Joint Spatial Division Research Articles

Equilibrium-Equation-Based Fast Recursive Principal Component Tracking With an Adaptive Forgetting Factor for Joint Spatial Division and Multiplexing Systems

Equilibrium-Equation-Based Fast Recursive Principal Component Tracking With an Adaptive Forgetting Factor for Joint Spatial Division and Multiplexing Systems

Neighbor-based joint spatial division and multiplexing in massive MIMO: user scheduling and dynamic beam allocation

AbstractTwo-stage precoding schemes have been developed to reduce the channel estimation overhead in FDD systems. By integrating user scheduling into these schemes, it becomes possible to meet the quality-of-service requirements of high-density wireless communication systems, despite the limitations on spatial resources and transmit power budget. In this paper, we propose a user scheduling and dynamic beam allocation method for neighbor-based joint spatial division multiplexing (N-JSDM) transmission. The user scheduling problem is formulated as a 0–1 quadratic programming problem to maximize effective spectral efficiency (ESE) using directional channel properties. To address the complexity issue, convex relaxation and linearization methods are employed to transform the problem into a 0–1 mixed integer linear programming, and a dimensionality reduction method is introduced. The proposed user scheduling-aided N-JSDM scheme reduces downlink training length and feedback of channel state information. Additionally, a dynamic configuration form is used for pre-beamforming matrix design based on user distribution, outperforming conventional approaches. Simulation results demonstrate higher ESE achieved by the proposed scheme compared to previous methods.

IRS-Aided Joint Spatial Division and Multiplexing for mmWave Multiuser MISO Systems

Intelligent reflecting surface (IRS)-aided millimeter wave (mmWave) communication systems have gained considerable attention recently. However, the benefits brought by IRS require the instantaneous channel state information (I-CSI) of the cascaded base station (BS)-IRS and IRS-user channel which is difficult to obtain in practice, especially for the multiuser scenario. To address this issue, in this paper, we combine two-timescale beamforming and multi-IRS aided joint spatial division and multiplexing (JSDM) in a mmWave multiuser system. Specifically, all the users are first divided into different groups and each group is associated with an IRS. Then, we propose a novel two-stage grouping-based randomized beamforming (TS-GRB) scheme, where the analog beamformer is designed based on the statistical CSI (S-CSI) in the first stage, and the short-term digital beamformer at the BS and long-term passive beam pattern control policy at the IRSs are jointly optimized in the second stage with both S-CSI and dimension-reduced effective I-CSI. In particular, in the first stage, the analog beamformer is designed to reduce the inter-group interference (IGI) and effective channel dimension, while in the second stage, a two-timescale randomized joint beamforming (TRJB) algorithm is proposed to maximize the proportional fairness utility (PFU). We show that through two-timescale beamforming, JSDM and proper problem reformulation, the pilot overhead of our TS-GRB scheme is significantly lower than existing schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed TS-GRB scheme.

Joint Spatial Division and Multiplexing for FDD in Intelligent Reflecting Surface-Assisted Massive MIMO Systems

Channel reciprocity, assumed in fifth-generation (5G) systems such as massive multiple-input-multiple-output (mMIMO), appears to be questioned in practice by recent studies on intelligent reflecting surface (IRS). Hence, contrary to previous works, we consider frequency division duplexing (FDD) to study the performance of an IRS-assisted mMIMO system. However, FDD is not suitable for large number of antennas architectures. For this reason we employ the joint spatial division and multiplexing (JSDM) approach exploiting the structure of the correlation of the channel vectors to reduce the channel state information (CSI) uplink feedback, and thus, allowing the use even of a large number of antennas at the base station. Specifically, we derive the sum spectral efficiency (SE) based on statistical CSI in terms of large-scale statistics by using the deterministic equivalent (DE) analysis while accounting for correlated Rayleigh fading. Subsequently, we formulate the optimization problem concerning the sum SE with respect to the reflecting beamforming matrix (RBM)and the total transmit power, which can be performed at every several coherence intervals by taking advantage of the slow time variation of the large-scale statistics. This notable property contributes further to the decrease of the feedback overhead. Numerical results, verified by Monte-Carlo (MC) simulations, enable interesting observations by elucidating how fundamental system parameters such as the rank of the covariance matrix and the number of groups of UEs affect the performance. For example, the selection of a high rank improves the channel conditioning but increases the feedback overhead.

