A low-complexity AMP detection algorithm with deep neural network for massive mimo systems

Signal detection plays an essential role in massive Multiple-Input Multiple-Output(MIMO)systems.However,existing detection methods have not yet made a good tradeoff between Bit Error Rate(BER)and computational complexity,resulting in slow convergence or high complexity.To address this issue,a low-complexity Approximate Message Passing(AMP)detection algorithm with Deep Neural Network(DNN)(denoted as AMP-DNN)is investigated in this paper.Firstly,an efficient AMP detection algorithm is derived by scalarizing the simplification of Belief Propagation(BP)algorithm.Secondly,by unfolding the obtained AMP detection algorithm,a DNN is specifically designed for the optimal performance gain.For the proposed AMP-DNN,the number of trainable parameters is only related to that of layers,regardless of modulation scheme,antenna number and matrix calculation,thus facilitating fast and stable training of the network.In addition,the AMP-DNN can detect different channels under the same distribution with only one training.The superior performance of the AMP-DNN is also verified by theoretical analysis and experiments.It is found that the proposed algorithm enables the reduction of BER without signal prior information,especially in the spatially correlated channel,and has a lower computational complexity compared with existing state-of-the-art methods.

Deep learning for joint channel estimation and feedback in massive MIMO systems

The great potentials of massive Multiple-Input Multiple-Output(MIMO)in Frequency Division Duplex(FDD)mode can be fully exploited when the downlink Channel State Information(CSI)is available at base stations.However,the accurate CsI is difficult to obtain due to the large amount of feedback overhead caused by massive antennas.In this paper,we propose a deep learning based joint channel estimation and feedback framework,which comprehensively realizes the estimation,compression,and reconstruction of downlink channels in FDD massive MIMO systems.Two networks are constructed to perform estimation and feedback explicitly and implicitly.The explicit network adopts a multi-Signal-to-Noise-Ratios(SNRs)technique to obtain a single trained channel estimation subnet that works well with different SNRs and employs a deep residual network to reconstruct the channels,while the implicit network directly compresses pilots and sends them back to reduce network parameters.Quantization module is also designed to generate data-bearing bitstreams.Simulation results show that the two proposed networks exhibit excellent performance of reconstruction and are robust to different environments and quantization errors.

Optimization of resource allocation in FDD massive MIMO systems

The performance of massive MIMO systems relies heavily on the availability of Channel State Information at the Transmitter(CSIT).A large amount of work has been devoted to reducing the CSIT acquisition overhead at the pilot training and/or CsI feedback stage.In fact,the downlink communication generally includes three stages,i.e.,pilot training,CsI feedback,and data transmission.These three stages are mutually related and jointly determine the overall system performance.Unfortunately,there exist few studies on the reduction of csIT acquisition overhead from the global point of view.In this paper,we integrate the Minimum Mean Square Error(MMSE)channel estimation,Random Vector Quantization(RVQ)based limited feedback and Maximal Ratio Combining(MRC)precoding into a unified framework for investigating the resource allocation problem.In particular,we first approximate the covariance matrix of the quantization error with a simple expression and derive an analytical expression of the received Signal-to-Noise Ratio(SNR)based on the deterministic equivalence theory.Then the three performance metrics(the spectral efficiency,energy efficiency,and total energy consumption)oriented problems are formulated analytically.With practical system requirements,these three metrics can be collaboratively optimized.Finally,we propose an optimization solver to derive the optimal partition of channel coherence time.Experiment results verify the benefits of the proposed resource allocation schemes under three different scenarios and illustrate the tradeoff of resource allocation between three stages.

