  We investigate the performance of multi-user multiple-antenna downlink
systems in which a BS serves multiple users via a shared wireless medium. In
order to fully exploit the spatial diversity while minimizing the passive
energy consumed by radio frequency (RF) components, the BS is equipped with M
RF chains and N antennas, where M < N. Upon receiving pilot sequences to obtain
the channel state information, the BS determines the best subset of M antennas
for serving the users. We propose a joint antenna selection and precoding
design (JASPD) algorithm to maximize the system sum rate subject to a transmit
power constraint and QoS requirements. The JASPD overcomes the non-convexity of
the formulated problem via a doubly iterative algorithm, in which an inner loop
successively optimizes the precoding vectors, followed by an outer loop that
tries all valid antenna subsets. Although approaching the (near) global
optimality, the JASPD suffers from a combinatorial complexity, which may limit
its application in real-time network operations. To overcome this limitation,
we propose a learning-based antenna selection and precoding design algorithm
(L-ASPA), which employs a DNN to establish underlaying relations between the
key system parameters and the selected antennas. The proposed L-ASPD is robust
against the number of users and their locations, BS's transmit power, as well
as the small-scale channel fading. With a well-trained learning model, it is
shown that the L-ASPD significantly outperforms baseline schemes based on the
block diagonalization and a learning-assisted solution for broadcasting systems
and achieves higher effective sum rate than that of the JASPA under limited
processing time. In addition, we observed that the proposed L-ASPD can reduce
the computation complexity by 95% while retaining more than 95% of the optimal
performance.
