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.