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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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]

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