Large Number Of Antenna Elements Research Articles

Synthesis of Antenna Array Radiation Pattern at Large Scanning Angles Using Genetic Algorithm

At present, in most modern communication systems, for example, in modern satellite terminals, the use of scanning beam antennas, i. e. antenna arrays is assumed. At the same time, at large scanning angles, the side lobe level (SLL) increases strongly and decrease in the gain is observed. In this regard, the problem of finding a procedure for synthesizing an amplitude-phase distribution (APD) with low SLL and high gain (G) at large scanning angles comes up. One of the ways to reduce SLL and compensate for the decrease in G is to synthesize the optimal APD (in terms of the maximum G and minimum SLL) using optimization algorithms. At the same time, taking into account the characteristics of the radiation pattern of the array emitters requires numerical electrodynamic calculation. The goal of this paper is to develop a procedure for the synthesis of APD with low SLL for linear and rectangular antenna arrays at various, including large, scanning angles and compensation for G reduction using a genetic algorithm and numerical electrodynamic calculation. The methods for studying the characteristics of antenna radiators are numerical electrodynamic modeling by the finite element method (FEM) in Ansys HFSS computer-aided design system and optimization of the APD for a given radiation pattern(RP) by a random search method using partial diagrams of antenna elements. The novelty is the combination of accurate numerical electrodynamic calculation of the RP of antenna elements and optimization search for APD for the synthesis of the required RP using partial diagrams. As a result, a procedure for APD synthesis of linear and uniform rectangular equidistant (for example, 8- and 64-element) antenna arrays has been developed, taking into account the exact electrodynamic characteristics of antenna elements and their mutual resistance. Radiation patterns were obtained taking into account the effect of neighboring elements, with the help of which, using a genetic algorithm, APDs on emitters were found at different scanning angles. The change in SLL and G of the antenna array is analyzed at different scanning angles using different APDs. The proposed algorithm allows to synthesize APD for a RP with low SLL and high G at scanning angles up to 40° for linear antenna array and up to 80° in the case of a uniform rectangular antenna array. The results of this work are relevant in the problems of radiation pattern synthesis, since the proposed solution provides a significant gain in the radiation pattern synthesis rate of APD of linear and rectangular antenna arrays, especially for systems with a large number of antenna elements. At the same time, it is possible to maintain a high G at large scanning angles, and achieve a significant reduction of SLL.

Investigation of mutual coupling coefficients in dual-polarized antenna arrays

Background. Antenna arrays are widely used in various fields of radio engineering, such as radio and telecommunications, satellite communication systems, etc. One of the important characteristics of an antenna array is its radiation pattern. The estimation of impedance matrices, scattering matrices, and partial radiation patterns is usually performed based on the results of numerical electrodynamic modelling. In the case of a large number of antenna elements, such modelling and optimization of the array requires significant time.
 Aim. To investigate the mutual coupling between dual- polarised antenna elements included in a linear antenna array.
 Methods. Modelling of antenna arrays based on cross-dipole elements was performed using methods of electrodynamic modelling software. The study of the mutual coupling of antenna elements in the antenna array and verification of the developed mathematical model were carried out by numerical methods.
 Results. A physical interpretation of that there is no almost interaction between the elements operating in orthogonal polarizations, and the coefficients of mutual coupling decrease with increasing distance between antenna elements is given. Proposed a simplified model of mutual coupling, which reduces the computational complexity of the problem of determining the mutual coupling matrices.
 Conclusion. It is developed a mathematical technique that allows to calculate the characteristics of antenna arrays with a large number of antenna elements, meanwhile electrodynamic modelling is carried out only for an isolated antenna element and a two-element array.

Analysis of MIMO methods for 5G and subsequent technologies: advantages and disadvantages

