Finite-SNR Diversity Multiplexing Tradeoff of SIMO diversity combining schemes under Nakagami-m fading

Multiple Antenna (MA) systems are fundamental in wireless communications. MA systems provide two kinds of advantages, namely diversity gain and multiplexing gain. However, there is an inherent tradeoff between the two, under slow fading conditions and is captured in [1] under asymptotically high signal to noise ratio (SNR). This is known as the Diversity Multiplexing Tradeoff (DMT). It has emerged as a performance criterion for wireless systems and has been generalized to finite-SNR in [2]. In this paper the finite-SNR DMT of rate-adaptive receive diversity combining schemes, namely Maximum Ratio Combining (MRC) and Selection Combining (SC) in presence of Nakagami-m fading, is derived. Closed form expressions of the finite-SNR DMT of Single Input Multiple Output (SIMO) diversity combining schemes are obtained. From the finite-SNR DMT curves, this paper concludes that at especially low SNR, i.e. SNR less than 20 dB, rate-adaptive SIMO-MRC scheme performs better than SIMO-SC, when the fading parameter m is same on all the paths. However, the performance of SIMO-SC catches up with that of SIMO-MRC at higher SNR.