In this work we present a full-duplex (FD) underwater acoustic (UWA) communication system capable of simultaneously transmitting and receiving acoustic signals in the same frequency bandwidth with a two-element FD transducer. The key challenge of implementing an FD system is to cancel the strong self-interference (SI) from the near-end transmitter. By using advanced adaptive filtering algorithms providing high accuracy channel estimates, a high level of SI cancellation can be achieved when the far-end signal is absent. However, the SI channel estimation performance is limited in FD scenarios since the far-end signal acts as an interference. In this paper, we propose an FD UWA communication system which alternates between the SI cancellation and far-end data demodulation. Advanced adaptive filters with high tracking performance are used for SI cancellation. An adaptive Rake combiner with multipath interference cancellation is implemented to improve the demodulation performance in time-varying multipath channels. The performance of the FD UWA system is evaluated in lake experiments and numerical simulations. The proposed adaptive Rake combiner with multipath interference cancellation significantly outperforms the conventional Rake combiner and an adaptive decision feedback equalizer in the experiments. With the adaptive Rake combiner, the detection performance of the proposed FD UWA system is comparable with that of the half-duplex system.

For direction of arrival (DOA) estimation based on graph signal processing (GSP), it has been assumed that there is a phase shift between adjacent snapshots of the received signals. However, this assumption does not hold for narrowband signals and thus affects the performance of the corresponding algorithms. To improve the performance, a new GSP-based DOA estimation method is proposed. By building a periodic directed graph based on a graph shift operator and computing the spectrum using the Kronecker product, the relationship between the input narrowband signals and the graph adjacency matrix of different direction coefficients is constructed. Simulation results show that this method performs better than existing algorithms based on GSP.

When applied to identification of time-varying systems, such as rapidly fading telecommunication channels, adaptive estimation algorithms built on the local basis function (LBF) principle yield excellent tracking performance but are computationally demanding. The subsequently proposed fast LBF (fLBF) algorithms, based on the preestimation principle, allow a substantial reduction in the complexity without significant performance losses. We propose a novel preestimator, called bidirectional, which further improves performance of the fLBF scheme.

The squared sine adaptive (SSA) algorithm is presented for identification scenarios, such as acoustic-echo cancellation (AEC) applications, in non-Gaussian environments. To devise the SSA algorithm, a novel cost function is constructed by exerting a sliding window-type squared sine function on the estimation error vector, which provides robustness in impulsive-noise environments and speeds up convergence when the input is colored. Theoretical results are presented for predicting the mean-weight, convergence, transient excess-mean-square-error (EMSE), and tracking behaviour. Moreover, the minimum EMSE and the optimum step size for tracking are presented. The computational complexity of the SSA algorithm has also been investigated. Numerical experiments demonstrate that results of the theoretical analysis match the simulated results very well and the proposed SSA algorithm outperforms known algorithms in AEC applications.

We consider the problem of identification of communication channels with a mix of static and time-varying parameters. Such scenarios are typical, among others, in underwater acoustics. In this paper, we further develop adaptive algorithms built on the local basis function (LBF) principle resulting in excellent performance when identifying time-varying systems. The main drawback of an LBF algorithm is its high complexity. The subsequently proposed fast LBF (fLBF) algorithms, based on the preestimation principle, allow a significant reduction in the complexity for recursively computable basis functions, such as the complex exponentials. We propose a debiased fLBF algorithm which exploits the fact that only a part of the system parameters are time-varying. We also propose an adaptive technique to identify whether a particular tap is static or time-varying.

We consider identification of sparse linear systems with a mix of static and time-varying parameters. Such systems are typical in underwater acoustics (UWA), for instance, in applications requiring identification of the acoustic channel, such as UWA communications, navigation and continuous-wave sonar. The recently proposed fast local basis function (fLBF) algorithm provides high performance when identifying time-varying systems. In this paper, we further improve the performance of the fLBF algorithm by exploiting properties of the system. Specifically, we propose an adaptive time-invariance test to identify whether a particular system tap is static or time-varying and exploit this knowledge for choosing the number of basis functions. We also propose a regularization scheme that exploits the system sparsity and an adaptive technique for estimating the regularization parameter. Finally, a debiasing technique is proposed to reduce an inherent bias of fLBF estimates. The high performance of the fLBF algorithm with the proposed techniques is demonstrated in scenarios of UWA communications, using numerical and real experiments.

