Exploit Channel Sparsity Research Articles

Channel Estimation for Underwater Acoustic Communications in Impulsive Noise Environments: A Sparse, Robust, and Efficient Alternating Direction Method of Multipliers-Based Approach

Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an l1−l1 optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method.

Turbo-HB: A Sub-Millisecond Hybrid Beamforming Design for 5G mmWave Systems

Hybrid beamforming (HB) architecture has been widely considered for 5G mmWave systems. It reduces hardware complexity by allowing the number of RF chains to be far fewer than the number of antennas. A major practical challenge for HB is to obtain a beamforming solution in real-time. In 5G NR, new frame structures with short TTIs are employed to support mmWave communications. Under such frame structures, it is necessary to obtain a beamforming solution with a time resolution varying from 1 ms to 125 us -- an extremely stringent time requirement considering the complexity involved in HB. In this paper, we present the design and implementation of Turbo-HB -- a novel beamforming design under the HB architecture that is capable of offering the beamforming matrices in less than 500 us. The key ideas of Turbo-HB include: (i) reducing the complexity of computation-intensive SVD operations by exploiting channel sparsity at mmWave frequencies, and (ii) achieving large-scale parallel computation with minimal memory access. We implement Turbo-HB on an off-the-shelf Nvidia GPU and conduct extensive experiments. Our experimental results demonstrate that Turbo-HB can obtain a beamforming solution in 500 us for up to 100 RBs and 10 MU-MIMO users on each RB while offering competitive throughput performance compared to state-of-the-art (non-real-time) algorithms.

Compressive sensing-based channel estimation for high mobile systems with delay Doppler effects

In this paper, channel overhead is reduced by exploiting channel sparsity for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system. Where, compressive sensing (CS) based dictionary design algorithms has been adopted as a channel estimation technique in high mobile systems with minimal number of pilots, such as high-speed train (HST) systems. A novel framework design of the dictionary-based CS was proposed considering both delay and Doppler effects in order to correctly recover the channel response. The channel under consideration is a 2 by 2 space-time block code (STBC) MIMO channel. Simulation tests according to the international telecommunication union (ITU) channel model demonstrated the suitability of the proposed dictionary for estimating the channel impulse response (CIR) of a liner time varying (LTV) channel with a mobility approaches 675 Km/h related to a Doppler frequency of 1500 Hz and 2.4 GHz carrier frequency. Two CS recovery algorithms were applied; orthogonal matching pursuit (OMP) and basis pursuit (BP), where by about 7 dB gain in signal to noise ratio (SNR) was achieved with mobility of 675 Km/h using OMP as compared to BP at a bit error rate (BER) of with 128 OFDM subcarriers.

Exploiting Sparsity for Underwater Acoustic Sensor Network Under Time-Varying Channels

As a time-frequency doubly selective channel, severe multipath, Doppler, as well as the large time-delay characteristics of the underwater acoustic (UWA) channel pose significant challenge to the research and design of UWA communication and network systems. To mitigate these negative factors, inherent sparsity contained in the UWA channel has been extensively investigated to improve UWA communication via a sparsity exploitation receiver. While the performance of the UWA sensor network is highly dependent on that of the physical layer, there are few investigations reported on exploiting channel sparsity from the viewpoint of UWA networking. In this article, a UWA sensor network adopting the sparsity exploitation physical layer is evaluated based on the network simulator 3 (NS-3) simulation tool. The simulation time-varying channel is generated by incorporating the Bellhop channel model with the statistical characteristics extracted from experimental shallow water channels. Three types of physical layers, i.e., those do not adopt sparse exploitation, adopting compressed sensing (CS), as well as the dynamic CS (DCS) technique, are employed for evaluation and comparison of network behavior under different media access control (MAC) protocols. The evaluation results verify the effectiveness of sparsity exploitation in improving UWA sensor network performance in the presence of time variations, while giving a quantitative comparison between enhancement achieved by the CS and DCS sparsity exploitation.

Dictionary Learning for Channel Estimation in Hybrid Frequency-Selective mmWave MIMO Systems

Exploiting channel sparsity at millimeter wave (mmWave) frequencies reduces the high training overhead associated with the channel estimation stage. Compressive sensing (CS) channel estimation techniques usually adopt the (overcomplete) Fourier transform matrix as sparsifying dictionary. This may not be the best choice when considering hardware impairments in practical arrays. We propose two dictionary learning (DL) algorithms to learn the best sparsifying dictionaries for channel matrices from observations obtained with practical hybrid frequency-selective mmWave multiple-input-multiple-output (MIMO) systems. First, we optimize the combined dictionary, i.e., the Kronecker product of transmit and receive dictionaries, as it is used in practice to sparsify the channel matrix. This stage operates as a calibration phase, since all the hardware imperfections are embedded into the learnt dictionaries. Second, considering the different array structures at the transmitter and receiver, we exploit separable DL to find the best transmit and receive dictionaries. Once the channel is expressed in terms of the optimized dictionaries, various CS-based sparse recovery techniques can be applied for low overhead channel estimation. The effectiveness of the proposed DL algorithms under low SNR conditions has been corroborated via numerical simulations with different system configurations, array geometries and hardware impairments.

