Sparse channel estimation for OFDM-based underwater cooperative systems with amplify-and-forward relaying

In this paper, an efficient channel estimation algorithm is proposed for amplify-and-forward (AF) cooperative relay based orthogonal frequency division multiplexing (OFDM) system in the presence of sparse underwater acoustic channels and of the correlative non-Gaussian noise. The algorithm is based on the combinations of the matching pursuit (MP) and the space-alternating generalized expectation-maximization (SAGE) technique, to improve the estimates of the channel taps and their location as well as the Gaussian mixture noise distribution parameters in an iterative way. Computer simulations show that underwater acoustic channel is estimated very effectively and the proposed algorithm has excellent symbol error rate (SER) and channel estimation performance, as compared to the existing ones.

In recent years, multiple-input multiple-output (MIMO) systems, which use several transmit and receive antennas, have attracted much attention for high performance radio systems. In MIMO systems, the channel estimation is important to distinguish transmit signals from multiple transmit antennas. While the space-alternating generalized expectation-maximization (SAGE) algorithm is known to offer good channel estimation and data detection. We proposed earlier the minimum mean square error (MMSE)-based SAGE algorithm for MIMO systems where the MMSE estimation is used for channel estimation. We showed that the proposed MMSE-based SAGE algorithm can achieve the better bit error rate (BER) than the maximum likelihood (ML) detection with training symbols. The MMSE channel estimation needs the knowledge of the maximum Doppler frequency F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> for deriving the covariance matrix of the channel and the variance sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of additive white Gaussian noise (AWGN). Additionally, the computation of the MMSE channel estimation requires O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where L is the transmitted frame length. Thus, its computational complexity is high. In this paper, we propose a zero-forcing (ZF)-based SAGE algorithm for channel estimation and data detection in MIMO systems that does not need the knowledge of Fd and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Since the computation of the proposed ZF-based SAGE algorithm requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where N is the number of transmit antennas, its computational complexity is low. We show that the proposed ZF-based tracking SAGE algorithm with less computational complexity can achieve almost the same BER as that of the MMSE-based tracking SAGE algorithm

In MIMO systems, channel estimation is important to distinguish transmit signals from multiple transmit antennas. The space-alternating generalized expectation-maximization (SAGE) algorithm is known to be good for channel estimation and data detection. However, the SAGE algorithm has not been applied to MIMO systems. In this paper, we propose a SAGE algorithm for the channel estimation and data detection in MIMO systems. In addition, we propose a simplified SAGE algorithm for the channel estimation and data detection by tracking the channel variation in MIMO systems. In the simplified SAGE algorithm, we divide a transmit frame into some subblocks and apply the SAGE algorithm to each subblock, and we use the channel estimates in the previous subblock as the initial channel estimates in the current subblock. According to the division of the transmit frame, the computational complexity is decreased. In addition, the simplified SAGE algorithm can track the channel variation by using the channel estimates transferred between the subblocks.

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).

Joint estimation of azimuth and elevation angles is of great importance in source localization and channel characterization. Firstly, some basic knowledge of three typical parametric estimation algorithms are introduced in this paper, i.e., multiple signal classification (MUSIC), Unitary estimation of signal parameter via rotational invariance technique (ESPRIT), and space-alternating generalized expectation-maximization (SAGE) algorithms. Each algorithm is capable of extracting both azimuth angle of arrival (AAoA) and elevation angle of arrival (EAoA) of multi-paths jointly. It is pointed out that the SAGE and MUSIC algorithms have higher complexity than the Unitary ESPRIT algorithm due to the iteration/angle searching procedure. Secondly, impacts of antenna number, closely spaced paths, and signal-to-noise ratio (SNR) on estimation performance of three algorithms are analyzed. Results show that the Unitary ESPRIT algorithm has lower accuracy in comparison with the MUSIC and SAGE algorithms when antenna number and SNR are large. Finally, three algorithms are applied to estimate multipath parameters in 16 GHz massive MIMO channel measurements. It is shown that the Unitary ESPRIT algorithm performs less satisfactory in MPCs extraction, while MUSIC can provide comparable results with the SAGE algorithm.

Various channel estimation methods have been proposed for shallow underwater communication channel with sparse channel type. A matching pursuit (MP), which is one of typical sparse channel estimation methods, can detect dominant components of sparse channel sequentially as a portion of matching. Mean squared error of MP, however, converges to fixed value even though signal-to-noise ratio (SNR) increases. This paper proposes a minimum mean squared error (MMSE) estimation method with constant false alarm (CFAR) detection for sparse channel estimation. Unlike MP, the mean squared error of the proposed method decreases as SNR increases and is lower than that of conventional MMSE estimators on the sparse channel. Experimental results show that the proposed method estimates sparse underwater communication channel efficiently.

This paper addresses the effective sparse channel estimation based on the most significant taps (MST) selection with high spectral efficiency and moderate computational complexity for orthogonal frequency division multiplexing (OFDM) systems. The main goal of this paper is to obtain an efficient time domain threshold and achieve the channel estimation performance approaching the least squares (LS) method with exact sparsity (exact number of non-zero channel taps) without using prior knowledge of both channel statistics and noise standard deviation. Firstly, classical LS method is used to get an initial channel impulse response (CIR) estimate. Then a novel effective threshold, estimated from the noise coefficients of the initial estimated CIR, is proposed. Finally, the obtained threshold is used to select the most significant taps. Simulations show that the proposed method is able to achieve good channel estimation performances for sparse channel within a comparatively wide range of sparsity with small number of pilots and moderate computational complexity.

