We derive a novel uplink-downlink duality principle for optimal joint precoding design under per-transmitter power and information constraints in fading channels. The information constraints model limited sharing of channel state information and data bearing signals across the transmitters. 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 using limited cooperation capabilities. 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 study involved information constraints going beyond the simple case of cluster-wise centralized precoding covered by previous techniques. Specifically, we show that the optimal joint precoders are, in general, given by an extension of the recently developed team minimum mean-square error method. As a particular yet practical example, we then solve the problem of optimal local precoding design in user-centric cell-free massive MIMO networks subject to per-AP power constraints.

翻译：我们针对衰落信道中每发射机功率与信息约束下的最优联合预编码设计，提出了一种创新的上下行对偶原理。信息约束刻画了各发射机之间信道状态信息与数据承载信号的共享限制。该原理主要应用于无小区网络，其中每个接入点（AP）需满足个体功率约束，并利用有限的协作能力生成发射信号。本文提出的对偶原理适用于由经典硬化界给出的遍历可达速率，可视为Yu与Lin针对确定性信道经典结果的重要推广。该推广使我们能够研究超出传统簇级集中式预编码简单场景的复杂信息约束。具体而言，我们证明了最优联合预编码通常由近期发展的团队最小均方误差方法的扩展形式给出。作为兼具普适性与实用性的典型案例，我们进一步解决了用户中心无小区大规模MIMO网络中受每AP功率约束的最优局部预编码设计问题。