In this paper, we develop a gradient-free optimization methodology for
efficient resource allocation in Gaussian MIMO multiple access channels. Our
approach combines two main ingredients: (i) an entropic semidefinite
optimization based on matrix exponential learning (MXL); and (ii) a one-shot
gradient estimator which achieves low variance through the reuse of past
information. This novel algorithm, which we call gradient-free MXL algorithm
with callbacks (MXL0+), retains the convergence speed of gradient-based
methods while requiring minimal feedback per iteration−a single scalar. In
more detail, in a MIMO multiple access channel with K users and M transmit
antennas per user, the MXL0+ algorithm achieves ϵ-optimality
within poly(K,M)/ϵ2 iterations (on average and with high
probability), even when implemented in a fully distributed, asynchronous
manner. For cross-validation, we also perform a series of numerical experiments
in medium- to large-scale MIMO networks under realistic channel conditions.
Throughout our experiments, the performance of MXL0+ matches−and
sometimes exceeds−that of gradient-based MXL methods, all the while operating
with a vastly reduced communication overhead. In view of these findings, the
MXL0+ algorithm appears to be uniquely suited for distributed massive MIMO
systems where gradient calculations can become prohibitively expensive.Comment: Final version; to appear in IEEE Transactions on Signal Processing;
16 pages, 4 figure