Weighted Minimum Mean Square Error Research Articles

A distortionless convolution beamformer design method based on the weighted minimum mean square error for joint dereverberation and denoising

This paper designs a weighted minimum mean square error (WMMSE) based distortionless convolution beamformer (DCBF) for joint dereverberation and denoising. By effectively using WMMSE with the constraint of distortionless, a DCBF is deduced, where the outputs of the weighted prediction error (WPE) filter and the WPE-based minimum variance distortionless response (MVDR) beamformer are combined to initialize target signal for balancing signal distortion, residual reverberation and residual noise. In addition, two optimization factors are introduced to reduce the reverberation and noise when the initialized target signal is used for the solution of beamformer. As a result, the designed beamformer is presented as a linear combination of the WMMSE-based convolution beamformer (CBF) and weighted power minimization distortionless response (WPD) filter. The experimental results demonstrate the superior performance of the designed beamformer for joint dereverberation and denoising compared to the reference methods.

A Single-Loop Algorithm for Weighted Sum Rate Maximization in Multiuser MIMO Systems With Per-Antenna Power Constraints

This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC) is considered. This problem is hard to solve due to its nonconvexity and the existence of multiple quadratic constraints. Conventional methods to tackle this problem, such as the iterative weighted minimum mean squared error (WMMSE) algorithm, typically consist of two nested loops and thus suffer from high computational complexity. By leveraging the inherent separability of the PAPC constraint set, we propose a low-complexity single-loop algorithm for solving the WSR maximization problem under PAPC, in which each updating step is done efficiently with closed form. Theoretically, we prove the convergence of the proposed algorithm to stationary solutions. Then we extend the proposed algorithm to the multi-carrier scenario where the power constraints are shared over the subcarriers. Complexity analysis and numerical results show that the proposed single-loop algorithm maintains the same WSR performance as existing methods but dramatically reduces the computational complexity.

A Survey on Challenges of Millimeter Wave Communications for Fifth-Generation Wireless Networks

Abstract-Cellular networks rely heavily on downlink beamforming; however, calculating beamformers that maximize the weighted sum rate (WSR) under power constraints is an NP-hard problem. A weighted minimum mean square error (WMMSE) algorithm variant is suggested for a MU-MISO downlink channel in order to address this trade-off between complexity and performance. This variation avoids bisection searches, eigendata compositions, and matrix inversions—all of which are challenging to implement as conventional network layers. With a reduced complexity, the suggested network architecture outperforms the WMMSE algorithm truncated to the same number of iterations and adapts well to variations in the channel distribution. Many use cases for vehicles that demand high capacity, extremely low latency, and high reliability can be made possible by 5G. To facilitate this, 5G For a MU-MISO downlink channel, a variation of the weighted minimum mean square error (WMMSE) algorithm is proposed to address this trade-off between complexity and performance. This variation avoids complex network layer implementations such as matrix inversions, eigendata compositions, and bisection searches. The suggested network architecture generalizes well to changes in the channel distribution and performs comparably to the WMMSE algorithm truncated to the same number of iterations, but at a lower complexity. Numerous automotive use cases requiring high capacity, extremely low latency, and high reliability can be made possible by 5G. 5G suggests using highly directed mm Wave system deployment and dense small cell technology to support this. To reduce the cost of signaling, however, enabling vehicular communication necessitates strong mobility management strategies. KEYWORD: Millimetre wave communications, propagation, channel measurements, channel models, MIMO, hybrid precoding, non-orthogonal multiple access (NOMA), multiple access techniques, simultaneous wireless information and power transfer (SWIPT), RF energy harvesting.

