Low-complexity RLS algorithms using dichotomous coordinate descent iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of O(N-2) operations per sample; N being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3N multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2N multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented

RLS adaptive filter with inequality constraints

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 nonnegative) or due to hardware constraints (such as in implementations using fixedpoint arithmetic). In this paper we propose a fast (that is, whose complexity grows linearly with the filter length) version of the dichotomous coordinate descent recursive least-squares 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 (LMS) and projected-gradient normalized LMS filters, which also include inequality constraints in the variables

Efficient use of space-time clustering for underwater acoustic communications

Underwater acoustic (UWA) communication channels are characterized by the spreading of received signals in space (direction of arrival) and in time (delay). The spread is often limited to a small number of space-time clusters. In this paper, the spacetime clustering is exploited in a proposed receiver designed for guard-free orthogonal frequency-division multiplexing (OFDM) with superimposed data and pilot signals. For separation of space clusters, the receiver utilizes a vertical linear array (VLA) of hydrophones, whereas for combining delay-spread signals within a space cluster, a time-domain equalizer is used. We compare a number of space-time processing techniques, including a proposed reduced-complexity spatial filter, and show that techniques exploiting the space-time clustering demonstrate an improved detection performance. The comparison is done using signals transmitted by a moving transducer, and recorded on a 14-element non-uniform VLA in sea trials at distances of 46 km and 105 km

Attitude-trajectory estimation for forward looking multi-beam sonar based on acoustic image registration

This work considers the processing of acoustic data from a multi-beam Forward Looking Sonar (FLS) on a moving underwater platform to estimate the platform’s attitude and trajectory. We propose an algorithm to produce an estimate of the attitude-trajectory for a FLS based on the optical flow between consecutive sonar frames. The attitude-trajectory can be used to locate an underwater platform, such as an Autonomous Underwater Vehicle (AUV), to a degree of accuracy suitable for navigation. It can also be used to build a mosaic of the underwater scene. The estimation is performed in three steps. Firstly, a selection of techniques based on the optical flow model are used to estimate a pixel displacement map (DM) between consecutive sonar frames represented in the native polar (range/bearing) format. The second step finds the best match between the estimated DM and DMs for a set of modeled sonar sensor motions. To reduce complexity, it is proposed to describe the DM with a small parameter vector derived from the displacement distribution. Thus, an estimate of the incremental sensor motion between frames is made. Finally, using a weighted regularized spline technique, the incremental inter-frame motions are integrated into an attitude-trajectory for the sonar sensor. To assess the accuracy of the attitude-trajectory estimate, it is used to register FLS frames from a field experiment dataset and build a high-quality mosaic of the underwater scene

Soft-Decision-Driven Sparse Channel Estimation and Turbo Equalization for MIMO Underwater Acoustic Communications

Multi-input multi-output (MIMO) detection based on turbo principle has been shown to provide a great enhancement in the throughput and reliability of underwater acoustic (UWA) communication systems. Benefits of the iterative detection in MIMO systems, however, can be obtained only when a high quality channel estimation is ensured. In this paper, we develop a new soft-decision-driven sparse channel estimation and turbo equalization scheme in the triply selective MIMO UWA. First, the Homotopy recursive least square dichotomous coordinate descent (Homotopy RLS-DCD) adaptive algorithm, recently proposed for sparse single-input single-output system identification, is extended to adaptively estimate rapid time-varying MIMO sparse channels. Next, the more reliable a posteriori soft-decision symbols, instead of the hard decision symbols or the a priori soft-decision symbols, at the equalizer output, are not only feedback to the Homotopy RLS-DCD-based channel estimator but also to the minimum mean-square-error (MMSE) equalizer. As the turbo iterations progress, the accuracy of channel estimation and the quality of the MMSE equalizer are improved gradually, leading to the enhancement in the turbo equalization performance. This also allows the reduction in pilot overhead. The proposed receiver has been tested by using the data collected from the SHLake2013 experiment. The performance of the receiver is evaluated for various modulation schemes, channel estimators, and MIMO sizes. Experimental results demonstrate that the proposed a posteriori soft-decision-driven sparse channel estimation based on the Homotopy RLS-DCD algorithm and turbo equalization offer considerable improvement in system performance over other turbo equalization schemes

