DocumentCode :
998513
Title :
On the Optimality of Beamforming with Quantized Feedback
Author :
Jafar, Syed Ali ; Srinivasa, Sudhir
Author_Institution :
California Univ., Irvine
Volume :
55
Issue :
12
fYear :
2007
Firstpage :
2288
Lastpage :
2302
Abstract :
The ergodic capacity of a fading vector channel with multiple transmit antennas and a single receive antenna is explored. Perfect channel information is assumed to be available at the receiver while the transmitter has only partial knowledge of the direction of the user´s channel vector based on quantized feedback. We present necessary and sufficient conditions for the optimality of beamforming in such systems. The conditions are applicable to all quantized feedback scenarios regardless of the channel distribution, number of transmit antennas, number of quantization vectors or transmit power. The optimality conditions are closely related to the iteration conditions of the Lloyd algorithm, revealing an interesting link between the optimality of beamforming and the optimality of the vector quantizers. Using the conditions, we prove the capacity optimality of beamforming for several quantized feedback scenarios such as the antenna-selection scheme. We also point out examples of quantized feedback scenarios where beamforming is not optimal. We find that for the independent identically distributed Rayleigh fading channel with more than a single bit of quantized feedback, there is no capacity benefit from increasing the number of antennas beyond the number of quantization vectors. Extensions of the necessary and sufficient optimality condition to the multiple-input multiple-output case are also provided.
Keywords :
MIMO communication; Rayleigh channels; antenna arrays; iterative methods; antenna-selection scheme; beamforming; channel distribution; distributed Rayleigh fading channel; ergodic capacity; fading vector channel; iteration conditions; multiple transmit antennas; perfect channel information; quantized feedback; single receive antenna; Antenna feeds; Array signal processing; Fading; Feedback; MIMO; Quantization; Receiving antennas; Sufficient conditions; Transmitters; Transmitting antennas; Beamforming; ergodic capacity; multiple-input; multiple-output (MIMO) channels; partial/limited feedback; quantized feedback;
fLanguage :
English
Journal_Title :
Communications, IEEE Transactions on
Publisher :
ieee
ISSN :
0090-6778
Type :
jour
DOI :
10.1109/TCOMM.2007.910697
Filename :
4395267
Link To Document :
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