Robust WMMSE Precoder With Deep Learning Design for Massive MIMO

In this paper, we investigate the downlink robust precoding with imperfect channel state information (CSI) for massive multiple-input-multiple-output (MIMO) communications. With the estimated channel and channel error statistics, the general design of the robust precoder is to maximize the ergodic sum rate subject to the total transmit power constraint. To make the problem more tractable, we find a lower bound of the ergodic sum rate and propose the robust weighted minimum mean-squared-error (WMMSE) precoder to maximize the bound. We characterize the structure of the precoding vectors by low-dimensional parameters, which are learned directly from the available CSI through a neural network. As such, the precoding vectors can be immediately computed without iterations. To extend the deep learning design to multi-antennas users, we present a flexible approach that allows the various antenna configurations at the user side to be handled. Simulation results show that the deep learning design can significantly reduce the computational complexity compared with the existing precoder designs while achieving near optimal performance.

Security design for integrated communication and computation networks through cooperative cognitive radios

AbstractIn this letter, a novel integrated communication and computation framework is proposed through cooperative cognitive radios, which includes a communication primary network (PN) and a computing secondary network. Specifically, two primary communication users intend to exchange their confidential information with the relay assistance of cognitive access point (CAP), meanwhile, multiple sensors share the spectrum of PN to transmit their concurrent sensing data to CAP. The CAP is assumed to be a potential eavesdropper and to ensure the secure communication of primary users (PUs) and computational performance of the CAP, it is proposed to maximize the sum achievable secrecy rate of PUs by jointly designing the transmit precoding, relay beamforming matrix, transmit scaling factors and aggregation beamforming vector, while satisfying the constraint of the computational mean square error of the CAP. A weighted minimum mean square error (WMMSE)‐based block coordinate descent (BCD) algorithm is developed to solve the formulated problem, and simulation results are provided to validate the effectiveness of our proposed schemes.

Coordinated Sum-Rate Maximization in Multicell MU-MIMO With Deep Unrolling

Coordinated weighted sum-rate maximization in multicell MIMO networks with intra- and intercell interference and local channel state at the base stations is recognized as an important yet difficult problem. A classical, locally optimal solution is obtained by the weighted minimum mean squared error (WMMSE) algorithm which facilitates a distributed implementation in multicell networks. However, it often suffers from slow convergence and therefore large communication overhead. To obtain more practical solutions, the unrolling/unfolding of traditional iterative algorithms gained significant attention. In this work, we demonstrate a complete unfolding of the WMMSE algorithm for transceiver design in multicell MU-MIMO interference channels with local channel state information. The resulting architecture termed GCN-WMMSE applies ideas from graph signal processing and is agnostic to different wireless network topologies, while exhibiting a low number of trainable parameters and high efficiency w.r.t. training data. It significantly reduces the number of required iterations while achieving performance similar to the WMMSE algorithm, alleviating the overhead in a distributed deployment. Additionally, we review previous architectures based on unrolling the WMMSE algorithm and compare them to GCN-WMMSE in their specific applicable domains.

Design Optimization for UAV Aided Sustainable 3D Wireless Communication at mmWaves

Unmanned aerial vehicles (UAVs) operating at different altitudes will be integral to the 5th generation and beyond (5G+) communication network to provide ubiquitous coverage. Though 5G+ communications target to operate in sub-6 GHz as well as millimeter wave range (mmWaves), sub-6 GHz being already congested, mmWaves are seen as a viable technology that can support high data rates. To this end, in this paper, we study the feasibility of using UAVs at mmWaves deployed at low altitudes to serve a user population higher than the number of RF chains available at the UAV. Since the UAVs are energy constrained devices, solar harvesting is considered for the UAVs to act as access nodes for an extended period of time. Practical 3-dimensional antenna array radiation pattern and the resulting inter-beam interference from the sidelobes are taken into account in the analysis. We devise a sub-array hybrid precoder that provides minimum rate support to all users across the wideband mmWave channel. The RF precoder is designed according to the users' locations. In addition, we propose a low complexity iterative joint subcarrier allocation and baseband precoder optimization algorithm with faster convergence. In the proposed algorithm, we employ weighted minimum mean squared error (WMMSE) to design baseband precoder to reduce inter-beam interference while jointly optimizing subcarrier allocation to maintain minimum user rate constraint. Next, we determine the optimal number of beams at UAV to optimize throughput while guaranteeing minimum user rate support for energy sustainable UAV operation. Finally, we compare the performance gain achieved by low-altitude UAV deployed at mmWaves over the UAV deployed at sub-6 GHz frequency range.

