TY - GEN
T1 - BER-Aware Link SNR Quantization for Relay Beamforming
T2 - 13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019
AU - Li, Wen Hsuan
AU - Wu, Jwo-Yuh
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/12/16
Y1 - 2019/12/16
N2 - Cooperative beamforming is a potentially useful technique for enhancing link reliability in modern wireless relay communications. To aid beamforming design, the signal-to-noise ratio (SNR) of the source-to-relay (S-R) channel links must be known at the destination node. Abdallah and Papadopoulos in IEEE Trans. Signal Processing, vol. 56, no. 10, 2008, proposed a beamforming system with relay-assisted SNR acquisition, that is, the S-R link SNR is first quantized at each relay and is then forwarded to the destination. An optimal quantizer design problem was proposed in that paper, aiming at reducing the system bit error rate; however, only the binary quantization case was considered therein, with the quantization threshold computed by a suggested rule of thumb. In this paper, we study the aforementioned quantizer design problem in the general multiple-bit setting. We show that the solutions to the first-order necessary condition for optimality can be obtained as a fixed point of a certain nonlinear map over the feasible threshold set. The existence, and uniqueness, of the fixed point are established by using, respectively, the Brouwer's and Schauder's fixed point theorems. Finally, we show that the fixed point thus obtained yields the globally optimal set of quantization thresholds. To the best of our knowledge, this paper is the first which leverages fixed point theories to rigorously solve SNR quantization problems in the context of wireless relay communication.
AB - Cooperative beamforming is a potentially useful technique for enhancing link reliability in modern wireless relay communications. To aid beamforming design, the signal-to-noise ratio (SNR) of the source-to-relay (S-R) channel links must be known at the destination node. Abdallah and Papadopoulos in IEEE Trans. Signal Processing, vol. 56, no. 10, 2008, proposed a beamforming system with relay-assisted SNR acquisition, that is, the S-R link SNR is first quantized at each relay and is then forwarded to the destination. An optimal quantizer design problem was proposed in that paper, aiming at reducing the system bit error rate; however, only the binary quantization case was considered therein, with the quantization threshold computed by a suggested rule of thumb. In this paper, we study the aforementioned quantizer design problem in the general multiple-bit setting. We show that the solutions to the first-order necessary condition for optimality can be obtained as a fixed point of a certain nonlinear map over the feasible threshold set. The existence, and uniqueness, of the fixed point are established by using, respectively, the Brouwer's and Schauder's fixed point theorems. Finally, we show that the fixed point thus obtained yields the globally optimal set of quantization thresholds. To the best of our knowledge, this paper is the first which leverages fixed point theories to rigorously solve SNR quantization problems in the context of wireless relay communication.
KW - Brouwer's
KW - Schauder's fixed point theorem
KW - cooperative beamforming
KW - cooperative communications
KW - fixed point theorem
KW - fixed point theory
KW - quantization
KW - relay communications
UR - http://www.scopus.com/inward/record.url?scp=85081991315&partnerID=8YFLogxK
U2 - 10.1109/ICSPCS47537.2019.9008706
DO - 10.1109/ICSPCS47537.2019.9008706
M3 - Conference contribution
AN - SCOPUS:85081991315
T3 - 2019, 13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019 - Proceedings
BT - 2019, 13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 16 December 2019 through 18 December 2019
ER -