Domain selective two-stage beamforming in 3D massive MIMO

In this paper, a two-stage beamforming scheme called domain selective neighbor-based joint spatial division and multiplexing (DS-NJSDM) scheme is proposed to reduce the overhead of pilot training and uplink feedback in Frequency Division Duplexing (FDD) three-dimensional (3D) massive multi-input multi-output (MIMO) systems. Inspired by the Kronecker product structure of the 3D channel model, a DS pre-beamformer is proposed to sparsify the channel matrix, which selects horizontal or vertical pre-beamformer to mitigate the interference from non-neighbors. The signal space can be effectively utilized with the DS pre-beamformer, and the complexity of beamforming is significantly reduced. After the pre-beamformer, the zero entries of the downlink channel matrix are randomly distributed, making pilot design difficult. Then, a pilot allocation scheme is proposed to design the pilot matrix. Simulation results are provided to validate the superiority of the proposed scheme in enhancing the spectral efficiency over the existing schemes.

Grouping-Based Joint Active User Detection and Channel Estimation With Massive MIMO

This paper considers an uplink massive machine-type communication scenario with a massive number of antennas, where a large number of user devices are connected to a base station (BS) and the user traffic is sporadic. We propose a novel hybrid message passing (HMP) algorithm to achieve joint active detection and channel estimation (JADCE) by exploiting the channel characteristics in both the angular domain and user domain, which is expected to enhance the performance of JADCE compared with the conventional approaches without the knowledge of such a consideration. The user grouping is performed simultaneously with JADCE, which provides the prerequisites of the joint spatial division and multiplexing to achieve significant savings both in the downlink training and feedback of channel state information at the transmitter. Based on the acquired knowledge of user grouping, we further propose a per-group processing based JADCE (PGP-JADCE) approach. It significantly reduces the computational overhead for JADCE and the BS is capable to process all the user groups in parallel. Further, the analysis of detection error probabilities and channel estimation error of PGP-JADCE is provided.

Joint Spatial Division and Coaxial Multiplexing for Downlink Multi-User OAM Wireless Backhaul

Orbital angular momentum (OAM) at radio frequency (RF) provides a novel approach of multiplexing a set of orthogonal modes on the same frequency channel to achieve high spectral efficiencies (SEs). However, the existing research on OAM wireless communications is mainly focused on point-to-point transmission in the line-of-sight (LoS) scenario. In this paper, we propose an overall scheme of the downlink multi-user OAM (MU-OAM) wireless backhaul based on uniform circular arrays (UCAs) for broadcasting networks, which can achieve the joint spatial division and coaxial multiplexing (JSDCM). A salient feature of the proposed downlink MU-OAM wireless backhaul systems is that the channel matrices are completely characterized by the position of each small base station (SBS), independent of the numbers of subcarriers and antennas, which avoids estimating large channel matrices required by the traditional downlink multi-user multiple-input multiple-output (MU-MIMO) wireless backhaul systems. Thereafter, we propose an OAM-based multi-user distance and angle of arrival (AoA) estimation method, which is able to simultaneously estimate the positions of multiple SBSs with a flexible number of training symbols. With the estimated distances and AoAs, a MU-OAM preprocessing scheme is applied to eliminate the co-mode and inter-mode interferences in the downlink MU-OAM channel. At last, the proposed methods are extended to the downlink MU-OAM-MIMO wireless backhaul system equipped with uniform concentric circular arrays (UCCAs), for which much higher spectral efficiency (SE) and energy efficiency (EE) than traditional MU-MIMO systems can be achieved. Both mathematical analysis and simulation results validate that the proposed scheme can effectively eliminate both interferences of the practical downlink MU-OAM channel and approaches the performance of the ideal MU-OAM channel.

Deep learning based user grouping for FD-MIMO systems exploiting statistical channel state information

The joint spatial division and multiplexing (JSDM) is a two-phase precoding scheme for massive multiple-input-multiple-output (MIMO) system under frequency division duplex (FDD) mode to reduce the amount of channel state information (CSI) feedback. To apply this scheme, users need to be partitioned into groups so that users in the same group have similar channel covariance eigenvectors while users in different groups have almost orthogonal eigenvectors. In this paper, taking the clustered user model into account, we consider the user grouping of JSDM for the downlink massive MIMO system with uniform planar antenna array (UPA) at base station (BS). A deep learning based user grouping algorithm is proposed to improve the efficiency of the user grouping process. The proposed grouping algorithm transfers the statistical CSI of all users into a picture, and utilizes the deep learning enabled objective detection model you look only once (YOLO) to divide the users into different groups rapidly. Simulation results show that the proposed user grouping scheme can achieve higher sum rate with less time delay.

