SEP Performance Using Equivalence in Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$</tex-math> </inline-formula> Fading Channels

Abstract

We show that an $L$ -branch maximal ratio combining (MRC) receiver with an average signal-to-noise ratio (SNR) $\bar{\gamma}$ in Nakagami- $m$ fading channels is equivalent to an $mL$ -branch MRC receiver with average SNR $\bar{\gamma}/m$ in Rayleigh fading channels in terms of symbol error probability (SEP) when $mL$ is an integer. Moreover, the orthogonal space–time block code (OSTBC) employing $M_\mathrm{t}$ transmit antennas and $M_\mathrm{r}$ receive antennas with the average SNR $\bar{\gamma}$ in Nakagami- $m$ fading channels is shown to be equivalent to an $mM_\mathrm{t}M_\mathrm{r}$ -branch MRC single-input–multiple-output (SIMO) receiver with the average SNR $\bar{\gamma}/mM_\mathrm{t}$ in Rayleigh fading channels.