Formulation of the problem. The global bandwidth shortage in the wireless communications sector has prompted the study and research of wireless access technology, known as mass Multiple Input/output (MIMO) technology. Mass MIMO is one of the key technologies for next-generation networks, which combines antennas in both the transmitter and receiver to provide high spectral and energy efficiency using relatively simple processing. Gaining a better understanding of the massive MIMO system to overcome the fundamental challenges of this technology is vital for the successful deployment of 5G and higher networks to implement various intelligent sensor system applications. Thus, in this paper, fully digital, analog and hybrid structures are analyzed and the method of multilevel massive MIMO transmission is described in detail. Purpose. Analysis of the main technologies needed to meet the demand for data transmission expected for 5G and 6G networks, with the allocation of transmission methods necessary for the mass implementation of MIMO. Practical significance. Evaluation of the MIMO system bandwidth, hardware and computational complexity, as well as energy efficiency, it is shown that massive MIMO circuits can rely on asymptotic linear independence when designing signal processing, given the large number of antennas used. Classical MIMO methods are not able to meet the technical requirements, so hybrid architectures use a combination of analog and digital areas to use the spatial resolution provided by a large number of antenna elements, but at the same time the number of energy-consuming and expensive radio frequency circuits remains within reasonable limits, and computational complexity is controlled. It becomes clear that there is no single structure/algorithm that would provide the best compromise between complexity and performance in all possible scenarios, rather, there is a need to adapt them to the characteristics of the application and channel when designing the system. As for optimizing the energy efficiency of the RF power supply, this is achievable using solutions such as multilayer massive MIMO.

CUDA-Optimized GPU Acceleration of 3GPP 3D Channel Model Simulations for 5G Network Planning

The simulation of massive multiple-input multiple-output (MIMO) channel models is becoming increasingly important for testing and validation of fifth-generation new radio (5G NR) wireless networks and beyond. However, simulation performance tends to be limited when modeling a large number of antenna elements combined with a complex and realistic representation of propagation conditions. In this paper, we propose an efficient implementation of a 3rd Generation Partnership Project (3GPP) three-dimensional (3D) channel model, specifically designed for graphics processing unit (GPU) platforms, with the goal of minimizing the computational time required for channel simulation. The channel model is highly parameterized to encompass a wide range of configurations required for real-world optimized 5G NR network deployments. We use several compute unified device architecture (CUDA)-based optimization techniques to exploit the parallelism and memory hierarchy of the GPU. Experimental data show that the developed system achieves an overall speedup of about 240× compared to the original C++ model executed on an Intel processor. Compared to a design previously accelerated on a datacenter-class field programmable gate array (FPGA), the GPU design has a 33.3% higher single-precision performance but a 7.5% higher power consumption. The proposed GPU accelerator can provide fast and accurate channel simulations for 5G NR network planning and optimization.

A Comparison of Faulty Antenna Detection Methodologies in Planar Array

Broadcasting, radar, sonar and space telecommunication systems use phased arrays to produce directed signals to be transmitted at the desired angle. This system requires a large number of antenna elements. The presence of faulty element(s) in an array causes asymmetry, which results in a deformed radiation pattern with higher sidelobe levels. Higher sidelobe levels indicate waste of energy by transmitting and receiving signals in unwanted directions. Hence, it is important to develop a method that detects faulty elements and corrects the radiation pattern. To correct the failed radiation pattern, failed elements in an array must be identified first. There have been various studies conducted on linear array failed radiation pattern correction and the finding of faulty elements, but investigation on the planar array is limited. Further, the optimization suggested for linear arrays does not necessarily work for the planar array. In this study, planar array faulty antenna detection was developed with pattern search (PS), simulated annealing (SA), and particle swarm optimization (PSO) methods by reducing the Signal to Noise Ratio (SNR) as the objective function. The analysis was varied for 8 × 8 and 6 × 6 planar arrays with different types of failures. The results were compared to find the best method to identify the faulty element’s location in a planar array. The pattern search method produced outstanding results in finding the faulty element’s locations by providing 100% accuracy for all types of failure, while other methods failed to do the same.

Energy Efficient Train-Ground mmWave Mobile Relay System for High Speed Railways

The rapid development of high-speed railways (HSRs) puts forward high requirements on the corresponding communication system. Millimeter wave (mmWave) can be a promising solution due to its wide bandwidth, narrow beams, and rich spectrum resources. However, with the large number of antenna elements employed, energy-efficient solutions at mmWave frequencies are in great demand. Based on a mmWave HSR communication system with multiple mobile relays (MRs) on top of the train, a dynamic power-control scheme for train-ground communications is proposed. The scheme follows the regular movement characteristics of high-speed trains and considers three phases of train movement: the train enters the cell, all MRs are covered in the cell, and the train leaves the cell. The transmit power is further refined according to the number of MRs in the cell and the distance between the train and the remote radio head. By minimizing energy consumption under the constraints of the transmitted data and transmit power budget, the transmit power is allocated to multiple MRs through the multiplier punitive function-based algorithm. Comprehensive simulation results, where the velocity estimation error is taken into account, are provided to demonstrate the effectiveness of the proposed scheme over several baseline schemes.