Sparse DFT Based Channel Estimation In OFDM Systems

Channel estimation is an essential part of Orthogonal Frequency Division Multiplexing (OFDM) communication systems. In this paper, two Discrete Fourier Transform (DFT) improvement algorithms are proposed and compared where the 1st one exploits channel sparsity concept while the other considers significant channel coefficients only. In the proposed algorithms; Enhanced and Sparse DFT (E-DFT and S-DFT), different number of significant channel components is selected either by a threshold determining procedure such as in E-DFT, or through determining channel sparsity level such as in S-DFT. In the presence of Doppler frequency shifts, the Inter Symbol Interference (ISI) effect on channel coefficients is successfully reduced using the proposed estimation algorithms. Vehicular A-ITU channel model is considered with a relatively high vehicle speed up to 68 Km/h in order to test the suitability of the proposed algorithms for mobile systems. E-DFT and S-DFT improves conventional as well as previous DFT improvement methods (I-DFT) suggested by [7], [8], [9], [15]. For 64 subcarriers, S-DFT outperforms E-DFT and I-DFT by about 3dB at a BER of 0.01 with a mobility reaches 45 Km/h, and by about 0.4dB and 2.5dB at a BER of 0.02 with a mobility reaches 68Km/h.

Precise Channel Estimation Approach for a mmWave MIMO System

Channel estimation is a formidable challenge in mmWave Multiple Input Multiple Output (MIMO) systems due to the large number of antennas. Therefore, compressed sensing (CS) techniques are used to exploit channel sparsity at mmWave frequencies to calculate fewer dominant paths in mmWave channels. However, conventional CS techniques require a higher training overhead for efficient recovery. In this paper, an efficient extended alternation direction method of multipliers (Ex-ADMM) is proposed for mmWave channel estimation. In the proposed scheme, a joint optimization problem is formulated to exploit low rank and channel sparsity individually in the antenna domain. Moreover, a relaxation factor is introduced which improves the proposed algorithm’s convergence. Simulation experiments illustrate that the proposed algorithm converges at lower Normalized Mean Squared Error (NMSE) with improved spectral efficiency. The proposed algorithm also ameliorates NMSE performance at low, mid and high Signal to Noise (SNR) ranges.

Joint Channel and Location Estimation of Massive MIMO System With Phase Noise

Massive multiple-input multiple-output (MIMO) is a key technique in the fifth-generation (5G) networks for its attractive advantages in wireless communication. Besides, it also provides localization capability with high accuracy, yet the massive MIMO localization problem is not well addressed with the presence of some physical impairments in the circuits, such as phase noise (PHN). In this paper, we consider localization problem with PHN, which is a critical bottleneck in massive MIMO. Traditionally, existing methods exploit channel sparsity by sampling the space into discrete grids to estimate the position of the user in the compressive sensing framework. However, as the PHN affects the received signal in a nonlinear manner, it is difficult to obtain accurate basis vectors for sparse channel recovery. Besides, they often suffer from performance loss due to the location quantization error introduced by the fixed location grid. To deal with the aforementioned problems, we introduced a sparse representation model for the channel with dynamic-grid parameters to eliminate the location quantization error and derived an approximation for the likelihood with the presence of PHN. Based on these, we proposed an efficient algorithm for joint estimation of user location and sparse channel utilizing the majorization-minimization algorithm, which is shown to achieve higher localization accuracy than existing methods with the presence of PHN.

Compressive RF Training for Massive MIMO With Channel Support Side Information

Hybrid beamforming (BF) is a promising solution for massive MIMO with limited RF chains. To reduce the amount of pilot overhead for channel estimation, compressed sensing techniques that exploit channel sparsity have been proposed. One key issue is how to design the RF (analog) training vectors to achieve higher BF gain with fewer pilots. Specifically, narrow-beam RF training requires large pilot overhead for finding strongest paths, and random RF training suffers from low BF gain. We propose to use a mixture of narrow-beam and random RF training vectors, and optimize the fraction of the two sets of RF training vectors based on channel support side information (CSSI) at the BS. We show that this optimized fraction exhibits a phase transition: when the CSSI accuracy exceeds a certain threshold, the maximum number of narrow-beam RF training vectors should be used to focus beams in all directions indicated by the CSSI. Otherwise, only random RF training vectors should be used to explore the unknown channel support. Moreover, we derive closed-form bounds on the channel estimation error. Both the analysis and simulations show that the proposed method can achieve substantial gains over various baseline methods.

