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

Large number of antennas and radio frequency (RF) chains at the base stations (BSs) lead to high energy consumption in massive MIMO systems. Thus, how to improve the energy efficiency (EE) with a computationally efficient approach is a significant challenge in the design of massive MIMO systems. With this motivation, a learning-based stochastic gradient descent algorithm is proposed in this article to obtain the optimal joint uplink and downlink EE with joint antenna selection and user scheduling in single-cell massive MIMO systems. Using Jensen's inequality and the characteristics of wireless channels, a lower bound on the system throughput is obtained. Subsequently, incorporating the power consumption model, the corresponding lower bound on the EE of the system is identified. Finally, learning-based stochastic gradient descent method is used to solve the joint antenna selection and user scheduling problem, which is a combinatorial optimization problem. Rare event simulation is embedded in the learning-based stochastic gradient descent method to generate samples with very small probabilities. In the analysis, both perfect and imperfect channel side information (CSI) at the BS are considered. Minimum mean-square error (MMSE) channel estimation is employed in the study of the imperfect CSI case. In addition, the effect of a constraint on the number of available RF chains in massive MIMO system is investigated considering both perfect and imperfect CSI at the BS.

This paper investigates the massive multi-input multi-output (MIMO) system in practical deployment scenarios, in which, to balance the economic and energy efficiency with the system performance, the number of radio frequency (RF) chains is smaller than the number of antennas. The base station employs antenna selection (AS) to fully harness the spatial multiplexing gain. Conventional AS techniques require full channel state information (CSI), which is time-consuming as the antennas cannot be simultaneously connected to the RF chains during the channel estimation process. To tackle this issue, we propose a novel joint channel prediction and AS (JCPAS) framework to reduce the CSI acquisition time and improve the system performance under temporally correlated channels. Our proposed JCPAS framework is a fully probabilistic model driven by deep unsupervised learning. The proposed framework is able to predict the current full CSI, while requiring only a historical window of partial observations. Extensive simulation results show that the proposed JCPAS can significantly improve the system performance under temporally correlated channels, especially for very large-scale systems with highly correlated channels. multi-output (MIMO) system in practical deployment scenarios, in which, to balance the economic and energy efficiency with the system performance, the number of radio frequency (RF) chains is smaller than the number of antennas. The base station employs antenna selection (AS) to fully harness the spatial multiplexing gain. Conventional AS techniques require full channel state information (CSI), which is time-consuming as the antennas cannot be simultaneously connected to the RF chains during the channel estimation process. To tackle this issue, we propose a novel joint channel prediction and AS (JCPAS) framework to reduce the CSI acquisition time and improve the system performance under temporally correlated channels. Our proposed JCPAS framework is a fully probabilistic model driven by deep unsupervised learning. The proposed framework is able to predict the current full CSI, while requiring only a historical window of partial observations. Extensive simulation results show that the proposed JCPAS can significantly improve the system performance under temporally correlated channels, especially for very large-scale systems with highly correlated channels.

Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI

Intelligent reflecting surface (IRS), which uses passive reflective elements instead of active radio frequency (RF) chains, is a cost and energy-efficient solution to improve the wireless system performance. With a similar objective, transmit antenna selection (AS) reduces the number of RF chains at the base station while harnessing the benefits of multiple antennas. In our work, we focus on joint optimization of antenna subset and transmit beamforming at the base station, and passive beamforming at the IRS to maximize the receive signal power. For single AS, we first derive a closed-form optimal rule. We then propose a simpler AS rule, which significantly reduces the computational complexity and the number of pilot transmissions required. For a system with Nt antennas at the base station and N IRS elements, the optimal AS rule requires N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> + N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> N pilots. However, the proposed simpler rule requires only 2N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +N pilots. For subset AS, we develop a manifold optimization based algorithm. To reduce its subset search complexity, which is exponential in the number of RF chains at the base station, we propose an alternating optimization based iterative algorithm. Our numerical results show that the proposed simpler AS rules are near optimal.

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.

In the multiuser multiple-input multiple-output (MU-MIMO) system, to reduce the influence of channel correlation on system performance, the base station (BS) should select the appropriate subset of user equipments (UEs) according to their channel state information (CSI). Due to a lack of channel reciprocity, the downlink CSI needs to be fed back to the BS in frequency division duplexing (FDD) mode. Some scholars have exploited kinds of deep neural networks (DNNs) for sensing and recovering CSI. However, user selection after all the CSI is reconstructed by DNNs will bring a great time delay. In this paper, we propose a deep learning-based CSI feedback scheme called US-CsiNet. Based on adversarial autoencoder (AAE), US-CsiNet can explicitly cover user schedule information while representing CSI. At the UE side, the encoder of US-CsiNet maps the CSI into codewords of which part are feature information for user schedule. Then the BS applies these partial codewords to separate the UEs into different groups and select active UEs. Finally, the decoder of AAE reconstructs the CSI of these active UEs. US-CsiNet can not only simplify the user selection process but also guarantee the accuracy of CSI reconstruction. The simulation results show that the proposed approach outperforms maximum channel gain (MCG) user selection algorithms and achieves the nearly same performance with semiorthogonal user selection (SUS) which needs full CSI of all users at the BS.

