Ergodic capacity and symbol error rate of distributed massive MIMO systems over Rayleigh-inverse Gaussian fading channels using ZF detectors

Distributed massive multiple-input multiple-output (DM-MIMO) system has attracted significant research interest in recent years. It is regarded as a potential technology in 5G communication network because of its capability to achieve substantial improvements in energy and spectral efficiency. In this paper, we consider Rayleigh-Inverse Gaussian (RIG) composite fading channels for DM-MIMO systems and investigate ergodic capacity and symbol error rate (SER) at the output of a zero forcing (ZF) detector. The DM-MIMO system comprises of multiple base stations (BSs) distributed across the cell and an arbitrarily located mobile unit. It is shown that for the considered DM-MIMO architecture signal to noise ratio (SNR) at the ZF output involves sum of several unequal Wishart channel matrices. This increases the difficulty in evaluating its performance compared to co-located MIMO (C-MIMO). In this regard, we first determine the ergodic capacity for finite receiving antennas and obtain the closed-form expression over small-scale fading over both correlated and uncorrelated channels. The output is compared with conventional C-MIMO configurations at various user locations. For massive MIMO system, the approximated SNR is expressed as a sum of unequal inverse Gaussian random variables. In such scenario, we formulate the closed form expression of asymptotic ergodic capacity and subsequently its lower bound for more practical insights. We demonstrate here that, the lower bound is consistently tight until coefficient of variation (CV) is less than or equal to unity and the tightness progressively decreases when CV is further increased beyond unity. We also assess SER performance of ZF detectors for both finite and infinite number of receiving antennas. The impact of various parameters such as number of transmitting and receiving antennas, shadowing parameters, locations of user and BSs etc. on the performance of ZF detectors are extensively investigated. Finally, the suitability of obtained expressions is validated through a set of Monte-Carlo simulations.