Two recursive least-squares (RLS) adaptive filtering algorithms are most often used in practice, the exponential and sliding (rectangular) window RLS algorithms. This popularity is mainly due to existence of low-complexity versions of these algorithms. However, these two windows are not always the best choice for identification of fast time-varying systems, when the identification performance is most important. In this paper, we show how RLS algorithms with arbitrary finite-length windows can be implemented at a complexity comparable to that of exponential and sliding window RLS algorithms. Then, as an example, we show an improvement in the performance when using the proposed finite-window RLS algorithm with the Hanning window for identification of fast time-varying systems.

This paper proposes a unified sparsity-aware robust recursive least-squares RLS (S-RRLS) algorithm for the identification of sparse systems under impulsive noise. The proposed algorithm generalizes multiple algorithms only by replacing the specified criterion of robustnessand sparsity-aware penalty. Furthermore, by jointly optimizing the forgetting factor and the sparsity penalty parameter, we develop the jointly-optimized S-RRLS (JO-S-RRLS) algorithm, which not only exhibits low misadjustment but also can track well sudden changes of a sparse system. Simulations in impulsive noise scenarios demonstrate that the proposed S-RRLS and JO-S-RRLS algorithms outperform existing techniques.

The shrinkage linear complex-valued least mean squares (SL-CLMS) algorithm with a variable step size overcomes the conflicting issue between fast convergence and low steady-state misalignment. To the best of our knowledge, the theoretical performance analysis of the SL-CLMS algorithm has not been presented yet. This letter focuses on the theoretical analysis of the excess mean square error transient and steady-state performance of the SL-CLMS algorithm. Simulation results obtained for identification scenarios show a good match with the analytical results.

This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate estimate update at each node. With the help of side information, the constraint is recursively updated in a diffusion strategy. Moreover, a control strategy for resetting the constraint is also proposed to retain good tracking capability when the estimated parameters suddenly change. Simulations show the superiority of the proposed algorithm over previously reported techniques in various impulsive noise scenarios.

This paper addresses the BEM (Basis Expansion Model) channel estimation in receivers of multicarrier communication signals. The estimation performance can be improved by choosing optimal basis functions or an optimal number of predefined basis functions; these approaches require knowledge of channel statistics. Another approach to improve the performance is to set the number of basis functions large enough to guarantee a negligible modeling error and optimize the regularization. In this paper, we adopt the latter approach and propose an adaptive regularization scheme based on the generalized cross-validation; the scheme does not require the knowledge of channel statistics. We demonstrate by simulation for LTE uplink scenarios that the proposed scheme allows a high estimation performance in a range of channels and noise levels.

Optimal detection does not require channel estimation and jointly processes the received data and pilot symbols to recover the transmitted data. However, the complexity of the optimal detector increases significantly with increase in the size of the data package, modulation order and number of transmit antennas. We propose an architecture for channel estimation and detection in Multi Input Multi Output (MIMO) OFDM systems that provides a great reduction in the complexity compared to the optimal detection, whereas providing a high detection performance. At first, we present a sequential interference cancellation scheme with reweighted Linear Minimum Mean Squares Error (RW-LMMSE) channel estimation. In this estimator, tentative data symbols used for channel estimation are recovered iteratively without decoding, thus reducing the complexity. Also, we propose an element-by-element selection scheme based on information obtained from the reweighted channel estimator to select symbols for optimal detection (selective optimal detection). This selection scheme applies the optimal detection only to a small number of received data not accurately estimated by the reweighted estimator. The selective optimal detection is shown to provide a significant improvement in the detection performance over the detection based on the RW-LMMSE channel estimator.

In practical implementations of estimation algorithms, designers usually have information about the range in which the unknown variables must lie either due to physical constraints (such as power always being non-negative) or due to hardware constraints (such as in implementations using fixed-point arithmetic). In this letter, we propose a fast (i.e., whose complexity grows linearly with the filter length) version of the dichotomous coordinate descent recursive least-squares (RLS) adaptive filter which can incorporate constraints on the variables. The constraints can be in the form of lower and upper bounds on each entry of the filter, or norm bounds. We compare the proposed algorithm with the recently proposed normalized non-negative least-mean-squares (N-NLMS) and projected-gradient normalized LMS (PG-NLMS) filters, which also include inequality constraints in the variables.

