Iterative Hard Thresholding with Combined Variable Step Size & Momentum-Based Estimator for Wireless Communication Systems with Dynamic Sparse Channels †
Abstract
:1. Introduction
- We propose an efficient dynamic channel estimator that is developed by deriving a combined variable step size mechanism and variable momentum and incorporating this into the traditional iterative hard thresholding. The estimator is named Iterative Hard Thresholding with Combined Variable Step Size and Momentum (IHT-wCVSSnM)-based estimator.
- We present a comparative study of the proposed IHT-wCVSSnM-based estimator with some other estimators when employed in a broadband wireless communication system that is operating in a dynamic sparse wireless channel.
2. Wireless System Model with Sparse Channel
3. The Proposed IHT-wCVSSnM-Based Estimator for Dynamic Sparse Wireless Channel
4. Computer Simulation Results and Computational Complexity Costs
Algorithm 1 Proposed IHT-wCVSSnM-based Estimator for Wireless Communication systems with Dynamic Sparse Channels |
Input:; ; ; ; ; Itr-Max; : stopping tolerance; : step size Output: Reconstructed sparse channel: Stage 1, Initialization of the Proposed IHT-wCVSSnM-based estimator: ; : Iteration counter : residue error; : Path delay support set of ; Stage 2, Iteration section of the Proposed IHT-wCVSSnM-based estimator: for do 1. While 2. 3. 4. 5. 6. 7. Stage 3, Stopping Criterion for the Proposed IHT-wCVSSnM-based estimator: 8. Until the stopping criterion is met: 9. or Itr-Max 10. end while 11. Return |
5. Conclusions and Future Research Directions
Author Contributions
Funding
Conflicts of Interest
References
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Reference | Contributions |
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[11] | The paper focused on estimation technique for underwater acoustic (UWA) channels where the channels impulses’ responses are said to possess large delays and Doppler spreads with few significant echoes. The proposed method (a flexible complexity-based recursive least-squares-based estimator) employed single-carrier waveforms for the estimation of doubly-selective single antenna channels, while neglecting the weakest taps. |
[12] | The problem of equalization of sparse channels with large delay was addressed in this paper. By taking advantage of the prior knowledge of the sparsity of the channel the authors proposed the use of a Matching Pursuit (MP) algorithm to obtain the nonzero weights in the channel response of the system. |
[13] | The papers considered communication problems that involve the estimation and equalization of channels with a large delay spread but with small nonzero support. By exploiting the sparse nature of the channel through the use of a matching pursuit (MP) algorithm, the authors developed a technique of obtaining near to accurate channel estimates for the system. |
[14] | The authors considered orthogonal frequency-division multiplexing (OFDM) system that is based on a dynamic parametric channel model. The channel model is assumed to be parameterized by a small number of distinct paths that are characterized by time-varying path delay and path gain. For this system, the authors proposed a sparse channel estimation and tracking method using the polynomial basis expansion model of [15]. |
[16] | To recover a d-dimensional m-sparse signal with high probability, the author proposed an extended Orthogonal Matching Pursuit (OMP)-based channel estimationa scheme that brings the required number of measurements for OMP closer to Basic Pursuit (BP)-based estimator. |
[17] | The reconstruction of sparse signals with and without noisy perturbations was considered in this paper. To achieve this, the authors developed a recovery technique for sparse signals sampled by employing the subspace pursuit (SP) algorithm. |
[18] | The authors proposed a signal reconstruction algorithm that is based on the OMP algorithm. The new algorithm is called CoSaMP and it incorporates several other ideas from some other previous works. The new ideas were incorporated to both accelerate the algorithm and provide strong guarantees that OMP failed to provide. |
[19] | The authors proposed a structured compressive sensing (SCS)-aided time-domain synchronous-OFDM scheme using wireless channel properties. These properties include the channel sparsity and the slow time-varying path delays which are usually not considered in conventional OFDM schemes. |
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[21] | Bayesian compressive sensing technique was proposed for the reconstruction of compressible signals on some linear basis. From this, the reconstruction of the signal can be executed accurately using only a small number of basis-function coefficients associated with the linear basis. |
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[23] | The authors proposed a structured compressive sensing algorithm named structured matching pursuit (SMP) for the reconstruction of dynamic sparse channels in broadband wireless communication systems. This is achieved by using temporal correlations associated with time-varying sparse channels for the reconstruction. |
