Space-Time Network Coding with Transmit Antenna Selection and Maximal-Ratio Combining

In this paper, we investigate space-time network coding (STNC) in cooperative multiple-input multiple-output networks, where U users communicate with a common destination D with the aid of R decode-and-forward relays. The transmit antenna selection with maximal-ratio combining (TAS/MRC) is adopted in user-destination and relay-destination links where a single transmit antenna that maximizes the instantaneous received signal-to-noise ratio is selected and fed back to transmitter by receiver and all the receive antennas are combined with MRC. In the presence of perfect feedback, we derive new exact and asymptotic closed-form expressions for the outage probability (OP) and the symbol error rate (SER) of STNC with TAS/MRC in independent but not necessarily identically distributed Rayleigh fading channels. We demonstrate that STNC with TAS/MRC guarantees full diversity order. To quantify the impact of delayed feedback, we further derive new exact and asymptotic OP and SER expressions in closed form. We prove that the delayed feedback degrades the full diversity order to (R+1)N_D, where N_D is the antenna number of the destination D. Numerical and Monte Carlo simulation results are provided to demonstrate the accuracy of our theoretical analysis and evaluate the impact of network parameters on the performance of STNC with TAS/MRC.