Number Of Antennas Research Articles

Low complexity detection algorithms based on ADMIN for massive MIMO

This paper proposes the alternating direction method of multipliers-based infinity-norm (ADMIN) with threshold (ADMIN-T) and with percentage (ADMIN-P) detection algorithms, which make full use of the distribution of the signal to interference plus noise ratio (SINR) for an uplink massive MIMO system. The ADMIN-T and ADMIN-P detection algorithms are improved visions of the ADMIN detection algorithm, in which an appropriate SINR threshold in the ADMIN-T detection algorithm and a certain percentage in the ADMIN-P detection algorithm are designed to reduce the overall computational complexity. The detected symbols are divided into two parts by the SINR threshold which is based on the cumulative probability density function (CDF) of SINR and a percentage, respectively. The symbols in higher SINR part are detected by MMSE. The interference of these symbols is then cancelled by successive interference cancellation (SIC). Afterwards the remaining symbols with low SINR are iteratively detected by ADMIN. The simulation results show that the ADMIIN-T and the ADMIN-P detection algorithms provide a significant performance gain compared with some recently proposed detection algorithms. In addition, the computational complexity of ADMIN-T and ADMIN-P are significantly reduced. Furthermore, in the case of same number of transceiver antennas, the proposed algorithms have a higher performance compared with the case of asymmetric transceiver antennas.

Integrated Microwave Photonics Coherent Processor for Massive-MIMO Systems in Wireless Communications

Massive-MIMO systems can achieve high capacities and data rates by increasing the number of operational antennas in the base station. As more antenna elements are introduced, the complexity of the signal processing operations increases accordingly and current electronic processors struggle to reach those requirements. To overcome these hurdles, we propose a novel theory to process the RF signals in the optical domain. We experimentally demonstrate the capabilities of theory using a non-integrated Dual Parallel Modulator as a 2×2 optical matrix multiplier, recovering satisfactorily previously mixed RF signals modulated following the standards in 5 G communications. Finally, we propose an integrated photonic architecture based on a core of Mach Zehnder Interferometers to physically process the information. Together with the optical core, we proposed the integration of RF modulators, microwave photonic filters and high-speed photodetectors. We present simulations on the expected performance of the circuit and analyze the impact of fabrication errors.

40-GHz Band Photodiode-Integrated Phased Array Antenna Module for Analog-Radio over Fiber toward Beyond 5G

In 5th generation (5G) and Beyond 5G mobile communication systems, it is expected that numerous antennas will be densely deployed to realize ultra-broadband communication and uniform coverage. However, as the number of antennas increases, total power consumption of all antennas will also increase, which leads to a negative impact on the environment and operating costs of telecommunication operators. Thus, it is necessary to simplify an antenna structure to suppress the power consumption of each antenna. On the other hand, as a way to realize ultra-broadband communication, millimeter waves will be utilized because they can transmit signals with a broader bandwidth than lower frequencies. However, since millimeter waves have a large propagation loss, a propagation distance is shorter than that of low frequencies. Therefore, in order to extend the propagation distance, it is necessary to increase an equivalent isotropic radiated power by beamforming with phased array antenna. In this paper, a phased antenna array module in combined with analog radio over fiber (A-RoF) technology for 40-GHz millimeter wave is developed and evaluated for the first time. An 8×8 phased array antenna for 40-GHz millimeter wave with integrated photodiodes and RF chains has been developed, and end-to-end transmission experiment including 20 km A-RoF transmission and 3-m over-the-air transmission from the developed phased array antenna has been conducted. The results showed that the 40-GHz RF signal after the end-to-end transmission satisfied the criteria of 3GPP signal quality requirements within ±50 degrees of main beam direction.

