Zero-forcing Algorithm Research Articles

Hybrid Beamforming for mm-Wave Massive MIMO Systems with Partially Connected RF Architecture

To satisfy the capacity requirements of future mobile systems, under-utilized millimeter wave frequencies can be efficiently exploited by employing massive multiple input-multiple output (MIMO) technology with highly directive beamforming. Hybrid analog-digital beamforming has been recognised as a promising approach for large-scale MIMO implementations with a reduced number of costly and power-hungry radio frequency (RF) chains. In comparison to fully connected architecture, hybrid beamforming (HBF) with partially connected RF architecture is particularly appealing for the practical implementation due to less complex RF power division and combining networks. In this paper, we first formulate single- and multi-user rate maximization problems as weighted minimum mean square error (WMMSE) and derive solutions for hybrid beamformers using alternating optimization. The algorithms are designed for the full-array- and sub-array-based processing strategies of partially connected HBF architecture. In addition, we propose lower complexity sub-array-based zero-forcing algorithms. The performance of the proposed algorithms is evaluated in two different channel models, a simple geometric model and a realistic statistical model. The performance results of the WMMSE HBF algorithms are meant to reveal the potential of partially connected HBF and serve as upper bounds for lower complexity methods. Numerical results imply that properly designed partially connected HBF has the potential to provide an good compromise between hardware complexity and system performance in comparison to fully digital beamforming.

Numtrical Evaluation of Optimal Precoding Algorithm and Zero Forcing Precoding in MU-MISO Channel with Channel Aging

In paper the numerical investigation of the impact of delayed channel state information (CSI) due to user movement and caused channel aging on the performance of multiuser precoder in downlink MISO system. The time variant CSI is obtained by the least squares channel estimation. We consider Zero Forcing algorithm and numerical optimization based solution of calculating precoder vectors maximizimg sum rate of multiuser system. For numerical simulation the QuaDRiGa channel model reflecting the real propagation conditions for moving users is used. The obtained performance of multiuser Zero Forcing and optimization based beamforming in spatially correlated channel are compared based on the empirical cumulative density function of the sum rate of multiple users.

Full-Duplex MIMO Relay-Assisted Interference Alignment Algorithm in K-user Interference Channels

In this paper, we investigate the transceiver design schemes for the full-duplex multiple-input multiple-output relay-assisted K-user single-input multiple-output interference channels. Firstly, we propose an iterative optimized reference vector for IA (IORV-IA) algorithm in the perfect channel state information (CSI) scenario. The proposed IORV-IA algorithm not only achieves the alignment of interference signals at each receiver, but also iteratively optimizes the IA reference vector by orthogonalizing the directions of the interference signals and the desired signal. With the optimized IA reference vector, the relay processing matrix and the receiving filter vectors are designed to further improve the system performance. Considering that the relay cannot obtain perfect CSIs in practice due to many factors, and the performance of the IA scheme is very sensitive to this error. Furthermore, we propose a robust transceiver design scheme based on mean square error (MSE) in the imperfect CSI scenario, which minimizes the sum of MSEs in the worst case through iteration. The proposed algorithms are evaluated in terms of the average sum rate and bit error rate performance and the simulation results show the advantages of the proposed algorithms over existing centralized IA and centralized zero-forcing algorithms.

Performance Evaluation of Hybrid Precoder Design for Multi-User Massive MIMO Systems with Low-Resolution ADCs/DACs

This paper presents a comprehensive analysis and design of a hybrid precoding system tailored for mmWave multi-user massive MIMO systems in both downlink and uplink scenarios. The proposed system employs a two-stage precoding approach, incorporating UQ and NUQ techniques, along with low-resolution DACs in downlink and ADCs in uplink to address hardware limitations. The system considers Zero Forcing and Minimum Mean Square Error algorithms as digital precoding methods for the uplink scenario, while exploring the impact of different DAC resolutions on system performance. Extensive simulations reveal that the proposed system surpasses conventional analog beamforming methods, particularly in multi-user scenarios involving inter-user interference. In downlink, the system demonstrates a trade-off between SE and EE, achieving higher Energy Efficiency with NUQ. In uplink, NUQ and UQ converters exhibit similar performance trends regardless of the chosen combiner algorithm. The proposed system attains enhanced Spectral and Energy Efficiency while maintaining reduced complexity and overhead. The study significantly contributes to the advancement of efficient and effective mmWave multi-user massive MIMO systems by providing a thorough analysis of various quantization schemes and precoding techniques. The findings of this research are expected to aid in the optimization of 5G and beyond technologies, particularly in high-density deployment scenarios.

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.

