Performance of BICM-SC and BICM-OFDM systems with diversity reception in non-gaussian noise and interference

In this paper, we present a general mathematical framework for performance analysis of single-carrier (SC) and orthogonal frequency division multiplexing (OFDM) systems employing popular bit-interleaved coded modulation (BICM) and multiple receive antennas. The proposed analysis is applicable to BICM systems impaired by general types of fading (including Rayleigh, Ricean, Nakagami-m, Nakagami-q, and Weibull fading) and general types of noise and interference with finite moments such as additive white Gaussian noise (AWGN), additive correlated Gaussian noise, Gaussian mixture noise, co-channel interference, narrowband interference, and ultra-wideband interference. We present an approximate upper bound for the bit error rate (BER) and an accurate closed-form approximation for the asymptotic BER at high signal-to-noise ratios for Viterbi decoding with the standard Euclidean distance branch metric. For the standard rate-1/2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at BERs of 10^-6 and 10^-12, respectively. However, if the code is punctured to higher rates (e.g. 2/3 or 3/4), the asymptotic approximation also becomes tight at a BER of 10^-6. Exploiting the asymptotic BER approximation we show that the diversity gain of BICM systems only depends on the free distance of the code, the type of fading, and the number of receive antennas but not on the type of noise. In contrast their coding gain strongly depends on the noise moments. Our asymptotic analysis shows that as long as the standard Euclidean distance branch metric is used for Viterbi decoding, BICM systems optimized for AWGN are also optimum for any other type of noise and interference with finite moments.