Massive multiple-input multiple-output (MIMO) precoders are typically designed by minimizing the transmit power subject to a quality-of-service (QoS) constraint. However, current sustainability goals incentivize more energy-efficient solutions and thus it is of paramount importance to minimize the consumed power directly. Minimizing the consumed power of the power amplifier (PA), one of the most consuming components, gives rise to a convex, non-differentiable optimization problem, which has been solved in the past using conventional convex solvers. Additionally, this problem can be solved using a proximal gradient descent (PGD) algorithm, which suffers from slow convergence. In this work, to overcome the slow convergence, a deep unfolded version of the algorithm is proposed, which can achieve close-to-optimal solutions in only 20 iterations compared to the 3500 plus iterations needed by the PGD algorithm. Results indicate that the deep unfolding algorithm is three orders of magnitude faster than a conventional convex solver and four orders of magnitude faster than the PGD.

翻译：大规模多输入多输出（Massive MIMO）预编码器的设计通常是在服务质量（QoS）约束下最小化发射功率。然而，当前的可持续发展目标促使人们寻求更具能效的解决方案，因此直接最小化消耗功率变得至关重要。功率放大器（PA）作为功耗最高的组件之一，其消耗功率的最小化问题可归结为一个凸但不可微的优化问题，该问题此前已通过传统凸优化求解器得以解决。此外，该问题也可采用近端梯度下降（PGD）算法进行求解，但该算法存在收敛速度缓慢的缺陷。为克服这一局限，本研究提出该算法的深度展开版本，该版本仅需20次迭代即可获得接近最优的解，而传统PGD算法则需要超过3500次迭代。实验结果表明，深度展开算法的求解速度比传统凸优化求解器快三个数量级，比PGD算法快四个数量级。