Machine Learning-Enabled Joint Antenna Selection and Precoding Design From Offline Complexity to Online Performance

Abstract : We investigate the performance of multi-user multiple-antenna downlink systems in which a base station (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 (CSI), 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 quality of service (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 deep neural network (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 [5] and a learning-assisted solution for broadcasting systems [29] 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.
 ? In order to validate the proposed algorithms, we have run numerical simulations and compare the performance to existing schemes. ? We show that the general RS scheme outperforms substantially state-of-the-art linear precoding schemes, especially with a moderately large number of users (e.g., 8), both in terms of achievable rates and of total transmit power. ? We have run numerical simulations showing that our RS solutions, even under practical constraints, can provide substantial performance gains over existing schemes. ? It is worth noting that since RS is linear, the implementation cost of the proposed algorithms are comparable to those applied in practical systems.
  It is worth noting that the optimal solution of problem is largely determined by the parameters y0. Thus, it is crucial to select proper values y0 such that the solution of is close to the optimal solution of . As such, we propose an iterative optimization algorithm to improve the performance of problem , shown in Algorithm The SDR-based reformulation in the previous subsection leverages the original problem’s non-convexity by working in a higher dimensional domain, which requires more memory. In this subsection, we solve based on difference-of-convex (DC) reformulation directly on the original variable domain
  To reduce the complexity on the precoder design and the decoding, we propose a new stream elimination algorithm which is then combined with the precoder design algorithm. The remaining streams are such that the searching space of the decoding order is essentially reduced. With such an adaptation, the general RS scheme can be applied even for a large number of users. Comparison among different algorithms reveals the substantial complexity reduction from the proposed stream selection algorithm. We propose a slight modification of the precoder design algorithms to account for the CSIT imperfection. Specifically, instead of reformulating entirely the problem, we introduce a regularization term in the precoder design formulation according to the CSIT accuracy.
 The main advantage of ML-aided communications lies in the capability of establishing underlying relations between system parameters and the desired objective, hence being able to shift the computation burden in real-time processing to the offline training phase. The authors of propose a beamforming neural network (BNN) for minimizing the transmit power of multiuser MISO systems, which employs convolutional neural networks (CNN) and a supervisedlearning method to predict the magnitude and direction of the beamforming vectors. This method is extended in for unsupervised-learning to maximize the system weighted sum-rate. In, a deep learning-aided transmission strategy is proposed for single-user MIMO system with limited feed back, which is capable of addressing both pilot-aided training and channel code selection.
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