Efficient Hybrid A/D Beamforming for Millimeter-Wave Systems Using Butler Matrices

Hybrid analog/digital (A/D) beamforming architectures are low complexity alternatives to fully digital designs in large antenna setups. Recent research efforts have been set out to find low-complexity algorithms, which have low implementation complexity in the analog domain. In this paper, we propose a two-stage hybrid precoding design assuming hardware constraints that avoid the use of adaptive phase-shifters (PSs) by introducing a novel combination of Butler matrices (BMs) to feed a uniform planar array (UPA). With several fixed beams, we propose an algorithm to design the analog precoding matrix in the first stage, while in the second stage, hybrid-beamforming (HBF)-weighted minimum mean square error (WMMSE) is proposed for baseband precoding by taking into account the analog precoding matrix designed in the first stage. The proposed algorithm shows fast convergence, thanks to the analog precoder design, which helps the HBF-WMMSE algorithm to converge within a few iterations. Compared with the classical matched filter (MF) and minimum mean square error (MMSE) solutions, HBF-WMMSE outperforms the latter in terms of sum-rate, especially in the low signal-to-noise-ratio (SNR) regime. Simulation results further show that the partially connected Butler matrices (PCBMS) approach implemented with fixed-PSs exhibit superior energy-efficiency while maintaining higher spectral-efficiency as compared to the partially connected analog phase shifting (PCAPS) network implemented with variable-PSs.

Joint Beamforming Design for Intelligent Omni Surface Assisted Wireless Communication Systems

Intelligent reflecting surface (IRS) has been widely considered as one of the key enabling techniques for future wireless communication networks owing to its ability of dynamically controlling the phase shift of reflected electromagnetic (EM) waves to construct a favorable propagation environment. While IRS only focuses on signal reflection, the recently emerged innovative concept of intelligent omni-surface (IOS) can provide the dual functionality of manipulating reflecting and transmitting signals. Thus, IOS is a new paradigm for achieving ubiquitous wireless communications. In this paper, we consider an IOS-assisted multi-user multi-input single-output (MU-MISO) system where the IOS utilizes its reflective and transmissive properties to enhance the MU-MISO transmission. Both power minimization and sum-rate maximization problems are solved by exploiting the second-order cone programming (SOCP), Riemannian manifold, weighted minimum mean square error (WMMSE), and block coordinate descent (BCD) methods. Simulation results verify the advancements of the IOS for wireless systems and illustrate the significant performance improvement of our proposed joint transmit beamforming, reflecting and transmitting phase-shift, and IOS energy division design algorithms. Compared with conventional IRS, IOS can significantly extend the communication coverage, enhance the strength of received signals, and improve the quality of communication links.

Rethinking WMMSE: Can Its Complexity Scale Linearly With the Number of BS Antennas?

Precoding design for maximizing weighted sum-rate (WSR) is a fundamental problem for downlink of massive multi-user multiple-input multiple-output (MU-MIMO) systems. It is well-known that this problem is generally NP-hard due to the presence of multi-user interference. The weighted minimum mean-square error (WMMSE) algorithm is a popular approach for WSR maximization. However, its computational complexity is cubic in the number of base station (BS) antennas, which is unaffordable when the BS is equipped with a large antenna array. In this paper, we consider the WSR maximization problem with either a sum-power constraint (SPC) or per-antenna power constraints (PAPCs). For the former, we prove that any nontrivial stationary point must have a low-dimensional subspace structure, and then propose a reduced-WMMSE (R-WMMSE) with linear complexity by exploiting the solution structure. For the latter, we propose a linear-complexity WMMSE approach, named PAPC-WMMSE, by using a novel recursive design of the algorithm. Both R-WMMSE and PAPC-WMMSE have simple closed-form updates and guaranteed convergence to stationary points. Simulation results verify the efficacy of the proposed designs, especially the much lower complexity as compared to the state-of-the-art approaches for massive MU-MIMO systems.

