Uplink Sparse Channel Estimation for Hybrid Millimeter Wave Massive MIMO Systems by UTAMP-SBL.

Massive multiple-input multiple-output (MIMO) enables reliability in low latency communication systems. This paper proposes a channel estimation scheme in orthogonal time frequency space (OTFS) massive MIMO systems, where the inherent channel cluster structure in Doppler-angle domain is considered. In our proposed scheme, a local Beta process (LBP) is utilized to characterize a two-dimensional (2-D) structure in Doppler-angle domain. The uplink channel estimation problem is modelled as a sparse channel reconstruction problem, and it is solved by estimating channel parameters (i.e., Doppler, angle and delay) with sparse Bayesian learning (SBL). Thus, downlink channel estimation can be performed with the help of these parameters. Finally, simulation results verify that the proposed algorithm can not only achieve ideal performance of channel estimation, but also have robust adaptation to variable Doppler.

Downlink channel estimation with low pilot overhead is an important and challenging problem in massive multiple‐input–multiple‐output (MIMO) systems due to the substantially increased MIMO channel dimension. A block iterative support detection (block‐ISD)‐based algorithm for downlink channel estimation to reduce the pilot overhead is proposed, which is achieved by fully exploiting the block sparsity inherent in the block‐sparse equivalent channel derived from the spatial correlations of MIMO channels. Furthermore, unlike conventional compressive sensing (CS) algorithms that rely on prior knowledge of the sparsity level, block‐ISD relaxes this demanding requirement and is thus more practically appealing. Simulation results demonstrate that block‐ISD yields better normalised mean square error (NMSE) performance than classical CS algorithms, and achieve a reduction of 84% pilot overhead compared with conventional channel estimation techniques.

Most existing downlink channel estimation methods rely on channel sparsity in the angular domain to reduce pilot overhead for massive multiple-input multiple-output (MIMO) systems. Compared with channel estimation methods based on predefined basis or offline dictionary learning, in this paper, we design an online two-timescale joint uplink/downlink dictionary learning and channel estimation (TTS-JDLCE) algorithm for dynamic scenarios, where the channel sparsity and angle reciprocity between uplink and downlink transmissions are both exploited to reduce the pilot overhead. The downlink channel estimation is constructed as a TTS stochastic optimization problem with a constraint coupled by the long-term dictionary and short-term sparse channel representations. Treating the dictionary as a learnable parameter, the proposed algorithm can capture dynamic spatial information for enhancing performance. By introducing a relaxed TTS primal-dual decomposition (PDD) framework, the original problem is decomposed into a long-term online dictionary learning subproblem and a family of short-term sparse channel estimation subproblems. Besides, the deep unfolding technique is employed to extract gradient information from short-term problems, which circumvents the non-closed form and non-convexity of long-term subproblem by constructing a convex surrogate problem. Finally, simulations show that the proposed method remarkably reduces the pilot overhead and achieves significant performance gains over various baselines.

In order to reduce the pilots overhead and improve the estimation accuracy of doubly selective sky wave channel estimation based on compressed sensing (CS), a new compressed sensing estimation scheme is proposed by exploiting the temporally correlated sparsity of channel coefficient in this paper. Combining with the transmission model of High-frequency (HF) orthogonal frequency division multiplexing (OFDM) system and the sparsity of sky wave channel in transformed domain, the channel estimation problem is formulated under the framework of compressed sensing. On this basis, the temporal correlation of channel coefficient sparsity is theoretically verified by proving that the channel coefficients in several successive OFDM symbols share the common support set. Since the temporal correlation enhances the sparsity of channel coefficients in time dimension, then higher reconstruction accuracy of compressed sensing and the reducuction of pilot overhead can be expected. Simulation results verify the effectiveness of the proposed scheme.

In filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) systems, a large pilot overhead is required due to the existence of the imaginary interference. In this paper, we present an approach to reduce the pilot overhead of channel estimation. A part of pilot overhead is used for transmitting data, and compensating symbols are required and designed to remove the imaginary interference. It is worthwhile to point out that the power of compensating symbols can be helpful for data recovery; hence, the proposed approach decreases the overhead of pilots significantly without the cost of additional pilot energy. In addition, the proposed scheme is extended into multiple input multiple output systems without the performance loss. Compared with the conventional preamble consisting of 3 columns symbols, the pilot overhead is equivalent to 2 column symbols in the proposed preamble. To verify the proposed preamble, numerical simulations are carried out with respects to bit error ratio.

