  Driven by green communications, energy efficiency (EE) has become a new
important criterion for designing wireless communication systems. However, high
EE often leads to low spectral efficiency (SE), which spurs the research on
EE-SE tradeoff. In this paper, we focus on how to maximize the utility in
physical 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, but
also 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 problem
into an equivalent convex problem, which has the same global optimum with the
original problem. Following the convexization procedure, we present a
centralized algorithm to solve the utility maximization problem, but it
requires the global information of all users. Thus we propose a primal-dual
distributed algorithm which does not need global information and just consumes
a small amount of overhead. Furthermore, we have proved that the distributed
algorithm can converge to the global optimum. Finally, the numerical results
show that our approach can both capture user diversity for EE-SE tradeoff and
ensure user fairness, and they also validate the effectiveness of our
primal-dual distributed algorithm.