A Study of a Competitive Reinforcement Learning Approach for Joint Spatial Division and Multiplexing in Massive MIMO

Massive Multiple-Input Multiple-Output (MIMO) is widely considered a pivotal communication technology for future generations of wireless networks. Massive MIMO uses a large number of antennas at the base station, which offers better effectiveness in spectral and energy use. However, a Frequency Division Duplex (FDD) system is challenging in reciprocity since it is difficult to estimate channels and requires feeding back channel state information. Joint Spatial Division and Multiplexing (JSDM) is a simplified FDD technique to provide massive MIMO gains. The main idea of JSDM is related to grouping users with approximately similar channel covariance. Many machine learning algorithms have been applied to conduct user grouping. In this paper, to improve the user grouping, we employ Reinforcement Guided Competitive Learning (RGCL) to the user grouping and then compare it with clustering techniques, including K-means, and sequential K-means to achieve the appropriate user grouping. The experimental results show that the RGCL technique represents better performance in computational time and system throughput than the other two above mentioned techniques, since RGCL can avoid being trapping in local minima.

An Efficient Interference-Aware Constrained Massive MIMO Beamforming for mm-Wave JSDM

Low-complexity beamformer design with practical constraints is an attractive research area for hybrid analog/digital systems in mm-wave massive multiple-input multiple-output (MIMO). This paper investigates interference-aware pre-beamformer (analog beamformer) design for joint spatial division and multiplexing (JSDM) which is a user-grouping based two-stage beamforming method. Single-carrier frequency domain equalization (SC-FDE) is employed in uplink frequency-selective channels. First, unconstrained slowly changing statistical analog beamformer of each group, namely, generalized eigenbeamformer (GEB) which has strong interference suppression capability is designed by maximizing the mutual information in reduced dimension. Then, constant-modulus constrained approximations of unconstrained beamformer are obtained by utilizing alternating minimization algorithms for fully connected arrays and fixed subarrays. In addition, a dynamic subarray algorithm is proposed where the connections between radio frequency (RF) chains and antennas are changed with changing channel statistics. Convergence of the proposed alternating minimization-based algorithms is provided along with their complexity analysis. It is observed that the additional complexity of proposed algorithms is insignificant for the overall system design. Although most of the interference is suppressed with the help of proposed constrained beamformers, there may be some residual interference after analog beamforming stage. Thus, minimum mean square error (MMSE) criterion based iterative block decision feedback equalization (IB-DFE) method, which takes the residual interference in reduced dimension into account, is promoted for digital beamforming stage. Simulation results verify the superiority of the proposed interference-aware constrained design over existing approaches in terms of beampattern, spectral efficiency, outage capacity, bit-error rate (BER), and channel estimation accuracy.

Joint Spatial Division and Multiplexing in Massive MIMO: A Neighbor-Based Approach

In this paper, we propose a joint spatial division and multiplexing (JSDM) beamforming based on a neighbor scheme for frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems. The neighbor-based JSDM (N-JSDM) can fully utilize signal space, leading to higher spectral efficiency over the conventional JSDMs. The reason is that for the neighbor scheme, neighbors and non-neighbors are classified adaptively by the angles of departure (AoD), and the prebeamformer is designed to mitigate the non-neighbors' interference by the statistical channel state information. The effective channel matrix after the prebeamformer then becomes a band matrix, from which the downlink training length (DTL) and the channel feedback length are much smaller than the number of antennas. Moreover, an optimal prebeamformer which is proved to be able to achieve the same system capacity as the full CSI system is proposed, followed by a suboptimal prebeamformer with constrained DTL, and a DFT-based prebeamformer. On the other hand, the neighbors' interference is mitigated using the banded channel state information. Simulation results validate the good performance of the proposed N-JSDM.

Interference-Aware Radio Resource Management for Cognitive High-Throughput Satellite Systems.

By providing interactive broadband services to geographical areas underserved by terrestrial infrastructure, multi-beam satellite systems play a central role in future wireless communications. Targeting the terabit throughput requirements in satellite communications, we introduce a cognitive radio-based high-throughput satellite (HTS) system architecture where full frequency reuse is employed among beams. Moreover, by analyzing the characteristics of the considered architecture, we discuss the design challenges of radio resource management in cognitive HTS systems exposed to both intra-system and inter-system co-channel interference. Furthermore, to combat interference with low overhead, we propose a generic interference-aware resource management framework based on joint spatial division and multiplexing (JSDM). Under this framework, user grouping along with two-stage precoding is studied to achieve substantial improvement in the overall system throughput. Finally, some future research directions and challenges are also given.