Weighted MMSE Precoding for Constructive Interference Region

In this letter, we propose a symbol-level precoding (SLP) design that aims to minimize the weighted mean square error between the received signal and the constellation point located in the constructive interference region (CIR). Unlike most existing SLP schemes that rely on channel state information (CSI) only, the proposed scheme exploits both CSI and the distribution information of the noise to achieve improved performance. We firstly propose a simple generic description of CIR that facilitates the subsequent SLP design. Such an objective can further be formulated as a nonnegative least squares (NNLS) problem, which can be solved efficiently by the active-set algorithm. Furthermore, the weighted minimum mean square error (WMMSE) precoding and the existing SLP can be easily verified as special cases of the proposed scheme. Finally, simulation results show that the proposed precoding outperforms the state-of-the-art SLP schemes in full signal-to-noise ratio ranges in both uncoded and coded systems without additional complexity over conventional SLP.

A Deep Learning-Based Framework for Low Complexity Multiuser MIMO Precoding Design

Using precoding to suppress multi-user interference is a well-known technique to improve spectra efficiency in multiuser multiple-input multiple-output (MU-MIMO) systems, and the pursuit of high performance and low complexity precoding method has been the focus in the last decade. The traditional algorithms including the zero-forcing (ZF) algorithm and the weighted minimum mean square error (WMMSE) algorithm failed to achieve a satisfactory trade-off between complexity and performance. In this paper, leveraging on the power of deep learning, we propose a low-complexity precoding design framework for MU-MIMO systems. The key idea is to transform the MIMO precoding problem into the multiple-input single-output precoding problem, where the optimal precoding structure can be obtained in closed-form. A customized deep neural network is designed to fit the mapping from the channels to the precoding matrix. In addition, the technique of input dimensionality reduction, network pruning, and recovery module compression are used to further improve the computational efficiency. Furthermore, the extension to the practical MIMO orthogonal frequency-division multiplexing (MIMO-OFDM) system is studied. Simulation results show that the proposed low-complexity precoding scheme achieves similar performance as the WMMSE algorithm with very low computational complexity.

DNN-Based Dynamic Transmit Power Control for V2V Communication Underlaid Cellular Uplink

Vehicle-to-vehicle (V2V) communication has been designed to afford improvements in the traffic congestion and traffic accidents by directly exchanging information between nearby vehicles. However, V2V communication may have difficulty providing service reliability due to interference between V2V links and vehicle-to-cellular user equipment links. In this paper, we consider the transmit power control algorithm to minimize interference among cellular users and vehicles in the context of V2V communication underlaid uplink cellular networks. First, we formulate the problem, which is an NP-hard combinatorial optimization problem with linear constraints. Addressing this problem with traditional optimization methods is ineffective; therefore, we design and train a deep neural network to address this optimization problem. Computational complexity analyses and simulation results reveal that the proposed algorithm outperforms weighted minimum mean squared error (WMMSE), fixed transmit power, and Dinkelbach's methods, and achieves near-global optimum with lower computation complexity than the exhaustive search (ES).

Deep unfolding for cooperative rate splitting multiple access in hybrid satellite terrestrial networks

Rate splitting multiple access (RSMA) has shown great potentials for the next generation communication systems. In this work, we consider a two-user system in hybrid satellite terrestrial network (HSTN) where one of them is heavily shadowed and the other uses cooperative RSMA to improve the transmission quality. The non-convex weighted sum rate (WSR) problem formulated based on this model is usually optimized by computational burdened weighted minimum mean square error (WMMSE) algorithm. We propose to apply deep unfolding to solve the optimization problem, which maps WMMSE iterations into a layer-wise network and could achieve better performance within limited iterations. We also incorporate momentum accelerated projection gradient descent (PGD) algorithm to circumvent the complicated operations in WMMSE that are not amenable for unfolding and mapping. The momentum and step size in deep unfolding network are selected as trainable parameters for training. As shown in the simulation results, deep unfolding scheme has WSR and convergence speed advantages over original WMMSE algorithm.

