Symbol Error Rate of Space - Time Network Coding in Nakagami-m Fading

In this paper, we analyze the symbol error rate (SER) of space-time network coding (STNC) in a distributed cooperative network over independent but not necessarily identically distributed (i.n.i.d.) Nakagami-m fading channels. In this network, multiple sources communicate with a single destination with the assistance of multiple decode-and-forward (DF) relays. We first derive new exact closed-form expressions for the SER with M-ary phase-shift keying modulation (M-PSK) and M-ary quadrature-amplitude modulation (M-QAM). We then derive new compact expressions for the asymptotic SER to offer valuable insights into the network behavior in the high signal-to-noise ratio (SNR) regime. Importantly, we demonstrate that STNC guarantees full diversity order, which is determined by the Nakagami-m fading parameters of all the channels but independent of the number of sources. Based on the new expressions, we examine the impact of the number of relays, relay location, Nakagami-m fading parameters, power allocation, and nonorthogonal codes on the SER.