Maximizing weighted sum-rate in the uplink of wireless systems using a second-order approximation

The capacity of the multiple-access channel (MAC) has been extensively studied before. In most works the focus was either on the theoretical fundamentals or on providing efficient algorithms for calculating special cases of the MAC. In this paper we concentrate on efficient algorithms for calculating the weighted-sum-rate capacity of the general case of the MIMO-OFDM MAC with an arbitrary number of transmitters, an arbitrary number of antennas both at the transmitters and the receiver and an arbitrary number of mutually orthogonal sub-bands. We provide compact closed-form formulas for the first and second derivatives of the objective function of the underlying non-linear convex optimization problem with respect to the transmit covariance matrices that allow for an efficient solution with an optimized general purpose solver. We apply this algorithm to different scenarios, amongst others to the uplink of a single wireless cell and a multi-point scenario with multiple base stations serving multiple terminals. It is shown that the proposed algorithm works reliably under different channel conditions. The influence of different parameters on the system performance is studied. The provided method for capacity-based performance studies is a solid and reliable basis for evaluating the efficiency of non-orthogonal transmission schemes, which are currently under investigation for future wireless systems.