Riemannian-Geometric Optimization Methods for MIMO Multiple Access Channels

Panayotis Mertikopoulos (1) , Aris L. Moustakas (2, 3)

1 MESCAL - Middleware efficiently scalable
2 E3S - Supélec Sciences des Systèmes
3 NKUA - National and Kapodistrian University of Athens

We analyze the problem of finding the optimal signal covariance matrix for MIMO multiple access channels by using an approach based on "exponential 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.

Domaines: Optimisation et contrôle [math.OC]

Panayotis Mertikopoulos, Aris L. Moustakas. Riemannian-Geometric Optimization Methods for MIMO Multiple Access Channels. ISIT '13: Proceedings of the 2013 IEEE International Symposium on Information Theory, 2013, Unknown, Unknown Region. ⟨hal-01382304⟩