Zero-forcing Beamforming Research Articles

Exploring the potential of swarm intelligence for optimal energy efficiency in IoT downlink system

This study delves into the energy optimization problem in Internet of Things (IoT) networks. We consider the downlink from multiple antenna Gateway (GW) and single antenna IoT devices. For this challenging nonconvex problem, we initially introduced the well-known zero-forcing beamforming (ZFBF) to eliminate inter-user interference, thereby transforming the energy efficiency maximization problem into a concave-convex fractional problem. Then, instead of applying a combination of ZFBF with power allocation, we propose the Particle Swarm Optimization (PSO) algorithm to allocate power to find the optimized beamforming matrix. Through extensive numerical analysis, we demonstrate the effectiveness of our proposed scheme in terms of energy efficiency and power achieved at the GW. The results underscore the significant benefits of our approach over conventional methods, paving the way for practical and efficient energy optimization in IoT networks.

Performance Analysis of RIS-Assisted SatComs Based on a ZFBF and Co-Phasing Scheme

In recent high-throughput satellite communication (SatCom) systems, the use of reconfigurable intelligent surfaces (RISs) has emerged as a promising solution to improve spectral efficiency and extend coverage in areas with limited terrestrial network access. However, the RIS may amplify the inter-beam interference (IBI) caused by multibeam transmission at the satellite, and multiple RISs can also cause inter-RIS interference (IRI) to terrestrial users. In this paper, the performance of the RIS-assisted SatCom system is asymptotically analyzed for both full and partial channel state information (CSI) scenarios. In particular, zero-forcing beamforming is considered as the active beamforming for data transmission, while the co-phasing scheme is considered as the passive beamforming for RIS reflection. Based on the asymptotic analyses, deterministic active and passive beamforming techniques using partial CSI are proposed that can gradually eliminate both IBI and IRI, ultimately achieving ideal performance. Simulation results validate the accuracy of asymptotic analyses and demonstrate the superiority of deterministic active and passive beamforming techniques using partial CSI. The simulation results also confirm that the proposed beamforming can achieve approximately 92.8% of the ideal performance, even though it only requires partial CSI.

On the Application of Quasi-Degradation to Network NOMA in Downlink CoMP Systems

The application of network non-orthogonal multiple access (N-NOMA) technique to coordinated multi-point (CoMP) systems has attracted significant attention due to its superior capability to improve connectivity and maintain reliable transmission for CoMP users simultaneously. Based on the concept of quasi-degraded channel for N-NOMA, this paper studies the precoding design for downlink N-NOMA scenarios with two base stations (BSs) equipped with multiple antennas. In specific, under quasi-degraded channels, simple linear precoding based N-NOMA can achieve the same minimal total transmission power as theoretically optimal but complicated dirty paper coding (DPC) scheme, when the users’ target rates and minimal transmission power of each BS are given. In this paper, the channel quasi-degradation (QD) condition is first rigorously derived for the scenario with single CoMP user and two NOMA users. The closed-form optimal precoders for N-NOMA under quasi-degraded channels are also provided. Then, based on QD condition, a novel hybrid N-NOMA (H-N-NOMA) scheme is proposed, which is a mixture of N-NOMA and conventional zero-forcing beamforming (ZFBF) scheme. Further, for the scenarios with more users, a low-complexity QD based user pairing (QDUP) algorithm is proposed, which is then combined with H-N-NOMA to make a novel scheme termed H-N-NOMA/QDUP into being. Numerical results are presented to reveal the impact factors on QD channels, and also demonstrate the superior performance of the proposed H-N-NOMA/QDUP scheme. It is shown that the proposed H-N-NOMA/QDUP scheme can effectively exploit the benefit of multi user diversity.

Random Caching Design for Multi-User Multi-Antenna HetNets With Interference Nulling

The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.

Performance analysis of multiuser massive MIMO with multi-antenna users: Asymptotic data rate and its application

Massive multiple-input multiple-output (MIMO) systems have become an essential feature in the fifth-generation (5G) wireless communication networks. Due to the commercialization of 5G mobile communication devices, the number of multi-antenna devices have increased over the years. Therefore, a precoding scheme based on multi-antenna users is an inevitable feature that needs to be analyzed in massive MIMO systems. The asymptotic ergodic sum-rate analysis of block diagonalization (BD) based multiuser MIMO systems is performed in this study. Based on the random matrix theory results derived from the massive base station antenna characteristics, the singular values of the block diagonalized channel are obtained asymptotically, and thereby, the closed-form expression for the BD based sum-rate is derived. The asymptotic sum-rate performance gap between the BD and the zero-forcing beamforming is then analyzed. Moreover, from the derived asymptotic sum-rate, the optimal number of users needed to maximize the ergodic sum-rate is proposed. Simulation results show that the derived asymptotic analyses are closely aligned to the sum-rate obtained by Monte Carlo simulations. In addition, the simulation results prove that the maximum ergodic sum-rate can be achieved by using the proposed number of users.

