We present a two-step method for computing the High-Resolution Spectrogram (HRS) of nonstationary signals. In the first step, a Weighted Short-Term Fourier Transform decomposes the signal using a bank of symmetric, tapered convolution operators, and the Hilbert transform extends each resulting component to its analytic form. In the second step, a single partial fraction decomposition is applied, corresponding to a first-order prediction error operator whose single pole is the first-order Burg reflection coefficient. A maximum-entropy autoregressive estimator then gives the instantaneous frequency of each locally monochromatic component within a sliding time window. The energy of each component is reassigned along the frequency axis to the pole location, producing sharply focused energy tracks and substantially improved time-frequency resolution. Summing all reassigned components reconstructs the original signal, which confirms invertibility and enables signal separation, denoising, and feature extraction. A systematic sensitivity analysis characterizes the method's valid operating range and parameter trade-offs, and quantitative evaluations show its robustness to white, colored, and impulsive noise across multiple SNR levels. Benchmarks against established high-resolution tools show competitive performance. The method is validated on synthetic signals, including a crossing chirp and a multi-component signal with stationary, frequency-modulated, swept, and impulsive constituents. It is then applied to a marine seismic trace and to the GW150914 gravitational wave signal recorded by the LIGO Hanford detector, demonstrating its effectiveness across a broad range of signal types and application domains.
In this paper, we develop two approaches for estimating the directions of arrival (DoAs) in hybrid analog/digital (HAD) receivers when the number of snapshots is too small for statistical averaging to be reliable. To the best of our knowledge, this is the only work to date that extracts DoAs in HAD receivers under stringent constraints on the number of available snapshots. To avoid averaging, the proposed approaches invoke the structure of the received signals in a matrix pencil method (MPM) framework. Unfortunately, the analog combiners at the front end of HAD receivers tangle the output signals, thereby hindering the application of the MPM framework. In addition to entanglement, these analog combiners effectively project the received signal onto a low-dimensional subspace, causing signals arriving from particular DoAs to be nullified or, at least, heavily attenuated. To eliminate this possibility, the proposed approaches cycle over an exhaustive set of analog combiners, which collectively span the entire space. The first approach can be applied to both fully-connected (FC) and partially-connected (PC) HADs and relies on the availability of periodic, potentially unknown, signals to disentangle the output of the HAD receiver. The second approach applies only to PC-HADs and eliminates the contingency on periodic signals by exploiting the block-diagonal structure underlying the PC-HAD architecture. Our numerical simulations and comparisons with the Cramér-Rao lower bound show that both approaches can perform reliably with as little as one snapshot per analog combiner, and that they can achieve a $97\%$ reduction in the root-mean-square error compared to their existing counterparts.
For testing underwater communication performance, model-driven channel simulators have high computational complexity, and the required dynamic environmental parameters are difficult to provide, making it challenging to generate realistic time-varying channels. In contrast, data-driven simulators do not suffer from these problems. Traditional underwater acoustic channel replay methods employ time-varying impulse responses; however, herein, a time-varying transfer function (TVTF) is employed to overcome the complexities associated with the large number of scattered acoustic paths in the time-delay domain. Singular value decomposition (SVD) is employed to implement stochastic acoustic channel replay by decomposing TVTF into principal and random components. A new random component can be generated randomly via the inverse process of the variable-parameter autoregressive (VPAR) model. To solve VPAR model, basis functions were used to translate frequency-dependent coefficients into constant coefficients, which can be estimated via a least square algorithm. SVD-VPAR replay (SVD-VPARR) method was proposed to generate realistic channel samples by inputting different complex noises into the inverse process of VPAR. The proposed simulator is validated using two measured channels from the WATERMARK benchmark and is compared with direct replay and an empirical mode decomposition-based stochastic replay method. Local time-frequency statistics and binary phase-shift keying / orthogonal frequency-division multiplexing communication results show that SVD-VPARR preserves the principal frequency-dependent channel characteristics and the major bit-error-rate variations with signal-to-noise ratio, time, and frequency.
Direct position determination (DPD) localizes a source directly from received array data, but its performance can degrade under model mismatch. In this work, we consider DPD in the presence of intermittent interfering sources, which lead to covariance contamination and spurious peaks in the DPD heatmap. To address this, we propose a covariance-enhancement approach based on the Riemannian geometry of the manifold of Hermitian positive definite matrices. The proposed enhancement procedure is built around the Riemannian mean of covariance matrices, and the resulting enhanced covariance is then used to compute the standard DPD heatmaps. We provide theoretical support, in several settings, showing that the Riemannian mean serves as a mechanism for attenuating intermittent interference. Numerical simulations demonstrate improved localization accuracy in challenging scenarios, including multiple desired transmitters and multiple intermittent interfering sources.
When a system operates under impulsive disturbances and conventional state estimation methods become ineffective, robust peak error reduction is required. In this paper, the error-to-error transfer function approach is used to compute the bias correction gain $\mathbf {K}$ for a robust recursive $\mathcal {L}_{2}$-to-$\mathcal {L}_\infty$ filter applied to discrete-time state-space models based on the backward Euler method. The disturbance is treated as a Gauss-Markov sequence, and the gain $\mathbf {K}$ is computed using the energy-to-peak lemma, a newly formulated theorem, and a linear matrix inequality. The performances of the $\mathcal {L}_{2}$-to-$\mathcal {L}_\infty$, $H_\infty$, unbiased finite impulse response (UFIR), and Kalman filters are compared numerically based on the quasi periodic harmonic model in terms of mean square error, robustness, and estimation quality. An experimental verification is provided for air quality monitoring in a significantly polluted city area. It is shown that the gain $\mathbf {K}$ of the $\mathcal {L}_{2}$-to-$\mathcal {L}_\infty$ filter obeys the previously formulated rule of thumb, i.e. it ranges between the gains of the UFIR and Kalman filters. In both numerical and experimental examples, the $\mathcal {L}_{2}$-to-$\mathcal {L}_\infty$ filter exhibited the smallest peak errors.
