On the ASEP of Decode-and-Forward Dual-Hop Networks with Pilot-Symbol Assisted M-PSK

We develop an analytical framework for the end-to-end (e2e) average symbol error probability (ASEP) of dual-hop relaying networks with pilot-symbol assisted M-ary phase-shift keying (M-PSK) modulation. The relays use the selective decode-and-forward protocol and are equipped with multiple receive antennas. The channels are estimated per antenna branch based on the least-squares estimation (LSE) technique by means of pilot symbols. Also, maximal-ratio combining and coherent detection are performed per receiving end. Exact e2e analytical ASEP expressions are derived for binary and quadrature phase-shift keying (BPSK and QPSK), while simple approximate expressions and bounds are obtained for high signal-to-noise ratio (SNR) when M ≥ 2. Our analysis is generic enough to account for any frequency-flat, time-selective, and/or arbitrarily correlated fading channel model per hop. As a case study, we further provide e2e ASEP expressions considering arbitrarily correlated Nakagami fading channels. For high SNR, closed-form expressions are derived, while the cooperation-gain and diversity-order are also extracted. In addition, two power allocation strategies are investigated and analytical solutions are provided. Comparisons between numerical and computer simulation results are finally presented to verify the validity of the proposed approach and the accuracy of the high-SNR approximate expressions.