Amplify-and-Forward Multihop Relaying with Adaptive M-QAM in Nakagami-m Fading

An amplify-and-forward (AF) multihop relaying system employing constant-power rate-adaptive M-QAM transmission is investigated. Accurate expressions for performance evaluation in Nakagami-m fading of adaptive continuous rate (ACR) and adaptive discrete rate (ADR) M-QAM are obtained. The analysis is based on a new approximation for the instantaneous end-to-end received SNR in the form of a scaled version of the harmonic mean of the individual per-hop SNRs. The scaling factor is determined based on the average link SNRs. Performance results evaluated using the proposed approximation are more accurate than the performance bounds obtained using the conventional harmonic- mean-based upper bound on the instantaneous received SNR, even though they are obtained with the same computational complexity. Numerical results show that the approximate performance results are very close to the exact results especially in small SNR regimes and for larger values of the Nakagami parameter. It is shown that the ACR QAM achieves an average spectral efficiency within a certain distance of the Shannon limit. The ADR QAM achieves smaller bit error rates than the target bit error rate but at the expense of an additional penalty on the average spectral efficiency, especially for smaller numbers of region boundaries.