Zero-Forcing Beamforming for RIS-Enhanced Secure Transmission

This article considers a reconfigurable intelligent surface (RIS) enhanced multi-antenna secure transmission system in the presence of both active eavesdroppers (AEves) and passive eavesdroppers (PEves). We propose a zero-forcing (ZF) beamforming strategy that can steer transmit beam to the null space of AEves' channel, while simultaneously enhancing the SNRs for a legitimate user equipment (UE) and PEves without perfect channel state information (CSI). The design goal is to maximize the SNR of UE subject to the transmit power constraint at the BS, SNR limitations on PEves, and reflection constraints at RIS. Due to the complexity of modeling, we first introduce a homogeneous Poisson point process (HPPP) to imitate the distribution of spatially random PEves, which derives a complicated non-convex problem. We then develop an efficient alternating algorithm where the transmit beamforming vector and the reflective beamforming vector are obtained by convex-concave procedure (CCP) and semi-definite relaxation (SDR) technique, respectively. Simulation results validate the performance advantages of the proposed optimized design.

Multi-Antenna Jammer-Assisted Secure Short Packet Communications in IoT Networks

In this work, we exploit a multi-antenna cooperative jammer to enable secure short packet communications in Internet of Things (IoT) networks. Specifically, we propose three jamming schemes to combat eavesdropping, i.e., the zero forcing beamforming (ZFB) scheme, null-space artificial noise (NAN) scheme, and transmit antenna selection (TAS) scheme. Assuming Rayleigh fading, we derive new closed-form approximations for the secrecy throughput with finite blocklength coding. To gain further insights, we also analyze the asymptotic performance of the secrecy throughput in the case of infinite blocklength. Furthermore, we investigate the optimization problem in terms of maximizing the secrecy throughput with the latency and reliability constraints to determine the optimal blocklength. Simulation results validate the accuracy of the approximations and evaluate the impact of key parameters such as the jamming power and the number of antennas at the jammer on the secrecy throughput.

Integrated single target sensing and multiuser communications based on zero-forcing beamforming

Integrated sensing and communication (ISAC) is a promising approach that utilizes a single waveform for both information transmission and target object acquisition. In this study, we focus on the challenges posed by inter-user and inter-ISAC-antenna interference, specifically the self-interference from ISAC transmit antennas to receive antennas. Further, the benefit of a multi-functional ISAC scheme is clarified by comparing it with single function-aware schemes: sensing- and communication-aware approaches. To address these issues, we investigate the application of a zero-forcing (ZF)-based beamforming and power allocation (PA) technique. A sum rate maximization problem with a target object sensing signal-to-noise (SNR) threshold is formulated and split into two subproblems for improved tractability. To tackle the first subproblem of precoder design, we develop a constraint-aware greedy algorithm that employs communication SNR ordering. Subsequently, we propose a feasibility test-based algorithm to solve the second subproblem of PA.Through an extensive performance evaluation, encompassing computational complexity, sum rate, and ISAC received SNR, we verify that relying solely on a single function-aware scheme is insufficient for accommodating ISAC's multifunctional capabilities. Additionally, we demonstrate that a naive switching strategy between two single function-aware schemes can result in inefficient communication performance. Considering both sensing and communication functions, we identify the need for an adaptive balance between sensing and communication capabilities in a multi-functional ISAC system. This can be achieved by dynamically adjusting the target object sensing SNR threshold within the optimization problem's constraint. The proposed ZF-based ISAC with the designed PA scheme offers an optimal strategy when the transmit power of the ISAC is low. Conversely, an equal PA to multiple users emerges as the best strategy when the transmit power of the ISAC is sufficiently high. In conclusion, our study highlights the significance of integrating sensing and communication functionalities in ISAC systems. Moreover, by providing insights into the interplay between target object sensing, beamforming, and power allocation, we contribute to the development of efficient and adaptable ISAC architectures.