Accurate channel estimation and hybrid beamforming using Artificial Intelligence for massive MIMO 5G systems

In a large-scale massive Multi User-Multiple Input Multiple Output (MU-MIMO) environment channel estimation and beamforming is a breathtaking task for enhancing the array gain without utilizing the many Radio Frequency (RF) chains. Somehow, several state-of-the-art works perform channel estimation and Hybrid Beamforming (HB) using Artificial Intelligence (AI) Algorithms but the massive computation intricacy and power consumption hindered the performance of the existing system. By considering the existing issues, we designed a DL-based Hybrid Beamformer for the MIMO environment with 5G communication technology (DLHB-MIMO 5G). The proposed HB design centers on three progressive processes such as accurate channel estimation, hybrid beamformer design, and hybrid beamforming. In the accurate channel estimation phase, the noise and interference-free channels are estimated using the Improved Extreme Learning Machine-Adaptive Orthogonal Matching Pursuit (IELM-AOMP) algorithm based on channel parameters and user feedback. In the HB design stage, the shortcoming of prior DL models is resolved by adopting Transfer Learning Lite Convolutional Neural Network (TL-LiteCNN) for designing a hybrid beamformer. Beforehand, we select the appropriate antenna numbers using Stackelberg Game Theory (StGT) using adequate parameters. In the hybrid beamforming stage, the problem of less Spectral Efficiency (SE) during low SNR conditions is fixed by adopting the Improved Proximal Policy Optimization (IPPO) algorithm with several beamforming parameters to generate highly resourceful hybrid beams. The realization of the proposed research is carried out using the MATLAB R2020a simulation tool and the performance of the proposed work is compared with the major state-of-the-art works in terms of useful performance metrics. The comparative results show that the proposed work beats the existing works.

Joint design of antenna selection and transmit linear array beamformer for integrated radar and communications

The design of integrated radar-communication (IRC) systems is seen as a promising solution to alleviate the congestion of spectrum resource in recent years. Additionally, with the deployment of large-scaled arrays in base stations, sparse array design via antenna selection has become prominent to reduce system overheads and alleviate mutual coupling effect. In this paper, we propose a joint design of antenna selection and transmit beamformer for IRC systems to realize the dual operations of radar and communications. Specifically, we propose a joint model that achieves a trade-off between minimizing the total number of antennas for IRC and suppressing the peak sidelobe level (PSL) of overall transmit beampattern with well-controlled mainlobe ripples. Unlike the existing schemes that focus on individual beamformer design with varying sparse array configurations, we impose a group sparsity on the beamforming matrix and jointly optimize multiple beamformers to obtain a common sparse array for the constellation of all communication symbols. To solve the resulting non-convex problem, we employ the alternating direction method of multipliers to split the original problem into parallel subproblems which are then solved iteratively. Simulation results illustrate the superiority of the proposed method over the conventional approaches in obtaining a lower PSL using fewer antennas with dual functions.

Beamforming Array Antenna Technique Based on Partial Update Adaptive Algorithms

The most important issues for improving the performance of modern wireless communication systems are interference cancellation, efficient use of energy, improved spectral efficiency and increased system security. Beamforming Array Antenna (BAA) is one of the efficient methods used for this purpose. Full band BAA, on the other hand, will suffer from a large number of controllable elements, a long convergence time and the complexity of the beamforming network. Since no attempt had previously been made to use Partial Update (PU) for BAA, the main novelty and contribution of this paper was to use PU instead of full band adaptive algorithms. PU algorithms will connect to a subset of the array elements rather than all of them. As a result, a common number of working antennas for the system's entire cells can be reduced to achieve overall energy efficiency and high cost-effectiveness. In this paper, we propose a new architectural model that employs PU adaptive algorithms to control and minimize the number of phase shifters, thereby reducing the number of base station antennas. We will concentrate on PU LMS (Least Mean Square) algorithms such as sequential-LMS, M-max LMS, periodic-LMS, and stochastic-LMS. According to simulation results using a Uniform Linear Array (ULA) and three communications channels, the M-max-LMS, periodic LMS, and stochastic LMS algorithms perform similarly to the full band LMS algorithm in terms of square error, tracking weight coefficients, and estimation input signal, with a quick convergence time, low level of error signal at steady state and keeping null steering's interference-suppression capability intact.

