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

TL;DR

This paper provides exact and asymptotic symbol error rate analyses for space-time network coding in cooperative networks over Nakagami-m fading channels, revealing full diversity order and factors affecting performance.

Contribution

It introduces new closed-form and asymptotic SER expressions for STNC in Nakagami-m fading, highlighting the impact of channel parameters and network configurations.

Findings

STNC achieves full diversity order determined by Nakagami-m parameters.

Derived exact and asymptotic SER expressions for M-PSK and M-QAM.

Performance influenced by relay number, placement, fading parameters, and power allocation.

Abstract

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.