Conventional Channel Estimation Algorithms Research Articles

Denoising Generalization Performance of Channel Estimation in Multipath Time-Varying OFDM Systems

Although Orthogonal Frequency Division Multiplexing (OFDM) technology is still the key transmission waveform technology in 5G, traditional channel estimation algorithms are no longer sufficient for the high-speed multipath time-varying channels faced by both existing 5G and future 6G. In addition, the existing Deep Learning (DL) based OFDM channel estimators are only applicable to Signal-to-Noise Ratios (SNRs) in a small range, and the estimation performance of the existing algorithms is greatly limited when the channel model or the mobile speed at the receiver does not match. To solve this problem, this paper proposes a novel network model NDR-Net that can be used for channel estimation under unknown noise levels. NDR-Net consists of a Noise Level Estimate subnet (NLE), a Denoising Convolutional Neural Network subnet (DnCNN), and a Residual Learning cascade. Firstly, a rough channel estimation matrix value is obtained using the conventional channel estimation algorithm. Then it is modeled as an image and input to the NLE subnet for noise level estimation to obtain the noise interval. Then it is input to the DnCNN subnet together with the initial noisy channel image for noise reduction to obtain the pure noisy image. Finally, the residual learning is added to obtain the noiseless channel image. The simulation results show that NDR-Net can obtain better estimation results than traditional channel estimation, and it can be well adapted when the SNR, channel model, and movement speed do not match, which indicates its superior engineering practicability.

Mixed-Timescale Deep-Unfolding for Joint Channel Estimation and Hybrid Beamforming

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.

Joint dictionary and deep learning for cosparse recovery of the millimeter wave massive MIMO channels

The channel estimation (CE) for millimeter wave (mmW) massive multiple input multiple output (mMIMO) is a challenging task because of the important number of transmit and receive antennas, which results in high pilot overhead. In conventional CE algorithms, the channel is modeled using pre-constructed dictionary. This often leads to a suboptimal solution which cannot guarantee CE accuracy. In this paper, an iterative two-stage CE algorithm is presented. In the first stage, training measurements under different conditions are collected and it is proposed to estimate the virtual sparse mmW mMIMO channel using a deep residual learning based orthogonal approximate message passing (DRL-OAMP) algorithm from these measurements. The estimated channel is used in the second stage to learn the dictionary via a projected gradient algorithm. Simulation results show that the proposal improves the CE accuracy with low pilot overhead.

Efficient Optical MIMO–OFDM Channel Estimation Based on Correntropy Compressive Sensing

The compressive sensing (CS) technique is widely used in the field of radio-frequency channel estimation. However, in optical wireless channel (OWC) estimation, CS needed to be adapted to cope with the nonlinear distortion resultant from the electrical-to-optical and optical-to-electrical conversion process of the OWC. Therefore, a robust CS channel estimation technique is proposed for the optical MIMO–OFDM system. The proposed CS channel estimation technique is based on higher-order statistics (HOS). In which, the correntropy is exploited as a HOS similarity measurement instead of the second-order statistics euclidean distance (ED) used with the conventional CS to handle the OWC nonlinear distortion. Herein, the ED is the most popular iterative CS algorithms such as orthogonal matching pursuits, sparsity adaptive matching pursuit, and self-aware step size sparsity adaptive matching pursuit is efficiently replaced by the HOS correntropy based CS to show the effectiveness of the proposed algorithm. Moreover, the most recent visible light communication system GLIM-OFDM is considered here to test the proposed technique. However, the pre-estimated channel state information (CSI) obtained from the previous OFDM frame is exploited as initial information in estimating the CSI of the current OFDM frame, which improves overall system performance. A comparison with the conventional CS reconstruction algorithms is conducted via extensive simulation analysis. The simulation results show the superiority of the bit error rate of the proposed correntropy based CS channel estimation scheme compared to the conventional CS-based channel estimation algorithms.