3-D Millimeter Wave Fast Imaging Technique Based on 2-D SISO/MIMO Array

In this article, a novel three-dimensional (3-D) imaging method based on the range decomposing algorithm (RDA) is proposed for millimeter wave imaging. We combined it with binomial theory and we derive the theoretical formulation of RDA applied to single-input–single-output (SISO)/multiple-input–multiple-output (MIMO) array; meanwhile, its computational complexity and computational error are analyzed. Compared to the classical Fourier algorithm, such as the range migration algorithm (RMA) and the phase shift migration (PSM), the proposed algorithm can replace the time-consuming interpolation and accumulation operations with reasonable approximations and transformations offering a more efficient approach, while maintaining the image quality. In addition, a method based on RDA which is applicable to the transformation between MIMO and SISO, is proposed to further enhance the processing efficiency. Proof-of-principle simulation using echo data collected from a large number of antennas, verifies that the proposed algorithm has higher efficiency. In order to better verify the feasibility of the proposed algorithm, a scanning prototype located in the millimeter wave band is designed. The experimental results of different targets demonstrate that the proposed algorithm achieves significantly higher reconstruction efficiency when compared to the traditional algorithms.

On CSI-Free Multiantenna Schemes for Massive Wireless-Powered Underground Sensor Networks

Radio-frequency wireless energy transfer (WET) is a promising technology to realize wireless-powered underground sensor networks (WPUSNs) and enable sustainable underground monitoring. However, due to the severe attenuation in harsh underground soil and the tight energy budget of the underground sensors, traditional WPUSNs relying on the channel state information (CSI) are highly inefficient, especially in massive WET scenarios. To address this challenge, we comparatively assess the feasibility of several state-of-the-art CSI-free multi-antenna WET schemes for WPUSNs, under a given power budget. Moreover, to overcome the extremely low WET efficiency in underground channels, we propose a distributed CSI-free system, where multiple power beacons (PBs) simultaneously charge a large set of underground sensors without any CSI. We consider the position-aware K-Means and the position-agnostic equally-far-from-center (EFFC) approaches for the optimal deployment of the PBs. Our results evince that the performance of the proposed distributed CSI-free system can approach or even surpass that of a traditional full-CSI WET strategy, especially when adopting an appropriate CSI-free scheme, applying the advisable PBs deployment approach, and equipping the PBs with an appropriate number of antennas. Finally, we discuss the impact of underground parameters, i.e., the burial depth of devices and the volumetric water content of soil, on the system’s performance, and identify potential challenges and research opportunities for practical distributed CSI-free WPUSNs deployment.

A Low-Complexity Digital Predistorter for Large-Scale MIMO Systems With Crosstalk

Massive multiple-input multiple-output (MIMO) technology is a key enabler for future wireless communication systems. On the other hand, crosstalk is inevitable in the highly integrated large-scale antenna array. The nonlinearity of power amplifiers (PAs) coupled with crosstalk is much more complicated when the number of antennas is large. Digital predistortion (DPD) can compensate for the PA nonlinearity without sacrificing efficiency and is widely applied in both base stations and mobile devices. Extending existing solutions to the large-scale MIMO system usually suffers from performance degradation or greatly increased complexity. In this paper, we consider the nonlinearity with crosstalk for the large-scale MIMO scenario. A much simplified DPD model is proposed by ignoring the high-order crosstalk terms generated from the complete nonlinear model. Compared to existing solutions, the proposed DPD can compensate for both the nonlinear and linear crosstalk of the system. It achieves satisfactory linearization performance with much reduced computational complexity. The complexity of the proposed DPD is linearly related to the number of transmitter branches. Thus, it is scalable in the large-scale MIMO scenario. Moreover, the proposed DPD can be extended to the partially-connected hybrid beamforming system with crosstalk. Simulation results validate the effectiveness of the proposed DPD scheme.