Efficient Hybrid Iterative Method for Signal Detection in Massive MIMO Uplink System over AWGN Channel

Massive multiple input multiple output (massive MIMO) is a key technology in fifth-generation (5G) and beyond fifth-generation (B5G) networks. It improves performance metrics such as gain, energy efficiency, spectral efficiency, and bit error rate (BER). Because of the large number of users and antennas, sophisticated processing is required to detect the transmitted message signal. One of the challenges in massive MIMO systems is transmitted message signal detection. To respond to these challenges, several detection algorithms have been developed, including minimum mean squared error (MMSE), zero forcing (ZF), matched filter (MF), conjugate-gradient (CG), gauss-seidel (GS), and optimized coordinate descent (OCD). Although the ZF and MMSE algorithms perform well, their computational complexity is high due to direct matrix inversion. When the number of users is much lower than the number of antennas, the MF algorithm performs well. However, as the number of users increases, the performance of the MF algorithm degrades. Although the OCD, CG, and GS algorithms have less computational complexity than the MMSE algorithm, they perform poorly in comparison. To address and resolve the shortcomings of existing methods, an efficient iterative algorithm has been proposed in this manuscript, which is a hybrid method possessing the combination of MMSE with the alternating direction method of multipliers (ADMM) technique and Gauss-Seidel method. The initial vector has a large influence on the performance, complexity, and convergence rate of such iterative algorithms. The proposed detector’s initial solution is determined using the diagonal matrix and MMSE with the ADMM technique. The proposed algorithm’s performance and complexity are compared with existing algorithms based on BER and the real number of multiplications, respectively. The numerical results revealed that the proposed algorithm achieves the desired performance with a small number of iterations and a significant reduction in computational complexity. At 8QAM, SNR = 20 dB, 80 × 120 massive MIMO antenna configuration, and n = 2, the percentage performance improvement of the proposed detector from the GS detector is 99.82%. At 32QAM, SNR = 25 dB, 120 × 180 antenna configuration, and n = 5, performance improvement of the proposed detector is 99.89%. At 64QAM, SNR = 28 dB, 80 × 120 antenna configuration, and n = 3, performance improvement of the proposed detector is 99.93%.

Hybrid Precoding-Based Millimeter Wave Massive MIMO-NOMA Systems

A symmetry-based hybrid precoder and combiner is a high spectral efficiency structure in millimeter-wave (mmWave) massive multiple-input multiple-output (mMIMO) non-orthogonal multiple access (NOMA) system. To improve the spectral efficiency of the mmWave mMIMO-NOMA system, we first propose a user grouping scheme to suppress the strong inter-user interference caused by NOMA, then the hybrid precoder based on user channel alignment and the zero-forcing algorithm is constructed to further improve the signal-to-interference-plus-noise ratio (SINR) of the receiver. Subsequently, the non-convex spectral efficiency optimization problem is transformed into a convex optimization problem of inter-cluster power allocation and the closed-form solution for the optimal power under the minimum rate constraint is obtained by solving the KKT condition to further improve the spectral efficiency. The simulation results show that the proposed scheme can achieve higher spectral efficiency compared to orthogonal multiple access (OMA), fixed power allocation (FPA), K-means, and cluster head selection (CHS).

Low-Complexity Joint Phase Adjustment and Receive Beamforming for Directional Modulation Networks via IRS

Intelligent reflecting surface (IRS) is a revolutionary and low-cost technology for boosting the spectrum and energy efficiencies in future wireless communication network. In order to create controllable multipath transmission in the conventional line-of-sight (LOS) wireless communication environment, an IRS-aided directional modulation (DM) network is considered. In this paper, to improve the transmission security of the system and maximize the receive power sum (Max-RPS), two alternately optimizing schemes of jointly designing receive beamforming (RBF) vectors and IRS phase shift matrix (PSM) are proposed: Max-RPS using general alternating optimization (Max-RPS-GAO) algorithm and Max-RPS using zero-forcing (Max-RPS-ZF) algorithm. Simulation results show that, compared with the no-IRS-assisted scheme and no-PSM optimization scheme, the proposed IRS-assisted Max-RPS-GAO method and Max-RPS-ZF method can significantly improve the secrecy rate (SR) performance of the DM system. Moreover, compared with the Max-RPS-GAO method, the proposed Max-RPS-ZF method has a faster convergence speed and a certain lower computational complexity.