Off-Grid Aware Channel and Covariance Estimation in mmWave Networks

The spectrum scarcity at sub-6 GHz spectrum has made millimeter-wave (mmWave) frequency band a key component of the next-generation wireless networks. While mmWave spectrum offers extremely large transmission bandwidths to accommodate ever-increasing data rates, unique characteristics of this new spectrum need special consideration to achieve the promised network throughput. In this work, we consider the off-grid targets (basis mismatch) problem for mmWave communications. The off-grid effect naturally appears in compressed sensing (CS) techniques adopting a discretization approach for representing the angular domain. This approach yields a finite set of discrete angle points, which are an approximation to the continuous angular space, and hence degrade the accuracy of related parameter estimation. In order to cope with the off-grid effect, we present a novel parameter-perturbation framework to efficiently estimate the channel and the covariance for mmWave networks. The proposed algorithms employ a smart perturbation mechanism in conjunction with a low-complexity greedy framework of simultaneous orthogonal matching pursuit (SOMP), and jointly solve for the off-grid parameters and weights. Numerical results show a significant performance improvement through our novel framework as a result of handling the off-grid effects, which is totally ignored in the conventional sparse mmWave channel or covariance estimation algorithms.

Sparse Channel Estimation for OFDM-Based Underwater Acoustic Systems in Rician Fading With a New OMP-MAP Algorithm

In this paper, a new channel estimation algorithm is proposed that exploits channel sparsity in the time domain for an orthogonal frequency division multiplexing (OFDM)-based underwater acoustical (UWA) communications systems in the presence of Rician fading. A path-based channel model is used, in which the channel is described by a limited number of paths, each characterized by a delay, Doppler scale, and attenuation factor. The resulting algorithm initially estimates the overall sparse channel tap delays and Doppler shifts using a compressed sensing approach, in the form of the orthogonal matching pursuit (OMP) algorithm. Then, a computationally efficient and novel channel estimation algorithm is developed by combining the OMP and maximum a posteriori probability (MAP) techniques for estimating the sparse complex channel path gains whose prior densities have complex Gaussian distributions with unknown mean and variance vectors, where a computationally efficient maximum likelihood algorithm is proposed for their estimation. Monte Carlo simulation results show that the mean square error and symbol error rate performances of the OMP–MAP algorithm uniformly outperforms the conventional OMP-based channel estimation algorithm, in case of uncoded OFDM-based UWA communications systems.

Turbo Receiver Channel Estimation for GFDM-Based Cognitive Radio Networks

Generalized frequency division multiplexing (GFDM) is a promising candidate for 5G waveforms because of its flexibility to meet the requirements of different scenarios and applications. Compared with the orthogonal frequency division multiplexing, the lower out-of-band radiation and higher spectrum efficiency make GFDM the qualified waveform solution for cognitive radio (CR). In CR networks, channel estimation is the necessity and premise to guarantee reliable spectrum sensing. Because of the block modulation structure for GFDM, conventional channel estimation algorithm cannot be applied to GFDM directly. Also, the feedback information in channel decoding is not fully utilized by the conventional algorithm. To solve these problems, in this paper, a modified turbo receiver is designed to utilize the feedback information for channel estimation. The modulator for the pilot insertion is also improved to make pilots orthogonal to data subcarriers. Based on the modified turbo receiver, an iterative channel estimation strategy combined with threshold control is proposed to cope with the noise enhancement. The symbols rebuilt for the iterative channel estimation are verified that only the credible symbols can be retained for the next iteration. Simulation results demonstrate that the proposed channel estimation method has the better bit error rate and mean-squared error performances over Rayleigh fading channel compared with the conventional algorithm.

Temporal-correlation-based compressive channel estimation for universal filtered multicarrier system over fast-fading channels

The universal filtered multicarrier technique is a competitive candidate multicarrier modulation scheme for 5G communication systems. Conventional channel-estimation algorithms suffer from significant performance losses due to the large spread in the delay of multipath channels in high-speed scenarios. To address this problem, we here propose a low-complexity, partial priori information-sparsity adaptive matching pursuit (PPI-SAMP) algorithm. Unlike the conventional SAMP algorithm, the PPI-SAMP algorithm improves performance over fast-fading channels by adequately exploiting the sparse characteristics and temporal correlation of wireless channels. First, the PPI-SAMP algorithm averages the channel impulse responses (CIRs) of consecutive symbols over the coherence time for achieving the accuracy required for coarse channel estimation. Second, the improved SAMP algorithm acquires the accurate CIRs with low complexity based on the coarse CIR. Moreover, the MSE performance and recovery probability with varying sizes of IBI-free region indicate that the proposed PPI-SAMP algorithm offers a longer CIR for multipath interference and is more robust against larger multipath-channel delay than the conventional SAMP and CoSaMP algorithms. The proposed algorithm also estimates channels more accurately than conventional SAMP and CoSaMP algorithms despite having a complexity reduced by approximately 52% compared to conventional SAMP algorithm.