Full-duplex (FD) distributed antenna system (DAS) can take advantage of both FD and DAS to dramatically improve system capacity. The challenges of designing such a system are self-interference at the base station (BS) and multiuser interference, as well as hardware cost, computational complexity and signaling overhead, especially for dense antenna deployments. To address these problems mentioned above, in this paper, we investigate an antenna selection strategy at the BS for FD DAS including FD-capable BS antennas and half-duplex (HD) users. In particular, we separately optimize the receive and transmit antenna selection problems to maximize the achievable sum rate. To reduce the computational complexity and signaling overhead, each user is restricted to selecting only the BS antennas in its virtual cell. The optimization problem is a nonconvex integer programming problem, for which it is difficult to find a globally optimal solution. Using variable relaxation and successive convex approximation, we present an iterative antenna selection algorithm based on difference of convex functions (D.C.) programming to obtain a suboptimal solution. The simulation results demonstrate that the proposed antenna selection algorithm can provide significant performance gain over various reference algorithms.

The objective of this paper is to study the performance of a multicell vector perturbation (MVP) precoding technique under practical situations in a network multiple-input multiple-output (MIMO) scheme employing joint transmission. The conventional perturbation strategy that minimizes the total power is considered, and the power at each base station (BS) is properly scaled to enforce per-BS power constraints. In our scenario, we consider multiple-antenna users and use block diagonalization (BD) as the linear front-end precoder for VP. The sum rate for the MVP in the case of uniformly distributed input and an asymptotic upper bound on the sum rate at high signal-to-noise ratios (SNRs) are derived. In addition, using the asymptotic upper bound on the individual user rates, we propose a proportionally fair (PF) user scheduling algorithm of lower complexity and better performance compared with the benchmark fair semiorthogonal user selection (SUS) algorithm. As opposed to the PF-SUS, the proposed PF scheduling algorithm requires no predefined correlation threshold. Furthermore, we study the impact of backhaul delay on the performance of both VP and BD by deriving bounds on the sum rate. The numerical results show that MVP in the case of perfect channel state information (CSI) outperforms multicell BD. In the presence of a backhaul delay, the performance of MVP significantly degrades, but the upper bound on the sum rate for MVP is still higher than for multicell BD.

The IEEE 802.16/WiMAX standard has fully embraced multi‐antenna technology and can, thus, deliver robust performance and high transmission rates. Nevertheless, due to its inherent cost concerns, a WiMAX mobile station (MS) should preferably contain fewer radio frequency (RF) chains than antenna elements. This is because the former is often substantially more expensive than the latter. Thus, antenna selection, wherein a subset of antennas is dynamically selected to connect to the limited number of RF chains for transceiving, is a highly appealing performance enhancement technique for multi‐antenna WiMAX terminals. In this paper, a novel protocol for antenna selection in space division multiple access (SDMA) transmission is developed for the next‐generation IEEE 802.16 mobile stations. Both locally and globally optimal selection rules are considered together with various linear precoding designs at the base station (BS). The proposed protocol can readily accommodate various channel situations (e.g., reciprocal and non‐reciprocal channels). As demonstrated by analysis and simulation, the proposed protocol delivers considerable performance improvement over conventional IEEE 802.16 terminals that lack antenna selection capability. Moreover, the proposed protocol leverages the existing signaling method defined in IEEE 802.16, thereby incurring a negligible signaling overhead and requiring only minimal modifications of the standard. To the best of our knowledge, this paper represents the first effort to support antenna selection capability for SDMA transmissions in IEEE 802.16 mobile stations. Copyright © 2009 John Wiley &amp; Sons, Ltd.

In this work, a new antenna selection algorithm is proposed for multiple-input multiple-output (MIMO) wireless communication systems. It is assumed that the channel state information (CSI) is exactly known at the receiver, and hence the antenna selection is considered only at the receiver. The goal of antenna selection is to find a tradeoff between the maximization of the channel capacity and the minimization of the pair-wise error probability (PEP). It turns out that the scheme of antenna selection plays an important part when dealing with high antenna correlation. It is shown that our proposed scheme for a system with two-transmit antennas and five-receive antennas offers better PEP performance than the algorithm based on the maximization capacity, but has little capacity loss. The simulation results indicate that our proposed scheme can jointly meet the capacity maximization and the PEP minimization.

