BER-Aware Link SNR Quantization for Relay Beamforming: A Fixed-Point Theory Approach

Wen Hsuan Li, Jwo Yuh Wu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publication2019, 13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728121949
DOIs
StatePublished - Dec 2019
Event13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019 - Gold Coast, Australia
Duration: 16 Dec 201918 Dec 2019

Publication series

Name2019, 13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019 - Proceedings

Conference

Conference13th International Conference on Signal Processing and Communication Systems, ICSPCS 2019
CountryAustralia
CityGold Coast
Period16/12/1918/12/19

Keywords

  • Brouwer's
  • cooperative beamforming
  • cooperative communications
  • fixed point theorem
  • fixed point theory
  • quantization
  • relay communications
  • Schauder's fixed point theorem

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