Low-complexity fractional phase estimation for totally blind channel estimation

To remove the scalar ambiguity in conventional blind channel estimation algorithms, totally blind channel estimation (TBCE) is proposed by using multiple constellations. To estimate the unknown scalar, its phase is decomposed into a fractional phase and an integer phase. However, the maximum-likelihood (ML) algorithm for the fractional phase does not have closed-form solutions and suffers from high computational complexity. By exploring the structures of widely used constellations, this paper proposes a low-complexity fractional phase estimation algorithm which requires no exhaustive search. Analytical expressions of the asymptotic mean squared error (MSE) are also derived. The theoretical analysis and simulation results indicate that the proposed fractional phase estimation algorithm exhibits almost the same performance as the ML algorithm but with significantly reduced computational burden.

An Adaptive Channel Estimation Based on Polynomial Fitting for LTE Uplink in High Doppler Spread Scenario

Channel estimation plays a crucial role in improving the overall system performance in long term evolution (LTE) systems. However, it is demonstrated that conventional channel estimation algorithms have poor performance in the presence of a large Doppler frequency shift. To mitigate the adverse effect of Doppler frequency shift on transmission signals, an adaptive anti-Doppler shift method based on polynomial fitting for LTE uplink is proposed in this paper. Furthermore, an adaptive strategy is exploited to improve estimation accuracy and reduce estimation mean square error (MSE), achieving better system performance. Simulations results validate the effectiveness of anti-Doppler algorithm.

Pilot Matrix Design for Estimating Cascaded Channels in Two-Hop MIMO Amplify-and-Forward Relay Systems

In this paper, we consider a two-hop multi-input-multi-output (MIMO) amplify-and-forward (AF) relay system consisting of a source node (SN), a destination node (DN), and a relay node (RN) that simply amplifies and forwards its received signal to the DN without any further processing. In this system, the overall channel from the SN to the DN is a cascade of the backward relay channel over the SN-RN hop, the amplifying matrix at the RN, and the forward relay channel over the RN-DN hop. We investigate the estimation of the two cascaded relay channels at the DN based on the predefined amplifying matrix applied at the RN and the corresponding overall channel obtained through the conventional channel estimation algorithms with the help of pilots transmitted by the SN. In particular, we find necessary and sufficient conditions on the pilot amplifying matrix sequence at the RN to ensure feasible relay channel estimation at the DN. Based on these conditions, we present rules to design diagonal or quasi-diagonal pilot amplifying matrices so that the cascaded relay channels can be estimated with minimum complexity at the RN. In the presence of imperfect overall channel state information at the DN, we further develop the approximate linear least-square estimation of the relay channels based on the designed pilot matrix sequence and demonstrate its performance by simulation results.

A Model Reduction Approach for OFDM Channel Estimation Under High Mobility Conditions

Orthogonal frequency-division multiplexing (OFDM) combines the advantages of high performance and relatively low implementation complexity. However, for reliable coherent detection of the input signal, the OFDM receiver needs accurate channel information. When the channel exhibits fast time variation as it is the case with several recent OFDM-based mobile broadband wireless standards (e.g., WiMAX, LTE, DVB-H), channel estimation at the receiver becomes quite challenging for two main reasons: 1) the receiver needs to perform this estimation more frequently and 2) channel time-variations introduce intercarrier interference among the OFDM subcarriers which can degrade the performance of conventional channel estimation algorithms significantly. In this paper, we propose a new pilot-aided algorithm for the estimation of fast time-varying channels in OFDM transmission. Unlike many existing OFDM channel estimation algorithms in the literature, we propose to perform channel estimation in the frequency domain, to exploit the structure of the channel response (such as frequency and time correlations and bandedness), optimize the pilot group size and perform most of the computations offline resulting in high performance at substantial complexity reductions.