On Optimal Scheduling for Joint Spatial Division and Multiplexing Approach in FDD Massive MIMO

Massive MIMO is widely considered as a key enabler of the next generation 5G networks. With a large number of antennas at the Base Station, both spectral and energy efficiencies can be enhanced. Unfortunately, the downlink channel estimation overhead scales linearly with the number of antennas. This burden is easily mitigated in TDD systems by the use of the channel reciprocity property. However, this is unfeasible for FDD systems and the method of two-stage beamforming was therefore developed to reduce the amount of channel state information feedback. The performance of this scheme being highly dependent on the users grouping and scheduling mechanims, we introduce in this paper a new similarity measure coupled with a novel clustering procedure to achieve the appropriate users grouping. We also proceed to formulate the optimal users scheduling policy in JSDM and prove that it is NP-hard. This result is of paramount importance since it suggests that, unless P=NP, there are no polynomial time algorithms that solve the general scheduling problem to global optimality and the use of sub-optimal scheduling strategies is more realistic in practice. We therefore use graph theory to develop a sub-optimal users scheduling scheme that runs in polynomial time and outperforms the scheduling schemes previously introduced in the literature for JSDM in both sum-rate and throughput fairness.

Joint Spatial Division and Diversity for Massive MIMO Systems

We propose a downlink beamforming scheme that combines spatial division and orthogonal space-time block coding (OSTBC) in multi-user massive MIMO systems. The beamformer is divided into two parts: a pre-beamforming matrix to separate the users into different beams with no interference between each other, which is designed based on the low rank covariance matrix of the downlink channel, and a linear precoding matrix using partial or even no channel state information (CSI) concatenated by an OSTBC. To construct the pre-beamforming matrix, a simple method that selects columns from DFT matrix is presented. To design the linear precoding matrix with partial CSI of the effective channel after the pre-beamforming, we solve an optimization problem to minimize the pairwise error probability (PEP) of the users under an individual power or sum power constraint, respectively. For the individual power constraint, a semi-definite relaxing (SDR) method with a sufficient condition achieving the globally optimal solution is proposed to provide a performance benchmark. In addition, an efficient iterative successive convex approximation (SCA) method is provided to achieve a suboptimal solution. Furthermore, closed form solutions are derived under some special cases. For the sum power constraint, we consider two different designs, i.e., minimizing the average PEP and minimizing the maximum PEP of all users. We find that both non-convex problems have a similar structure, and proposed a unified SCA-Alternating Direction Method of Multipliers (ADMM) algorithm to handle them. The SCA-ADMM method can be implemented in a parallel manner, and thus is with great efficiency. Simulation results show the efficiency of our proposed JSDD scheme and the optimization method.

Outage Analysis of Relay-Assisted mmWave Cellular Systems Employing JSDM

In this paper, the outage probabilities of relay-assisted millimeter wave (mmWave) cellular systems employing joint spatial division and multiplexing (JSDM) are investigated. It is assumed that the macro base station (BS) equipped with a large number of antennas serves the single antenna relay and users simultaneously and that the relay is located at the edge of the macro cell. Theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) outage probabilities of each user with and without the second stage precoding is first obtained, respectively. The cell SINR outage probabilities are then derived. Under the noise-limited assumption, simplified closed-form expressions of the outage probabilities are given as well. The simulation results demonstrating the performance improvement due to the relay are provided. Overall, the impact of deploying a relay in the mmWave cellular systems on the outage probabilities is characterized.

Massive MIMO interference coordination for 5G broadband access: Integration and system level study

Upcoming 5G systems are called to face a huge growth of mobile traffic compared to the current 4G technology. To meet this challenge, the Massive Multiple-Input Multiple-Output (mMIMO) emerged as an essential and capable transmission technique, able to concurrently serve a large number of users, while guaranteeing a very high spectral efficiency. Moreover, some other additional approaches, like the Joint Spatial Division and Multiplexing precoding scheme and the multi-cell coordinated beamforming technique for interference reduction, could be used to further improve the overall system performance and reduce the mMIMO implementation complexity. Unfortunately, the current scientific literature does not provide a clear overview on how and in which conditions these mechanisms can be successfully harmonized, configured, and adopted in real 5G deployments. To bridge this gap, this paper deeply investigates the configuration and the integration of these promising transmission techniques. Moreover, it also evaluates, from the system level perspective, their behavior in different operating conditions. From one side, obtained results clearly show the performance gain that these new techniques offer with respect to the existing 4G technology. From another side, however, they also identify the scenarios where the proper combination of these emerging techniques is really fruitful for meeting the expected quality requirements defined for the 5G.

