Precise SER Analysis and Performance Results of OSTBC MIMO-OFDM Systems over Uncorrelated Nakagami-m Fading Channels

Abstract

Although the topic of multiple-input multiple-output (MIMO) based orthogonal frequency division multiplexing (OFDM) over different fading channels is well investigated, its closed form symbol error rate (SER) expressions and performance results employing orthogonal space time block codes (OSTBCs) over uncorrelated frequency-selective Nakagami-m fading channels are still not available. The closed form expressions are extremely useful for evaluating system's performance without carrying out time consuming simulations. Similarly, the performance results are also quite beneficial for determining the system's performance in the sense that many practical wireless standards extensively employ MIMO-OFDM systems in conjunction with M-ary quadrature amplitude modulation (M-QAM) constellation. This paper thus, derives exact closed form expressions for the SER of M-ary Gray-coded one and two dimensional constellations when an OSTBC is employed and Nt transmit antennas are selected for transmission over frequency-selective Nakagami-m fading channels. For this purpose, first an exact closed-form of average SER expression of OSTBC based MIMO-OFDM system for M-ary phase shift keying (M-PSK) using traditional probability density function (PDF) approach is derived. We then compute exact closed form average SER expressions for M-ary pulse amplitude modulation (M-PAM) and M-QAM schemes by utilizing this generalized result. These expressions are valid over both frequency-flat and frequency-selective Nakagami-m fading MIMO channels and can easily be evaluated without using any numerical integration methods. We also show that average SER of MIMO-OFDM system using OSTBC in case of frequency-selective Rayleigh fading channels remains independent to the number of taps, L of that fading channel and the performance of the same system for two-tap un-correlated Rayleigh and Nakagami-m fading channels is better than that of the correlated one. Moreover, Monte Carlo simulation of MIMO-OFDM system using multiple transmit and receive antennas for different modulations is presented to validate our theoretical results. Finally, due to availability of closed form expressions, we further provide the performance results of MIMO-OFDM system over frequency-selective Nakagami-m fading channels employing (M-QAM) using OSTBCs under the transmission rate equal to 1, 2 and 3 bit(s)/s/Hz, respectively.