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.

Variable kernel‐based computing algorithms for estimating sparse multipath channels

SummaryAccurate channel estimation algorithms are required to mitigate the frequency‐selective fading in the broadband wireless communication systems. Many physical experiments revealed that finite impulsive responses are distributed as sparse in delayed time domain. Hence, the inherent sparse information can be exploited by state‐of‐the‐art computing algorithms, in order to improve channel accuracy. Existing computing algorithms, zero‐attracting recursive least square (ZA‐RLS) and reweighted ZA‐RLS (RZA‐RLS), have been developed to exploit channel sparsity. However, optimization theory implies that accuracy of the computing algorithms can be further improved to exploit more sparsity information. To further improve the estimation performance, this paper proposes a correntropy induced metric (CIM)‐penalized RLS (CIM‐RLS) based sparse channel estimation algorithm. Here, sparse constraint is performed by CIM function, while error constraint term is computed by RLS. In particular, Gaussian kernel is adopted for computing the CIM, and its variable kernel width (VKW) is computed for adaptively exploiting the channel sparsity. Monte Carlo simulation results are conducted to verify the proposed algorithm in different scenarios.

Auto Regulated Data Provisioning Scheme with Adaptive Buffer Resilience Control on Federated Clouds

We investigate the channel state information (CSI) in multi-input multi-output (MIMO) cooperative networks that employ the amplify-and-forward transmission scheme. Least squares and expectation conditional maximization have been proposed in the system. However, neither of these two approaches takes advantage of channel sparsity, and they cause estimation performance loss. Unlike linear channel estimation methods, several compressed channel estimation methods are proposed in this study to exploit the sparsity of the MIMO cooperative channels based on the theory of compressed sensing. First, the channel estimation problem is formulated as a compressed sensing problem by using sparse decomposition theory. Second, the lower bound is derived for the estimation, and the MIMO relay channel is reconstructed via compressive sampling matching pursuit algorithms. Finally, based on this model, we propose a novel algorithm so called sparsity adaptive expectation maximization (SAEM) by using Kalman filter and expectation maximization algorithm so that it can exploit channel sparsity alternatively and also track the true support set of time-varying channel. Kalman filter is used to provide soft information of transmitted signals to the EM-based algorithm. Various numerical simulation results indicate that the proposed sparse channel estimation technique outperforms the previous estimation schemes.

Shallow water acoustic channel estimation across fluctuations in channel support

Estimating the shallow water acoustic channel across rapidly varying multipath fluctuations have been an open challenge for decades. Recently, sparse sensing techniques have been employed to take advantage of the heavy-tailed distribution of channel components in the Delay-Doppler domain. Despite noticeable improvement over channel estimator performance by exploiting channel sparsity compared to traditional least-squared based techniques, a key challenge remains. Most sparse recovery techniques are designed to estimate high-amplitude components across static or slowly varying support. Depending on wind and sea conditions, the underlying distribution of the channel components may change unpredictably, leading to fluctuations in the channel support that are difficult to model or track efficiently with high precision. Furthermore, not all channel components are high-energy and therefore, may be unintentionally suppressed by a sparse optimization technique. We will present the current state-of-the-art on applying sparse sensing, particularly mixed norm techniques, to shallow water channel tracking. In particular, we will present extensions to prior work on channel estimation that exploit a non-convex metric to converge faster to the same solution offered by the traditional (and convex) Lasso metric. We will present how non-convex optimization can navigate varying channel sparsity and present results based on experimental field data.

Sign Function Based Sparse Adaptive Filtering Algorithms for Robust Channel Estimation under Non-Gaussian Noise Environments

Robust channel estimation is required for coherent demodulation in multipath fading wireless communication systems which are often deteriorated by non-Gaussian noises. Our research is motivated by the fact that classical sparse least mean square error (LMS) algorithms are very sensitive to impulsive noise while standard SLMS algorithm does not take into account the inherent sparsity information of wireless channels. This paper proposes a sign function based sparse adaptive filtering algorithm for developing robust channel estimation techniques. Specifically, sign function based least mean square error (SLMS) algorithms to remove the non-Gaussian noise that is described by a symmetric α-stable noise model. By exploiting channel sparsity, sparse SLMS algorithms are proposed by introducing several effective sparse-promoting functions into the standard SLMS algorithm. The convergence analysis of the proposed sparse SLMS algorithms indicates that they outperform the standard SLMS algorithm for robust sparse channel estimation, which can be also verified by simulation results.

