Jointly Sparse Support Recovery via Deep Auto-encoder with Applications in MIMO-based Grant-Free Random Access for mMTC

In this paper, a data-driven approach is proposed to jointly design the common sensing (measurement) matrix and jointly support recovery method for complex signals, using a standard deep auto-encoder for real numbers. The auto-encoder in the proposed approach includes an encoder that mimics the noisy linear measurement process for jointly sparse signals with a common sensing matrix, and a decoder that approximately performs jointly sparse support recovery based on the empirical covariance matrix of noisy linear measurements. The proposed approach can effectively utilize the feature of common support and properties of sparsity patterns to achieve high recovery accuracy, and has significantly shorter computation time than existing methods. We also study an application example, i.e., device activity detection in Multiple-Input Multiple-Output (MIMO)-based grant-free random access for massive machine type communications (mMTC). The numerical results show that the proposed approach can provide pilot sequences and device activity detection with better detection accuracy and substantially shorter computation time than well-known recovery methods.Comment: 5 pages, 8 figures, to be publised in IEEE SPAWC 2020. arXiv admin note: text overlap with arXiv:2002.0262

Covariance-domain Dictionary Learning for Overcomplete EEG Source Identification

We propose an algorithm targeting the identification of more sources than channels for electroencephalography (EEG). Our overcomplete source identification algorithm, Cov-DL, leverages dictionary learning methods applied in the covariance-domain. Assuming that EEG sources are uncorrelated within moving time-windows and the scalp mixing is linear, the forward problem can be transferred to the covariance domain which has higher dimensionality than the original EEG channel domain. This allows for learning the overcomplete mixing matrix that generates the scalp EEG even when there may be more sources than sensors active at any time segment, i.e. when there are non-sparse sources. This is contrary to straight-forward dictionary learning methods that are based on the assumption of sparsity, which is not a satisfied condition in the case of low-density EEG systems. We present two different learning strategies for Cov-DL, determined by the size of the target mixing matrix. We demonstrate that Cov-DL outperforms existing overcomplete ICA algorithms under various scenarios of EEG simulations and real EEG experiments

Novel Algorithms for Analyzing the Robustness of Difference Coarrays to Sensor Failures

Sparse arrays have drawn attention because they can identify O(N²) uncorrelated source directions using N physical sensors, whereasuniform linear arrays (ULA) find at most N−1 sources. The main reason is that the difference coarray, defined as the set of differences between sensor locations, has size of O(N²) for some sparse arrays. However, the performance of sparse arrays may degrade significantly under sensor failures. In the literature, the k-essentialness property characterizes the patterns of k sensor failures that change the difference coarray. Based on this concept, the k-essential family, the k-fragility, and the k-essential Sperner family provide insights into the robustness of arrays. This paper proposes novel algorithms for computing these attributes. The first algorithm computes the k-essential Sperner family without enumerating all possible k-essential subarrays. With this information, the second algorithm finds the k-essential family first and the k-fragility next. These algorithms are applicable to any 1-D array. However, for robust array design, fast computation for the k-fragility is preferred. For this reason, a simple expression associated with the k-essential Sperner family is proposed to be a tighter lower bound for the k-fragility than the previous result. Numerical examples validate the proposed algorithms and the presented lower bound