Exact SER analysis of OSTBC MIMO-OFDM systems over uncorrelated Nakagami-m fading channels

Although the topic of multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) over different fading channels is well investigated, but its exact closed form symbol error rate (SER) expression employing orthogonal space-time block codes (OSTBCs) over uncorrelated Nakagami-m fading channels for M-ary phase shift keying (M-PSK) is still not available. The closed form expressions are very useful for evaluating system's performance without carrying out time consuming simulations. In this paper, we thus, derive exact closed form expression for average SER of MIMO-OFDM systems employing gray coded M-PSK modulation using the traditional probability density function (PDF) approach over uncorrelated Nakagami-m fading channels using OSTBCs. We further deduce the closed form expressions of average SER for gray coded binary phase-shift keying (B-PSK), quadrature phase-shift keying (Q-PSK) and eight phase-shift keying (8-PSK) modulation schemes by computing the value of the parameter, g for M = 2, 4 and 8, respectively. These expressions are valid for both frequency-flat and frequency-selective Nakagami-m fading MIMO channels and can be evaluated without any numerical integration techniques. We also show that average BER and SER in case of frequency-selective Rayleigh fading channels remain independent to the number of taps, L of the multipath fading channel used in the system. Moreover, by utilizing the encoding and decoding algorithms for various OSTBCs, Monte Carlo simulation of MIMO-OFDM systems using multiple transmit and receive antennas for different gray coded phase-shift keying modulations is presented. Theoretical results and the simulation results are drawn on the same figures in order to show the validity of our analytical results.