Power Allocation for SE Maximization in Uplink Massive MIMO System Under Minimum Rate Constraint

In this paper,we optimize the spectrum efficiency(SE)of uplink massive multiple-input multiple-output(MIMO)system with imperfect channel state information(CSI)over Rayleigh fading channel.The SE optimization problem is formulated under the constraints of maximum power and minimum rate of each user.Then,we develop a near-optimal power allocation(PA)scheme by using the successive convex approximation(SCA)method,Lagrange multiplier method,and block coordinate descent(BCD)method,and it can obtain almost the same SE as the benchmark scheme with lower complexity.Since this scheme needs three-layer iteration,a suboptimal PA scheme is developed to further reduce the complexity,where the characteristic of massive MIMO(i.e.,numerous receive antennas)is utilized for convex reformulation,and the rate constraint is converted to linear constraints.This suboptimal scheme only needs single-layer iteration,thus has lower complexity than the near-optimal scheme.Finally,we joint design the pilot power and data power to further improve the performance,and propose an two-stage algorithm to obtain joint PA.Simulation results verify the effectiveness of the proposed schemes,and superior SE performance is achieved.

Network-Assisted Full-Duplex Cell-Free mmWave Massive MIMO Systems with DAC Quantization and Fronthaul Compression

In this paper,we investigate networkassisted full-duplex(NAFD)cell-free millimeter-wave(mmWave)massive multiple-input multiple-output(MIMO)systems with digital-to-analog converter(DAC)quantization and fronthaul compression.We propose to maximize the weighted uplink and downlink sum rate by jointly optimizing the power allocation of both the transmitting remote antenna units(T-RAUs)and uplink users and the variances of the downlink and uplink fronthaul compression noises.To deal with this challenging problem,we further apply a successive convex approximation(SCA)method to handle the non-convex bidirectional limited-capacity fronthaul constraints.The simulation results verify the convergence of the proposed SCA-based algorithm and analyze the impact of fronthaul capacity and DAC quantization on the spectral efficiency of the NAFD cell-free mmWave massive MIMO systems.Moreover,some insightful conclusions are obtained through the comparisons of spectral efficiency,which shows that NAFD achieves better performance gains than cotime co-frequency full-duplex cloud radio access network(CCFD C-RAN)in the cases of practical limited-resolution DACs.Specifically,their performance gaps with 8-bit DAC quantization are larger than that with1-bit DAC quantization,which attains a 5.5-fold improvement.

Intelligent reflecting surface for sum rate enhancement in MIMO systems

The research for the Intelligent Reflecting Surface(IRS)which has the advantages of cost and energy efficiency has been studied.Channel capacity can be effectively increased by appropriately setting the phase value of IRS elements according to the channel conditions.However,the problem of obtaining an appropriate phase value of IRs is difficult to solve due to the non-convex problem.This paper proposes an iterative algorithm for the alternating optimal solution in the Single User Multiple-Input-Multiple-Output(SU-MIMO)systems.The proposed iterative algorithm finds an alternating optimal solution that is the phase value of IRS one by one.The results show that the proposed method has better performance than that of the randomized IRS systems.The number of iterations for maximizing the performance of the proposed algorithm depends on the channel state between the IRS and the receiver.

Optimal AP Deployment in Cell-Free Massive MIMO Systems with LoS/NLoS Transmissions:A Stochastic Geometry Approach

Cell-free massive multiple-input multipleoutput(MIMO)is a promising technology for future wireless communications,where a large number of distributed access points(APs)simultaneously serve all users over the same time-frequency resources.Since users and APs may locate close to each other,the line-of-sight(Lo S)transmission occurs more frequently in cell-free massive MIMO systems.Hence,in this paper,we investigate the cell-free massive MIMO system with Lo S and non-line-of-sight(NLo S)transmissions,where APs and users are both distributed according to Poisson point process.Using tools from stochastic geometry,we derive a tight lower bound for the user downlink achievable rate and we further obtain the energy efficiency(EE)by considering the power consumption on downlink payload transmissions and circuitry dissipation.Based on the analysis,the optimal AP density and AP antenna number that maximize the EE are obtained.It is found that compared with the previous work that only considers NLo S transmissions,the actual optimal AP density should be much smaller,and the maximized EE is actually much higher.