Implementation of small cell antenna based massive MIMO system for high spectrum and energy efficiencies

In order to achieve high data rates (DR) in the fifth generation (5G), Massive Multiple Input Multiple Output (m-MIMO) systems must be altered to boost spectral efficiency. These systems must be used in conjunction with Small Cell Antennas (SCA). When compared to a number of User Terminals (UTs) provided in the same time-frequency resource without significant inter-user interference, m-MIMO enables a significant increase in spectrum efficiency. This is accomplished by deploying a large number of antenna elements at the base station, anywhere from tens to hundreds. The evolution of SC technology has resulted in decreased latency, decreased energy consumption, and increased data rates, all of which are necessary conditions for the deployment of 5G. In this study, we construct an m-MIMO system with SCAs that takes into account partial channel state information. We do this by reaching DR in the lower limit by repeating pilot sequences in time division duplex. In this way, we are able to achieve our goal (TDD). Either implementing massive MIMO at the base stations (BSs) or overlaying SCAs on top of the infrastructure already in place may help improve the energy efficiency of cellular networks. We present some intriguing results that demonstrate that combining Massive MIMO with small cells may be able to drastically cut total power usage. Beam-forming techniques with a low level of complexity, such as the proposed multi-flow RZF beam-forming, also have the potential to

Low-complexity soft-output signal detector based on AI-SSOR preconditioned conjugate gradient method over massive MIMO correlated channel

Massive multiple-input multiple-output (MIMO) techniques with a large number of antenna elements at base station (BS) have been proved as an alternative to provide potential opportunity to increase the spectrum and energy efficiency. However, in the system, there generally exists a spatial correlation effect due to insufficient antenna elements spacing and/or the lack of rich scattering at BS. The minimum mean square error (MMSE) method performs signal detection at the expense of large-scale matrix inversion operation. Thus, the conjugate gradient (CG) method has received a lot of attentions to realize the MMSE detection efficiently. Unfortunately, this efficiency can be compromised due to the ill-conditioned equalization matrix of MMSE method over the correlated channel environments. Moreover, the hard output signal detection exhibits a sharply degradation in performance for higher-order quadrature amplitude modulation (QAM). Therefore, the modern communication systems use the soft-output information, i.e., log-likelihood ratio (LLR) along with the forward error-correcting code (FEC) to achieve satisfactory performance. The LLR computation along with a higher-order QAM remains challenging due to the exhaustive search of symbol in the modulation constellation. In this paper, a low-complexity soft-output signal detector based on approximate inverse symmetric successive over-relaxation preconditioned conjugate gradient (AI-SSOR-CG-SOD) method is proposed to realize MMSE method detection for uplink multiuser massive MIMO correlated channel. In the proposed method, a new preconditioner, an AI-SSOR, which is based on the Neumann series approximation of the inverse of the conventional SSOR preconditioner is firstly developed to handle ill-conditioned matrix, and then incorporated with CG method to improve the convergence rate and performance. According to the characteristic of the Gray-coding that adjacent symbols in the constellation set have only one different bit, the constellation set is divided multiple times based on the bits of the inphase and the quadrature components of the symbol, which reduces the complexity of the LLR computation of the transmitted bits by avoiding the exhaustive search process. Simulation results show that the AI-SSOR preconditioner is robust against spatial correlation effect, and the proposed detector converges at 3 iterations. Simulation results also show that the proposed detector achieves a better trade-off between the complexity and the performance compared to other existing detectors.

On Computational Offloading in Massive MIMO-Enabled Next-Generation Mobile Edge Computing

Next-generation wireless communication networks are expected to support massive connectivity with high data rate, low power consumption, and computational latency. However, it can significantly enhance the existing network complexity, which results in high latency. To ease this situation, mobile edge cloud and massive multiple input and multiple output (MIMO) have recently emerged as the effective solutions. Mobile edge cloud has the ability to overcome the constraints of low power and finite computational resources in next-generation communication systems by allowing devices to offload their extensive computation to maximize the computation rate. On the other hand, MIMO can enhance network spectral efficiency by using large number of antenna elements. The integration of mobile edge cloud with massive MIMO also helps to increase the energy efficiency of the devices; as a result, more bits are computed with minimal energy consumption. In this work, a mathematical model is formulated by considering the devices’ energy constraint, which is nonconvex in nature. Following that, to overcome this, we transformed the original optimization problem using the first approximation method and solved the partial offloading schemes. Results reveal that the proposed scheme outperforms the others by considering computational rate as a performance matrix.

