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Covariance matrix reconstruction has been the most widely used guiding objective in gridless direction-of-arrival (DoA) estimation for sparse linear arrays. Many semidefinite programming (SDP)-based methods fall under this category. Although deep learning-based approaches enable the construction of more sophisticated objective functions, most methods still rely on covariance matrix reconstruction. In this paper, we propose new loss functions that are invariant to the scaling of the matrices and provide a comparative study of losses with varying degrees of invariance. The proposed loss functions are formulated based on the scale-invariant signal-to-distortion ratio between the target matrix and the Gram matrix of the prediction. Numerical results show that a scale-invariant loss outperforms its non-invariant counterpart but is inferior to the recently proposed subspace loss that is invariant to the change of basis. These results provide evidence that designing loss functions with greater degrees of invariance is advantageous in deep learning-based gridless DoA estimation. 

Sparse Bayesian Learning (SBL) is a popular sparse signal recovery method, and various algorithms exist under the SBL paradigm. In this paper, we introduce a novel re-parameterization that allows the iterations of existing algorithms to be viewed as special cases of a unified and general mapping function. Furthermore, the re-parameterization enables an interesting beamforming interpretation that lends insights to all the considered algorithms. Utilizing the abstraction allowed by the general mapping viewpoint, we introduce a novel neural network architecture for learning improved iterative update rules under the SBL framework. Our modular design of the architecture enables the model to be independent of the size of the measurement matrix and provides us a unique opportunity to test the generalization capabilities across different measurement matrices. We show that the network when trained on a particular parameterized dictionary generalizes in many ways hitherto not possible; different measurement matrices, both type and dimension, and number of snapshots. Our numerical results showcase the generalization capability of our network in terms of mean square error and probability of support recovery across sparsity levels, different signal-to-noise ratios, number of snapshots and multiple measurement matrices of different sizes. 

Localizing more sources than sensors with a sparse linear array (SLA) has long relied on minimizing a distance between two covariance matrices and recent algorithms often utilize semidefinite programming (SDP). Although deep neural network (DNN)-based methods offer new alternatives, they still depend on covariance matrix fitting. In this paper, we develop a novel methodology that estimates the co-array subspaces from a sample covariance for SLAs. Our methodology trains a DNN to learn signal and noise subspace representations that are invariant to the selection of bases. To learn such representations, we propose loss functions that gauge the separation between the desired and the estimated subspace. In particular, we propose losses that measure the length of the shortest path between subspaces viewed on a union of Grassmannians, and prove that it is possible for a DNN to approximate signal subspaces. The computation of learning subspaces of different dimensions is accelerated by a new batch sampling strategy called consistent rank sampling. The methodology is robust to array imperfections due to its geometry-agnostic and data-driven nature. In addition, we propose a fully end-to-end gridless approach that directly learns angles to study the possibility of bypassing subspace methods. Numerical results show that learning such subspace representations is more beneficial than learning covariances or angles. It outperforms conventional SDP-based methods such as the sparse and parametric approach (SPA) and existing DNN-based covariance reconstruction methods for a wide range of signal-to-noise ratios (SNRs), snapshots, and source numbers for both perfect and imperfect arrays. 

The frequency-dependent nature of hearing loss poses many challenges for hearing aid design. In order to compensate for a hearing aid user’s unique hearing loss pattern, an input signal often needs to be separated into frequency bands, or channels, through a process called sub-band decomposition. In this paper, we present a real-time filter bank for hearing aids. Our filter bank features 10 channels uniformly distributed on the logarithmic scale, located at the standard audiometric frequencies used for the characterization and fitting of hearing aids. We obtained filters with very narrow passbands in the lower frequencies by employing multi-rate signal processing. Our filter bank offers a 9.1× reduction in complexity as compared to conventional signal processing. We implemented our filter bank on Open Speech Platform, an open-source hearing aid, and confirmed real-time operation. 

We propose a new adaptive feedback cancellation (AFC) system in hearing aids (HAs) based on a well-posed optimization criterion that jointly considers both decorrelation of the signals and sparsity of the underlying channel. We show that the least squares criterion on subband errors regularized by a p-norm-like diversity measure can be used to simultaneously decorrelate the speech signals and exploit sparsity of the acoustic feedback path impulse response. Compared with traditional subband adaptive filters that are not appropriate for incorporating sparsity due to shorter sub-filters, our proposed framework is suitable for promoting sparse characteristics, as the update rule utilizing subband information actually operates in the fullband. Simulation results show that the normalized misalignment, added stable gain, and other objective metrics of the AFC are significantly improved by choosing a proper sparsity promoting factor and a suitable number of subbands. More importantly, the results indicate that the benefits of subband decomposition and sparsity promoting are complementary and additive for AFC in HAs. 

We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion directly penalizes subband errors and includes a sparsity penalty term which is minimized using the damped regularized Newton’s method. The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the system identification problem via computer simulations. Specifically, we study the effects of using different numbers of subbands and various sparsity penalty terms for quasi-sparse, sparse, and dispersive systems. The results show that the benefit of increasing the number of subbands is larger than promoting sparsity of the estimated filter coefficients when the target system is quasi-sparse or dispersive. On the other hand, for sparse target systems, promoting sparsity becomes more important. More importantly, the two aspects provide complementary and additive benefits to the GPtNSAF for speeding up convergence. 

Acoustic feedback control continues to be a challenging prob- lem due to the emerging form factors in advanced hearing aids (HAs) and hearables. In this paper, we present a novel use of well-known all-pass filters in a network to perform frequency warping that we call “freping.” Freping helps in breaking the Nyquist stability criterion and improves adaptive feedback can- cellation (AFC). Based on informal subjective assessments, dis- tortions due to freping are fairly benign. While common ob- jective metrics like the perceptual evaluation of speech quality (PESQ) and the hearing-aid speech quality index (HASQI) may not adequately capture distortions due to freping and acoustic feedback artifacts from a perceptual perspective, they are still instructive in assessing the proposed method. We demonstrate quality improvements with freping for a basic AFC (PESQ: 2.56 to 3.52 and HASQI: 0.65 to 0.78) at a gain setting of 20; and an advanced AFC (PESQ: 2.75 to 3.17 and HASQI: 0.66 to 0.73) for a gain of 30. From our investigations, freping provides larger improvement for basic AFC, but still improves overall system performance for many AFC approaches.