This paper addresses adaptive filtering for sparse identification. Proportionate affine projection algorithms (PAPAs) are known to be efficient techniques for this purpose. We show that the PAPA performance may improve with an increase in the projection order M (for example, such as M = 512), which, however, also results in an increased complexity; the complexity is in general O(M 2 N) or at least O(MN) operations per sample, where N is the filter length. We show that PAPAs are equivalent to specific sliding-window recursive least squares (SRLS) adaptive algorithms with time-varying and tap-varying diagonal loading (SRLS-VDLs). We then propose an approximation to the SRLS-VDLs based on dichotomous coordinate descent (DCD) iterations with a complexity of O(N u N), which does not depend on M; it depends on the number of DCD iterations N u , which as we show can be significantly smaller than M, thus allowing a low-complexity implementation of PAPA adaptive filters.

This paper presents a simple approach for matrix inversion by using dichotomous coordinate descent (DCD) algorithm. The idea of the approach is that the DCD algorithm obtains separately the individual columns of the inverse of the matrix. Owing to the low complexity of hardware implementation of the individual DCD algorithm, a block of DCD processors can be adopted to obtain the columns of the inverse of the channel correlation matrix in parallel with reduced hardware occupation.

In this letter, we propose a low-complexity channel-estimate based adaptive linear equalizer. The equalizer exploits coordinate descent iterations for computation of equalizer coefficients. The proposed technique has as low complexity as operations per sample, where and are the equalizer and channel estimator length, respectively, and is the number of iterations such that and . Moreover, with dichotomous coordinate descent iterations, the computation of equalizer coefficients is multiplication-free and division-free, which makes the equalizer attractive for hardware design. Simulation shows that the proposed adaptive equalizer performs close to the minimum mean-square-error equalizer with perfect knowledge of the channel.

In this paper, a joint data-aided channel and frequency offset estimator is proposed for doubly-selective fading channels. The joint estimator is based on the B-spline model approximating the fading process and the dichotomous search frequency estimation technique. The estimator relies on the Bayesian approach. It is examined for different scenarios in Rayleigh fading channels. Simulation results show that the proposed estimator achieves a high accuracy performance, which is close to that with perfect knowledge of the frequency offset, over a wide range of signal to noise ratios, for different Doppler frequencies and throughout all the frequency acquisition range.

An optimal detector for orthogonal frequency-division multiplexing (OFDM) signals with pilot symbol assisted modulation in multiple-input multiple-output (MIMO) frequency selective fading channels with imperfect channel estimation is derived. This detector does not estimate the channel explicitly but maximises the likelihood function incorporating received data and pilot symbols to recover the data. The authors investigate and compare its performance with that of mismatched detectors treating maximum likelihood (ML), regularised ML or minimum mean squared error (MMSE) channel estimates as perfect channel information in spatially uncorrelated MIMO channels with binary phase shift keying (BPSK) and 16-quadrature amplitude modulation (QAM) by simulation. The authors use basis functions to model the channel frequency response and compare the performance of different basis expansion models in frequency selective fading channels with different delay spread. In single-input single-output (SISO) channels, the performance of the optimal detector is close to that of the mismatched detector with MMSE channel estimates, which provides the best performance among these mismatched detectors. However, the optimal detector significantly outperforms the mismatched detectors in MIMO channels.

In this paper, we propose a new multichannel filtered-x affine projection algorithm based on dichotomous coordinate descent (DCD) iterations for active noise control (ANC) systems. It includes a fast recursive filtering procedure with the filter update incorporated in the DCD iterations. It is shown that the proposed algorithm has a lower complexity, and superior convergence properties than the multichannel filtered-x LMS algorithm. Also, it compares favorably to a previously published DCD based algorithm for ANC systems.

In this paper, we present an FPGA implementation of a Recursive Least Squares adaptive filtering algorithm based on dichotomous coordinate descent iterations. The algorithm is simple for finite precision implementation, requires small chip resources, and exhibits numerical stability. For arbitrary regressors (as in antenna array beamforming), the proposed implementation allows significant increase in the weight update rate compared to implementations based on QR decomposition; for 9 and 32-element arrays, the update rates are as high as 162 kHz and 31 kHz, respectively. For 16-tap and 64-tap transversal filters, the proposed implementation provides the weight update rate 207 kHz and 76 kHz, respectively.