Design of Channel Estimation for Hybrid Beamforming Millimeter-Wave Systems in the Presence of Beam Squint

In this article, channel estimation for millimeter-wave massive multiple-input–multiple-output (MIMO) systems with hybrid beamforming is considered. With a large number of antenna elements, a progressive time delay across antenna elements incurs a change in the beam direction as a function of subcarriers in an orthogonal frequency-division multiplexing system. Considering the difference in delay across the entire array, a new channel estimation framework is proposed by using a maximum likelihood criterion as a function of the analog training beam and pilot subcarrier assignment. The resulting design achieves asymptotic orthogonality among the channel paths and minimizes the mean squared error. An extension of the proposed design to a uniform planar array is discussed. The Cramér–Rao lower bound for joint channel estimation with hybrid beamforming is derived to verify the effectiveness of the proposed design.

Performance analysis of sparse array based massive MIMO via joint convex optimization

Massive multiple-input multiple-output (MIMO) technology enables higher data rate transmission in the future mobile communications. However, exploiting a large number of antenna elements at base station (BS) makes effective implementation of massive MIMO challenging, due to the size and weight limits of the masssive MIMO that are located on each BS. Therefore, in order to miniaturize the massive MIMO, it is crucial to reduce the number of antenna elements via effective methods such as sparse array synthesis. In this paper, a multiple-pattern synthesis is considered towards convex optimization (CO). The joint convex optimization (JCO) based synthesis is proposed to construct a codebook for beamforming. Then, a criterion containing multiple constraints is developed, in which the sparse array is required to full-fill all constraints. Finally, extensive evaluations are performed under realistic simulation settings. The results show that with the same number of antenna elements, sparse array using the proposed JCO-based synthesis outperforms not only the uniform array, but also the sparse array with the existing CO-based synthesis method. Furthermore, with a half of the number of antenna elements that on the uniform array, the performance of the JCO-based sparse array approaches to that of the uniform array.

Low-Complexity and Robust Framework of Precoding for Multi-Panel Massive MIMO

Massive multiple-input multiple-output (m-MIMO) is used to improve the robustness of data transmission and high sum spectral efficiency in 5G systems. For 5G New Radio (NR) systems need to be designed to reduce cost and complexity, most notably hybrid analog-digital beamforming with large-scale antenna array which has become a major research target. In the downlink transmission, we propose a robust and low-complexity framework of precoding design to implement hybrid beamforming (BF) of large antenna arrays without limitation on the size of the antenna. Furthermore, a large number of antenna elements can be coupled into multiple panels m-MIMO for the purpose of reducing costs and saving power. This study proposes to use both azimuth and elevation angles parameters to provide low complexity adaptive beam control in panels m-MIMO system. In contrast to existing works, that aim to eliminate inter-user interference, this work is distinguished by adopting polarization function and space-time block code to the m-MIMO antenna arrays. We also propose a new multi-panel codebook design correspondingly with control parameters. The performance of the proposed framework is analysed with state-of-the-art research comparisons. To this end, the important factor of beamforming which is the Error Vector Magnitude (EVM) will be analyzed and simulated.