Massive MIMO Receiver Design with Channel State Information

In order to achieve an astounding data transfer rate, 5G Technology’s is essential obligation, this is the primal reason while the world considers it as an pivotal active research topic, Amongst numerous techniques available to attain the transfer rate, opted Massive Multiple-Input Multiple-Output (MIMO) system receivers with respect to CSI assuming the mathematic computations and complex equations would be deduced in a primordial passion, is examined in this study. For the uplink, we show the possible transfer rate for both receivers with perfect and imperfect channel state information (CSI), considering that the base station (BS) deploys maximum ratio combining (MRC) or zero-forcing (ZF) receivers. Channel estimation is carried out by transmitting pilot symbols when there is insufficient information about the channel state to establish its properties. Additionally, the influence of channel state information on the power scaling rule is illustrated, and a numerical analysis for combiner is derived. In this study, we compare the competence of receivers under ideal and imperfect CSI. In case of perfect CSI, Value of data rate is 84 bits/sec/Hz for ZF receiver and 45 bits/sec/Hz. In case of imperfect CSI, Value of data rate is 60 bits/sec/Hz for ZF receiver and 37 bits/sec/Hz with number of antennas being 500 and number of pilot bits as 10.

A power method based user selection for reconfigurable intelligent surface (RIS) assisted multiuser massive MISO systems

Reconfigurable intelligent surfaces (RISs) have recently emerged as effective solutions for providing massive connectivity. However, an effective RIS user selection method that can support massive devices remains undeveloped. In this study, a power method (PM)-based RIS user selection algorithm for RIS-assisted massive multiple-input multiple-output systems is proposed. It is proven that minimizing the condition number (CN) of the aggregated downlink channel matrix results in the same performance as maximizing the sum rate. Based on this analysis, a PM-based RIS user selection algorithm that utilizes a CN as an RIS user selection metric is proposed here. Although the complexity of conventional user selection algorithm is proportional to the square of the number of base station (BS) antennas ( M 2 ), that of the proposed algorithm is linearly proportional to the number of BS antennas ( M ). Simulation results demonstrate that, under a practical RIS control link, the proposed PMUS algorithm achieves better performance and lower complexity than the conventional user selection algorithm.

Performance Analysis of DoA Estimation for FDD Cell Free Systems Based on Compressive Sensing Technique

The concept of cell free (CF) massive MIMO systems is a prospective fifth generation communication technology that effort with base stations for the privilege of user-centric coverage. Most studies on the CF massive MIMO system in the past imply that systems that use time division duplexing (TDD), even despite the systems using frequency division duplex (FDD) predominate in today’s wireless communications. When the number of antennas increases in FDD systems, channel state information (CSI) collection and feedback overhead become major issues. In order to mitigate these issues, we make use of the condition that the so-called uplink and downlink multipath components are comparable. Base station takes use of the angle reciprocity may immediately obtain information on channel parameters from the uplink training signal. In this paper, for CF massive MIMO system based on FDD, we provide compressive sensing (CS) of directions of arrival (DoAs) estimation approach of access point cooperation based on the channel parameters. The suggested estimation approach outperforms the established subspace-based technique, according to simulation findings. Additionally, we showed that the results of our compressive sensing estimator against the conventional estimation method. The former demonstrates way far better outcome and performance accordingly than the latter.

Robust Precoding for HF Skywave Massive MIMO

In this paper, we investigate the robust precoding with imperfect channel state information (CSI) for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications. Starting with a sparse beam based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> channel model for the available imperfect CSI at the base station (BS), we prove that the robust precoder for ergodic sum-rate maximization can be designed by optimizing the beam domain robust precoder (BDRP) without any loss of optimality. Furthermore, the asymptotic optimal precoder is beam structured for a sufficiently large number of antennas at the BS, involving a low-dimensional BDRP. As a result, the beam structured robust precoding is asymptotic optimal and can be efficiently implemented based on chirp z-transform. We then derive an iterative algorithm to design the BDRP using majorization-minimization (MM). Furthermore, we develop a low-complexity BDRP design with an ergodic sum-rate upper bound, simplifying the MM based design algorithm. Based on our simulation results, the proposed beam structured robust precoding can achieve a near-optimal performance with significantly reduced complexity in various scenarios.