Gaussian Mixture-Learned Approximate Message Passing(GM-LAMP)Based Hybrid Precoders for mmWave Massive MIMO Systems

Hybrid precoder design is a key technique providing better antenna gain and reduced hardware complexity in millimeter-wave(mmWave)massive multiple-input multiple-output(MIMO)systems.In this paper,Gaussian Mixture learned approximate message passing(GM-LAMP)network is presented for the design of optimal hybrid precoders suitable for mmWave Massive MIMO systems.Optimal hybrid precoder designs using a compressive sensing scheme such as orthogonal matching pursuit(OMP)and its derivatives results in high computational complexity when the dimensionality of the sparse signal is high.This drawback can be addressed using classical iterative algorithms such as approximate message passing(AMP),which has comparatively low computational complexity.The drawbacks of AMP algorithm are fixed shrinkage parameter and non-consideration of prior distribution of the hybrid precoders.In this paper,the fixed shrinkage parameter problem of the AMP algorithm is addressed using learned AMP(LAMP)network,and is further enhanced as GMLAMP network using the concept of Gaussian Mixture distribution of the hybrid precoders.The simula-tion results show that the proposed GM-LAMP network achieves optimal hybrid precoder design with enhanced achievable rates,better accuracy and low computational complexity compared to the existing algorithms.

A Hybrid Small-Cell and Clustered Cell-Free Massive MIMO System under Mobility Scenarios

Recently,cell-free(CF)massive multipleinput multiple-output(MIMO)becomes a promising architecture for the next generation wireless communication system,where a large number of distributed access points(APs)are deployed to simultaneously serve multiple user equipments(UEs)for improved performance.Meanwhile,a clustered CF system is considered to tackle the backhaul overhead issue in the huge connection network.In this paper,taking into account the more realistic mobility scenarios,we propose a hybrid small-cell(SC)and clustered CF massive MIMO system through classifications of the UEs and APs,and constructing the corresponding pairs to run in SC or CF mode.A joint initial AP selection of this paradigm for all the UEs is firstly proposed,which is based on the statistics of estimated channel.Then,closed-form expressions of the downlink achievable rates for both the static and moving UEs are provided under Ricean fading channel and Doppler shift effect.We also develop a semi-heuristic search algorithm to deal with the AP selection for the moving UEs by maximizing the weight average achievable rate.Numerical results demonstrate the performance gains and effective rates balancing of the proposed system.

Performance Analysis of ZF and RZF in Low-Resolution ADC/DAC Massive MIMO Systems

Large number of antennas and higher bandwidth usage in massive multiple-input-multipleoutput(MIMO)systems create immense burden on receiver in terms of higher power consumption.The power consumption at the receiver radio frequency(RF)circuits can be significantly reduced by the application of analog-to-digital converter(ADC)of low resolution.In this paper we investigate bandwidth efficiency(BE)of massive MIMO with perfect channel state information(CSI)by applying low resolution ADCs with Rician fadings.We start our analysis by deriving the additive quantization noise model,which helps to understand the effects of ADC resolution on BE by keeping the power constraint at the receiver in radar.We also investigate deeply the effects of using higher bit rates and the number of BS antennas on bandwidth efficiency(BE)of the system.We emphasize that good bandwidth efficiency can be achieved by even using low resolution ADC by using regularized zero-forcing(RZF)combining algorithm.We also provide a generic analysis of energy efficiency(EE)with different options of bits by calculating the energy efficiencies(EE)using the achievable rates.We emphasize that satisfactory BE can be achieved by even using low-resolution ADC/DAC in massive MIMO.

Low-complexity signal detection for massive MIMO systems via trace iterative method

Linear minimum mean square error(MMSE)detection has been shown to achieve near-optimal performance for massive multiple-input multiple-output(MIMO)systems but inevitably involves complicated matrix inversion,which entails high complexity.To avoid the exact matrix inversion,a considerable number of implicit and explicit approximate matrix inversion based detection methods is proposed.By combining the advantages of both the explicit and the implicit matrix inversion,this paper introduces a new low-complexity signal detection algorithm.Firstly,the relationship between implicit and explicit techniques is analyzed.Then,an enhanced Newton iteration method is introduced to realize an approximate MMSE detection for massive MIMO uplink systems.The proposed improved Newton iteration significantly reduces the complexity of conventional Newton iteration.However,its complexity is still high for higher iterations.Thus,it is applied only for first two iterations.For subsequent iterations,we propose a novel trace iterative method(TIM)based low-complexity algorithm,which has significantly lower complexity than higher Newton iterations.Convergence guarantees of the proposed detector are also provided.Numerical simulations verify that the proposed detector exhibits significant performance enhancement over recently reported iterative detectors and achieves close-to-MMSE performance while retaining the low-complexity advantage for systems with hundreds of antennas.