In this paper, a box-constrained MIMO detector is considered that allows simple FPGA implementation and provides improvement in the detection performance compared to the MMSE detector. The box-constrained detector is implemented using dichotomous coordinate descent iterations. We investigate the design throughput against the BER performance and the design complexity in terms of the number of logic slices. The proposed design requires as few as 637, 658, and 667 slices for 4 times 4, 8 times 8, and 16 times 16 MIMO systems, respectively, which is significantly less than that required by known designs of the MMSE detector.

In this paper, we derive an optimal detector for pilot-assisted transmission in Rayleigh fading channels with imperfect channel estimation. The classical approach is based on obtaining channel estimates and treating them as perfect in a minimum distance detector (this is called mismatched detector). The optimal detector jointly processes the received pilot and data symbols to recover the data. The optimal detector is specified for fast frequency-flat fading channels.We consider spline approximation of the channel gain time variations and compare the detection performance of different mismatched detectors with the optimal one. Further, we investigate the detection performance of an iterative receiver in a system transmitting turbo-encoded data, where a channel estimator provides either maximum likelihood estimates, minimum mean square error (MMSE) estimates or statistics for the optimal detector. Simulation results show that the optimal detector outperforms the mismatched detectors. However, the improvement in the detection performance compared to the mismatched detector with the MMSE channel estimates is modest.

In this paper, we derive an optimal detector for pilot-assisted transmission in Rayleigh frequency-flat fast fading channels. The classical detector based on obtaining channel estimates and treating them as perfect in a minimum distance detector is called mismatched detector. The optimal detector jointly processes the received pilot and data symbols to recover the data with a minimum error. We consider spline approximation of the channel gain time variations and compare the detection performance of mismatched detectors using maximum likelihood channel estimates with the optimal one. Further, we investigate the detection performance of a receiver that iteratively improves the channel and data information in a system transmitting turbo-encoded data, where a channel estimator provides either maximum likelihood estimates or statistics for the optimal detector. Simulation results show that the optimal detector significantly outperforms the mismatched detectors.

In this letter, a new low-complexity implementation of the affine projection (AP) adaptive filtering algorithm is proposed and investigated by simulation. The proposed algorithm uses a novel low complexity recursive filtering technique and filter update that is incorporated in dichotomous coordinate descent (DCD) iterations. If the projection order is significantly smaller than the filter lengthL, the complexity of the proposed DCD-AP algorithm is as small as aboutLmultiplications per sample.

The FPGA design of an adaptive antenna array beamformer is presented. The complex-valued array weights are calculated using the MVDR algorithm whose implementation is based on dichotomous coordinate descent (DCD) iterations. The DCD algorithm allows the multiplication-free solution of the normal equations, resulting in an area-efficient FPGA design that requires approximately 400 slices for the DCD core. Antenna beampatterns obtained from weights calculated in the fixed-point FPGA platform are compared with those of a floating-point simulation. The comparison shows good match of the results for linear arrays of as large as 64 elements. For a 64-element array, the proposed design could provide a weight update rate as high as 28 kHz.

For feedforward multichannel active noise control (ANC) systems, the use of adaptive finite-impulse response (FIR) filters is a popular solution, and the multichannel filtered-x least-mean-square (FX-LMS) algorithm is the most commonly used algorithm. The drawback of the FX-LMS is the slow convergence speed, especially for broadband multichannel systems. Recently, some fast affine projection algorithms have been introduced for multichannel ANC, as an interesting alternative to the FX-LMS algorithm. They can provide a significantly improved convergence speed at a reasonable additional computational cost. Yet, the additional computational cost or the potential numerical instability in some of the recently proposed algorithms can prevent the use of those algorithms for some applications. In this paper, we propose two pseudo-affine projection algorithms for multichannel ANC: one based on the Gauss-Seidel method and one based on dichotomous coordinate descent (DCD) iterations. It is shown that the proposed algorithms typically have a lower complexity than the previously published fast affine projection algorithms for ANC, with very similar good convergence properties and good numerical stability. Thus, the proposed algorithms are an interesting alternative to the standard FX-LMS algorithm for ANC, providing an improved performance for a computational load of the same order