Effective channel estimation for massive multiple-input-multiple-output (MIMO) systems based on frequency division duplex (FDD) protocol is a crucial problem. To reduce pilot overhead, we consider the joint sparsity of the multi-path channel in delay-angle domain. Based on the joint sparsity, we propose a decoupling pilot design scheme. In the proposed scheme, the pilot design is decoupled into two parts. In the first part, a global optimal selection greedy iterative algorithm (GOS-GIA) is proposed to obtain the near-optimal pilot subcarrier pattern. In the second part, a random Rademacher distribution pilot matrix is used as the angle-domain pilot matrix. Accordingly, a two-stage channel estimation strategy is also provided and analyzed. The first stage of the strategy is concerned with retrieving the positions of non-zero dominant taps in the delay domain. The second stage focuses on estimating the channel coefficients at these taps. Algorithm complexity analysis shows that the GOS-GIA can reduce the computational complexity at least one order of magnitude, and the proposed channel estimation strategy reduces the computational complexity by more than two orders of magnitude. Simulation results verify that the proposed pilot design scheme achieves better performance with lower pilot overhead.

Compressive sensing (CS) techniques have been shown to enhance the performance of sparse channel estimation. This paper addresses CS-based sparse channel estimation in practical systems where the measurements are quantized to a finite number of bits. In these systems, quantization introduces two kinds of errors into the CS framework: quantization errors and saturation errors. To combat the effect of quantization error on estimating the sparse channel, a new complex-valued cost function is formulated based on the quantization model. To minimize this cost function, a multi-bit iterative hard thresholding algorithm is proposed. The channel estimate performance is evaluated by modeling the quantization error as white Gaussian noise. Our simulation results quantify the number of bits needed for our proposed quantized CS-based sparse channel estimate to achieve satisfactory performance.

The huge pilot overhead required for channel estimation is one of the key issues for massive multiple-input multiple-output (MIMO) systems. Existing compressed sensing and deep learning methods generally implement pilot compression under the assumption of the huge number of antennas and strict channel sparsity, while the channel estimation performance decreases sharply under quasi-sparse channel environment. Motivated by the powerful learning ability of deep learning for extracting the major characteristics of the target, we propose approximate message passing (AMP) algorithm-based multi-stage training optimization architecture to solve the above problem, where the whole system is considered as a deep neural network (DNN). In the first stage, the optimized sensing matrix of the AMP algorithm is learned by training to match the quasi-sparse channel. In the second stage, we optimize the linear coefficients and nonlinear shrinkage parameters of AMP to further improve the performance. In the third stage, all parameters are jointly optimized by training to make the whole system optimal. Numerical simulation results show that the proposed architecture can achieve high precision channel estimation under the premise of reducing pilot overhead effectively.

In this paper, we propose a manifold optimization empowered two-timescale channel estimation (MO-TTCE) scheme for reconfigurable intelligent surface (RIS)-assisted multiuser millimeter wave massive MIMO systems. Since the base station (BS) and RIS remain relatively stationary while the user equipments (UEs) are mobile, the coherence time of the RIS-BS channel is significantly longer than that of the UErelated channels, namely the UE-RIS and UE-BS channels. Therefore, it is sufficient to estimate the RIS-BS channel only once in the large timescale, while frequently estimating the UErelated channels in the small timescale. We leverage the sparse and low-rank properties of the RIS-BS channel and transform the channel estimation problem into a series of sparse lowrank matrix recovery (SLRMR) problems, specifically ℓ1-norm regularized constrained optimization problems with the feasible region being a complex bounded-rank (CBR) matrix set. To ensure the differentiability of the objective function, we employ a differentiable Huber-γ function as a substitute for the ℓ1-norm. To handle the non-convex nature of the CBR matrix set, we treat the complex fixed-rank (CFR) matrix set as a CFR manifold and consider the CBR matrix set as a collection of CFR manifolds, thereby employing manifold optimization techniques to solve the problem. Furthermore, in the small timescale, we utilize the downlink pilot transmission and uplink feedback scheme to simultaneously estimate all UE-RIS channels. Simulation results show that the proposed MO-TTCE scheme can enhance the accuracy of channel estimation and reduce pilot overhead.

Underwater acoustic channels typically exhibit clustered-sparse structure, and sparse channel recovery based on the clustered-sparse structure can achieve smaller structural error. We propose a novel clustered-sparse Bayesian model for sparse channel estimation in underwater acoustic (UWA) orthogonal frequency-division multiplexing (OFDM) communication systems. In this model, the sparsity and temporal correlation of channel impulse responses (CIRs) are controlled by a set of hyperparameters. For continuously transmitted OFDM blocks in one frame, the auto-regressive (AR) process is used to characterize temporal correlation of time-varying UWA channels, and different clusters are considered to have different AR model coefficients, as they are usually generated according to different transmission routes. A joint cluster partition and sparse Bayesian learning algorithm (JCP-SBL) is proposed to learn the clustered-sparse structure of UWA channels when the cluster partition is unknown. Results of numerical simulation and lake trial demonstrate the effectiveness of the JCP-SBL channel estimator in time-varying UWA channel, which achieve better channel estimation performance and lower bit error rate (BER) compared with the orthogonal matching pursuit (OMP), simultaneous OMP (SOMP) and temporal multiple sparse Bayesian learning (TMSBL).