Pilot Decontamination in Wideband Massive MIMO Systems by Exploiting Channel Sparsity

This paper strives to reduce pilot contamination, a bottleneck for massive multiple-input multiple-output (MIMO) systems, by exploiting channel sparsity. Considering that typical wideband massive MIMO channel is correlated in both space and frequency domains, we employ Karhunen–Loeve Transform (KLT) and Discrete Fourier Transform (DFT) to capture the hidden sparsity of the channel. KLT basis is optimal in extracting the uncorrelated information from channel, but requires channel statistical information. As a suboptimal alternative, DFT basis can be determined without channel statistics, which is more viable for practical use. By representing the channel with DFT basis, we find that the subspaces of the desired and interference channels are approximately orthogonal, even when the number of antennas is not so large. Inspired by this observation, we propose a pilot decontamination method, where a pilot assignment policy is designed to help identify the subspace of the desired channel, and a desired channel subspace aware least square channel estimator is derived to remove the pilot contamination. The proposed method does not need channel statistics and pilot co-ordination. By exploiting channel stationary, the method does not introduce extra training overhead. Simulation results demonstrate substantial sum rate gain of the proposed method over existing methods.

Compensation Estimation Method for Fast Fading MIMO-OFDM Channels Based on Compressed Sensing

In this paper, a compensation estimation algorithm is developed for Multiple-Input-Multiple-Output (MIMO) Orthogonal Frequency-Division-Multiplexing (OFDM) systems operating in a fast fading environment. In order to satisfy the constraint frequency mask, the pulse signal spectrum must be limited in the mask band. We investigate a channel estimator that exploit channel sparsity in the time and/or Doppler domain, where the channel is described by a limited number of paths, each characterized by a delay, Doppler scale, and attenuation factor, and derive the exact inter-carrier-interference pattern. The algorithm works with channel sparsity by jointly estimating the sparse coefficients vector and by reconstructing dynamic mathematical model of pulse wave functions. The proposed method exploits the intrinsic relationship between the sparse channels and the mathematical model. A dynamic mathematical model of pulse wave functions is used to construct the sparse channels. The dynamic mathematical model reconstruction is used to update the sensing matrix. The pulse signal which is band and time concentrated distribution, is conducive to optimization design of sparse MIMO- OFDM channel. The simulation results show that the proposed channel estimator can provide a considerable performance improvement in estimating doubly selective channels with few pilots and computational complexity.

Time reversal communications in a time-varying sparse channel

Recently, time reversal (TR) communications has been extended to time-varying channels. The basic idea is to implement it on a block-by-block basis such that within each block the channel remains time-invariant and subsequently is updated using detected symbols (decision-directed mode). Using experimental data (12–20 kHz) collected in shallow water, this letter investigates three different block-based TR approaches: (1) without explicit phase tracking, (2) with phase tracking, and (3) exploiting channel sparsity. The TR approaches then are compared to a conventional adaptive multichannel equalizer. It is found that approach (3) generally provides the best performance and robustness.

Time reversal communication in a time-varying sparse channel

Recently time reversal (TR) communications has been extended to time-varying channels. The basic idea is to implement it on a block-by-block basis such that within each block the channel remains time-invariant and subsequently is updated using detected symbols (decision-directed mode). Using experimental data (12-20 kHz) collected in shallow water, this letter investigates three different block-based TR approaches: (1) without explicit phase tracking, (2) with phase tracking, and (3) exploiting channel sparsity. The TR approaches then are compared to a conventional adaptive multichannel equalizer. It is found that approach (3) generally provides the best performance and robustness.

Sparse Channel Estimation for Multicarrier Underwater Acoustic Communication: From Subspace Methods to Compressed Sensing

In this paper, we investigate various channel estimators that exploit channel sparsity in the time and/or Doppler domain for a multicarrier underwater acoustic system. We use a path-based channel model, where the channel is described by a limited number of paths, each characterized by a delay, Doppler scale, and attenuation factor, and derive the exact inter-carrier-interference (ICI) pattern. For channels that have limited Doppler spread we show that subspace algorithms from the array processing literature, namely Root-MUSIC and ESPRIT, can be applied for channel estimation. For channels with Doppler spread, we adopt a compressed sensing approach, in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms, and utilize overcomplete dictionaries with an increased path delay resolution. Numerical simulation and experimental data of an OFDM block-by-block receiver are used to evaluate the proposed algorithms in comparison to the conventional least-squares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating ICI, the compressed sensing algorithms can effectively handle channels with significant Doppler spread.