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 previously. In most works the focus was either on the theoretical fundamentals or on providing efficient algorithms for calculating special cases of the multiple access channel. In this article we concentrate on efficient algorithms for calculating the capacity of the genaral 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 subchannels. We provide closed form formulas for the first and second derivatives of the objective function of the underlying non-linear convex optimiztion problem 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 staions 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. This work provides a reliable method for studying the capacity of uplink transmission, which is a solid basis for evaluating the efficiency of non-orthogonal transmission schemes which are currently under investigation for future wireless systems.