Space–Time Network Coding With Antenna Selection

Abstract

In this paper, we investigate the space–time network coding (STNC) with antenna selection (AS) in the cooperative multiple-input–multiple-output (MIMO) network, where $U$ users communicate with a common destination $D$ with the aid of $R$ decode-and-forward (DF) relays. In this network, the best transmit/receive antenna pair with the highest signal-to-noise (SNR) ratio is selected to perform the signal transmission and reception over the user–destination and relay–destination links. To quantify the performance degradation of STNC with AS due to time delay between instants of channel state information (CSI) estimation and data transmission, we derive the symbol error rate (SER) and capacity expressions over flat Rayleigh fading channels. The asymptotic SER expression reveals that STNC with AS guarantees full diversity order of $(N_u \!+\! \sum_{r = 1}^R N_r)N_{D}$ , where $N_u$ , $N_r$ , and $N_{D}$ are the antenna numbers of user $u$ , relay $r$ , and the destination $D$ , respectively, when the AS is performed based on perfect CSI, and outdated CSI degrades the full diversity order to $R+\mbox{1}$ . We also examine the effect of spatial correlation on the performance of STNC with AS by obtaining new closed-form expression for the asymptotic SER, which indicates that STNC with AS achieves the full diversity order over flat correlated Rayleigh channels, regardless of the value of spatial correlation coefficient. Numerical and simulation results are provided to demonstrate the accuracy of our theoretical analysis and evaluate the performance of STNC with AS.