IRS-Assisted Multicell Multiband Systems: Practical Reflection Model and Joint Beamforming Design

Intelligent reflecting surface (IRS) has been regarded as a promising and revolutionary technology for future wireless communication systems owing to its capability of tailoring signal propagation environment in an energy/spectrum/ hardware-efficient manner. However, most existing studies on IRS optimizations are based on a simple and ideal reflection model that is impractical in hardware implementation, which thus leads to severe performance loss in realistic wideband/multi-band systems. To deal with this problem, in this paper we first propose a more practical and more tractable IRS reflection model that describes the difference of reflection responses for signals at different frequencies. Then, we investigate the joint transmit beamforming and IRS reflection beamforming design for an IRS-assisted multi-cell multi-band system. Both power minimization and sum-rate maximization problems are solved by exploiting popular second-order cone programming (SOCP), Riemannian manifold, minimization-majorization (MM), weighted minimum mean square error (WMMSE), and block coordinate descent (BCD) methods. Simulation results illustrate the significant performance improvement of our proposed joint transmit beamforming and reflection design algorithms based on the practical reflection model in terms of power saving and rate enhancement.

Rate-Splitting Multiple Access for Downlink Multiuser MIMO: Precoder Optimization and PHY-Layer Design

Rate-Splitting Multiple Access (RSMA) has recently appeared as a powerful and robust multiple access and interference management strategy for downlink Multi-user (MU) multi-antenna communications. In this work, we study the precoder design problem for RSMA scheme in downlink MU systems with both perfect and imperfect Channel State Information at the Transmitter (CSIT) and assess the role and benefits of transmitting multiple common streams. Unlike existing works which have considered single-antenna receivers (Multiple-Input Single-Output–MISO), we propose and extend the RSMA framework for multi-antenna receivers (Multiple-Input Multiple-Output–MIMO) and formulate the precoder optimization problem with the aim of maximizing the Weighted Ergodic Sum-Rate (WESR). Precoder optimization is solved using Sample Average Approximation (SAA) together with the proposed vectorization and Weighted Minimum Mean Square Error (WMMSE) based approach. Achievable sum-Degree of Freedom (DoF) of RSMA is derived for the proposed framework as an increasing function of the number of transmitted common and private streams, which is further validated by the Ergodic Sum Rate (ESR) performance using Monte Carlo simulations. Conventional MU–MIMO based on linear precoders and Non-Orthogonal Multiple Access (NOMA) schemes are considered as baselines. Numerical results show that with imperfect CSIT, the sum-DoF and ESR performance of RSMA is superior to those of the two baselines, and is increasing with the number of transmitted common streams. Moreover, by better managing the interference, RSMA not only has significant ESR gains over baseline schemes but is more robust to CSIT inaccuracies, network loads and user deployments.

Dynamic Channel Access and Power Control in Wireless Interference Networks via Multi-Agent Deep Reinforcement Learning

Due to the scarcity in the wireless spectrum and limited energy resources especially in mobile applications, efficient resource allocation strategies are critical in wireless networks. Motivated by the recent advances in deep reinforcement learning (DRL), we address multi-agent DRL-based joint dynamic channel access and power control in a wireless interference network. We first propose a multi-agent DRL algorithm with centralized training (DRL-CT) to tackle the joint resource allocation problem. In this case, the training is performed at the central unit (CU) and after training, the users make autonomous decisions on their transmission strategies with only local information. We demonstrate that with limited information exchange and faster convergence, DRL-CT algorithm can achieve 90% of the performance achieved by the combination of weighted minimum mean square error (WMMSE) algorithm for power control and exhaustive search for dynamic channel access. In the second part of this paper, we consider distributed multi-agent DRL scenario in which each user conducts its own training and makes its decisions individually, acting as a DRL agent. Finally, as a compromise between centralized and fully distributed scenarios, we consider federated DRL (FDRL) to approach the performance of DRL-CT with the use of a central unit in training while limiting the information exchange and preserving privacy of the users in the wireless system. Via simulation results, we show that proposed learning frameworks lead to efficient adaptive channel access and power control policies in dynamic environments.

