TY - JOUR
T1 - Optimal selective feedback policies for opportunistic beamforming
AU - Samarasinghe, Tharaka
AU - Inaltekin, Hazer
AU - Evans, Jamie S.
PY - 2013/5
Y1 - 2013/5
N2 - This paper studies the structure of downlink sum-rate maximizing selective decentralized feedback policies for opportunistic beamforming under finite feedback constraints on the average number of mobile users feeding back. First, it is shown that any sum-rate maximizing selective decentralized feedback policy must be a threshold feedback policy. This result holds for all fading channel models with continuous distribution functions. Second, the resulting optimum threshold selection problem is analyzed in detail. This is a nonconvex optimization problem over finite-dimensional Euclidean spaces. By utilizing the theory of majorization, an underlying Schur-concave structure in the sum-rate function is identified, and the sufficient conditions for the optimality of homogenous threshold feedback policies are obtained. Applications of these results are illustrated for well-known fading channel models such as Rayleigh, Nakagami, and Rician fading channels. Rather surprisingly, it is shown that using the same threshold value at all mobile users is not always a rate-wise optimal feedback strategy, even for a network in which mobile users experience statistically the same channel conditions. For the Rayleigh fading channel model, on the other hand, homogenous threshold feedback policies are proven to be rate-wise optimal if multiple orthonormal data carrying beams are used to communicate with multiple mobile users simultaneously.
AB - This paper studies the structure of downlink sum-rate maximizing selective decentralized feedback policies for opportunistic beamforming under finite feedback constraints on the average number of mobile users feeding back. First, it is shown that any sum-rate maximizing selective decentralized feedback policy must be a threshold feedback policy. This result holds for all fading channel models with continuous distribution functions. Second, the resulting optimum threshold selection problem is analyzed in detail. This is a nonconvex optimization problem over finite-dimensional Euclidean spaces. By utilizing the theory of majorization, an underlying Schur-concave structure in the sum-rate function is identified, and the sufficient conditions for the optimality of homogenous threshold feedback policies are obtained. Applications of these results are illustrated for well-known fading channel models such as Rayleigh, Nakagami, and Rician fading channels. Rather surprisingly, it is shown that using the same threshold value at all mobile users is not always a rate-wise optimal feedback strategy, even for a network in which mobile users experience statistically the same channel conditions. For the Rayleigh fading channel model, on the other hand, homogenous threshold feedback policies are proven to be rate-wise optimal if multiple orthonormal data carrying beams are used to communicate with multiple mobile users simultaneously.
KW - Majorization
KW - opportunistic beamforming (OBF)
KW - selective feedback
KW - sum-rate
KW - vector broadcast channels
UR - http://www.scopus.com/inward/record.url?scp=84876760443&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP0984862
UR - http://purl.org/au-research/grants/arc/DP110102729
U2 - 10.1109/TIT.2013.2239355
DO - 10.1109/TIT.2013.2239355
M3 - Article
AN - SCOPUS:84876760443
SN - 0018-9448
VL - 59
SP - 2897
EP - 2913
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 5
ER -