On the Multi-cell Processing Capacity of the Cellular MIMO Uplink Channel in Correlated Rayleigh Fading Environment

In the context of cellular systems, it has been shown that multicell processing can eliminate inter-cell interference and provide high spectral efficiencies with respect to traditional interference-limited implementations. Moreover, it has been proved that the multiplexing sum-rate capacity gain of multicell processing systems is proportional to the number of Base Station (BS) antennas. These results have been also established for cellular systems, where BSs and User Terminals (UTs) are equipped with multiple antennas. Nevertheless, a common simplifying assumption in the literature is the uncorrelated nature of the Rayleigh fading coefficients within the BS-UT MIMO links. In this direction, this paper investigates the ergodic multicell-processing sum-rate capacity of the Gaussian MIMO Cellular Multiple-Access Channel in a correlated fading environment. More specifically, the multiple antennas of both BSs and UTs are assumed to be correlated according to the Kronecker product model. Furthermore, the current system model considers Rayleigh fading, uniformly distributed User Terminals (UTs) over a planar coverage area and powerlaw path loss. Based on free probabilistic arguments, the empirical eigenvalue distribution of the channel covariance matrix is derived and it is used to calculate both Optimal Joint Decoding and Minimum Mean Square Error (MMSE) Filtering capacity. In addition, numerical results are presented, where the per-cell sum-rate capacity is evaluated while varying the cell density of the system, as well as the level of fading correlation. In this context, it is shown that the capacity performance is greatly compromised by BS-side correlation, whereas UT-side correlation has a negligible effect on the system’s performance. Furthermore, MMSE performance is shown to be greatly suboptimal but more resilient to fading correlation in comparison to optimal decoding