We propose novel low-complexity iterative channel estimators based on B-splines. Local splines are adopted for computational simplicity. Minimum mean square error (MMSE) local splines with integral sampling are derived. The MSE of the proposed estimators depends on signal-to-noise ratio, fading rate, sampling interval, spline order and the number of weighting coefficients; these dependencies are investigated. The linear and cubic local splines with as few as seven weighting coefficients are capable of achieving MSE and BER performance comparable to those of the Wiener filter and the spheroidal basis expansion. However, a significantly lower complexity is achieved using B-splines

Spectral domain B-spline identification is proposed for acoustic echo cancellation. Two approaches are considered. The first is based on the solution of normal equations; we describe an efficient technique for such a solution, which benefits from the sparseness of the system matrix due to B-splines. The second approach is based on using local splines, enabling further simplification. We also show how the proposed techniques can be used for efficient double-talk detection. The echo cancellation performance and complexity of the proposed techniques are compared with that of a low-complexity cross-spectral technique and the affine projection (AP) algorithm possessing high cancellation performance. The B-spline identification allows cancellation performance comparable with that of the AP algorithm and complexity close to that of the cross-spectral algorithm.

A novel B-spline iterative channel estimation technique over fast flat fading channels is proposed. Both local linear and parabolic splines are considered. The optimal sampling interval is found by simulations and then approximated by a simple equation. Comparisons with the Wiener filtering approach in mean square error (MSE), bit error rate (BER) and complexity are given. The BER performance of the iterative receiver with the proposed estimators is very close, within 0.3 dB for BER = 10/sup -4/ of that of the Wiener estimator for fading rates up to f/sup d/T/sup s/ = 0.02. However, the proposed estimators require only a few multiplications per symbol per iteration which is only a small fraction of that of the Wiener filter.

We propose a new approach for real-time implementation of the fast affine projection (FAP) algorithm. This is based on exploiting the recently introduced dichotomous coordinate descent (DCD) algorithm, which is especially efficient for solving systems of linear equations on real-time hardware and software platforms since it is free of multiplication and division. The numerical stability of the DCD algorithm allows the new combined DCD-FAP algorithm also to be stable. The convergence and complexity of the DCD-FAP algorithm is compared with that of the FAP, Gauss-Seidel FAP (GS-FAP), and modified GS-FAP algorithms in the application to acoustic echo cancellation. The DCD-FAP algorithm demonstrates a performance close to that of the FAP algorithm with ideal matrix inversion and the complexity smaller than that of the Gauss-Seidel FAP algorithms.

We investigate how pilot signals affect complexity and accuracy of maximum likelihood (ML) frequency estimation in frequency-flat channels with transmit diversity. We show that for arbitrary pilot signals, the complexity can be as low as O(N/sub t/), where N/sub t/ is the number of transmit antennas. For linearly dependent pilot signals this can be further reduced down to O(1) with even better estimation accuracy. Lower and upper bounds of the Cramer-Rao lower bound (CRLB) over possible channel gains are derived. We define locally optimal pilot signals as those minimising the upper bound and show how to find such signals. The CRLB characterises local properties of ML estimates, while the ambiguity function allows analysis of global properties of estimates in the whole acquisition range. We analyse the ambiguity function for binary pilot signals, in particular Hadamard sequences and show how it relates to behaviour of frequency estimates over the signal-to-noise ratio and frequency acquisition range.

Maximum-likelihood (ML) data-aided frequency estimation in multipath Rayleigh-fading channels with sparse impulse responses is investigated. We solve this problem under the assumption that the autocorrelation matrix of the pilot signal can be approximated by a diagonal matrix, the fading of different path amplitudes are independent from each other, and the additive noise is white and Gaussian. The ML frequency estimator is shown to be based on combining nonlinearly transformed path periodograms. We have derived the nonlinear function for the two cases: known and unknown fading variances. The new frequency estimators lead, in particular cases, to known ML frequency estimators for nonsparse multipath fading channels. The use of a priori information about the mean number of paths in the channel allows a significant improvement of the accuracy performance. Exploiting the sparseness of the channel impulse response is shown to significantly reduce the threshold signal-to-noise ratio at which the frequency error departs from the Cramer-Rao lower bound. However, precise knowledge of the channel sparseness is not required in order to realize this improvement.

