Exact closed-form expression for the bit error rate of orthogonal STBC in Nakagami fading channels

We consider the bit error rate (BER) performance of multiple-input multiple-output (MIMO) systems employing transmit diversity through orthogonal space-time block coding (STBC). First, we derive a formula for the characteristic function of the output signal-to-noise ratio (SNR) at the receiver in the presence of Nakagami fading, expressing it in terms of the system diversity order, the code-rate of the employed orthogonal design, and the average SNR per receive antenna. Then, based on a recently proposed general BER expression tor one-and two-dimensional amplitude modulations (PAM and QAM) in AWGN channels (Yoon, D. et al., 2000; Cho, K. and Yoon, 2002), we derive exact closed-form expressions for the BER of Gray-coded PAM and QAM modulations when STBC is employed in the presence of Nakagami fading. We also consider the BER of STBC, when used in conjunction with M-ary phase shift keying (M-PSK), for which we derive a tight closed-form approximation.