An analytical framework for the incorporation of non-orthogonal pilots in massive MIMO systems

Training-based cellular communication systems use orthogonal pilot sequences to limit pilot contamination.However,the orthogonality constraint imposes a certain pilot length,and therefore,in communication systems with a large number of users,time-frequency resources are wasted significantly in the training phase.In cellular massive MIMO systems,the time-frequency resources can be used more efficiently by replacing the orthogonal pilots with shorter non-orthogonal pilot sequences in such a way that more space is available for the transmission of additional data symbols,and thus achieving higher data rates.Of course,the use of non-orthogonal pilots introduces additional pilot contamination,so the performance improvement could be achieved under certain system conditions,which are thoroughly investigated in this paper.We first provide a performance analysis framework for the uplink of cellular massive MIMO systems in which the effect of user pilot non-orthogonality has been analytically modelled.In this framework,we derive analytical expressions for the channel estimation,user Signal-to-Interference-plus-Noise-Ratio(SINR),and the average channel capacity per cell.We then use the proposed framework to evaluate the achievable spectral efficiency gain obtained by replacing orthogonal pilots with non-orthogonal counterparts.In particular,the existing trade-off between pilot lengths and the additional data symbols that can be transmitted by reducing the number of pilot symbols,is numerically quantified over a wide range of system parameters.

Passive Beamforming Design for Intelligent Reflecting Surface Assisted MIMO Systems

Intelligent reflecting surfaces(IRSs)constitute passive devices,which are capable of adjusting the phase shifts of their reflected signals,and hence they are suitable for passive beamforming.In this paper,we conceive their design with the active beamforming action of multiple-input multipleoutput(MIMO)systems used at the access points(APs)for improving the beamforming gain,where both the APs and users are equipped with multiple antennas.Firstly,we decouple the optimization problem and design the active beamforming for a given IRS configuration.Then we transform the optimization problem of the IRS-based passive beamforming design into a tractable non-convex quadratically constrained quadratic program(QCQP).For solving the transformed problem,we give an approximate solution based on the technique of widely used semidefinite relaxation(SDR).We also propose a low-complexity iterative solution.We further prove that it can converge to a locally optimal value.Finally,considering the practical scenario of discrete phase shifts at the IRS,we give the quantization design for IRS elements on basis of the two solutions.Our simulation results demonstrate the superiority of the proposed solutions over the relevant benchmarks.

Uplink capacity analysis of single-user SA-MIMO system

A novel framework of which combines smart antennas multiple antenna systems, （SA） with multiple-input multiple-output （MIMO） at the receiver, is proposed. The uplink SA-MIMO system is investigated. The joint optimization problem corresponding to the uplink capacity of the single-user SA-MIMO system is deduced. Then the closedform expression of the capacity is obtained in the case of equal power allocation and the same direction-of-arrivals （DOAs） from different transmit antennas at the same antenna array, and an upper bound of the capacity is also given in the case of different DOAs at the same antenna array. After that, for the general case, a suboptimal method for the capacity optimization problem is presented. Some numerical results are also given to compare the capacities of conventional MIMO and SA-MIMO systems and show that the proposed method is viable.

Adaptive modulation MIMO system based on minimizing transmission power

Adaptive modulation (AM) is an effective technique to approach the theoretical bound of multi-input and multi-output (MIMO) channel. In most previous studies, the AM parameters were obtained by maximizing the transmission rate for a given total transmit power. In this paper, a novel AM-MIMO algorithm is presented, which is based on minimizing total transmit power when the link’s QoS requirements are given. By taking the QoS requirements into account directly, the proposed algorithm not only makes the system more flexible, but also makes the cross layer design of wireless network easier. At last, the numerical results of the proposed scheme are presented.