Beamspace MIMO can utilize beam selection to reduce the number of required RF chains in mmWave massive MIMO systems. However, beam selection requires the information of beamspace channel of large size. This is a challenging task, since the user mobility usually leads to the fast variation of mmWave beamspace channels, and the real-time channel estimation involves unaffordable pilot overhead. To solve this problem, in this paper we propose a priori-aided (PA) channel tracking scheme. Specifically, by considering a practical user motion model, we first excavate a temporal variation law of the physical direction between the base station and each mobile user. Then, based on the special sparse structure of mmWave beamspace channels, we propose to utilize the obtained beamspace channels in the previous time slots to predict the prior information of the beamspace channel in the following time slot. Finally, aided by the obtained prior information, the time-varying beamspace channels can be tracked with low pilot overhead. Simulation results verify that the proposed PA channel tracking scheme can achieve much better performance than conventional schemes.

To deal with the estimation problem of non-stationary channel in massive Multiple-Input Multiple-Output (MIMO) up-link, the 2D channels' sparse structure information in temporal-spatial domain is used, to design an iterative channel estimation algorithm based on Dirichlet Process (DP) and Variational Bayesian Inference (VBI), which can improve the accuracy under a lower pilot overhead and computation complexity. On account of that the stationary channel models is not suitable for massive MIMO systems anymore, a non-stationary channel prior model utilizing Dirichlet Process is constructed, which can map the physical spatial correlation channels to a probabilistic channel with the same sparse temporal vector. By applying VBI technology, a channel estimation iteration algorithm with low pilot overhead and complexity is designed. Experiment results show the proposed channel method has a better performance on the estimation accuracy than the state-of-art method, meanwhile it works robustly against the dynamic system key parameters.<br/><br/>

One major practical issue for the implementation of frequency division duplex (FDD) massive MIMO systems is that the acquisition of channel state information at the transmitter side (CSIT) requires overwhelming pilot training and feedback overhead. Recently, compressive sensing (CS) based CSIT estimation approaches have been proposed to reduce the pilot training overhead for massive MIMO systems. However, it is very difficult to compute the minimum required pilot training overhead at the base station because of loose restricted isometry property (RIP) bounds for successful CS recovery and unknown sparsity levels. In this paper, we consider a framework of closed-loop compressive CSIT estimation with 1 bit feedback to learn the minimum required pilot overhead to achieve a certain target CSIT MSE without explicit knowledge of channel sparsity. We analyze the convergence behaviors of the multi-loop pilot overhead adaptation based on the Lyapunov approach. Simulations show that the proposed closed-loop compressive CSIT estimation framework has substantial performance gain over conventional open-loop algorithms and is very robust to dynamic sparsity as well as model mismatch.

This paper presents sparse Bayesian learning (SBL)-based schemes for approximately sparse channel estimation in an orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) wireless system. The parameterized prior-based SBL framework is employed to present a pilot scheme for an ill-posed OSTBC MIMO-OFDM channel estimation scenario. Maximum likelihood symbol detection (MLSD) has been incorporated in the expectation-maximization framework for SBL-based channel estimation. This has led to the development of a novel scheme for joint approximately sparse channel estimation and symbol detection. The proposed scheme performs SBL-based channel estimation in the E-step followed by a modified ML decision metric-based symbol detection in the M-step. Bayesian Cramer–Rao bounds are obtained for the genie minimum mean-squared error estimators corresponding to the SBL schemes. Closed-form bit error probability expressions are derived for the MLSD in the presence of SBL-based channel estimation errors. Simulation results are presented towards the end to validate the theoretical bounds and illustrate the performance of the proposed techniques.

Massive Multiple Input Multiple Output (MIMO) system has gathered lately a huge interest from researchers and it has been known as a backbone technology for the 5th generation because it can greatly improve the capacity of wireless communication and it can potentially provide energy efficiency and security. Before ensuring the full advantages, massive MIMO system has to overcome many challenges. One of them is to accurate an exact estimation of the Channel Impulse response (CIR) between each transmit-receive antenna pair. The other problem arises when implementing such a system in presence of High Power Amplifiers (HPA) which imposes a nonlinear distortion on the transmitted signals. This paper proposes contributions in three key areas. Firstly, we investigate the nonlinear effects of memoryless HPA, which is modeled using Saleh model, by deriving its Bit Error Rate expression (BER) in massive MIMO Orthogonal Frequency Division Multiplexing (OFDM) system. Secondly, we highlight the necessity of providing the accurate channel characteristics by estimating it using Compressive Sensing (CS) techniques. Moreover, we propose also a CS compensation algorithm based on Orthogonal Matching Pursuit (OMP) to mitigate the nonlinear distortion in the receiver. The proposed CS-based compensation technique has been compared to the Neural Network (NN) pre and post compensation technique and it has shown a good performance not only in terms of BER but also in terms of complexity.