Diversity Order and Coding Gain of General-Order Rectangular QAM in MIMO Relay With TAS/MRC in Nakagami- $m$ Fading

Recently, multiple-input–multiple-output (MIMO) relay networks have been an active area of research, particularly with combining single transmit antenna selection (TAS) and receiver maximal ratio combining (MRC). Moreover, general-order rectangular quadrature amplitude modulation (QAM) has received much attention for its high spectral efficiency and flexible modulation scheme. However, the analytical performance of general-order rectangular QAM has not been found in the literature for MIMO relay with TAS/MRC in Nakagami-
$m$
fading channels in spite of its practical usefulness. In addition, the analytical performance of general-order rectangular QAM often comes with enormous computational complexity. Therefore, it is hardly possible to understand the analytical solution unless the symbol error probability (SEP) is plotted graphically. In this paper, we present the SEP of general-order rectangular QAM in a MIMO relay with TAS/MRC using the sampling property of the delta impulse function. The SEP of MIMO relay networks is shown in terms of diversity order and coding gain. The proposed sampling method can also significantly reduce the computational complexity of the SEP of general-order rectangular QAM.