Priori-Information Aided Iterative Hard Threshold: A Low-Complexity High-Accuracy Compressive Sensing Based Channel Estimation for TDS-OFDM

Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in the measurement vector leading to a poor performance when the noise no longer follows the Gaussian assumption but, instead, is better characterized by heavier-than-Gaussian tailed distributions. In this paper, we propose a robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse signals in the presence of impulsive noise. To address this problem, we use a Lorentzian cost function instead of the $L_2$ cost function employed by the traditional IHT algorithm. We also modify the algorithm to incorporate prior signal information in the recovery process. Specifically, we study the case of CS with partially known support. The proposed algorithm is a fast method with computational load comparable to the LS based IHT, whilst having the advantage of robustness against heavy-tailed impulsive noise. Sufficient conditions for stability are studied and a reconstruction error bound is derived. We also derive sufficient conditions for stable sparse signal recovery with partially known support. Theoretical analysis shows that including prior support information relaxes the conditions for successful reconstruction. Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments. Numerical results also demonstrate that the partially known support inclusion improves the performance of the proposed algorithm, thereby requiring fewer samples to yield an approximate reconstruction.

Compressed sensing (CS) is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, we apply the iterative hard thresholding (IHT) algorithm for compressed sensing on the speech signal. The interested speech signal is transformed to the frequency domain using Discrete Fourier Transform (DCT) and then compressed sensing is applied to that signal. The compressed signal can be reconstructed using the recently introduced Iterative Hard Thresholding (IHT) algorithm and also by the tradditional \( \ell_{1} \) minimization (basic pursuit) for comparison. It is shown that the compressed sensing can provide better root mean square error (RMSE) than the tradition DCT compression method, given the same compression ratio.

Wearable ECG monitoring devices, often limited by power constraints, require efficient methods to reduce energy consumption and extend battery life for continuous health tracking. This work proposes a digital compressed sensing approach for ECG (DCS-ECG), featuring a suitable sensing matrix, effective sparse signal recovery algorithms, and an optimized number of bits for quantization (BM). The framework is designed to achieve high compression ratios (CR) with minimal signal distortion and parameter extraction without the reconstruction of the original signal. The following five sensing matrices are examined: deterministic block binary diagonal (DBBD) matrix, random binary (RBin) matrix, random Bernoulli (RBen) matrix, random Gaussian (RG) matrix, and random sparse fixed binary (RSB) matrix. These are paired with a sparsifying matrix (ψ), a hybrid of identity matrix (I), discrete sine transform matrix (S), and discrete cosine transform matrix (C) (i.e. ψ = [I S C]). The following five sparse reconstruction algorithms are evaluated: iterative hard thresholding (IHT) algorithm, orthogonal matching pursuit (OMP) algorithm, smoothed ℓ0 (SL0) algorithm, ℓ1 least square (L1LS) algorithm, and subspace matching pursuit (SMP) algorithm. The proposed DCS-ECG system was tested on ECG signals from the MIT-BIH arrhythmia database. The configuration using the DBBD sensing matrix and OMP recovery algorithm with the sparsifying matrix achieved a low average percentage of root mean square difference (PRD) of 3.75 ± 1.43% at CR = 12.5%, which also offers fast reconstruction. For CR = 12.5% and BM = 8, the CS measurement generation on the Arduino Due consumes 2.02 mJ, while reconstruction on the Raspberry Pi requires 1.13 J. The wireless transmission energy is 1.2973 J. Overall, the proposed CS-based system achieves an 86.24% total energy saving compared to the without CS approach, demonstrating its suitability for low-power IoT-enabled wearable edge ECG health monitoring applications.

