Channel Impulse Response Estimation 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.

Bayesian Learning-Assisted Joint Frequency Tracking and Channel Estimation for OFDM Systems

Orthogonal frequency division multiplexing (OFDM) is very sensitive to the carrier frequency offset (CFO). The CFO estimation precision heavily makes impacts on the OFDM performance. In this paper, a new Bayesian learning-assisted joint CFO tracking and channel impulse response estimation is proposed. The proposed algorithm is modified from a Bayesian learning-assisted estimation (BLAE) algorithm in the literature. The BLAE is expectation-maximization (EM)-based and displays the estimator mean square error (MSE) lower than the Cramer-Rao bound (CRB) when the CFO value is near zero. However, its MSE value may increase quickly as the CFO value goes away from zero. Hence, the CFO estimator of the BLAE is replaced to solve the problem.

Supervised identification and equalization of transmission channel using reproducing kernel Hilbert space

The subject matter of the article is to identify and equalize the parameters of telecommunication channels. The goal is to develop a new mathematical approach based on positive definite kernels on a Hilbert space. The tasks to be solved are: (a) to formulate a mathematical procedure based on a kernel; a kernel is a function that maps pairs of data points to a scalar value, and positive definite kernels are widely used in machine learning and signal processing applications; (b) to identify the channel parameters using the proposed method; and (c) to apply the Zero Forcing and MMSE equalizer to measure the performance of the proposed system. This article introduces a new method to address the problem of supervised identification of transmission channel parameters based on the positive definite kernel on Hilbert space, which implements Gaussian kernels. The input sequence, used as an input for a system or process, is assumed to be independent, have a zero mean, a non-Gaussian distribution, and be identically distributed. These assumptions are made to simplify the analysis and modeling. The proposed method for estimating the parameters of the channel impulse response yields promising results, indicating that the estimated parameters are close to the measured parameters of the model for various channels. The convergence of the estimated parameters toward the measured parameters of the model is particularly noticeable for BRAN A (indoor) and BRAN E (outdoor) channels. The method has been tested with different channel models, and the results remain consistent. Overall, the proposed method appears to be a reliable and effective approach for estimating channel impulse response parameters. The accuracy of the estimated parameters is particularly noteworthy considering the challenges inherent in modeling wireless channels, which can be influenced by various factors such as obstacles and interference. These findings have important implications for the design and optimization of wireless communication systems. Accurate estimates of channel impulse response parameters are essential for predicting and mitigating the effects of channel distortion and interference, and the proposed method represents a promising tool for achieving this goal. Further research and testing are needed to validate and refine the method and to explore its potential applications in different settings and scenarios. We evaluated the performance of the system using the estimated parameters obtained from the proposed method. Two equalizers, MMSE and ZF, were used, and the results show that MMSE outperforms ZF. Both equalizers produced highly satisfactory outcomes.

Low-Complexity Channel Estimation Using Supercomplementary Blocks of Sequences

The paper analyzes channel impulse response (CIR) estimation using aperiodic transmit sequences and a receiver which removes carrier frequency offset (CFO) after correlation. It is shown that when there are guard intervals between the transmit sequences longer than the CIR, a class of sequence sets previously introduced can be applied to achieve CIR estimation without any correlation sidelobes for an arbitrary CFO. As having these guard intervals may be viewed as a waste of on-air time, the same problem is solved when they are eliminated by introducing a new class of sequence blocks. Furthermore, for binary sequence blocks, it is shown that by careful construction of the base Hadamard matrices the minimum sizes of these blocks can be halved. The price to pay are the correlation sidelobes that are minimized but generally are not zero anymore, except for zero CFO and a couple of small Hadamard matrix sizes.

Deep Learning based Wireless Channel Prediction: 5G Scenario

In the area of wireless communication, channel estimation is a challenging problem due to the need for real-time implementation as well as system dependence on the estimation accuracy. This work presents a Long-Short Term Memory (LSTM) based deep learning (DL) approach for the prediction of channel response in real-time and real-world non-stationary channels. The model uses the pre-defined history of channel impulse response (CIR) data along with two other features viz. transmitter-receiver update distance and root-mean-square delay spread values which are also changing in time with the channel impulse response. The objective is to obtain an approximate estimate of CIRs using prediction through the DL model as compared to conventional methods. For training the model, a sample dataset is generated through the open-source channel simulation software NYUSIM which realizes samples of CIRs for measurement-based channel models based on various multipath channel parameters. From the model test results, it is found that the proposed DL approach provides a viable lightweight solution for channel prediction in wireless communication.