Optimality of Linear MIMO Detection for 5G Systems via 1-Opt Local Search

Multiple input multiple output (MIMO) symbol detection problem belongs to non-deterministic polynomial acceptable hard combinatorial optimization (CO) class. One of the key trials in design of MIMO scheme is to develop a low complexity detection algorithm without much compromise in performance. Detection approaches proposed in the literature can be split into non-linear and linear algorithms. Vertical Bell-Labs Layered Space Time (V-BLAST) and Sphere Decoder (SD) are non-linear methods used for extracting transmitted data; whereas, Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) detections are comparatively in complex and effectual linear techniques. In this work, the heuristic 1-Opt local search method used for solving computationally hard combinatorial optimization problems is applied to the ZF and MMSE detection algorithms. First, simple MIMO decoding using ZF and MMSE is accomplished to find the estimated symbol then the transmitted symbol is calculated using the heuristic 1-opt approach by means of the estimated symbol. Simulation results demonstrate that 1-opt search when applied to the ZF and MMSE displays better bit error rate (BER) performance than the simple ZF and MMSE detectors. It is also verified through simulations that the proposed 1-Opt based detectors display better BER performance as compared to the complex nonlinear VBLAST and SD at considerably reduced complexity. Hence, the proposed detectors are appropriate for effective hardware implementations.

Principle of Computation Power Optimization in Millimeter Wave Massive MIMO Systems

The computation power of baseband units (BBUs) is a major source of power consumption in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with a large number of users due to complex signal processing. The effective reduction of computation power is critical for improving system energy efficiency. In this paper, the principle of reducing the computation power of BBUs is first investigated in mmWave massive MIMO systems with a hybrid precoding structure. A recursive constraint in decomposing the baseband precoding matrix is derived for reducing the computation power of hybrid precoding systems. Furthermore, the optimal number of sub-matrices minimizing the maximum error in decomposing the baseband precoding matrix is obtained. Based on the proposed principle, consisting of the recursive constraint and the optimal number of sub-matrices, a fast Monte Carlo baseband precoding (FMCBP) algorithm is developed to reduce the computation power of BBUs and improve system energy efficiency. Simulation results show that the total transmission rate and energy efficiency of mmWave systems are coupled with the computation power of BBUs, based on the FMCBP algorithm. Moreover, the FMCBP algorithm maximally improves the energy efficiency of multi-user mmWave massive MIMO communication systems by 124 percent, compared with the conventional equivalent zero-forcing algorithm.

Equalization-Based Beamforming for Secure Multicasting in Multicast Wiretap Channels

In this paper, a beamforming scheme is proposed to maximize a secrecy multicast rate (SMR) in the multicast wiretap channel, in which the multiple unauthorized users overhear the multicast messages. The SMR is formulated by the ratio of multicast rate and information leakage in the numerator and denominator, respectively. By exploiting the SMR structure, we propose three doubly equalizing beamforming approaches: i) zero-forcing algorithm, ii) bottom-first algorithm, and iii) top-first algorithm. Depending on the algorithms, either the legitimate user channels or the unauthorized user channels are fully equalized, and the other set of channels are then equalized through a least-squares approach. While the zero-forcing algorithm optimizes the strength of legitimate user channels, the bottom-first and the top-first algorithms find the balance between the strengths of legitimate user channels and unauthorized user channels. The top-first algorithm encompasses the bottom-first algorithm, where the bottom-first algorithm encompasses the zero-forcing algorithm. Consequently, the proposed top-first algorithm outperforms the other two algorithms. The proposed top-first algorithm improves SMR by effectively preventing overhearing while sustaining almost maximum multicast rate and provide comparable SMR to the multicast rate obtained without unauthorized users. These results are verified by simulation.

Low-complexity soft-output signal detector for massive MIMO with higher order QAM constellations

As the number of base station (BS) antennas in massive multiple-input multiple-output (MIMO) systems is dramatically increased, linear detection methods are able to achieve the near optimal performance at the expense of performing the complicated matrix inversion of a high dimensional matrix, which makes hardware implementation infeasible. Meanwhile, the straightforward application of the hard symbol-to-bit decision algorithm yields a very poor performance for the higher order quadrature amplitude modulation (QAM) that is widely adopted as an efficient tool to accommodate high demand of data throughput in modern wireless systems. In this work, we propose a low-complexity soft-output signal detector for multiuser massive MIMO communication systems employing Gray-coded higher order QAM with square constellations. In the proposed detector, the two-dimensional double successive projection (2D-DSP) algorithm is utilized to iteratively realize zero-forcing (ZF) algorithm for multiuser signal recovery, which circumvents the matrix inverse operation. Moreover, a simplified implementation of Max-Log-MAP algorithm is developed to calculate log likelihood ratios (LLRs) for soft-input channel decoding by fully exploiting the bit-flipping property of Gray-coded modulation scheme along with the utilization of the channel hardening property of the massive MIMO systems. Numerical results show that the proposed soft-output detector provides a relatively good tradeoff between the complexity and performance compared with several existing detectors, and approaches the performance of the ZF algorithm with only 3 iterations.