Multi-antenna Jammer assisted covert communications in data collected IoT with NOMA

In this paper, we investigate covert communications in data collected IoT with NOMA, where the paired sensor nodes S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> transmit covert messages to a legitimate receiver (Bob) in the presence of a Warden (Willie). To confuse the detection at Willie, an extra multi-antenna friendly jammer (Jammer) has been employed to transmit artificial noise (AN) with random power. Based on the CSI of Willie is available or not at Jammer, three AN transmission schemes, including null-space artificial noise (NAN), transmit antenna selection (TAS), and zero-forcing beamforming (ZFB), are proposed. Furthermore, the closed-form expressions of expected minimum detection error probability (EMDEP) and joint connection outage probability (JCOP) are derived to measure covertness and reliability, respectively. Finally, the maximum effective covert rate (ECR) is obtained with a given covertness constraint. The numerical results show that ZFB scheme has the best maximum ECR in the case of the number of antennas satisfies N > 2, and the same maximum ECR can be achieved in ZFB and NAN schemes with N =3D 2. Moreover, TAS scheme also can improve the maximum ECR compared with the benchmark scheme (i.e., signal-antenna jammer). In addition, a proper NOMA node pairing can further improve the maximum ECR.

Regularized Zero-Forcing Aided Hybrid Beamforming for Millimeter-Wave Multiuser MIMO Systems

This paper considers hybrid beamforming consisting of analog beamforming (ABF) coupled with digital baseband beamforming (DBF) which is designed for multi-user (MU) multiple input multiple output (MIMO) millimeter-wave (mmWave) communications. ABF uses a limited number of radio frequency (RF) chains and finite-resolution phase-shifters to alleviate the power consumption at the base station (BS), while DBF uses either zero-forcing beamforming (ZFB) or regularized zero forcing beamforming (RZFB) to restrain MU interference. The joint design of ABF and DBF constitutes a computationally challenging mixed discrete continuous optimization problem. The paper develops efficient algorithms for its solution, which iterate scalable-complex expressions. Furthermore, we conceive a new class of MU RZFB for attaining higher rates. Simulations are provided to demonstrate the viability of the proposed algorithms and the advantages of the conceived RZFB.

Machine Learning-Based CSI Feedback With Variable Length in FDD Massive MIMO

To fully unlock the benefits of multiple-input multiple-output (MIMO) networks, downlink channel state information (CSI) is required at the base station (BS). In frequency division duplex (FDD) systems, the CSI is acquired through a feedback signal from the user equipment (UE). However, this may lead to an important overhead in FDD massive MIMO systems. Focusing on these systems, in this study, we propose a novel strategy to design the CSI feedback. Our strategy allows to optimally design variable length feedback, that is promising compared to fixed feedback since users experience channel matrices differently sparse. Specifically, principal component analysis (PCA) is used to compress the channel into a latent space with adaptive dimensionality. To quantize this compressed channel, the feedback bits are smartly allocated to the latent space dimensions by minimizing the normalized mean squared error (NMSE) distortion. Finally, the quantization codebook is determined with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means clustering. Numerical simulations show that our strategy improves the zero-forcing beamforming sum rate by 17%, compared to CsiNetPro. The number of model parameters is reduced by 23.4 times, thus causing a significantly smaller offloading overhead. At the same time, PCA is characterized by a lightweight unsupervised training, requiring eight times fewer training samples than CsiNetPro.

Spectral Efficiency of Time-Variant Massive MIMO Using Wiener Prediction

Massive multiple-input multiple-output (MIMO) serves as technological pillar in current 5G deployments. The spectral efficiency (SE) reduction due to time-variance of the wireless channel, and respective mitigation strategies, are still not sufficiently understood. In this paper, we propose a multi-step Wiener predictor with a general temporal covariance function to quantify the impact of time-variance on the SE for different numbers of consecutive pilot symbols and prediction horizons. We provide asymptotic expressions of the SE for maximum ratio combining (MRC) beam-forming that show excellent agreement to numerical simulations. We investigate the channel hardening capability of massive MIMO systems in time-variant propagation channels and show that it is largely independent of the prediction horizon. The numerical evaluations show that channel prediction allows to double SE utilizing four instead of one uplink pilot symbol for a prediction horizon of 0.3 λ for both MRC and regularized zero-forcing (RZF) beam-forming.

Optimal Transmit Power and Channel-Information Bit Allocation With Zeroforcing Beamforming in MIMO-NOMA and MIMO-OMA Downlinks

In downlink, a base station (BS) with multiple transmit antennas applies zeroforcing beamforming to transmit to single-antenna mobile users in a cell. We propose the schemes that optimize transmit power and the number of bits for channel direction information (CDI) for all users to achieve the max-min signal-to-interference plus noise ratio (SINR) fairness. The optimal allocation can be obtained by a geometric program for both non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA). For NOMA, 2 users with highly correlated channels are paired and share the same transmit beamforming. In some small total-CDI rate regimes, we show that NOMA can outperform OMA by as much as 3 dB. The performance gain over OMA increases when the correlation-coefficient threshold for user pairing is set higher. To reduce computational complexity, we propose to allocate transmit power and CDI rate to groups of multiple users instead of individual users. The user grouping scheme is based on K-means over the user SINR. We also propose a progressive filling scheme that performs close to the optimum, but can reduce the computation time by almost 3 orders of magnitude in some numerical examples.