SSP based underwater CIR estimation with S-BiFPN

In underwater sensor networks (USN), channel impulse response (CIR) estimation based on sound speed profile (SSP) ensures link reliability. We propose a separate bi-directional feature pyramid network (S-BiFPN) that estimates the CIR using deep learning based on SSP. The proposed method enlarges the small variation of SSP by converting 1-dimension into 2-dimension, extracts various features using a fused feature map obtained from the separate paths, and estimates the CIR. Simulations are performed using the practically measured SSPs and CIRs, and the results show that the proposed method has the lowest mean square error (MSE) and a reasonable running time compared to conventional methods.

Amplitude Modeling of Specular Multipath Components for Robust Indoor Localization.

Ultra-Wide Bandwidth (UWB) and mm-wave radio systems can resolve specular multipath components (SMCs) from estimated channel impulse response measurements. A geometric model can describe the delays, angles-of-arrival, and angles-of-departure of these SMCs, allowing for a prediction of these channel features. For the modeling of the amplitudes of the SMCs, a data-driven approach has been proposed recently, using Gaussian Process Regression (GPR) to map and predict the SMC amplitudes. In this paper, the applicability of the proposed multipath-resolved, GPR-based channel model is analyzed by studying features of the propagation channel from a set of channel measurements. The features analyzed include the energy capture of the modeled SMCs, the number of resolvable SMCs, and the ranging information that could be extracted from the SMCs. The second contribution of the paper concerns the potential applicability of the channel model for a multipath-resolved, single-anchor positioning system. The predicted channel knowledge is used to evaluate the measurement likelihood function at candidate positions throughout the environment. It is shown that the environmental awareness created by the multipath-resolved, GPR-based channel model yields higher robustness against position estimation outliers.

2D BiLSTM Based Channel Impulse Response Estimator for Improving Throughput in Underwater Sensor Network

In underwater acoustic (UWA) sensor network, the channel impulse response (CIR) at the transmitter is important to increase the link reliability and the throughput. The CIR feedback to the transmitter decreases the throughput due to the feedback propagation delay, and the estimation of the CIR at the transmitter is also difficult since the sound of speed profile (SSP) may not be continuously measured. This paper proposes a deep learning based CIR estimator that estimates the SSP from only one water temperature sensor at a depth of the transmitter. The proposed CIR estimator consists of a 2-dimensional temperature network, 2-dimensional bidirectional long short term memory (2D BiLSTM), and a fully connected layer. The proposed algorithm learns the SSP variation with the depth and the time using 2D BiLSTM and estimates the CIR from the SSP. The estimated CIRs are utilized for the multi-user diversity to increase the link reliability and the throughput of the UWA sensor network. The computer simulations and practical ocean experiments were executed to evaluate the estimation error, the bit error rate and the throughput of the proposed algorithm. The proposed CIR estimator demonstrated better performance than other 1D conventional algorithms.

Estimation of Acoustic Channel Impulse Response at Low Frequencies Using Sparse Bayesian Learning for Nonuniform Noise Power

Sparse Bayesian learning (SBL) has been extended to estimate acoustic channel impulse responses (CIRs) at low frequencies, where matched filter (MF)-based CIR estimation suffers from low resolution due to a limited frequency band. In this study, the extended SBL was developed to account for nonuniform noise power in a signal model for the CIR via a formulation that considers inconsistent noise and multiple measurements, which cannot be handled in the conventional SBL. The extended SBL is applied to simulated and measured acoustic data and then compared with the MF and existing SBLs. With the advancement in the schemes, the time resolution and denoising are enhanced; especially, the results of the extended SBL on the simulated data show that it clearly distinguishes the two adjacent arrivals with moderate errors in the estimated time delays. Additionally, as a result of applying it to the measured array data, the extended SBL can achieve a high resolution in the CIR estimation, which retains assured arrivals with a single measurement, while some arrivals are weakened by the insufficient measurement for the extended SBL.

