Information-theoretic capacity limits in multi-cell joint processing systems

Multicell Joint Processing has emerged as a new paradigm of cooperative communications, which aims at pushing the capacity limits of cellular systems by eliminating inter-cell interference. Its operation is based on the concept of Base Station cooperation, which is enabled through wideband error-free low-latency links to a central signal processor. This processor is responsible for jointly encoding or decoding the signals, which are transmitted to or received from the User Terminals of the cellular system. The rationale behind this cooperation is that spatially distributed Base Stations are able to act as multiple antennas of a single universal transceiver, which servers the entire cellular system. In this context, the objective is to determine the capacity performance of a multicell joint processing system under the limitations imposed by a practical cellular channel. Towards this end, a comprehensive cellular channel model is proposed, which accommodates continuous path loss functions, distributed User Terminals, multiple antennas and correlated flat fading. Focusing on the uplink channel, the per-cell sum-rate capacity is determined using asymptotic analysis and the derived closed-forms are verified through Monte Carlo simulations. The core of the analysis is based on free probability and random matrix theory, which provide the mathematical tools for studying the asymptotic eigenvalue distribution of the channel matrix. Based on this setting, it is observed that multicell processing effectively removes the interference-limited behavior of conventional cellular systems, since increasing the system power always results in higher capacity. The exact sum-rate capacity depends on the total received power across the system, which is determined by the user distribution, the cell density and the path loss. Including multiple antennas at the Base Stations results in a linear capacity scaling, whereas multiple antennas at the User Terminals do not provide a capacity enhancement. Similarly, antenna correlation at the Base Station side degrades the capacity, while correlation at the User Terminal has no effect. Furthermore, the distribution of the sum-rate capacity across individual User Terminal rates is investigated in terms of fairness. It is observed that by first decoding strong-channel User Terminals, rate fairness is promoted, but equal rate sharing can only be achieved by employing power control in parallel with heuristic user ordering. Focusing on the downlink channel, the per-cell sum-rate capacity is evaluated using duality principles and the individual user rates are calculated considering channel-dependent and random encoding orders. More specifically, three types of power allocations are considered: a) optimal power allocation with system power constraint as an upper bound, b) optimal power allocation with the more appropriate per-cell power constraint and c) uniform power allocation in the dual uplink domain. In this context, it is shown that the upper bound calculated considering a system power constraint is tight for the considered range of cellular parameters and it can be utilized to closely estimate the realistic downlink capacity of a per-cell power constrained system. Furthermore, the downlink user rate vectors are greatly affected by the employed encoding order. More specifically, by considering a user ordering which favours the deep-fade User Terminals, the fairness over the downlink rates can be promoted, while uniform power allocation favours user rate fairness on the expense of the sum-rate capacity.