A POMDP-Based Approach to Joint Antenna Selection and User Scheduling for Multi-User Massive MIMO Communication

We devise a partially observable Markov decision process (POMDP) based joint antenna selection and user scheduling (JASUS) policy for a massive MIMO base station, equipped with only a small number of RF chains, that serves a large number of users. The users are served at different time slots within a frame. Relying on partial CSI obtained from training between the selected antennas and the users, at the beginning of each frame, the BS assigns each user to a time slot in the frame and selects a subset of antennas to serve the users scheduled in each time slot. Assuming that the channels evolve according to a Markov process and relying on zero-forcing beamforming, we formulate our JASUS problem using a POMDP framework to devise a real-time decision-making policy that maximizes the expected long-term sum-rate. We rigorously prove that for positively correlated two-state channel models, the myopic policy provides the optimal solution to our POMDP-based JASUS problem for any number of RF chains and for any number of users. Based on this, we model the Rayleigh fading channels as first-order Gauss-Markov processes and devise a low-complexity myopic policy-based JASUS algorithm for massive MU-MIMO systems that only relies on partial CSI.

IRS-Aided Uplink Transmission Scheme in Integrated Satellite-Terrestrial Networks

This paper proposes an intelligent reflecting surface (IRS)-aided uplink transmission scheme to expand the wireless coverage and improve spectral efficiency for an integrated satellite-terrestrial network (ISTN). Here, multiple earth stations communicate with the satellite via non-orthogonal multiple access (NOMA) technology, while multiple direct users and blockage users access the cellular network through space division multiple access and IRS-aided NOMA technology, respectively. In particular, we first aim at maximizing the ergodic sum rate of the ISTN subject to the quality-of-service requirements and transmit power budgets of all users, yielding a constrained optimization problem. Then, based on the assumption that only the statistical channel state information (CSI) is available, we propose a two-layer alternating algorithm to solve the non-convex original problem. The algorithm combines successive convex approximation with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> -procedure approach to calculate the phase shifts of IRS and transmit powers of all users in the first layer, and uses Charnes-Cooper method with semi-definite programming to calculate beamforming vectors at the BS in the second layer. Furthermore, with the help of the zero-forcing beamforming principle, we propose a low-complexity algorithm to solve the problem that can reduce the computational load effectively. Finally, simulation results demonstrate that our proposed algorithms can obtain a higher ergodic sum rate than the benchmarks.

System throughput maximization in IRS-assisted phase cooperative NOMA networks

This work investigates performance of system throughput in intelligent reflecting surfaces (IRSs)-enabled phase cooperative non-orthogonal multiple access (NOMA) framework. By exploiting heterogeneous cognitive radio networks concept the aim is to maximize the sum rate of secondary users in the proposed phase cooperative downlink network configuration via optimization solutions. However, the optimization problem comes out to be NP-hard and precludes direct solution. Hence, an alternating optimization is applied at the primary network to solve the maximization problem by exploiting the transmit beamforming (BF) at the power station (PS) and phase shift optimization at the IRS. Later, sum rate maximization for secondary network is performed by utilizing phase shifts of primary network via phase cooperation. In order to find global optimal solutions for active beamformers at both PSs, a branch-reduce-and-bound (BRnB) method is used whereas, passive phase shift optimization at the primary PS is performed via a simple iterative solution, i.e., the element-wise block coordinate descent method. For the proposed framework, Monte-Carlo simulations are performed where the optimality of the global solution is compared with heuristic BF methods including minimum-mean-square-error/regularized zero-forcing-beamforming (ZFBF) and ZFBF. The BRnB algorithm sets an upper performance bound by improving the sum rate of users in comparison with the conventional heuristic BF schemes. This work signifies the utilization of phase cooperation in IRS-assisted NOMA networks for a multi-user environment.