The recently proposed compressed sensing theory equips us with methods to recover exactly or approximately, high resolution images from very few encoded measurements of the scene. The traditional ill-posed problem of MRI image recovery from heavily under-sampled κ-space data can be thus solved using CS theory. Differing from the soft thresholding methods that have been used earlier in the case of CS MRI, we suggest a simple iterative hard thresholding algorithm which efficiently recovers diagnostic quality MRI images from highly incomplete κ-space measurements. The new multi-scale redundant systems, curvelets and contourlets having high directionality and anisotropy, and thus best suited for curved-edge representation are used in this iterative hard thresholding framework for CS MRI reconstruction and their performance is compared. The κ-space under-sampling schemes such as the variable density sampling and the more conventional radial sampling are experimented at the same sampling rate and the effect of encoding scheme on iterative hard thresholding compressed sensing reconstruction is studied.

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).

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.

Iterative hard thresholding algorithm (IHT) is a novel and efficient method to solve signal and image reconstruction in compressed sensing, but it is sensitive to the initial point and converges to a local optimal solution. Therefore, to overcome its shortcoming, in this paper a hybrid hard thresholding algorithm (HHT) is derived by introducing the simulated annealing algorithm (SA) into the IHT. And a series of experiments are provided on signal and image reconstruction to assess performance of the algorithm. The experiments and applications show that the proposed algorithm uses less sampling to construct the signal and image and is more stable, as compared with IHT.

As an essential task for enabling dynamic spectrum sharing, spectrum sensing in wideband cognitive radio (CR) networks becomes quite challenging due to high sampling pressure, huge data transmission overheads and serious channel fading. To overcome these challenges, this paper proposes a collaborative spectrum sensing scheme based on 1-bit compressed sensing (CS). Each SU performs local 1-bit CS and obtains its own estimated support set via signal reconstruction. To make use of joint sparsity, all the support sets are fused in the fusion center (FC) and the fused result is used as priori information to guide the next local signal reconstruction. The weighted binary iterative hard thresholding (BIHT) algorithm with support estimate vector is proposed to implement the second reconstruction. Simulation results show that our proposed scheme can achieve effective spectrum detection at low communication and computation load.

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.

Massive multi input multi output (MIMO) systems incorporate orthogonal frequency division multiplexing (OFDM) technology to render high data rate services for future wireless communication applications. The channel estimator (CE) employed by a reliable massive MIMO-OFDM system requires huge amount of overhead in the form of known and null data transmissions, hence limiting the system spectral efficiency (SE). Often, CE design is a tradeoff between SE and system reliability. In this paper, CE with three different overhead arrangements, namely time domain synchronous (TDS), comb type with cyclic prefix (CTCP), 2D grid type with cyclic prefix (GTCP) are investigated and a GTCP based CE is proposed which offers both high SE and improved system reliability. The proposed CE uses autocorrelation based denoising threshold for channel impulse response (CIR) estimation and does not require any knowledge of channel statistics (KCS). A 4 x 16 MIMO-OFDM system is simulated in a rayleigh fading channel environment with U-shaped doppler spectrum. From the bit error rate (BER) performance results inWiMax SUI-4, Advanced Television Technology Center (ATTC) and Brazil A channel environments, it is verified that the proposed CE with GTCP overhead and proposed denoising scheme, indeed improves both SE and system reliability. Hence it is suitable for application in all massive MIMO-OFDM systems.

— Performance of pilot-aided channel estimation techniques such as the Least Squares (LS) method depends on not only on the signal-to-noise ratio (SNR), channel conditions and pilot ratio, but also on the choice of interpolation method for deriving channel estimates at non-pilot subcarriers. This paper investigates the bit-error-rate (BER) performance of linear, spline and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation methods in LS channel estimation over the three extended ITU channel profiles defined for Long Term Evolution (LTE) testing. Simulation results show that applying the linear interpolation method produces the best BER performance over the fading channel with the smallest multipath delay spread. It is also shown that the choice of best interpolation method actually depends on the SNR in some of the fading channel profiles. Index Terms—ITU, LS, LTE, PCHIP, spline. I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) technology has been adopted in many of the next generation communication systems such as Long Term Evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX) [1]. OFDM is preferred not only because it offers high data rate transmission but also because of its flexibility and robustness against multipath fading [1]. Multipath channel fading exists when multiple delayed copies of a transmitted signal are received at the receiver, thereby resulting in the distortion of the transmitted signal. These distortions are collectively termed „channel fading‟, causing reception errors and hence increased bit-error-rate (BER). Channel fading can be broadly classified as time-selective and/or frequency selective, depending on the relationship between the fading channel and the transmitted signal parameters [2]. To combat multipath fading and improve BER, some form of channel estimation method is required in order to estimate the channel distortion effect for each of the active subcarriers within an OFDM symbol [3].