In this paper, the space alternating generalized expectation-maximization (SAGE) method is applied to derive receivers for coded CDMA systems. In the so-called SAGE receiver, hard decision code symbols are fed back from the single user decoders to the joint channel estimator and interference canceler. Using multivariate Gaussian approximations, the SAGE receiver is then modified such that soft values of code symbols are fed back from the single user decoders. We refer to this modified receiver as SAGE-based receiver. Compared to the SAGE receiver, the SAGE-based receiver considers the statistical properties of the code symbols, thus the channel estimation and the interference cancellation take symbol estimation errors into account. A performance improvement in terms of bit error rate (BER) and system load of the SAGE-based receiver compared to the SAGE receiver and other receivers is shown by means of Monte Carlo simulations.

Multiple-input multiple-output (MIMO) systems combined with orthogonal frequency division multiplexing (OFDM), can improve communication quality and capacity. In this paper, we consider channel estimation issue in a MIMO-OFDM system using low-density parity-check (LDPC) codes at transmitter and iterative detection based on a maximum a posteriori (MAP) demodulator and a soft LDPC decoder at receiver. We first consider a previously proposed solution based on least-square estimator (USE). Since matrix inversion is required in LSE algorithms, their computational cost for implementation is high. Then, we resort to the expectation-maximization (EM)-type algorithms, which significantly reduce the complexity of the channel estimation, and propose a modified turbo receiver for LDPC-coded MIMO-OFDM systems which performs the channel estimation by space alternating generalized EM (SAGE) algorithm. Based on simulation results, the performance of the proposed receiver is quite satisfying.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

Millimeter wave (mmWave) channels can provide new frequency bands for communications together with improved accuracy and resolution for sensing and target localization. Those require parametric channel estimation methods capable of operating with very short coherence times in case of large Doppler spread. In this paper, we address this problem in orthogonal frequency division multiplexing (OFDM) uplink channel estimation. We first observe that it is a variation of the multidimensional harmonic retrieval (MHR) problem in which one has no direct access to the channel tensor due to the strongly time-varying channel. We then derive an improvement of the OFDM space-alternating generalized expectation-maximization (SAGE) algorithm for channel estimation. It is able to solve the problem under intense Doppler spreads and carrier frequency offset (CFO). The proposed method exploits the shift-invariance properties of the OFDM channel tensor to perform efficient coordinate descent steps. We also derive a threshold with probability of false alarm (PFA) guarantees to probe the quality of path initializations. The algorithm estimates the number of significant multipath components by progressively adding paths until the likelihood function reaches a threshold value derived from the noise distribution. We show via numerical examples that the proposed method outperforms the state-of-the-art methods both in channel tensor estimation accuracy as well as in the model order estimation performance.

Underwater acoustic (UWA) communication is a critical part of information exchange among marine equipment in the Internet of Underwater Things (IoUT). The impact of the marine environment on UWA communication manifests through physical channels, which exhibit multipath propagation, Doppler spread, and time-varying characteristics. The dynamic compressed sensing (DCS) framework, represented by Kalman Filtered CS (KF-CS) algorithm, is introduced to dynamically adapt support sets by real-time tracking of observations. Meanwhile, channel modeling in Delay-Doppler (DD) domain offers a more stable representation for doubly-selective UWA channels, revealing a potential for channel estimation. In this paper, we transform the time-domain channel estimation into the DD domain channel estimation, and formulate the DD domain channel estimation under the DCS framework to exploit the time-varying sparsity of the UWA channel in the DD domain. In addition, to solve the DD model, the classic algorithms need to search for the sparse solution in the extremely large two-dimensional space of the entire UWA channel. Since only a few multipath arrivals within the large time-delay spread of the entire UWA channel have the Doppler value, we propose the multipath arrivals-Doppler function-based DCS channel estimation approach (DCS-MAD) to solve the DD model. The proposed DCS-MAD can remodel the traditional DD model as multipath arrivals and Doppler model, and search for the sparse solution in the two-dimensional space of multipath arrivals, instead of on the entire channel, so as to effectively reduce system complexity and better focus on Doppler value estimation at the UWA channel’s multipath arrivals. Specifically, we first estimate the multipath arrival delay of the UWA channel using the DCS algorithm. Then, the two-dimensional space search is performed specifically at the multipath arrivals and Doppler domains under the DCS framework to exploit the time-varying sparsity. Finally, the results of numerical simulation and sea experiments validate the superiority of the proposed schemes, compared to the benchmark algorithms.

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This paper studies the pilot design for compressed sensing (CS)-based sparse channel estimation in multi-input–multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. To improve the performance of estimating multiple jointly sparse channels, based on the assumption that the modulus of the pilot symbol at each pilot carrier position is equal to a constant, the pilot is currently allocated by means of lowering the sensing matrix’s total coherence (TC). However, according to the block compressed sensing (BCS) theory, the recovery ability of the sensing matrix is determined by the block coherence (BC) and subblock coherence (SC), which should be as small as possible. Therefore, we propose a novel scheme, which designs the pilot by simultaneously minimizing the TC, BC, and SC of the sensing matrix to improve the channel estimation accuracy. We first formulate the jointly sparse channel estimation as a block sparse signal recovery problem, and the pilot allocation problem is comprised of allocating the pilot index for each transmitter and allocating the pilot symbol at each carrier. Then, we derive the error bound of BCS-based channel estimation, where the pilot symbols bear any value. Finally, a novel sequential joint criterion design (SJCD) method is proposed to design pilots with a joint criterion, where the pilot pattern and pilot power are designed by BC and TC, respectively. Simulation results show that, compared with existing algorithms, the proposed algorithm can achieve a better channel estimation performance in terms of normalized mean square error (NMSE) and bit error rate (BER).

MMP-DCD-CV based sparse channel estimation algorithm for underwater acoustic transform domain communication system