Demodulate-and-Forward Relaying with Higher Order Modulations: Impact of Channel State Uncertainty

In this paper, we study the impact of uncertain channel state information (CSI) on the performance of demodulate-and-forward relaying protocols with higher order modulation formats such as pulse-amplitude modulation (PAM) and rectangular quadrature-amplitude modulation (QAM). Assuming a single source and a single destination node assisted by $N$ relay nodes, we study the average bit error probability (BEP) performance of $M$-ary PAM and rectangular QAM constellations with Gray code mapping and imperfect CSI at the relay nodes as well as the destination. The main contributions of this paper are the derivation of closed-form expressions for $a)$ the cumulative distribution functions of the demodulator test statistics, $b)$ the transition probability of error at a given relay, and $c)$ the average BEP for independent and not necessarily identically distributed Rayleigh fading channels with imperfect receiver CSI.

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