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Driven by green communications, energy efficiency (EE) has become a newimportant criterion for designing wireless communication systems. However, highEE often leads to low spectral efficiency (SE), which spurs the research onEE-SE tradeoff. In this paper, we focus on how to maximize the utility inphysical layer for an uplink multi-user multiple-input multipleoutput (MU-MIMO)system, where we will not only consider EE-SE tradeoff in a unified way, butalso ensure user fairness. We first formulate the utility maximization problem,but it turns out to be non-convex. By exploiting the structure of this problem,we find a convexization procedure to convert the original nonconvex probleminto an equivalent convex problem, which has the same global optimum with theoriginal problem. Following the convexization procedure, we present acentralized algorithm to solve the utility maximization problem, but itrequires the global information of all users. Thus we propose a primal-dualdistributed algorithm which does not need global information and just consumesa small amount of overhead. Furthermore, we have proved that the distributedalgorithm can converge to the global optimum. Finally, the numerical resultsshow that our approach can both capture user diversity for EE-SE tradeoff andensure user fairness, and they also validate the effectiveness of ourprimal-dual distributed algorithm.

Utility Maximization for Uplink MU-MIMO: Combining Spectral-Energy Efficiency and Fairness