Spectral and Energy Efficiency Trade-Off in UAV-Based Olive Irrigation Systems

Precision agriculture, also referred to as smart farming, is one of the main pillars of modern society to achieve the Sustainable Development Goals (SDGs). Precision agriculture aims to improve the quality and quantity of production while conserving scarce natural resources. Smart farming has grown in recent years thanks to the adoption of modern technologies, including artificial intelligence (AI) and the Internet of Things (IoT). In this work, we consider an irrigation system for olive orchards based on unmanned aerial vehicles (UAVs). Specifically, UAVs ensure remote sensing (RS), which offers the advantage of collecting vital information on a large temporal and spatial scale (which cannot be achieved with traditional technologies). However, UAV-based irrigation systems face tremendous challenges due to the various requirements of a powerful computing ability, battery capacity, energy efficiency, and spectral efficiency for different connected devices. This paper addresses the energy efficiency and spectral efficiency trade-off problem of UAV-based irrigation systems. We propose to adopt massive multiple input, multiple output (M-MIMO) technology to ensure wireless communication. In fact, this technology plays a significant role in future sixth-generation (6G) wireless mobile networks and has the potential to enhance the energy efficiency as well as the spectral efficiency. We design a network model with a three-layered architecture and analytically compute the achievable spectral efficiency and the energy efficiency of the studied system. Then, we numerically determine the optimal number of ground base station antennas as well as the optimal number of IoT devices that should be used to ensure the maximum energy efficiency while guaranteeing a high spectral efficiency. The numerical results prove that the proposed UAV-based irrigation system outperforms conventional systems and demonstrate that the best spectral and energy efficiency trade-off is obtained by using the M-MMSE combiner.

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.

Design of Multi-User Noncoherent Massive SIMO Systems for Scalable URLLC.

This paper develops and optimizes a non-orthogonal and noncoherent multi-user massive single-input multiple-output (SIMO) framework, with the objective of enabling scalable ultra-reliable low-latency communications (sURLLC) in Beyond-5G (B5G)/6G wireless communication systems. In this framework, the huge diversity gain associated with the large-scale antenna array in the massive SIMO system is leveraged to ensure ultra-high reliability. To reduce the overhead and latency induced by the channel estimation process, we advocate for the noncoherent communication technique, which does not need the knowledge of instantaneous channel state information (CSI) but only relies on large-scale fading coefficients for message decoding. To boost the scalability of noncoherent massive SIMO systems, we enable the non-orthogonal channel access of multiple users by devising a new differential modulation scheme to ensure that each transmitted signal matrix can be uniquely determined in the noise-free case and be reliably estimated in noisy cases when the antenna array size is scaled up. The key idea is to make the transmitted signals from multiple geographically separated users be superimposed properly over the air, such that when the sum signal is correctly detected, the signal sent by each individual user can be uniquely determined. To further enhance the average error performance when the array antenna number is large, we propose a max-min Kullback-Leibler (KL) divergence-based design by jointly optimizing the transmitted powers of all users and the sub-constellation assignments among them. The simulation results show that the proposed design significantly outperforms the existing max-min Euclidean distance-based counterpart in terms of error performance. Moreover, our proposed approach also has a better error performance compared to the conventional coherent zero-forcing (ZF) receiver with orthogonal channel training, particularly for cell-edge users.

Homogeneous microwave near-field power focusing using a cylindrical antenna array

This paper presents an investigation of a microwave near-field power focusing (NFPF) analytical approach utilizing a cylindrical array of electric line sources along the z-axis, applicable to any arbitrary homogeneous linear medium. A novel parameter, termed the “focus ability” (FA), is introduced to quantitatively assess a method's capabilities in achieving power focusing. In the following, the phases and amplitudes of the excitation signals of the array elements are obtained with optimization to maximize FA over a certain studied area. Each stage of the theoretical analysis is supported through COMSOL full-wave simulations, ensuring the validity of the results. Theoretical results relevant to focused power are then compared to outcomes obtained from CST full-wave simulations with the same array configuration while employing half-wave dipole antenna elements with excitations obtained via optimization. These comparisons indicate that the excitation signals obtained by theoretical analysis can be used for power focusing when the array of half-wave dipole antenna sources is utilized. Furthermore, the proposed method leads to a significant reduction in the optimization time. Also, in the provided examples, the FA parameter and NFPF are investigated for the different conditions consisting of the type of the homogeneous medium and the number of antennas.