Maximum likelihood (ML) data-aided frequency estimation in multipath Rayleigh fading channels with sparse impulse responses is investigated. We solve this problem under the assumption that the autocorrelation matrix of the pilot signal can be approximated by a diagonal matrix, the fading of different path amplitudes are independent from each other, and the additive noise is white and Gaussian. The ML frequency estimator is shown to be based on combining nonlinear transformed path periodograms. We have found the nonlinear function for the two cases: known and unknown fading variances. The new frequency estimators lead, in particular cases, to known ML frequency estimators for non-sparse multipath fading channels. Exploiting the sparseness of the channel impulse response is shown to significantly reduce the threshold signal-to-noise ratio (SNR) at which the frequency error departs from the Cramer-Rao lower bound. However, precise knowledge of the channel sparseness is not required in order to realise this improvement. The assumption of a diagonal autocorrelation matrix is shown to affect the accuracy performance only at high SNRs which however can often be outside the SNRs of interest.

Provides an abstract of articles to be presented in a forthcoming issue.

This paper concerns the estimation of a frequency offset of a known (pilot) signal propagated through a slowly fading multipath channel, such that channel parameters are considered to he constant over the observation interval. We derive a maximum-likelihood (ML) frequency estimation algorithm for additive Gaussian noise and path amplitudes having complex Gaussian distribution when covariance matrices of the fading and noise are known; we consider in detail the algorithm for the white noise and Rayleigh fading, in particular, for independent fading of path amplitudes and pilot signals with diagonal autocorrelation matrices. For the latter scenario, we also derive an ML frequency estimator when the power delay profile is unknown, but the noise variance and bounds for the path amplitude variances are specified; in particular, this algorithm can be used when path delays and amplitude variances are unknown. Finally, we consider frequency estimators which do not use a priori information about the noise variance; these algorithms are also operable without timing synchronization. All the frequency estimators exploit the multipath diversity by combining periodograms of multipath signal components and searching for the maximum of the combined statistic. For implementation of the algorithms, we use a fast Fourier transform-based coarse search and fine dichotomous search. We perform simulations to compare the algorithms. The simulation results demonstrate high accuracy performance of the proposed frequency estimators in wide signal-to-noise ratio and frequency acquisition range.

This paper concerns the estimation of the frequency offset of a known (pilot) signal propagated through a slowly fading multipath channel, such that channel parameters are considered to be constant over the observation interval. We derive a Cramer-Rao lower bound (CRLB) and maximum likelihood (ML) frequency estimation algorithm for additive Gaussian noise and path amplitudes having complex zero-mean Gaussian distribution when covariance matrices of the fading and noise are known. In particular, we consider the scenarios with white noise, independent fading of path amplitudes and pilot signals with a diagonal correlation matrix. We compare simulation results for the ML estimator with the CRLB. We also show that the results obtained can be extended to scenarios with fast fading channels.

High-speed communications over the underwater acoustic channel are difficult due to time-varying multipath propagation and Doppler scattering. These phenomena, however, can be effectively used for joint multipath-Doppler diversity of received signals similarly to multipath diversity in a conventional RAKE receiver. We present a new signal processing technique for data transmission over fast fading underwater acoustic channel by using OFDM signals. This technique exploits multipath-Doppler diversity which is based on the channel model as a sum of macro-rays characterised by delays, Doppler parameters and transfer functions. Delay and Doppler estimation involves calculation of the cross-ambiguity function for a pilot signal; transfer function estimation exploits frequency domain B-spline approximation. Experimental results demonstrate high BER performance of the proposed algorithm for various propagation scenarios.

We propose an algorithm for joint channel estimation and detection in application to a practical scenario of detection of random access bursts in the W-CDMA UMTS system. The proposed algorithm is based on using the FFT algorithm for matched filtration and further signal processing with symbol rate sampling; as a result, it is well suited to implementation with modest DSP resources. We have performed simulation of the algorithm in different multiuser, multipath and frequency uncertainty environments; the simulation has shown high detection performance of the proposed algorithm.