A HOS-based Blind Signal Extraction Method for Chaotic MIMO Systems

A novel method to extract multiple input and multiple output (MIMO) chaotic signals was proposed using the blind neural algorithm after transmitting in nonideal channel. The MIMO scheme with different chaotic signal generators was presented. In order to separate the chaotic source signals only by using the sensor signals at receivers, a blind neural extraction algorithm based on higher-order statistic (HOS) technique was used to recover the primary chaotic signals. Simulation results show that the proposed approach has good performance in separating the primary chaotic signals even under nonideal channel.

Antenna selection based on large-scale fading for distributed MIMO systems

An antenna selection algorithm based on large-scale fading between the transmitter and receiver is proposed for the uplink receive antenna selection in distributed multiple-input multiple-output(D-MIMO) systems. By utilizing the radio access units(RAU) selection based on large-scale fading,the proposed algorithm decreases enormously the computational complexity. Based on the characteristics of distributed systems,an improved particle swarm optimization(PSO) has been proposed for the antenna selection after the RAU selection. In order to apply the improved PSO algorithm better in antenna selection,a general form of channel capacity was transformed into a binary expression by analyzing the formula of channel capacity. The proposed algorithm can make full use of the advantages of D-MIMO systems,and achieve near-optimal performance in terms of channel capacity with low computational complexity.

Low Complexity Joint Hybrid Precoding for Millimeter Wave MIMO Systems

In millimeter wave(mmWave) multiple-input multiple-output(MIMO) systems, hybrid precoding has been widely used to overcome the severe propagation loss. In order to improve the spectrum efficiency with low complexity, we propose a joint hybrid precoding algorithm for single-user mmWave MIMO systems in this paper. By using the concept of equivalent channel, the proposed algorithm skillfully utilizes the idea of alternating optimization to complete the design of RF precoder and combiner. Then, the baseband precoder and combiner are computed by calculating the singular value decomposition of the equivalent channel. Simulation results demonstrate that the proposed algorithm can achieve satisfactory performance with quite low complexity. Moreover, we investigate the effects of quantization on the analog components and find that the proposed scheme is effective even with coarse quantization.

Hybrid Precoding for mm Wave Massive MIMO Systems with Different Antenna Arrays

In this paper, the performance of hybrid precoding is investigated for mmWave massive MIMO systems with different antenna arrays. The hybrid precoding with partially connected architecture (PCA) is adopted. The spectral efficiency (SE) and received energy efficiency (EE) are investigated by considering four types of antenna arrays, including uniform linear array (ULA), uniform rectangular planar array (URPA), uniform hexagonal planar array (UHPA), and uniform circular planar array (UCPA), respectively. We focus on analysis at the antenna response vector and utilize the idea of orthogonal matching pursuit algorithm to seek the optimal hybrid precoder. Furthermore, the trade-off of precoding architectures is studied between SE and received EE. Simulation results show that if the uniform planar array antenna is more concentrated, the SE and receive EE will be higher. Considering SE and received EE, the performance of planar arrays outperform linear array. There exist different optimal radio-frequency chain numbers to maximize the SE for planar array and linear array. In addition, the PCA can achieve relatively higher received EE while the SE is close to the fully connected architecture and the full digital architecture.

Spectral Efficiency and Power Allocation for Mixed-ADC Massive MIMO System

This paper investigates the achievable uplink spectral efficiency(SE) of a massive multi-input multi-output(MIMO) system with a mixed analog-to-digital converter(ADC) receiver architecture, in which some antennas are equipped with full-resolution ADCs while others are deployed with low-resolution ADCs. We derive the theoretical results and corresponding approximate expressions of the achievable SE in multi-cell systems with maximum ratio combining(MRC) detector and in single-cell systems with zero-forcing(ZF) detector. Based on approximated results, the effects of physical parameters, including the transmit power, the number of antennas, the proportion of full-resolution ADCs and the quantization precision of the low-resolution ADCs on the achievable SE are revealed. Furthermore, we propose the power allocation algorithms based on the lower bound and upper bound of approximate achievable SE. Our results show that the total achievable SE improves by increasing the number of BS antennas, the signal-to-noise ratio(SNR), and the quantization precision. Results showcase that proposed power allocation algorithms remarkably improve the total achievable SE comparing to the equal power allocation algorithm, which verifies the effectiveness of our proposed schemes.