Zero-forcing Beamforming for Jamming Aided Covert Communication in MIMO Systems

This paper investigates covert wireless communication in a multi-input multi-output (MIMO) system, where a multi-antenna transmitter transmits covert signal to a multi-antenna receiver with the assistance of a multi-antenna jammer employing zero-forcing (ZF) beamforming to avoid detection by a warden equipped with single antenna. For the given scenario, we first provide theoretical modeling for the minimum detection error probability at warden and covert rate from transmitter to receiver. We then explore the optimal beamformer design of the jammer to maximize the covert rate, subjecting to the constraints of covertness, upper bounds of transmitter and jammer transmit power, and beamformer on jammer. We further devise an iterative algorithm to determine the related optimal precoding matrix for covert rate maximization. Finally, we provide extensive numerical results to illustrate the impact of system parameters on covert performance.

Joint Optimization of Transmit Beamforming and Base Station Cache Allocation in Multi-Cell C-RAN

This paper studies a downlink cloud radio access network (C-RAN) consisting of a centralized processor (CP) and multiple cells each one of which has one cache-enabled base station (BS) connected to the CP through wireless backhaul links. In such a network, we aim to determine sizes of the cache allocated to the BSs such that the long-term delivery time of the available files is minimized. Considering the two-stage nature of this problem, we formulate a beamforming optimization problem and a cache allocation problem. The purpose of the first one is to deliver un-cached portions of files to the BSs in the shortest possible time during the beamforming stage. The second problem aims to minimize long-term expectation of delivery time through optimal cache allocation during the cache allocation stage. We rigorously prove that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-varying beamformers</i> can be assumed to be piece-wise constant functions of time. Based on this finding, the beamforming optimization problem does not appear to be amenable to a computationally efficient solution. Hence, we resort to the zero-forcing (ZF) beamforming approach to tackle the beamforming optimization problem. Using the results of the beamforming optimization problem, we prove that the cache allocation problem is a convex optimization problem; hence it can be solved by any convex optimization solvers. Simulation results show that the loss of optimality due to adopting ZF beamforming is negligible. Moreover, the superiority of our proposed cache allocation scheme over several other heuristic schemes including proportional cache size allocation is shown.

Energy-Efficient IRS-Aided NOMA Beamforming for 6G Wireless Communications

This manuscript presents an energy-efficient alternating optimization framework based on intelligent reflective surfaces (IRS) aided non-orthogonal multiple access beamforming (NOMA-BF) system for 6G wireless communications. Specifically, this work proposes a centralized IRS-enabled design for the NOMA-BF system to optimize the active beamforming and power allocation coefficient (PAC) of users at the transmitter in the first stage and passive beamforming at IRS in the 2nd stage to maximize the energy efficiency (EE) of the network. However, an increment in the number of supportable users with the NOMA-BF system will lead to NOMA user interference and inter-cluster interference (ICI). To mitigate the effect of ICI, first zero-forcing beamforming along with efficient user clustering algorithm is exploited and then NOMA user interference is tackled efficiently through a proposed iterative algorithm that computes PAC of NOMA user through simplified closed-form expression under the required system constraints. In the 2nd stage, the problem of passive beamforming is solved through a technique based on difference-of-convex (DC) programming and successive convex approximation (SCA). Simulation results demonstrate that the proposed alternating framework for energy-efficient IRS-assisted NOMA-BF system can achieve convergence within a few iterations and provide efficient performance in terms of EE of the system with low complexity.

Reinforcement learning-based cost-efficient service function chaining with CoMP zero-forcing beamforming in edge networks

As two promising paradigms in emerging 6G wireless systems, service function chaining (SFC) and mobile edge computing (MEC) have attracted insensitive attentions from both industry and academia, and would bring more close-proximity services to 6G users with communication, computing and caching (3C) resources, yet also faced with challenges arising in time-varying channel conditions and resource dynamics. In this work, boosted by recent advents in artificial intelligence and reinforcement learning, we investigate the on-line SFC deployment in the edge of 6G wireless systems via the actor–critic learning framework. First, one long-run cost-efficient SFC deployment problem is investigated, and the coordinated multiple points (CoMP)-based zero-forcing beamforming is utilized to cancel the interference across SFCs. Then, by exploiting the Markov decision processes (MDP) property of long-run SFC deployment, one natural gradient-based actor–critic framework is proposed to characterize edge network dynamics, and meanwhile facilitates the training of neural networks to the global optimum. Next, to lower the size of action space, we follow the principle that a subproblem is embedded into each state–action pair’s critic to solve the reward function, and then utilize both the ℓp(0<p<1) norm-based successive convex approximation (SCA) and proximal center-based dual decomposition to approach the global optimum and accelerate the convergence. Finally, numerical results are used to validate proposed actor–critic approach, showing that the communication resource management deserves special attentions in the SFC deployment in the edge of 6G wireless systems.