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.

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.

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.

Joint Flexible Duplexing and Power Allocation with Deep Reinforcement Learning in Cell-Free Massive MIMO System

Network-assisted full duplex(NAFD)cellfree(CF)massive MIMO has drawn increasing attention in 6G evolvement.In this paper,we build an NAFD CF system in which the users and access points(APs)can flexibly select their duplex modes to increase the link spectral efficiency.Then we formulate a joint flexible duplexing and power allocation problem to balance the user fairness and system spectral efficiency.We further transform the problem into a probability optimization to accommodate the shortterm communications.In contrast with the instant performance optimization,the probability optimization belongs to a sequential decision making problem,and thus we reformulate it as a Markov Decision Process(MDP).We utilizes deep reinforcement learning(DRL)algorithm to search the solution from a large state-action space,and propose an asynchronous advantage actor-critic(A3C)-based scheme to reduce the chance of converging to the suboptimal policy.Simulation results demonstrate that the A3C-based scheme is superior to the baseline schemes in term of the complexity,accumulated log spectral efficiency,and stability.

Grant-Free Random Access in Pilot-Reused Multicell Massive MIMO Systems with Backoff Mechanisms

Grant-free random access(RA)is attractive for future network due to the minimized access delay.In this paper,we investigate the grantfree RA in multicell massive multiple-input multipleoutput(MIMO)systems with pilot reuse.With backoff mechanism,user equipments(UEs)in each cell are randomly activated,and active UEs randomly select orthogonal pilots from a predefined pilot pool,which results in a random pilot contamination among cells.With the help of indicators that capture the uncertainties of UE activation and pilot selection,we derive a closed-form approximation of the spectral efficiency per cell after averaging over the channel fading as well as UEs’random behaviors.Based on the analysis,the optimal backoff parameter and pilot length that maximize the spectral efficiency can be obtained.We find that the backoff mechanism is necessary for the system with large number of UEs,as it can bring significant gains on the spectral efficiency.Moreover,as UE number grows,more backoff time is needed.

Error Probability Analysis for Ultra-Massive MIMO System and Near-Optimal Signal Detection

In this paper,average bit error probability(ABEP)bound of optimal maximum likelihood(ML)detector is first derived for ultra massive(UM)multiple-input-multiple-output(MIMO)system with generalized amplitude phase modulation(APM),which is confirmed by simulation results.Furthermore,a minimum residual criterion(MRC)based lowcomplexity near-optimal ML detector is proposed for UM-MIMO system.Specifically,we first obtain an initial estimated signal by a conventional detector,i.e.,matched filter(MF),or minimum mean square error(MMSE)and so on.Furthermore,MRC based error correction mechanism(ECM)is proposed to correct the erroneous symbol encountered in the initial result.Simulation results are shown that the performance of the proposed MRC-ECM based detector is capable of approaching theoretical ABEP of ML,despite only imposing a slightly higher complexity than that of the initial detector.

Low-complexity soft-output signal detector based on adaptive pre-conditioned gradient descent method for uplink multiuser massive MIMO systems

In multiuser massive Multiple Input Multiple Output(MIMO)systems,a large amount of antennas are deployed at the Base Station(BS).In this case,the Minimum Mean Square Error(MMSE)detector with soft-output can achieve the near-optimal performance at the cost of a large-scale matrix inversion operation.The optimization algorithms such as Gradient Descent(GD)method have received a lot of attention to realize the MMSE detection efficiently without a large scale matrix inversion operation.However,they converge slowly when the condition number of the MMSE filtering matrix(the coefficient matrix)increases,which can compromise the efficiency of their implementation.Moreover,their soft information computation also involves a large-scale matrix-matrix multiplication operation.In this paper,a low-complexity soft-output signal detector based on Adaptive Pre-conditioned Gradient Descent(APGD-SOD)method is proposed to realize the MMSE detection with soft-output for uplink multiuser massive MIMO systems.In the proposed detector,an Adaptive Pre-conditioner(AP)matrix obtained through the Quasi-Newton Symmetric Rank One(QN-SR1)update in each iteration is used to accelerate the convergence of the GD method.The QN-SR1 update supports the intuitive notion that for the quadractic problem one should strive to make the pre-conditioner matrix close to the inverse of the coefficient matrix,since then the condition number would be close to unity and the convergence would be rapid.By expanding the signal model of the massive MIMO system and exploiting the channel hardening property of massive MIMO systems,the computational complexity of the soft information is simplified.The proposed AP matrix is applied to the GD method as a showcase.However,it also can be used by Conjugate Gradient(CG)method due to its generality.It is demonstrated that the proposed detector is robust and its convergence rate is superlinear.Simulation results show that the proposed detector converges at most four iterations.Simulation results also show that the proposed approach achieves a better trade-off between the complexity and the performance than several existing detectors and achieves a near-optimal performance of the MMSE detector with soft-output at four iterations without a complicated large scale matrix inversion operation,which entails a big challenge for the efficient implementation.