[24] | The tracking of a dynamic sparse channel in a broadband wireless communication system was considered in this paper. The authors proposed a dynamic CS algorithm named differential orthogonal matching pursuit (D-OMP) based on the standard OMP algorithm to track a dynamic sparse channel. |
[25] | The authors proposed a differential simultaneous orthogonal matching pursuit (DSOMP) algorithm-based joint multi-symbol channel estimation to estimate dynamic channel parameters. The authors took advantage of the complex exponential basis expansion model (CE-BEM) in the time domain and exploiting the channel sparsity in the delay domain. |
[26] | Differential block simultaneous orthogonal matching pursuit (DBSOMP) algorithm based on jointly sparsity in different complex basis expansion mode (CE-BEM) order was proposed to estimate a dynamic sparse channel in the massive MIMO systems with better recovery performance and lower computational complexity. |
[27] | A new greedy channel estimation technique that is capable of tracking dynamic sparse signals is proposed for millimeter-wave (mmWave) communication systems. Some of the signals tracked by estimation techniques include time-varying angle of departure (AoD), angle of arrival (AoA), and channel gain amplitudes of mmWave channel. |
[28] | Kalman Filtered Compressed Sensing (KF-CS) estimation of the time-varying underwater acoustic channel is studied in this paper. The authors modeled the time-varying underwater acoustic (UWA) channels as sparse. This consists of both constant and time-varying supports. The KF-CS-based estimator is then employed to enhance the underwater acoustic communication systems’ performance. |
[29] | The problem of estimating sparse communication channels in the OFDM system is considered in this paper. The modified likelihood function’s maximization for the system is performed with the aid of the Expectation–Maximization (EM) algorithm. |
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[32] | An Adaptive Channel Estimation (ACE) technique that exploited the sparsity in time-varying broadband wireless channels is proposed. The estimator is named Variable Step Size Sign Data Sign Error NLMS (VSS-SDSENLMS)-based estimator and it is used to track sparse channels in the considered system. |
[33] | Both downlink (DL) and uplink (UL) channel estimation for the time-varying massive MIMO networks is studied in this paper. An expectation maximization-based sparse Bayesian learning framework is developed to learn the model parameters of the sparse virtual channel. |
[34] | The authors investigated the estimation of the sparse multi-user massive MIMO channels via multi-task (MT)-sparse Bayesian learning (SBL) that is employed in learning dynamic sparse channels in the uplink paths of multi-user massive MIMO-OFDM systems. Specifically, the dynamic information of the sparse channel is used to initialize the hyper-parameters in the multi-task (MT)-sparse Bayesian learning (SBL) MT-SBL procedure for the next time step. |
[35] | A new method for channel estimation in space-time block coding (STBC) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. This is achieved by using the sparsity and the inherent temporal correlation of the time-varying wireless channel. Specifically, an adaptive multi-frame averaging (AMA) and improved mean square error (MSE) optimal threshold (IMOT)-based channel estimation method is proposed by the authors. |
[36] | The authors investigated the estimation and prediction of the sparse time-varying channel in underwater acoustic (UWA) communication systems, in which they proposed a decision-directed-based sparse adaptive predictor that works in the delay-Doppler domain for dynamic UWA channels. The proposed technique extrapolates the channel knowledge estimated from a block of training symbols, and the predicted channel is used to decode consecutive data blocks. |
[37] | The authors proposed a channel estimator that is based on iterative hard thresholding (IHT) algorithm. This is achieved by using the temporal correlation that is associated with the dynamic sparse wireless channel. The proposed estimator is named the iterative hard thresholding with memory (IHT-wM)-based estimator. The proposed estimator also employs its memory term to enhance channel estimation procedure in the system. |
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Oyerinde, O.O.; Flizikowski, A.; Marciniak, T. Iterative Hard Thresholding with Combined Variable Step Size & Momentum-Based Estimator for Wireless Communication Systems with Dynamic Sparse Channels. Electronics 2021, 10, 842. https://doi.org/10.3390/electronics10070842
Oyerinde OO, Flizikowski A, Marciniak T. Iterative Hard Thresholding with Combined Variable Step Size & Momentum-Based Estimator for Wireless Communication Systems with Dynamic Sparse Channels. Electronics. 2021; 10(7):842. https://doi.org/10.3390/electronics10070842
Chicago/Turabian StyleOyerinde, Olutayo Oyeyemi, Adam Flizikowski, and Tomasz Marciniak. 2021. "Iterative Hard Thresholding with Combined Variable Step Size & Momentum-Based Estimator for Wireless Communication Systems with Dynamic Sparse Channels" Electronics 10, no. 7: 842. https://doi.org/10.3390/electronics10070842