Relay Cooperative Beamforming Algorithm Based on Probabilistic Constraint in SWIPT Secrecy Networks

We explore physical layer security of simultaneous wireless information and power transfer (SWIPT) relay network in this paper. Modeling channel error between relay and eavesdroppers (Eves) as random channel state information (CSI) error, we present an algorithm to optimize secret rate of SWIPT in the constraints of relay forward power, receiver signal-to-interference-plus-noise ratio (SINR) and Eves SINR. A slack variable is introduced to decompose original non-convex problem into upper and lower sub-problems, meanwhile, Bernstein-type inequality is used to convert probability constraint of lower sub-problems to linear matrix inequality constraints. Simulation experiments show that the proposed algorithm obtains higher secret rate than that of zero-forcing algorithm and worst-case algorithm.

Trade‐offs between the quality of service, computational cost and cooling complexity in interference‐dominated multi‐user SDMA systems

The future fifth generation (5G) systems will aim to design low-cost phased array base station antenna systems at mm-waves for simultaneous multiple beamforming with enhanced spatial multiplexing, limited interference, acceptable power consumption, suitable processing complexity, and passive cooling. In this study, a multi-user space division multiple access (SDMA) model is developed to investigate the trade-off between the quality of service (QoS), computational complexity in beamforming and cooling requirements for various use cases, and a number of users. The QoS at the user ends is rated by assessing the statistical signal-to-interference-plus-noise ratios (SINRs). Two beamforming algorithms, namely conjugate beamforming (CB) and zero-forcing (ZF), are considered and compared. Depending on the deployment scenario, rotated and optimised array layouts are proposed to be used in CB with the least computational complexity while providing relatively good QoS. Different reduced-complexity ZF algorithms are introduced as a compromise between the SINR performance and computational burden. The impact of the number of simultaneously served users on the thermal management in active integrated 5G base station antenna arrays is investigated as well.

4 × 4 MIMO fiber-wireless transmission based on an integrated four-channel directly modulated optical transceiver

In this paper, an integrated compact four-channel directly modulated analog optical transceiver is proposed and fabricated. The 3 dB bandwidth of this optical transceiver exceeds 20 GHz, and the measured spurious-free dynamic range is up to 91.2 dB·Hz2/3. The optical coupling efficiency (CE) is improved by using a precise submicron alignment technique for lens coupling in a transmitter optical subassembly, and the highest CE is achieved when the oblique angle of the arrayed waveguide grating using a silica-based planar lightwave circuit (AWG-PLC) in receiver optical sub assembly is set to 42°. Based on the proposed optical transceiver, we have experimentally demonstrated a 6.624 Gbit/s 4×4 multi-input multioutput (MIMO) 16-quadrature amplitude modulation orthogonal frequency division multiplexing (16QAM-OFDM) radio signal over 15.5 km standard single mode fiber, together with 1.2 m wireless transmission in both an uplink and a downlink. To cope with the channel interference and noise of the fiber-wireless transmission system, a low-complexity MIMO demodulation algorithm based on lattice reduction zero-forcing (LR-ZF) is designed. In our experiment, 1.6 dB power penalty is achieved by using the proposed LR-ZF algorithm, compared to the commonly used zero-forcing algorithm. Moreover, this LR-ZF algorithm has much less complexity than the optimal maximum-likelihood sequence estimation (MLSE) at a given transmission performance. These results not only demonstrate the feasibility of the integrated optical transceiver for MIMO fiber-wireless application but also validate that the proposed LR-ZF algorithm is effective to eliminate the interference for hybrid fiber-wireless transmission.

Hybrid precoding with phase shifter reduction for 5G massive antenna multi‐user systems in millimetre wave

In this study, the performances of commonly used precoding schemes are evaluated based on channel measurements carried out at 28 GHz in a railway station for a massive antenna system configuration. And a hybrid precoding algorithm for a fifth generation (5G) multi-user antenna system is proposed and its performance is evaluated based on real measured channels. Specifically, An upper bound for achievable sum-rate of phased zero forcing (PZF) algorithm is derived and a precoding technique by reduction of phase shifters (PSs) named reduced-PZF (RPZF) is proposed, which can obviously reduce power consumption in hybrid precoding systems. In addition, the authors give the closed-form expression for achievable sum-rate when RPZF is used. There are no requirements in the authors’ proposed scheme with complicated matrix decomposition and optimisation techniques. The simulation results show that it is possible to reduce 30 and 50% of the PSs by using the proposed hybrid precoder with better system performance in the line-of-sight (LoS) and non-LoS scenarios, respectively. In addition, the digital PSs with 3 bits low resolution can achieve the similar performance when using analogue ones.

