Quasi-Concavity for Gaussian Multicast Relay Channels

Mohit Thakur; Gerhard Kramer

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arXiv · 1506.02703

Quasi-Concavity for Gaussian Multicast Relay Channels

Mohit Thakur·Gerhard Kramer

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Abstract

Standard upper and lower bounds on the capacity of relay channels are cut-set (CS), decode-forward (DF), and quantize-forward (QF) rates. For real additive white Gaussian noise (AWGN) multicast relay channels with one source node and one relay node, these bounds are shown to be quasi-concave in the receiver signal-to-noise ratios and the squared source-relay correlation coefficient. Furthermore, the CS rates are shown to be quasi-concave in the relay position for a fixed correlation coefficient, and the DF rates are shown to be quasi-concave in the relay position. The latter property characterizes the optimal relay position when using DF.

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Mohit Thakur, Gerhard Kramer. 2015-06-08. Quasi-Concavity for Gaussian Multicast Relay Channels. https://arxiv.org/abs/1506.02703

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