Abstract
This work considers quantize–forward (QF) relay channels with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -ary phase shift keying at the source and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -bit uniform phase quantization at the relay. A cooperative linear combining (CLC) detection which linearly combines the received signals at the destination is proposed in the QF relay channel by deriving an equivalent signal-to-noise ratio for the source-relay-destination link. Furthermore, the proposed detection is simplified by approximating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> function in two directions: small <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> and large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> . The CLC detection and its simplified version are also extended to multi-relay channels. Simulation results verify that the CLC and simplified CLC detections achieve reasonable performance with less complexity than the maximum-likelihood detection. It demonstrates that applying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\log _{2} M+2)$</tex-math></inline-formula> -bit uniform phase quantization at the relay and the simplified CLC detection at the destination can be an appropriate choice in terms of performance, complexity, and memory.
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