UL-DL duality for cell-free massive MIMO with per-AP power and information constraints

We derive a novel uplink-downlink duality principle for optimal joint precoding design under per-transmitter power and information constraints in fading channels. The main application is to cell-free networks, where each access point (AP) must typically satisfy an individual power constraint and form its transmit signal on the basis of possibly partial sharing of data bearing signals and channel state information. Our duality principle applies to ergodic achievable rates given by the popular hardening bound, and it can be interpreted as a nontrivial generalization of a previous result by Yu and Lan for deterministic channels. This generalization allows us to cover more involved information constraints, and to show that optimal joint precoders can be obtained using a variation of the recently developed team minimum mean-square error method. As particular examples, we solve the problems of optimal centralized and local precoding design in user-centric cell-free massive MIMO networks subject to per-AP power constraints.