Matrix exponential learning: Distributed optimization in MIMO systems

We analyze the problem of finding the optimal signal covariance matrix for multiple-input multiple-output (MIMO) multiple access channels by using an approach based on ”ex-ponential learning”, a novel optimization method which applies more generally to (quasi-)convex problems defined over sets of positive-definite matrices (with or without trace constraints). If the channels are static, the system users converge to a power allocation profile which attains the sum capacity of the channel exponentially fast (in practice, within a few iterations); otherwise, if the channels fluctuate stochastically over time (following e.g. a stationary ergodic process), users converge to a power profile which attains their ergodic sum capacity instead. An important feature of the algorithm is that its speed can be controlled by tuning the users´ learning rate; correspondingly, the algorithm converges within a few iterations even when the number of users and/or antennas per user in the system is large.