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Highlights • In this paper, we focus on the recursive least-squares algorithm for bilinear forms, i.e., RLS-BF. • The bilinear term is defined with respect to the impulse responses of a spatiotemporal model. • Low-complexity versions of the RLS-BF algorithm are proposed, based on the DCD method. • A robust variable-regularized RLS-BF (VR-RLS-BF) algorithm is developed, using an estimate of the SNR. • Low-complexity versions of the VR-RLS-BF algorithm are derived, involving the DCD method. Abstract Due to its fast convergence rate, the recursive least-squares (RLS) algorithm is very popular in many applications of adaptive filtering, including system identification scenarios. However, the computational complexity of this algorithm represents a major limitation in applications that involve long filters. Moreover, when the parameter space becomes large, the system identification problem is more challenging and the adaptive filters should be able to cope with this aspect. In this paper, we focus on the identification of bilinear forms, where the bilinear term is defined with respect to the impulse responses of a spatiotemporal model. From this perspective, the solution requires a multidimensional adaptive filtering technique. Recently, the RLS algorithm tailored for bilinear forms (namely RLS-BF) was developed for this purpose. In this framework, the contribution of this paper is mainly twofold. First, in order to reduce the computational complexity of the RLS-BF algorithm, two versions based on the dichotomous coordinate descent (DCD) method are proposed; due to its arithmetic features, the DCD algorithm represents one of the most attractive alternatives to solve the normal equations. However, in the bilinear context, we need to consider the particular structure of the input data and the additional related challenges. Second, in order to improve the robustness of the RLS-BF algorithm in noisy environments, a regularized version is developed, together with a method to find the regularization parameters, which are related to the signal-to-noise ratio (SNR). Furthermore, using a proper estimation of the SNR, a variable-regularized RLS-BF algorithm is designed and two DCD-based low-complexity versions are proposed. Due to their nature, these variable-regularized algorithms have good robustness features against additive noise, which make them behave well in different noisy condition scenarios. Simulation results indicate the good performance of the proposed low-complexity RLS-BF algorithms, with appealing features for practical implementations. [ABSTRACT FROM AUTHOR]

Abstract The affine projection (AP) algorithm is one of the most celebrated adaptive filtering algorithms, and it achieves a good tradeoff between the convergence rate and computational complexity. However, the complexity of the AP algorithm increases with the projection order. A wealth of fast AP algorithms have been proposed to reduce the complexity in the last two decades. However, those low-complexity methods have not been well analyzed and compared. To fill this gap, this paper reviews the fast AP algorithms, including both fast filtering approaches and efficient solutions of the linear system of equations. The advantages and disadvantages of each fast implementation version are clarified based on an extensive performance evaluation, which could be useful to engineers when selecting a suitable algorithm for their specific applications and could also be a starting point for experts in this field to develop better solutions. [ABSTRACT FROM AUTHOR]

Massive (or large-scale) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system is widely acknowledged as a key technology for future communication. One main challenge to implement this system in practice is the high dimensional channel estimation, where the large number of channel matrix entries requires prohibitively high computational complexity. To solve this problem efficiently, a channel estimation approach using few number of pilots is necessary. In this paper, we propose a weighted Homotopy based channel estimation approach which utilizes the sparse nature in MIMO channels to achieve a decent channel estimation performance with much less pilot overhead. Moreover, inspired by the fact that MIMO channels are observed to have approximately common support in a neighborhood, an information exchange strategy based on the proposed approach is developed to further improve the estimation accuracy and reduce the required number of pilots through joint channel estimation. Compared with the traditional sparse channel estimation methods, the proposed approach can achieve more than 2 dB gain in terms of mean square error (MSE) with the same number of pilots, or achieve the same performance with much less pilots. [ABSTRACT FROM AUTHOR]

Abstract: Locating an unknown-position source using received signal strength (RSS) measurements in an accurate and low-complexity manner is addressed in this paper. Given that the source transmit power is unknown, we employ the differential RSS information to devise two computationally attractive localization methods based on the weighted least squares (WLS) approach. The main ingredients in the first algorithm development are to obtain the unbiased estimates of the squared ranges and introduce an extra variable. The second method improves the first version by implicitly exploiting the relationship between the extra variable and source location through a second WLS step. The performance of the two estimators is analyzed in the presence of zero-mean white Gaussian disturbances. Numerical examples are also included to evaluate their localization accuracy by comparing with the maximum likelihood approach and Cramér–Rao lower bound. [Copyright &y& Elsevier]

To locate mixed far-field (FF) and near-field (NF) sources, most existing methods require two or three steps to first find the direction-of-arrival (DOA) and then retrieve the range parameters based on the DOA estimates. Hence, the range estimation performance highly relies on the DOA estimation accuracy in these methods. On the other hand, the MUSIC-like or on-grid sparse methods require discretization of the angle and range spaces which may bring in high computations and grid mismatch problem. In this paper, we propose a new method named Gridless OnE-Step (GOES) to jointly retrieve the DOA and range without requiring the pairing and discretization of the angle and range. In particular, we first construct a virtual single-snapshot signal model by the fourth-order cumulants, and then formulate a semidefinite programming (SDP) based on the atomic norm technique to simultaneously estimate the angle and range information. To reduce the computational complexity, we also propose a projected Wirtinger gradient descent algorithm Wirtinger-GOES (W-GOES) for the implementation. Because of the one-step procedure, our method not only has higher resolution than many existing methods in distinguishing both the angles and the ranges of different sources, but also can locate multiple NF or mixed FF and NF sources closely-located in angle domain or even with the same DOA. Extensive simulations are carried out to verify the superiorities of our method. [ABSTRACT FROM AUTHOR]