Low-Complexity Joint CFO and Channel Estimation for RIS-Aided OFDM Systems

Accurate channel estimation is essential for achieving the performance gains offered by reconfigurable intelligent surface (RIS)-aided wireless communications. A variety of channel estimation methods have been proposed for such systems; however, none of the existing methods takes into account the effect of synchronization errors such as carrier frequency offset (CFO). In general, CFO can significantly degrade the channel estimation performance of orthogonal frequency division multiplexing (OFDM) systems. Motivated by this, we investigate the effect of CFO on channel estimation for RIS-aided OFDM systems. Furthermore, we propose a joint CFO and channel impulse response (CIR) estimation method for these systems. Simulation results demonstrate the effectiveness of our proposed method, and also demonstrate that the use of time-domain rather than frequency-domain estimation in this context results in an improvement in the mean-squared error (MSE) performance of channel estimation as well as in a significantly lower overall computational complexity.

Motion Estimation of Underwater Platforms Using Impulse Responses From the Seafloor

Autonomous underwater vehicles require accurate navigation. Techniques such as image registration using consecutive acoustic images from a sonar have shown promising results for this task. The implementation of such techniques using sonar images augmented with deep learning (DL) networks demonstrate high navigation accuracy; this is possible even with highly compressed images. The sonar images are estimates of sampled in time (with a ping period) magnitudes of channel impulse responses representing the underwater acoustic environment. More information about the environment is contained in (almost) continuous in time estimates of the channel impulse responses. Such estimates can be obtained using full-duplex technology. Rather than using sonar images, this paper investigates the use of channel impulse response estimates for underwater platform motion estimation. The proposed system uses a single projector and a small number of receiving transducers installed on the moving platform. A DL network is used to estimate the motion in two degrees of freedom (forward/backward and sideways), using two or more consecutive impulse response estimates as the input. To train the DL network, a specially designed simulator is used to model the underwater acoustic environment, populated with multiple objects spread on the seafloor. The proposed technique can significantly reduce the acoustic hardware and processing complexity of the DL network and obtain a higher accuracy of motion estimation, compared with techniques based on the processing of sonar images, e.g., the error achieved with the technique proposed in this paper is 1.7% of the maximum platform displacement, compared to 4% achieved with a technique using sonar images. The navigation accuracy is further illustrated by examples of estimation of complex trajectories.

Estimation of Compressible Channel Impulse Response for OFDM Modulated Transmissions

Channel estimation scheme for OFDM modulated transmissions usually combines an initial block-pilot-assisted stage with a tracking one based on comb or scattered pilots distributed among user data in the signal frame. The channel reconstruction accuracy in the former stage has a significant impact on tracking efficiency of the channel variations and the overall transmission quality. The paper presents a new block-pilot-assisted channel reconstruction procedure based on the DFT-based approach and the Least Square impulse response estimation. The proposed method takes into account a compressibility feature of the channel impulse response and restores its coefficients in groups of automatically controlled size. The proposition is analytically explained and tested in a OFDM simulation environment. The popular DFT-based methods including compressed sensing oriented one were used as references for comparison purposes. The obtained results show a quality improvement in terms of Bit Error Rate and Mean Square Error measures in low and mid ranges of signal-to-noise ratio without significant computational complexity growth in comparison to the classical DFT-based solutions. Moreover, additional multiplication operations can be eliminated, compared to the competitive, in terms of estimation quality, compressed sensing reconstruction method based on greedy approach.

