Recursive Compressed Sensing

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining the next one, and b) recursive decoding, where the signal estimate from the previous window is utilized in order to achieve faster convergence in an iterative optimization scheme applied to decode the new one. To remove estimation bias, a two-step estimation procedure is proposed comprising support set detection and signal amplitude estimation. Estimation accuracy is enhanced by a non-linear voting method and averaging estimates over multiple windows. We analyze the computational complexity and estimation error, and show that the normalized error variance asymptotically goes to zero for sublinear sparsity. Our simulation results show speed up of an order of magnitude over traditional CS, while obtaining significantly lower reconstruction error under mild conditions on the signal magnitudes and the noise level.Comment: Submitted to IEEE Transactions on Information Theor

Decentralized Massive MIMO Processing Exploring Daisy-chain Architecture and Recursive Algorithms

Algorithms for Massive MIMO uplink detection and downlink precoding typically rely on a centralized approach, by which baseband data from all antenna modules are routed to a central node in order to be processed. In the case of Massive MIMO, where hundreds or thousands of antennas are expected in the base-station, said routing becomes a bottleneck since interconnection throughput is limited. This paper presents a fully decentralized architecture and an algorithm for Massive MIMO uplink detection and downlink precoding based on the Stochastic Gradient Descent (SGD) method, which does not require a central node for these tasks. Through a recursive approach and very low complexity operations, the proposed algorithm provides a good trade-off between performance, interconnection throughput and latency. Further, our proposed solution achieves significantly lower interconnection data-rate than other architectures, enabling future scalability.Comment: Manuscript accepted for publication in IEEE Transactions on Signal Processin

Sensor-Based Estimation of BTEX Concentrations in Water Samples Using Recursive Least Squares and Kalman Filter Techniques

This work investigates sensor signal processing approaches that can be used with a sensor system for direct on-site monitoring of groundwater, enabling detection and quantification of BTEX (benzene, toluene, ethylbenzene and xylene) compounds at μg/L (ppb) concentrations in the presence of interferents commonly found in groundwater. A model for the sensor response to water samples containing multiple analytes was first formulated based on experimental results. The first signal processing approach utilizes only RLSE (recursive least squares estimation) whereas the second, a two-step processing technique, utilizes both RLSE and bank of Kalman filters for the estimation process. The estimation techniques were tested using actual sensor responses to contaminated groundwater samples. Results indicate that relatively accurate concentration estimates (within ±15–23% for benzene) can be obtained in near-real time using these techniques. The two-step processing technique gave more accurate results. This approach allows the use of a single sensor, even for multiple analyte detection and quantification

A New Approach to Extract Fetal Electrocardiogram Using Affine Combination of Adaptive Filters

The detection of abnormal fetal heartbeats during pregnancy is important for monitoring the health conditions of the fetus. While adult ECG has made several advances in modern medicine, noninvasive fetal electrocardiography (FECG) remains a great challenge. In this paper, we introduce a new method based on affine combinations of adaptive filters to extract FECG signals. The affine combination of multiple filters is able to precisely fit the reference signal, and thus obtain more accurate FECGs. We proposed a method to combine the Least Mean Square (LMS) and Recursive Least Squares (RLS) filters. Our approach found that the Combined Recursive Least Squares (CRLS) filter achieves the best performance among all proposed combinations. In addition, we found that CRLS is more advantageous in extracting FECG from abdominal electrocardiograms (AECG) with a small signal-to-noise ratio (SNR). Compared with the state-of-the-art MSF-ANC method, CRLS shows improved performance. The sensitivity, accuracy and F1 score are improved by 3.58%, 2.39% and 1.36%, respectively.Comment: 5 pages, 4 figures, 3 table

Estimation of pulse heights and arrival times

The problem is studied of estimating the arrival times and heights of pulses of known shape observed with white additive noise. The main difficulty is estimating the number of pulses. When a maximum likelihood formulation is employed for the estimation problem, difficulties similar to the problem of estimating the order of an unknown system arise. The problem may be overcome using Rissanen's shortest data description approach. An estimation algorithm is described, and its consistency is proved. The results are illustrated by a simulation study using an example from seismic data processing also studied by Mendel