A Transmitter Design for the Multi-beam CC-OFDM Azimuth Scanning MIMO Radar

A conventional phased array radar provides a high gain by transmitting coherent signals over a large number of antenna elements. However, it does not provide a full time-on-target because it produces beams that scan the whole angular view of the radar. This paper describes an implementation of circulating codes (CC) in azimuth scanning MIMO radar that adopts OFDM waveform. The CC MIMO technique can produce a beam toward a certain angle by applying an appropriate delay difference between the MIMO antennas that transmit the same waveform across the azimuth. The adoption of OFDM waveform in the CC MIMO radar, gives the possibility to apply the phase difference for beamforming in the frequency domain of the OFDM signals. CC-OFDM MIMO with spectrum division into sub-bands and use of orthogonal codes, allow for simultaneous transmission of orthogonal OFDM symbols that generate orthogonal beams toward different angles. This strategy makes it possible for the radar system to have multiple and simultaneous beamforming to provide a full-time coverage. Furthermore, the transmission of a series of orthogonal OFDM symbols in each beam enables the detection of long-range targets. By taking as an example the design of long-range surveillance radar, the paper discusses further issues pertinent to the implementation of the CC OFDM MIMO radar, including the beam squinting problem and its remedy, arrangement of the multiple beams, the radar system structure, use of Golay codes for orthogonalization and PAPR mitigation, use of software-defined radar that eliminates the need of amplitude and phase control in each transmitter, transmit scheduling for multi-beam long-range target detection, and multidimensional ambiguity function analysis. The latter indicates that the CC OFDM MIMO radar can achieve a high resolution in angle, range, and velocity, with beam isolation of -30 dB for neighboring beams and co-channel beams.

Deep Unfolded Recovery of Sub-Nyquist Sampled Ultrasound Images.

The most common technique for generating B-mode ultrasound (US) images is delay-and-sum (DAS) beamforming, where the signals received at the transducer array are sampled before an appropriate delay is applied. This necessitates sampling rates exceeding the Nyquist rate and the use of a large number of antenna elements to ensure sufficient image quality. Recently, we proposed methods to reduce the sampling rate and the array size relying on image recovery using iterative algorithms based on compressed sensing (CS) and the finite rate of innovation (FRI) frameworks. Iterative algorithms typically require a large number of iterations, making them difficult to use in real time. In this article, we propose a reconstruction method from sub-Nyquist samples in the time and spatial domain, which is based on unfolding the iterative shrinkage thresholding algorithm (ISTA), resulting in an efficient and interpretable deep network. The inputs to our network are the subsampled beamformed signals after summation and delay in the frequency domain, requiring only a subset of the US signal to be stored for recovery. Our method allows reducing the number of array elements, sampling rate, and computational time while ensuring high-quality imaging performance. Using in vivo data, we demonstrate that the proposed method yields high-quality images while reducing the data volume traditionally used up to 36 times. In terms of image resolution and contrast, our technique outperforms previously suggested methods as well as DAS and minimum-variance (MV) beamforming, paving the way to real-time applicable recovery methods.

An overview of wireless communication technology using deep learning

With the development of 5G, the future wireless communication network tends to be more and more intelligent. In the face of new service demands of communication in the future such as super-heterogeneous network, multiple communication scenarios, large number of antenna elements and large bandwidth, new theories and technologies of intelligent communication have been widely studied, among which Deep Learning (DL) is a powerful technology in artificial intelligence(AI). It can be trained to continuously learn to update the optimal parameters. This paper reviews the latest research progress of DL in intelligent communication, and emphatically introduces five scenarios including Cognitive Radio (CR), Edge Computing (EC), Channel Measurement (CM), End to end Encoder/Decoder (EED) and Visible Light Communication (VLC). The prospect and challenges of further research and development in the future are also discussed.

Maximizing the spectral efficiency of finite dimensional multiuser massive MIMO

In this paper, we derive a closed-form approximation for the achievable uplink ergodic rate of the users in a single-cell multi-user multiple-input multiple-output (MIMO) system, where the angular domain in the physical channel model is divided into a finite number of separate directions and the base station (BS) is equipped with a large number of antenna elements. Then, we develop an approximation for the spectral efficiency of various detectors such as maximum-ratio combining (MRC), zero-forcing (ZF), and linear minimum mean square error (LMMSE). We also propose a resource allocation scheme in which the pilot power, data power, and training duration are optimally chosen in order to maximize the spectral efficiency in a given total power budget. By employing the proposed power allocation scheme, the simulation results illustrate a notable improvement in the achievable spectral efficiency. Moreover, the results show that the performance of the proposed method is much superior when the number of channel directions or the number of antennas at BS increases. Furthermore, while the advantage of the proposed method is more notable in the case of ZF and LMMSE receivers, it still outperforms the equal power allocation method for the MRC receiver in terms of spectral efficiency.