Recently it has been shown that it is possible to improve the performance of multiple-input multiple-output (MIMO) systems by employing a larger number of antennas than actually used and selecting the optimal subset based on the channel state information. Existing antenna selection algorithms assume perfect channel knowledge and optimize criteria such as Shannon capacity or various bounds on error rate. This paper examines MIMO antenna selection algorithms where the set of possible solutions is large and only a noisy estimate of the channel is available. In the same spirit as traditional adaptive filtering algorithms, we propose simulation based discrete stochastic optimization algorithms to adaptively select a better antenna subset using criteria such as maximum mutual information, bounds on error rate, etc. These discrete stochastic approximation algorithms are ideally suited to minimize the error rate since computing a closed form expression for the error rate is intractable. We also consider scenarios of time-varying channels for which the antenna selection algorithms can track the time-varying optimal antenna configuration. We present several numerical examples to show the fast convergence of these algorithms under various performance criteria, and also demonstrate their tracking capabilities.

This paper addresses channel state information (CSI) estimation in a wireless relay network, which consists of a base station (BS), a relay station (RS), and a mobile station (MS). We propose a method for the BS to obtain the instantaneous CSIs of the three links (BS-RS, BS-MS, and RS-MS links) with minimized overhead. The CSI availability plays an important role for the BS to adapt its transmission strategies to the given channel conditions. Our proposed method exploits the fact that the link condition between fixed BS and fixed RS tends to be stable, and the frequent CSI update is not necessary for this link. In order for the BS to obtain the CSI of the distant link (i.e. RS-MS link), RS amplifies a pilot signal received from MS with a pre-defined amplification factor, and forwards it to BS. This enables the BS to obtain the CSI of the RS-MS link based on the received pilot signal and pre-knowledge on the CSI of BS-RS link. We show by computer simulation that our proposed method can reduce the required overhead for CSI estimation with little degradation on the accuracy of the obtained CSI.

In this paper, the performance of coded OFDM transmission over multiple antennas is explored when joint transmit and receive antenna selection is employed. The channel is assumed as Rayleigh frequency selective fading channel and only receiver is assumed to have perfect channel state information (CSI). The performance of MIMO OFDM system using pragmatic coding techniques such as convolutional coding (CC) and space-time block coding (STBC) with antenna selection based on subcarrier groups and other types such as all-tone, per-tone and hybrid techniques are obtained via computer simulations. The results suggests that joint antenna selection particularly based on subcarrier groups can be a desirable option in Worldwide Interoperability for Microwave Access (WiMAX) and Long Term Evolution (LTE) standards.

Knowledge of the propagation channel makes it possible for multiple-input multiple-output (MIMO) links to achieve higher system capacities by means of beamforming on the stronger channel eigenvectors. Assigning dedicated low bit rate feedback links is an efficient and practical method of providing transmitters with the required channel state information. One of the key problems in limited feedback precoding is the design of finite indexed codebooks known a priori to both the transmitter and receiver.Previous design methods include signal-to-noise ratio maximization through Grassmannian line packing, distortion minimization via vector quantization and antenna selection algorithms. In this paper we propose a new method that utilizes the dominant right singular vector of the MIMO channel to construct quantized unitary precoders. We show that although sub-optimum, this method can produce full diversity order codebooks. Using Monte-Carlo simulations, we compare the performance of the this method with optimum Grassmannian precoders and also antenna selection and subset selection algorithms.

Coordinated Beamforming (CB) is an effective technique to maximize weighted sum rate (WSR) targeting at on-demand network capacity. However, the channel state information (CSI) of the base stations (BSs) far away can’t be measured accurately, which will lead to the invalidation of the traditional WSR-maximization beamformer design and eventually result in capacity decrease. This letter proposes a tractable user-centric CSI model and a robust CB design to maximize WSR with partially accurate CSI. Specifically, the CSI model of the coordinated BSs is built for each user, where the inaccurate CSI of BSs far away from this user is modeled according to its static statistic characteristic. To derive a robust beamformer, deterministic equivalent method is adopted to obtain an approximate closed-form expression of the ergodic sum rate. Moreover, the performance of the robust CB design with different model parameters is considered to provide guidance for practical network deployment. Simulation results show that the proposed robust CB design has 30% capacity gain through careful interference management compared with traditional beamforming.