Smartphone-based Handwritten Signature Verification using Acoustic Signals

Handwritten signature verification techniques, which can facilitate user authentication and enable secure information exchange, are still important in property safety. However, on-line automatic handwritten signature verification usually requires dynamic handwritten patterns captured by a special device, such as a sensor-instrumented pen, a tablet or a smartwatch on the dominant hand. This paper presents SonarSign, an on-line handwritten signature verification system based on inaudible acoustic signals. The key insight is to use acoustic signals to capture the dynamic handwritten signature patterns for verification. Particularly, SonarSign exploits the built-in speakers and microphones of smartphones to transmit a specially designed training sequence and record the corresponding echo for channel impulse response (CIR) estimation, respectively. Based on the sensitivity of CIR to the tiny surrounding environment changes including handwritten signature actions, SonarSign designs an attentional multi-modal Siamese network for end-to-end signatures verification. First, multi-modal CIR streams are fused to extract representative signature pattern features from spatio-temporal dimensions. Then an attentional Siamese network is elaborated to verify whether the given two signatures are from the same signatory. Extensive experiments in real-world scenarios show that SonarSign can achieve accurate and robust signatures verification with an AUC (Area Under ROC (Receiver Operating Characteristic) Curve) of 98.02% and an EER (Equal Error Rate) of 5.79% for unseen users.

MSE analysis for the finite order joint frequency tracking and channel estimation in OFDM systems

ABSTRACT The technique of orthogonal frequency division multiplexing is very sensitive to the carrier frequency offset (CFO). The requirement for high estimation accuracy when we acquire the CFO value is demanding. An efficient high-order approximation algorithm for jointly estimating the CFO and the channel impulse response (CIR) has been presented in the literature. From their simulation results, it is found that the estimator mean-square error (MSE) values are very close to the Cramer-Rao bound values, indicating that the highest estimation accuracy is achieved. However, no theoretical analysis is provided to confirm this assertion. In this article, we derive the theoretical formulas for the CFO MSE and the average CIR MSE for the estimators. It is found that the theoretical MSE for a joint CFO and CIR estimation problem approximates the Cramer-Rao bound when the signal-to-noise ratio (SNR) is high and the generalized CAZA sequence is used as the preamble. From our simulations, the theoretical results still hold true even for an SNR as low as 5 dB. Consequently, the range of SNR for which the theoretical analysis is valid is quite large.

Linear frequency modulation signal for channel impulse response measurement in shallow water environment

Understanding the characteristics of channel propagation plays a very important role in the design of underwater acoustic communication. Underwater acoustic channel (UAC) model is usually carried out by measuring directly at a specific location and time. This paper presents the use of Linear Frequency Modulation (LFM) signal for channel impulse response estimation and power delay profile (PDP) measurement in a shallow water environment. Measurements were made in a laboratory-scale towing tank with three variations of distance and depth. Furthermore, the measurement results are compared with the existing underwater acoustic channel model. The measurement results show that the response impulses at the three distances have almost the same pattern and the resulting amplitude is similar to the existing underwater acoustic channel model simulation. The RMS delay spread generated from the three distances has a value of about 0,2 msec. Meanwhile, the maximum excess delay obtained at a distance of 120 m has the highest value, which is 29 msec.

Variational autoencoder based receiver for orthogonal time frequency space modulation

The emerging orthogonal time frequency space (OTFS) modulation is demonstrated to offer reliable communication performance advantages over orthogonal frequency division multiplexing (OFDM) in doubly-dispersive fading channel. However, the existing embedded pilot-aided method to estimate channel impulse response (CIR) requires enormous spectral overhead to avoid the contamination of pilot symbols. In this paper, we present a variational autoencoder (VAE) based receiver for OTFS modulation that achieve a joint estimation and detection without pilot in delay-Doppler (DD) domain. The variational approach is considered to simplify the problem, and evidence lower bound (ELBO) is derived as loss function. In encoder step, an approximate posterior probability is introduced and utilized to minimize the Kullback-Leibler (KL) distance. Then we estimate CIR in decoder step and maximize the ELBO at last. From our simulation results, the proposed VAE based receiver for OTFS modulation enjoys a promising performance with other methods.

