Approximate ergodic capacity of multiuser massive multiple input multiple output in a Rayleigh fading uplink channel with variance profile

The effect of large-scale fading variations over massive multiple input multiple output (MIMO) antenna array on sum-capacity of massive MIMO system has not been thoroughly investigated in the literature. This study considers a multiuser massive MIMO system with a Rayleigh fading channel that takes into account large-scale fading variations over base station antenna array. Two scenarios are investigated: distributed antenna base station and linear array base station. In both scenarios, the authors obtain an approximate closed-form expressions for uplink ergodic sum-capacity for both low and high signal-to-noise ratio (SNR) regimes. It is shown that the proposed closed-form expressions are accurate in a wide range of practical SNRs; for example, the approximation error is below 10% for SNRs lower than -10 dB and higher than 17 dB for low-SNR and high-SNR closed-form expressions, respectively. It is also shown that the proposed closed-form expressions are not only valid for massive MIMO scenario but also for a system with a few number of base station antennas. The numerical results show that the proposed closed-form expressions have much less computational complexity than previous works.