IEEE TSP Article

In the second part of the series papers, we set out to study the algorithmic efficiency of sparsity-constrained sensing. Stemmed from co-prime sampling/array, we propose a generalized framework, termed Diophantine sensing, which utilizes generic Diophantine equation theory and higher-order sparse ruler to strengthen the sampling time (delay), the degree of freedom (DoF), and the sampling sparsity, simultaneously. It is well known that co-prime sensing can reconstruct the autocorrelation of a sequence with significantly more lags based on Bézout theorem.

This paper considers the problem of outlier censoring from secondary data, where the number, amplitude and location of outliers is unknown. To this end, a novel sparse recovery technique based on joint block sparse learning via iterative minimization (BSLIM) and model order selection (MOS), called JBM, is proposed which exploits the inherent sparse nature of the outliers in homogeneous background. The cost function proposed here, unlike many similar works in this field, does not require a dictionary matrix.

In this paper, new results in random matrix theory are derived, which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. 

In this paper, we show that the adaptive projected subgradient method (APSM) is bounded perturbation resilient. To illustrate a potential application of this result, we propose a set-theoretic framework for MIMO detection, and we devise algorithms based on a superiorized APSM. Various low-complexity MIMO detection algorithms achieve excellent performance on i.i.d. Gaussian channels, but they typically incur high performance loss if realistic channel models (e.g., correlated channels) are considered.

We consider the problem of monostatic radar sensing with orthogonal frequency-division multiplexing (OFDM) joint radar-communications (JRC) systems in the presence of phase noise (PN) caused by oscillator imperfections. We begin by providing a rigorous statistical characterization of PN in the radar receiver over multiple OFDM symbols for free-running oscillators (FROs) and phase-locked loops (PLLs). 

Recently, affine projection algorithm has been extensively studied in the Gaussian noise environment. However, the performance of affine projection algorithm will deteriorate rapidly in the presence of impulsive noise and other non-Gaussian noise. To address this issue, this paper proposes a novel affine projection algorithm based on the complex Gaussian kernel function, called widely linear maximum complex correntropy criterion affine projection algorithm (WL-MCCC-APA). 

The large antenna arrays with hybrid analog and digital (HAD) architectures can provide a large aperture with low cost and hardware complexity, resulting in enhanced direction-of-arrival (DOA) estimation and reduced power consumption. This paper investigates the trade-off between DOA estimation and power consumption in large antenna arrays with HAD architectures.

We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). By applying the kernel method and the representer theorem to perform linear quadratic estimation in a functional space, we derive a Bayesian recursive state estimator for a general nonlinear dynamical system in the original input space. Unlike existing nonlinear extensions of the Kalman filter where the system dynamics are assumed known, the state-space representation for the Functional Bayesian Filter (FBF) is completely learned online from measurement data in the form of an infinite impulse response (IIR) filter or recurrent network in the RKHS, with universal approximation property.

In this paper, we propose CE-BASS, a particle mixture Kalman filter which is robust to both innovative and additive outliers, and able to fully capture multi-modality in the distribution of the hidden state. Furthermore, the particle sampling approach re-samples past states, which enables CE-BASS to handle innovative outliers which are not immediately visible in the observations, such as trend changes.

Time-of-arrival (TOA) based localization plays a central role in current and future localization systems. Such systems, exploiting the fine delay resolution properties of wideband and ultra-wideband (UWB) signals, are particularly attractive for ranging under harsh propagation conditions in which significant multipath may be present. While multipath has been traditionally considered detrimental in the design of TOA estimators, it can be exploited to benefit ranging.