Space-Time Network Coding With Multiple AF Relays Over Nakagami-m Fading Channels

This paper first analyzes the symbol error rate (SER) performance of the space-time network coding (STNC) over independent but not necessarily identically distributed (i.n.i.d) Nakagami-m fading channels, where multiple sources transmit information symbols to a destination through multiple helping amplify-and-forward (AF) relays. The exact expressions of the overall end-to-end received signal-to-noise ratio (SNR) via multiple STNC-AF relays and its moment generating function (MGF) are derived. Based on these results, the closed-form expression of STNC-AF for the SER withM-ary phase-shift keying andM-ary quadrature-amplitude modulation (QAM) modulations are then presented by adopting the unified MGF method. Furthermore, an approximate SER expression with low computational complexity is also given. In order to observe the performance limit, the diversity order and the nonorthogonality of STNC codes are discussed. Simulation results demonstrate our analytical results and it is illustrated that the diversity order of the STNC with multiple AF relay nodes is a sum function of the fading index of the direct link and the minimal fading indices of the multiple two-hop links.