Background: To resist the time-variant underwater acoustic (UWA) channel, large amounts of channel estimation algorithms for the UWA orthogonal frequency division multiplexing (OFDM) are presented. An updated review of the recent UWA OFDM channel estimators is suggested in this article. Objective: The goal of this work is to review and conclude the development of different types of channel estimators. The possible perspectives about the future UWA channel estimator design are also discussed. Methodology: The principles and performances of the linear channel estimators, the compressed sensing (CS)-based channel estimators, and the neural network (NN)-based channel estimators are reviewed and discussed. Simulations are conducted to compare the typical implementations of the different methods. Conclusion: To take more channel state characteristics into account, the data-driven methods have been applied in the channel estimator design. Compared with the linear and CS-based methods, the NN-based channel estimator shows the higher performance, robustness and lower complexity, which is promising to be applied with the proper structure and training sets.

In this letter, the authors propose block normalised iterative hard thresholding (BNIHT) algorithm for the recovery of block sparse signal, in which the non-zero elements are presented in clusters. Based on block restricted isometry property, the sufficient conditions to guarantee the convergence of BNIHT are derived. In addition, the number of required iterations is obtained. The simulation experiment shows that BNIHT algorithm is superior to the block IHT (BIHT) algorithm when the step size satisfies μ < 1 .

Compressive radar imaging has attracted considerable attention because it substantially reduces imaging time through directly compressive sampling. However, a problem that must be addressed for compressive radar imaging systems is the high computational complexity of reconstruction of sparse signals. In this paper, a novel algorithm, called two-dimensional (2D) normalized iterative hard thresholding (NIHT) or 2D-NIHT algorithm, is proposed to directly reconstruct radar images in the matrix domain. The reconstruction performance of 2D-NIHT algorithm was validated by an experiment on recovering a synthetic 2D sparse signal, and the superiority of the 2D-NIHT algorithm to the NIHT algorithm was demonstrated by a comprehensive comparison of its reconstruction performance. Moreover, to be used in compressive radar imaging systems, a 2D sampling model was also proposed to compress the range and azimuth data simultaneously. The practical application of the 2D-NIHT algorithm in radar systems was validated by recovering two radar scenes with noise at different signal-to-noise ratios, and the results showed that the 2D-NIHT algorithm could reconstruct radar scenes with a high probability of exact recovery in the matrix domain. In addition, the reconstruction performance of the 2D-NIHT algorithm was compared with four existing efficient reconstruction algorithms using the two radar scenes, and the results illustrated that, compared to the other algorithms, the 2D-NIHT algorithm could dramatically reduce the computational complexity in signal reconstruction and successfully reconstruct 2D sparse images with a high probability of exact recovery.

In the new generation wireless communication systems where high data rates are desired, orthogonal frequency division multiplexing (OFDM) has become the standard method because of its advantages over single carrier modulation schemes on multi-path, frequency selective fading channels. However, inter-carrier interference due to Doppler frequency shifts, and multi-path fading severely degrades the performance of OFDM systems. Estimation of channel parameters is required at the receiver. In this paper, we present a time-varying channel modeling and estimation method based on the discrete evolutionary transform that provides a time-frequency procedure to obtain a complete characterization of a multi-path, fading and frequency selective channel. Performance of the proposed method is tested on different levels of channel noise, and Doppler frequency shifts.