Bayesian Iterative Channel Estimation and Turbo Equalization for Multiple-Input–Multiple-Output Underwater Acoustic Communications

This article investigates a robust receiver scheme for a single carrier, multiple-input-multiple-output (MIMO) underwater acoustic (UWA) communications, which uses the sparse Bayesian learning algorithm for iterative channel estimation embedded in Turbo equalization (TEQ). We derive a block-wise sparse Bayesian learning framework modeling the spatial correlation of the MIMO UWA channels, where a more robust expectation-maximization algorithm is proposed for updating the joint estimates of channel impulse response, residual noise, and channel covariance matrix. By exploiting the spatially correlated sparsity of MIMO UWA channels and the second-order a priori channel statistics from the training sequence, the proposed Bayesian channel estimator enjoys not only relatively low complexity but also more stable control of the hyperparameters that determine the channel sparsity and recovery accuracy. Moreover, this article proposes a low complexity space-time soft decision feedback equalizer (ST-SDFE) with successive soft interference cancellation. Evaluated by the undersea 2008 Surface Processes and Acoustic Communications Experiment, the improved sparse Bayesian learning channel estimation algorithm outperforms the conventional Bayesian algorithms in terms of the robustness and complexity, while enjoying better estimation accuracy than the orthogonal matching pursuit and the improved proportionate normalized least mean squares algorithms. We have also verified that the proposed ST-SDFE TEQ significantly outperforms the low-complexity minimum mean square error TEQ in terms of the bit error rate and error propagation.

Adaptive Blind Channel Estimation for MIMO-OFDM Systems Based on PARAFAC

In order to track the changing channel in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, it is prior to estimate channel impulse response adaptively. In this paper, we proposed an adaptive blind channel estimation method based on parallel factor analysis (PARAFAC). We used an exponential window to weight the past observations; thus, the cost function can be constructed via a weighted least squares criterion. The minimization of the cost function is equivalent to the decomposition of third-order tensor which consists of the weighted OFDM data symbols. To reduce the computational load, we adopt a recursive singular value decomposition method for tensor decomposition; then, the channel parameters can be estimated adaptively. Simulation results validate the effectiveness of the proposed algorithm under diverse signalling conditions.

Subcarrier modulation identification of underwater acoustic OFDM based on block expectation maximization and likelihood

The low identification rate of the Orthogonal frequency division multiplexing (OFDM) based subcarrier modulation in underwater acoustic multipath channel is an important issue. Therefore, we proposed a novel Expectation Maximization-Block-Quasi Hybrid Likelihood Ratio Test (EM-Block-QHLRT) method which effectively improved the identification rate while using the blind channel impulse response (CIR) estimation and likelihood. Initially, CIR is obtained by using clustering, and then the CIR is updated iteratively by EM-Block method. Further, the subcarrier modulation is identified using QHLRT. The influence of iteration times, the length of symbol and influence of the number of blocks in EM are analyzed by using extensive simulation. The identification rate of subcarrier modulation of binary phase shift keying (BPSK), QPSK, 8PSK and 16QAM are presented using different signal noise ratio (SNR). In addition, the identification rate of subcarrier modulation based on Average Likelihood Rate Test (ALRT) as well as QHLRT with EM are compared. Simulation results showed that the identification rate of the proposed EM-Block-QHLRT method can reach to more than 90% when SNR is higher than 5 dB. Finally, the performance of the proposed EM-Block-QHLRT method is verified using sea trial data.

Joint MAP channel estimation and data detection for OFDM in presence of phase noise from free running and phase locked loop oscillator

This paper addresses a computationally compact and statistically optimal joint Maximum a Posteriori (MAP) algorithm for channel estimation and data detection in the presence of Phase Noise (PHN) in iterative Orthogonal Frequency Division Multiplexing (OFDM) receivers used for high speed and high spectral efficient wireless communication systems. The MAP cost function for joint estimation and detection is derived and optimized further with the proposed cyclic gradient descent optimization algorithm. The proposed joint estimation and detection algorithm relaxes the restriction of small PHN assumptions and utilizes the prior statistical knowledge of PHN spectral components to produce a statistically optimal solution. The frequency-domain estimation of Channel Transfer Function (CTF) in frequency selective fading makes the method simpler, compared with the estimation of Channel Impulse Response (CIR) in the time domain. Two different time-varying PHN models, produced by Free Running Oscillator (FRO) and Phase-Locked Loop (PLL) oscillator, are presented and compared for performance difference with proposed OFDM receiver. Simulation results for joint MAP channel estimation are compared with Cramer-Rao Lower Bound (CRLB), and the simulation results for joint MAP data detection are compared with “NO PHN” performance to demonstrate that the proposed joint MAP estimation and detection algorithm achieve near-optimum performance even under multipath channel fading.