Downlink Precoding for Massive MIMO Systems Exploiting Virtual Channel Model Sparsity

In this paper, the problem of designing a forward link linear precoder for massive multiple-input multiple-output (MIMO) systems in conjunction with quadrature amplitude modulation (QAM) is addressed. A challenge in such system design is to consider finite alphabet inputs, especially with larger constellation sizes, such as $M\geq 16$ . First, we employ a novel and efficient methodology that allows for an orthogonal, sparse representation of multiple users and groups in a fashion similar to joint spatial division and multiplexing (JSDM), thus offering an extension of JSDM to finite alphabet data symbols. We term the new approach JSDM for finite alphabets (JSDM-FA). JSDM-FA employs virtual channel model beams in order to explore the orthogonality between different groups. Then, we present a natural generalization of JSDM-FA to the frequency-selective case with orthogonal frequency-division multiplexing (OFDM) and also enhance OFDM with combined frequency and spatial division and multiplexing. This configuration offers high flexibility in Massive MIMO systems, as it is capable of offering separate decoding of each user data within a group or increase the spectral efficiency of spatially overlapping groups without sacrificing the overall cell spectral efficiency. The proposed methodology is next applied jointly with the complexity-reducing Per-Group Processing within groups technique, on a per user group basis, in conjunction with QAM modulation and in simulations, for constellation size up to $M=64$ . We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder or the plain beamformer and with $M\geq 16$ .

New Beamforming Designs for Joint Spatial Division and Multiplexing in Large-Scale MISO Multi-User Systems

In this paper, we study a joint spatial division multiplexing (JSDM) beamforming scheme, which enables large-scale spatial multiplexing gains for massive multi-input multi-output downlink systems. In contrast to the conventional JSDM, which employs a block diagonalization method as a pre-beamformer, we aim to maximize sum-rate by applying minimum-mean-squared error (MMSE) approaches when designing a pre-beamformer and a multi-user precoder sequentially. First, to suppress inter-group interference, we design the pre-beamformer, which minimizes an upper bound of the sum mean-squared-error in the large-scale array regime. Then, to mitigate same-group interference, we present the multi-user precoder based on the weighted MMSE (WMMSE) optimization method, which requires the same channel state information overhead as the conventional JSDM. Also, in order to reduce the computational complexity, we compute deterministic equivalents of the WMMSE beamforming parameters to generate the beamformers by employing asymptotic results of large system analysis. Through simulation results, we confirm that the proposed two-step beamforming methods bring substantial performance gains in terms of sum-rate over the conventional JSDM schemes especially in a low and medium signal-to-noise ratio regime with comparable complexity.

Massive MIMO Channel Subspace Estimation From Low-Dimensional Projections

Massive MIMO is a variant of multiuser MIMO (Multi-Input Multi-Output) system, where the number of base-station antennas $M$ is very large and generally much larger than the number of spatially multiplexed data streams. Unfortunately, the front-end A/D conversion necessary to drive hundreds of antennas, with a signal bandwidth of 10 to 100 MHz, requires very large sampling bit-rate and power consumption. To reduce complexity, Hybrid Digital-Analog architectures have been proposed. Our work in this paper is motivated by one of such schemes named Joint Spatial Division and Multiplexing (JSDM), where the downlink precoder (resp., uplink linear receiver) is split into product of a baseband linear projection (digital) and an RF reconfigurable beamforming network (analog), such that only $m \ll M$ A/D converters and RF chains is needed. In JSDM, users are grouped according to similarity of their signal subspaces, and these groups are separated by the analog beamforming stage. Further multiplexing gain in each group is achieved using the digital precoder. Therefore, it is apparent that extracting the signal subspace of the $M$ -dim channel vectors from snapshots of $m$ -dim projections , with $m \ll M$ , plays a fundamental role in JSDM implementation. In this paper, we develop efficient subspace estimation algorithms that require sampling only $m=O(2 \sqrt{M})$ antennas and, for a given $p \ll M$ , return a $p$ -dim beamformer (subspace) that has a performance comparable with the best $p$ -dim beamformer designed from the full knowledge of the exact channel covariance matrix. We assess the performance of our proposed estimators both analytically and empirically via numerical simulations.

User Grouping and Scheduling for Joint Spatial Division and Multiplexing in FDD Massive MIMO System

Massive multiple-input multiple-output (MIMO) is a key technology for the 5th Generation wireless communication systems. Joint spatial division and multiplexing (JSDM) method can reduce the cost of downlink training and feedback for CSIT of frequency-division duplexing (FDD) system. In this paper, we studied user grouping and user scheduling problems based on JSDM, and proposed an improved greedy user scheduling algorithm with lower complexity. Numerical results show that the user grouping and scheduling based on the proposed improved algorithm have much lower computational complexity while resulting in only a slight loss in system performance.