Channel Feedback
Krishna Kiran Mukkavilli, Ashutosh Sabharwal, and Behnaam Aazhang Department of Electrical and Computer Engineering Rice University, Houston, Texas

2 Introduction Demand for high data rates in wireless communications
High spectral efficiency schemes Fading phenomenon Diversity schemes Multiple antenna Overcomes fading Capacity grows linearly with min(t,r) [Telatar95] Capacity achieved via space-time codes

3 Background Slow (block) fading channel Feedback
Increase spectral efficiency Decrease frame error rate Spatial water filling [Telatar95] Maximizes mutual information Requires substantial channel information No guarantees for practical low dimensional codebooks

4 Our Focus Practical management of unknown channel condition
Limited feedback Practical codebook design issues Our approach Role of feedback in codebook design Role of phase information Role of amplitude information

5 Codebook Design with Feedback
Objective: Error minimizing codebooks Unknown channel condition with reduced dimension feedback Issues: what feedback? what codebook? Dominant spatial direction is the key parameter Chernoff bound analysis Transmission schemes with phase and amplitude feedback

6 System and Channel Model
h1,i L Y X Block Fading m tx antennas n rx antennas hm,i Channel realization known at the receiver Error free feedback channel

7 Chernoff Bound Minimize pairwise error probability given H
Use X = Wd x where Wd is the eigenvector corresponding to the maximum singular value of H, max Observations: Reduced dimension feedback required Gaussian channel codebooks

8 Feedback Cases Dominant eigenvector solution
Captures relevant channel phase and amplitude information (2m – 2) real numbers Analyze the cases of Phase information only Amplitude information only Outage probability performance

9 Beamforming with Phase Information
Problem : find such that minimizes error probability where x is the information vector Solution: Choose whose components satisfy

10 Special Cases m =2 ,n = 1 m=2, n = n m=m, n = 1

11 Features of Beamforming with Phase Feedback
Less feedback information (m-1 real numbers) No need for singular value decomposition Performance loss compared to dominant eigenvector solution, for n=1 Loss is 0.49 dB for 2 tx and 1 rx antenna Loss is about 1.05 dB for 1 rx antenna and large m

12 Beamforming with Amplitude Information
Problem: find such that minimizes error probability where x is the information vector; Solution (selection diversity) : Set hi= 1 for the antenna with the “best channel”, hi =0 for others Additional amplitude information does not help

13 Features of Selection Diversity
Finite feedback of log(m) bits per frame Maximum diversity achieved Performance loss compared to dominant eigenvector, for n=1, given by For large m, with n=1, loss approximated by

14 Simulation Results (1) 2 transmit antennas and 2 receive antennas
Rayleigh block fading Antipodal signaling No channel code

15 3 transmit antennas and 2 receive antennas
Simulation Results (2) 3 transmit antennas and 2 receive antennas

16 Outage Probability Analysis
Useful concept for non-ergodic (delay constrained) channels Lower bound on frame error rate Same slope for outage for all the schemes Given by the maximum spatial diversity Sufficient condition based on channel norm for attaining maximum slope for outage probability [ISIT 2002]

17 Conclusion and Future Work
Summary Designed and analyzed various transmission and feedback schemes Future work Address tradeoff between phase and amplitude information with finite feedback Framework for performance analysis normalized by the extent of feedback


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