Matrix-Inverse-Free Deep Unfolding of the Weighted MMSE Beamforming Algorithm

Downlink beamforming is a key technology for cellular networks. However, computing beamformers that maximize the weighted sum rate (WSR) subject to a power constraint is an NP-hard problem. The popular weighted minimum mean square error (WMMSE) algorithm converges to a local optimum but still exhibits considerable complexity. In order to address this trade-off between complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm for a MU-MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE into trainable neural network layers. However, the formulation of the WMMSE algorithm, as provided in Shi <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , involves matrix inversions, eigendecompositions, and bisection searches. These operations are hard to implement as standard network layers. Therefore, we present a variant of the WMMSE algorithm i) that circumvents these operations by applying a projected gradient descent and ii) that, as a result, involves only operations that can be efficiently computed in parallel on hardware platforms designed for deep learning. We demonstrate that our variant of the WMMSE algorithm convergences to a stationary point of the WSR maximization problem and we accelerate its convergence by incorporating Nesterov acceleration and a generalization thereof as learnable structures. By means of simulations, we show that the proposed network architecture i) performs on par with the WMMSE algorithm truncated to the same number of iterations, yet at a lower complexity, and ii) generalizes well to changes in the channel distribution.

User Rate Optimization for Fronthaul-Constrained Cell-Free Massive MIMO-OFDM Systems: A Quadratic Transform-Based Approach

As a promising candidate for the future generations of mobile communication networks, the cell-free (CF) massive multiple-input multiple-output (mMIMO) networks have been shown to provide high spectral efficiency (SE) and more uniform signal coverage than cellular mMIMO networks, enabling smart cities more diverse application services. The fronthaul link in such networks, defined as the transmission link between the central processing unit and the access point, requires a high capacity, but is often constrained. Hence, the optimization of the user rate under the limited capacity of fronthaul is the key problem to be solved in a CF networks. In this paper, we consider the downlink transmission of CF mMIMO orthogonal frequency division multiplexing (OFDM) systems with constrained transmit power and fronthaul capacity. Based on the min-max and sum-max principles, quadratic transform-min max (QT-MM) and quadratic transform-sum max (QT-SM) optimization algorithms are proposed, respectively. Simulation results show that compared with the weighted minimum mean square error (WMMSE) algorithm, both of the proposed algorithms can effectively prevent very low user rates when the fronthaul capacity is limited. When the fronthaul link capacity constraint is high, the QT-SM algorithm has better rate performance than the distributed WMMSE-d algorithm and the centralized WMMSE-c algorithm.

Globally Optimal Spectrum- and Energy-Efficient Beamforming for Rate Splitting Multiple Access

Rate splitting multiple access (RSMA) is a promising non-orthogonal transmission strategy for next-generation wireless networks. It has been shown to outperform existing multiple access schemes in terms of spectral and energy efficiency when suboptimal beamforming schemes are employed. In this work, we fill the gap between suboptimal and truly optimal beamforming schemes and conclusively establish the superior spectral and energy efficiency of RSMA. To this end, we propose a successive incumbent transcending (SIT) branch and bound (BB) algorithm to find globally optimal beamforming solutions that maximize the weighted sum rate or energy efficiency of RSMA in Gaussian multiple-input single-output (MISO) broadcast channels. Numerical results show that RSMA exhibits an explicit globally optimal spectral and energy efficiency gain over conventional multi-user linear precoding (MU-LP) and power-domain non-orthogonal multiple access (NOMA). Compared to existing globally optimal beamforming algorithms for MU-LP, the proposed SIT BB not only improves the numerical stability but also achieves faster convergence. Moreover, for the first time, we show that the spectral/energy efficiency of RSMA achieved by suboptimal beamforming schemes (including weighted minimum mean squared error (WMMSE) and successive convex approximation) almost coincides with the corresponding globally optimal performance, making it a valid choice for performance comparisons. The globally optimal results provided in this work are imperative to the ongoing research on RSMA as they serve as benchmarks for existing suboptimal beamforming strategies and those to be developed in multi-antenna broadcast channels.