완전 디지털 능동배열 레이다를 위한 빔 도메인 국부 적응 빔 형성 기법

Digital adaptive beamforming is applied to the radar system to ensure system performance in an interference environment. For real time application to an actual radar system with a large number of antenna elements, the dimensions of the adaptive beamforming coefficient must be reduced. In this paper, we propose a beam domain localized adaptive beamforming algorithm based on linear constrained minimum variance (LCMV) that considers system applicability while maintaining the performance of fully adaptive beamforming. Jammer detection and angle estimation are performed using a passive listening signal, and the dimensions are reduced by localizing the signal to the beam domain based on jammer information and pre-determined linear constraints. Estimation of the interference covariance matrix and adaptive beamforming are performed in the reduced beam domain to ensure real-time operation and applicability. To verify the performance of the proposed algorithm, we analyzed the results compared to the fully adaptive beamforming in terms of signal-to-interference plus noise ratio (SINR) loss and maximum side lobe level in the presence of a jamming signal.

A Partial CSI Estimation Approach for Downlink FDD massive-MIMO System with Different Base Transceiver Station Topologies

Massive multiple-input multiple-output (massive-MIMO) is a promising technology for next generation wireless communications systems due to its capability to increase the data rate and meet the enormous ongoing data traffic explosion. However, in non-reciprocal channels, such as those encountered in frequency division duplex (FDD) systems, channel state information (CSI) estimation using downlink (DL) training sequence is to date very challenging issue, especially when the channel exhibits a shorter coherence time. In particular, the availability of sufficiently accurate CSI at the base transceiver station (BTS) allows an efficient precoding design in the DL transmission to be achieved, and thus, reliable communication systems can be obtained. In order to achieve the aforementioned objectives, this paper presents a feasible DL training sequence design based on a partial CSI estimation approach for an FDD massive-MIMO system with a shorter coherence time. To this end, a threshold-based approach is proposed for a suitable DL pilot selection by exploring the statistical information of the channel covariance matrix. The mean square error of the proposed design is derived, and the achievable sum rate and bit-error-rate for maximum ratio transmitter and regularized zero forcing precoding is investigated over different BTS topologies with uniform linear array and uniform rectangular array. The results show that a feasible performance in the DL FDD massive-MIMO systems can be achieved even when a large number of antenna elements are deployed by the BTS and a shorter coherence time is considered.

Passive-Shaped Beam Synthesis Using Pattern Diversity Dielectric Resonator Antenna Array

The passive antenna array is attractive for energy-efficient base station antenna. However, due to the absence of active elements, a large number of antenna elements are required to provide adequate degree of freedoms (DoFs) for shaped beam synthesis. This results in a bulky antenna structure of the conventional passive antenna array. In this work, pattern diversity dielectric resonator antenna (DRA) is first utilized for passive antenna array-shaped beam synthesis. Pattern diversity DRA can provide extra DoFs by exciting orthogonal transverse electric (TE) and transverse magnetic (TM) modes with diverse ports. For demonstration, a four-element linear pattern diversity DRA array is designed to verify its feasibility on shaped beam synthesis. Array configurations and desired user patterns are formulated and optimized by the artificial fish swarm algorithm. Its synthesis performances on six pattern shapes with different peaks and nulls are evaluated and compared with a conventional four-element phase array. It was found that the proposed passive antenna array has better synthesis ability with a smaller mean square error than that of the conventional phased array. The measured results verify the feasibility of using pattern diversity DRA as a passive scheme for energy-efficient base station antenna.

Mean‐based reciprocity calibration in TDD massive MIMO system

Non-reciprocity limits the potential of time division duplexing (TDD) massive multiple-input and multiple-output (MIMO) systems. Due to the reciprocal channel, there is no need for downlink (DL) pilot transmission implies computational complexity reduction and saving precious time resources. In this study, the DL channel matrix is estimated using the uplink channel matrix by a novel reciprocity calibration technique. Non-reciprocity arises due to the hardware mismatch (HM) across the base station (BS) and the user terminal (UT)/both. Its detrimental effect causes amplitude and phase impairment in the downlink signal transmission. Since a massive MIMO network has a large number of antenna elements across the BS, hence the instantaneous HM coefficient cannot be determined accurately. For solving such a problem, the authors use the statistical response of the hardware unit. Considering a complex Gaussian hardware response across each antenna terminal, the probability density function (PDF) of amplitude and phase mismatch is derived. They also derive the joint PDF of amplitude and phase mismatch, considering the HM. Simulation results address the sensitivity and complexity for evaluating the sum-rate capacity under three linear precoders (matched filter, regularized zero-forcing, and zero-forcing), which validate their effectiveness in this scenario.