Multibranch Autocorrelation Method for Doppler Estimation in Underwater Acoustic Channels

In underwater acoustic (UWA) communications, Doppler estimation is one of the major stages in a receiver. Two Doppler estimation methods are often used: the cross-ambiguity function (CAF) method and the single-branch autocorrelation (SBA) method. The former results in accurate estimation but with a high complexity, whereas the latter is less complicated but also less accurate. In this paper, we propose and investigate a multibranch autocorrelation (MBA) Doppler estimation method. The proposed method can be used in communication systems with periodically transmitted pilot signals or repetitive data transmission. For comparison of the Doppler estimation methods, we investigate an orthogonal frequency-division multiplexing (OFDM) communication system in multiple dynamic scenarios using the Waymark simulator, allowing virtual UWA signal transmission between moving transmitter and receiver. For the comparison, we also use the OFDM signals recorded in a sea trial. The comparison shows that the receiver with the proposed MBA Doppler estimation method outperforms the receiver with the SBA method and its detection performance is close to that of the receiver with the CAF method, but with a significantly lower complexity

TDA-MAC : TDMA without clock synchronization in underwater acoustic networks

This paper investigates the application of underwater acoustic sensor networks for large scale monitoring of the ocean environment. The low propagation speed of acoustic signals presents a fundamental challenge in coordinating the access to the shared communication medium in such networks. In this paper, we propose two medium access control (MAC) protocols, namely, Transmit Delay Allocation MAC (TDA-MAC) and Accelerated TDA-MAC, that are capable of providing time division multiple access (TDMA) to sensor nodes without the need for centralized clock synchronization. A comprehensive simulation study of a network deployed on the sea bed shows that the proposed protocols are capable of closely matching the throughput and packet delay performance of ideal synchronized TDMA. The TDA-MAC protocols also significantly outperform T-Lohi, a classical contention-based MAC protocol for underwater acoustic networks, in terms of network throughput and, in many cases, end-To-end packet delay. Furthermore, the assumption of no clock synchronization among different devices in the network is a major advantage of TDA-MAC over other TDMA-based MAC protocols in the literature. Therefore, it is a feasible networking solution for real-world underwater sensor network deployments

MMP-DCD-CV based Sparse Channel Estimation Algorithm for Underwater Acoustic Transform Domain Communication System

In this paper, we propose a computationally efficient multipath matching pursuit (MMP) channel estimation algorithm for underwater acoustic (UWA) transform domain communication systems (TDCSs). The algorithm, referred to as the MMP-DCD-CV algorithm, is based on the dichotomous coordinate descent (DCD) iterations and cross validation (CV). The MMP-DCD-CV sparse channel estimator in each iteration searches for multiple promising path candidates most relevant to a residual vector and chooses the best candidate. The DCD iterations are used to solve the corresponding least squares problem with low complexity and numerical stability. The CV provides a stopping criterion of the algorithm without a priori information on the channel sparsity and noise level and examines whether the algorithm overfits its data, thus improving the estimation accuracy. The performance of the proposed algorithm is evaluated under simulated sparse UWA channels. The numerical results show that the algorithm achieves better performance than the original MMP algorithm, has lower complexity, and does not require prior knowledge on the channel sparsity and noise level. We also propose an UWA TDCS with sparse channel estimation based on the proposed MMP-DCD-CV algorithm. The proposed UWA communication system is tested by the Waymark simulator, providing the virtual signal transmission in the UWA channel, with a measured Sound Speed Profile and bathymetry. Numerical results demonstrate that the UWA TDCS with the proposed sparse channel estimator offers considerable improvement in system performance compared to other TDCS schemes

Performance Analysis of Shrinkage Linear Complex-Valued LMS Algorithm

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