Efficient Channel Equalization and Performance Analysis for Uplink FBMC/OQAM-Based Massive MIMO Systems

For offset quadratic amplitude modulation filter bank multi-carrier (FBMC/OQAM) based massive multiple-input multiple-output (MIMO) systems, a response difference phenomenon in the process of designing multi-tap equalizers is founded in this paper, which degrades the equalization performance. To address this issue, we propose a multi-stage equalization based design scheme of multi-tap equalizers with low implementation complexity. The scheme can alleviate the impact brought by the phenomenon effectively and improve the equalization performance significantly. Besides, we analyze the signal-to-interference-plus-noise ratio (SINR) and ergodic achievable rate performance of the proposed scheme, and further elaborate its self-equalization property that inter-user interference and noise vanishes as the number of BS antennas increases. In this case, there only remains some residual interference within the same user, which is tiny enough to be ignored. Thus, SINR can approach the signal-to-interference ratio (SIR) upper bound, i.e., the SIR in single-input single-output (SISO) scenario when the channel response is unit impulse. Simulation results confirm the performance analysis and show that the proposed scheme with shorter equalizer length can outperform other schemes with longer equalizer length. Moreover, even with finite number of BS antennas, the interference brought by the channels can be almost eliminated.

Performance of Multi-Antenna Proactive Eavesdropping in 5G Uplink Systems

This paper studies the performance of multi-antenna proactive eavesdropping in 5G uplink systems with spatially correlated Rayleigh fadings, where the base station (BS) serves an illegal user and a multi-antenna legitimate monitor eavesdrops the suspicious link with the help of jamming attack. Based on a practical assumption of channel state information (CSI) in 5G uplink, i.e., imperfect instantaneous CSI of the suspicious link at the BS and that of eavesdropping link at the monitor, and only jamming channel statistics at the monitor, we first give a statistical jamming beamforming design. Then, semi-closed form expressions of eavesdropping non-outage probability and relative average eavesdropping rate are, respectively, derived for delay-sensitive and delay-tolerant scenarios. Via reasonable approximations and asymptotic analysis, we gain many insights on the effect of key system parameters, e.g., location-dependent channel path loss and angular spread, jamming energy and the number of antennas. Further, we provide the optimal energy allocation between pilot and data jamming and the optimal antenna allocation between jamming and eavesdropping under total energy constraint and total antenna number, respectively, which are both explicit functions of system parameters. Finally, simulation results validate our analytical results.

RIS Partitioning Based Scalable Beamforming Design for Large-Scale MIMO: Asymptotic Analysis and Optimization

In next-generation wireless networks, reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems are foreseeable to support a large number of antennas at the transceiver as well as a large number of reflecting elements at the RIS. To fully unleash the potential of RIS, the phase shifts of RIS elements should be carefully designed, resulting in a high-dimensional non-convex optimization problem that is hard to solve with affordable computational complexity. In this paper, we address this scalability issue by partitioning RIS into sub-surfaces, so as to optimize the phase shifts in sub-surface levels to reduce complexity. Specifically, each sub-surface employs a linear phase variation structure to anomalously reflect the incident signal to a desired direction, and the sizes of sub-surfaces can be adaptively adjusted according to channel conditions. We formulate the achievable rate maximization problem by jointly optimizing the transmit covariance matrix and the RIS phase shifts. Under the RIS partitioning framework, the RIS phase shifts optimization reduces to the manipulation of the sub-surface sizes, the phase gradients of sub-surfaces, as well as the common phase shifts of sub-surfaces. Then, we characterize the asymptotic behavior of the system with an infinitely large number of transceiver antennas and RIS elements. The asymptotic analysis provides useful insights on the understanding of the fundamental performance-complexity tradeoff in RIS partitioning design. We show that in the asymptotic domain, the achievable rate maximization problem has a rather simple form with an explicit physical meaning of optimization variables. We develop an efficient algorithm to find an approximately optimal solution to the asymptotic problem via a one-dimensional (1D) grid search. Moreover, we discuss the insights and impacts of the asymptotic result on finite-size system design. By applying the asymptotic result to a finite-size system with necessary modifications, we show by numerical results that the proposed design achieves a favorable tradeoff between system performance and computational complexity.