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：在衰落信道中，针对每发射机功率与信息约束下的最优联合预编码设计，我们推导出一种新颖的上行-下行对偶原理。信息约束描述了发射机间信道状态信息与数据承载信号的有限共享。该原理主要应用于无蜂窝网络，其中每个接入点（AP）必须满足个体功率约束，并利用有限协作能力形成其发射信号。我们的对偶原理适用于由流行的硬化界给出的遍历可达速率，可被解释为Yu与Lane关于确定性信道先前结果的一个非平凡推广。这一推广使我们能够研究超越先前技术所覆盖的簇级集中式预编码简单情况的信息约束问题。具体而言，我们证明最优联合预编码器通常可由近年发展的团队最小均方误差方法的扩展形式给出。作为兼具实用性的特例，我们还求解了面向每AP功率约束的用户中心无蜂窝大规模MIMO网络中局部最优预编码的设计问题。