#### [J32] - Fast optimization with zeroth-order feedback in distributed multi-user MIMO systems

O. Bilenne, P. Mertikopoulos, and E. V. Belmega. IEEE Transactions on Signal Processing, vol. 68, pp. 6085-6100, October 2020.

##### Abstract

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 method 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 $\varepsilon$-optimality within $\mathrm{poly}(K,M)/\varepsilon^{2}$ 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.