Symbol Error Probability Analysis for Multihop Relaying over Nakagami Fading Channels

In this paper, we derive closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular I × J-ary quadrature amplitude modulation (QAM) in cooperative amplify-and-forward (A&F) relaying systems, when no direct line-of-sight exists between the source and the destination nodes and when the links between the K successive nodes forming the multihop cooperation chain (including the source and the destination nodes) follow independent but not-necessarily identical Nakagami-m fading distributions with arbitrary real indexes {m
_k
}
_k=1
^K
not less than 1/2 and arbitrary average power levels {γ̅k}
_k=1
^K
. The average SEP of rectangular QAM for this set-up is provided in closed-form as a linear combination of the first Lauricella's multivariate hypergeometric function, F
_A
^(K+1)
, K being the number of multihop links, which can be efficiently evaluated using standard numerical softwares. Simulation results sustaining our analysis are provided, and the impacts of various parameters on the overall multihop system performance are investigated.