Error Rate Analysis of ZF and MMSE Decoders for Massive Multi Cell MIMO Systems in Impulsive Noise Channels

In wireless channels, Non-Gaussian noise is one of the most common noise models that is observed. This type of noise has a severe impact on wireless systems with linear and multiuser detection devices. In this paper, We study the performance of zero forcing (ZF) and minimum mean square error (MMSE) ZF detection methods in Impulsive multi-cell MIMO channels. We start by showing the Bit Error Rate performance in non-Gaussian channels for ZF Detection, then we extend the derivations for MMSE ZF system. We clearly show the lower and upper bound derivations and verify it through simulations. The sum rate analysis for this case is also examined. Finally, we address the ZF matrix inversion complexity problem, and propose a simple ZF algorithm that does not necessitate the matrix inversion. We then investigate the convergence of such a detector and look at the Symbol Error rate SER performance through simulation again.

Hybrid Beamforming Design for mmWave Joint Unicast and Multicast Transmission

In this letter, we investigate the beamforming design for millimeter-wave (mmWave) joint unicast and multicast (JUM) systems, in which the common and private signals are transmitted simultaneously. Due to the hardware limitation, the conventional fully digital beamforming methods are infeasible. We propose a suboptimal low-complexity hybrid zero-forcing (ZF) beamforming scheme for the mmWave JUM systems. The analog precoder and combiner are first optimized to maximize the effective channel gains. The ZF algorithm is then used to decide the unicast beamforming directions for cancelling the inter-user interference so that the optimization problem is reduced. With the unicast beamforming directions, the unicast power allocation and multicast beamformer are finally optimized by employing successive convex approximation (SCA) iteratively. The simulation results demonstrate that the sum-rate of the proposed algorithm is slightly inferior to the fully digital beamforming algorithm, but outperforms the orthogonal multiple access scheme.

Performance analysis of a LDPC coded OAM-based UCA FSO system exploring linear equalization with channel estimation over atmospheric turbulence

A low-density parity-check (LDPC) coded orbital angular momentum (OAM)-based uniform circular array (UCA) free space optical (FSO) system exploring linear equalization is investigated with channel estimation over the atmospheric turbulence fading channels. On the basis of the proposed system model, the least square (LS) channel estimator is adopted to obtain the channel state information (CSI) of this OAM-FSO system. Then, the average bit error ratio (ABER) expressions with MP-ary phase shift keying (MPPSK) modulation scheme are derived by ensemble average with the aid of the large number theorem. Besides, LDPC codes are applied in the simulation to improve the ABER performance, and subsequently the probability expressions of the estimated signals with zero forcing (ZF) and minimum mean squared error (MMSE) equalizers for LDPC decoder are achieved, respectively. Results show that the ABER performance of the OAM-FSO system degrades with increasing turbulence strengths. With ZF and MMSE equalization algorithms, the ABER performance is significantly enhanced with an increase in the number of receive antennas for considerable diversity gain. Furthermore, a substantial coding gain can be attained by LDPC codes in this OAM-FSO system, especially under strong turbulence condition. This work will benefit the research and development of OAM-FSO system.

Interference mitigation and capacity enhancement using constraint field of view ADR in downlink VLC channel

The continued increase in several mobile applications forces to replace existing limited spectrum indoor radio-frequency wireless connections with high-speed ones. Visible light communication (VLC) is a promising license free indoor wireless technology that could offer high-speed connections. However, both co-channel interference (CCI) from more neighbour transmitters and inter-symbol interferences (ISI) from multipath reflections limit the performance of VLC downlink channel. In this study, a constraint field of view angular diversity receiver (CFOV-ADR) is proposed to mitigate these limitations. By optimising the photodetector's (PD) field of view (FOV) angle, the line of sight CCI could be totally eliminated and the ISI could be significantly reduced. The optimal range for FOV angle is calculated in a typical indoor scenario. Furthermore, the zero-forcing (ZF) algorithm is applied to the conventional ADR (ADR-ZF) which can significantly eliminate the ISI components. The received optical signal-to-interference-plus-noise ratio (SINR) is tested at various room positions. The simulation results show that the proposed CFOV-ADR can achieve higher SINR performance than single receiver, conventional ADR, and ADR-ZF at all positions and orientations.