Massive MIMO Channels Under the Joint Power Constraints

Abstract

Massive MIMO has been recognized as a key technology for 5G systems due to its high spectral efficiency. The capacity and optimal signaling for a MIMO channel under the total power constraint (TPC) are well-known and can be obtained by the water-filling (WF) procedure. However, much less is known about optimal signaling under the per-antenna power constraint constraint (PAC) or under the joint power constraints (TPC+PAC). In this thesis, we consider a massive MIMO Gaussian channel under favorable propagation (FP) and obtain the optimal transmit covariance under the joint constraints. The effect of the joint constraints on the optimal power allocation (OPA) is shown. While it has some similarities to the standard WF, it also has number of notable differences. The numbers of active streams and active PACs are obtained, and a closed-form expression for the optimal dual variable is given. A capped water-filling interpretation of the OPA is given, which is similar to the standard WF, where a container has both floor and ceiling profiles. An iterative water-filling algorithm is proposed to find the OPA under the joint constraints, and its convergence to the OPA is proven.

The robustness of optimal signaling under FP is demonstrated in which it becomes nearly optimal for a nearly favorable propagation channel. An upper bound of the sub-optimality gap is given which characterizes nearly (or eps)-favorable propagation. This upper bound quantifies how close the channel is to the FP.

A bisection algorithm is developed to numerically compute the optimal dual variable. Newton-barrier and Monte-Carlo algorithms are developed to find the optimal signaling under the joint constraints for an arbitrary channel, not necessarily for a favorable propagation channel.

When the diagonal entries of the channel Gram matrix are fixed, it is shown that a favorable propagation channel is not necessarily the best among all possible propagation scenarios capacity-wise.

We further show that the main theorems in [1] on favorable propagation are not correct in general. To make their conclusions valid, some modifications as well as additional assumptions are needed, which are given here.