High-SNR Second-Order Statistics of Amplify-and-Forward Relaying with Variable Gains and Multiple Hops

Reginaldo Nunes de Souza, Edgar Eduardo Benitez Olivo, Lucas Catão de Freitas Ferreira, Carlos R. N. da Silva, José Cândido Silveira Santos Filho

DOI: 10.14209/SBRT.2020.1570649504

Evento: XXXVIII Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT2020)

Keywords: amplify-and-forward variable-gain LCR AFD

Abstract

We analyze the high-SNR behavior of the level crossing rate and average fade duration for a variable-gain amplify-and-forward relaying system composed of an arbitrary number of hops under Rayleigh fading. Most studies on the second-order statistics of multi-hop amplify-and-forward relaying assume fixed gains at the relays and analyze the end-to-end channel gain (from source to destination). Such analysis leads to the so-called cascaded product channel, being mathematically attractive, yet ignoring the accumulation of noise along the hops. Here, in turn, we take the noise into account by analyzing the end-to-end SNR, which ultimately governs the system performance. Also, aiming at the benchmark for transparent relaying, we assume variable gains at the relays. We obtain simple closed-form asymptotic expressions for the investigated second-order statistics and, as a byproduct, for the associated outage probability.

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