QBFO-BOMP Based Channel Estimation Algorithm for mmWave Massive MIMO Systems

At present,the traditional channel estimation algorithms have the disadvantages of over-reliance on initial conditions and high complexity.The bacterial foraging optimization(BFO)-based algorithm has been applied in wireless communication and signal processing because of its simple operation and strong self-organization ability.But the BFO-based algorithm is easy to fall into local optimum.Therefore,this paper proposes the quantum bacterial foraging optimization(QBFO)-binary orthogonal matching pursuit(BOMP)channel estimation algorithm to the problem of local optimization.Firstly,the binary matrix is constructed according to whether atoms are selected or not.And the support set of the sparse signal is recovered according to the BOMP-based algorithm.Then,the QBFO-based algorithm is used to obtain the estimated channel matrix.The optimization function of the least squares method is taken as the fitness function.Based on the communication between the quantum bacteria and the fitness function value,chemotaxis,reproduction and dispersion operations are carried out to update the bacteria position.Simulation results showthat compared with other algorithms,the estimationmechanism based onQBFOBOMP algorithm can effectively improve the channel estimation performance of millimeter wave(mmWave)massive multiple input multiple output(MIMO)systems.Meanwhile,the analysis of the time ratio shows that the quantization of the bacteria does not significantly increase the complexity.

Design of a Neural Network Based Stable State Observer for Mimo Systems

MIMO (Multiple Input Multiple Output) is a key technology underpinning fourth generation or 4G networks. This technology allows 4G networks to increase throughput. However, the dynamics of the MIMO system are not under control due to the many uncertainties that destabilize the system. This work is therefore very relevant in the sense that an observer can be used to monitor the dynamics of such a system. This work presents a neuro-adaptive observer based on a radial basis function neural network for generic non-linear MIMO systems. Unlike most neuro-adaptive observers, the proposed observer uses a neural network that is non-linear in its parameters. It can therefore be applied to systems with high degrees of nonlinearity without any a priori knowledge of the system dynamics. Indeed, in addition to the fact that neural networks are very good nonlinear approximators, their adaptive behavior makes them powerful tools for observing the state without any a priori knowledge of the dynamics of the system. The learning rule of the neural network is an approach based on the modified backpropagation algorithm: A term has been added to guarantee the robustness of the observer. The proposed approach is not limited by a strong assumption. The stability of the neuro-adaptive observer is demonstrated by the direct Lyapunov method. Simulation results are presented in the context of MIMO signal transmission applied in LTE, to demonstrate the performance of our observer.

A TSE based design for MMSE and QRD of MIMO systems based on ASIP

A Taylor series expansion(TSE) based design for minimum mean-square error(MMSE) and QR decomposition(QRD) of multi-input and multi-output(MIMO) systems is proposed based on application specific instruction set processor(ASIP), which uses TSE algorithm instead of resource-consuming reciprocal and reciprocal square root(RSR) operations.The aim is to give a high performance implementation for MMSE and QRD in one programmable platform simultaneously.Furthermore, instruction set architecture(ISA) and the allocation of data paths in single instruction multiple data-very long instruction word(SIMD-VLIW) architecture are provided, offering more data parallelism and instruction parallelism for different dimension matrices and operation types.Meanwhile, multiple level numerical precision can be achieved with flexible table size and expansion order in TSE ISA.The ASIP has been implemented to a 28 nm CMOS process and frequency reaches 800 MHz.Experimental results show that the proposed design provides perfect numerical precision within the fixed bit-width of the ASIP, higher matrix processing rate better than the requirements of 5G system and more rate-area efficiency comparable with ASIC implementations.

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.