Omid Taheri

Sparse channel estimation with l p -norm and reweighted l 1 -norm penalized least mean squares

The least mean squares (LMS) algorithm is one of the most popular recursive parameter estimation methods. In its standard form it does not take into account any special characteristics that the parameterized model may have. Assuming that such model is sparse in some domain (for example, it has sparse impulse or frequency response), we aim at developing such LMS algorithms that can adapt to the underlying sparsity and achieve better parameter estimates. Particularly, the example of channel estimation with sparse channel impulse response is considered. The proposed modifications of LMS are the lp-norm and reweighted l1-norm penalized LMS algorithms. Our simulation results confirm the superiority of the proposed algorithms over the standard LMS as well as other sparsity-aware modifications of LMS available in the literature.

Segmented Compressed Sampling for Analog-to-Information Conversion: Method and Performance Analysis

A new segmented compressed sampling (CS) method for analog-to-information conversion (AIC) is proposed. An analog signal measured by a number of parallel branches of mixers and integrators (BMIs), each characterized by a specific random sampling waveform, is first segmented in time into segments. Then the subsamples collected on different segments and different BMIs are reused so that a larger number of samples (at most ) than the number of BMIs is collected. This technique is shown to be equivalent to extending the measurement matrix, which consists of the BMI sampling waveforms, by adding new rows without actually increasing the number of BMIs. We prove that the extended measurement matrix satisfies the restricted isometry property with overwhelming probability if the original measurement matrix of BMI sampling waveforms satisfies it. We also prove that the signal recovery performance can be improved if our segmented CS-based AIC is used for sampling instead of the conventional AIC with the same number of BMIs. Therefore, the reconstruction quality can be improved by slightly increasing (by times) the sampling rate per each BMI. Simulation results verify the effectiveness of the proposed segmented CS method and the validity of our theoretical results. Particularly, our simulation results show significant signal recovery performance improvement when the segmented CS-based AIC is used instead of the conventional AIC with the same number of BMIs.

Permutation Meets Parallel Compressed Sensing: How to Relax Restricted Isometry Property for 2D Sparse Signals

Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which increases the storage and computational complexity significantly. To solve this problem, the multidimensional signal is reshaped into a 2D signal, which is then sampled and reconstructed column by column using the same sensing matrix. This approach is referred to as parallel compressed sensing, and it has much lower storage and computational complexity. For a given reconstruction performance of parallel compressed sensing, if a so-called acceptable permutation is applied to the 2D signal, the corresponding sensing matrix is shown to have a smaller required order of restricted isometry property condition, and thus, lower storage and computation complexity at the decoder are required. A zigzag-scan-based permutation is shown to be particularly useful for signals satisfying the newly introduced layer model. As an application of the parallel compressed sensing with the zigzag-scan-based permutation, a video compression scheme is presented. It is shown that the zigzag-scan-based permutation increases the peak signal-to-noise ratio of reconstructed images and video frames.

2D signal compression via parallel compressed sensing with permutations

In this paper, we propose a new scheme to compress 2D signals using parallel compressed sensing. According to this scheme, the reconstruction at the decoder can be performed in parallel. By performing certain permutation on a 2D signal, all columns are insured to have approximately the same density level and can be sampled using the same measurement matrix. In this way, vectorization of a 2D signal can be avoided, and thus the size of the measurement matrix can be dramatically reduced. We prove that with a good permutation, we can have a tighter upper bound on reconstruction mean square error. To illustrate this scheme, we apply it to video compression and use two kinds of permutations for different frames: the zigzag-scan-based permutation for reference frames and the block-test-based permutation for non-reference frames. Simulation results show that under the same compression ratio, the peak signal-to-noise ratio can be improved by approximately 3-7 dB compared to the case without permutation.

Calibrated Layer-Stripping Technique for Level and Permittivity Measurement With UWB Radar in Metallic Tanks

A method to measure liquid level and electrical properties based on ultra-wideband pulsed radar is developed in this paper. Current methods of material property measurement using free-space radar typically use computationally intensive frequency-domain analysis or finite time-domain methods. The method presented is modified from layer-stripping algorithms and includes several improvements over previous techniques, such as an antenna array that allows measurement in a metallic tank environment and a method of calibration that characterizes path-loss and near-field effects for accurate amplitude-distance prediction. The method presented here also estimates the material loss properties and uses accumulated power with noise compensation to predict reflected pulse power. The method extends the use of pulsed radar for liquid-level measurement in tanks to the evaluation of liquid permittivity and the estimation of liquid height in liquids consisting of multiple layers. The accuracy of the presented method is evaluated using a transmitting single antenna element, a four-element antenna array, and an eight-element antenna array for measurement in a metallic tank environment. Accuracy is improved with larger antenna arrays, but the calibration becomes more critical. The accuracy for varying layer heights and materials is investigated to demonstrate the method reliability.

Segmented compressed sampling for analog-to-information conversion

A new segmented compressed sampling method for analog-to-information conversion (AIC) is proposed. According to this method, signal is first segmented and passed through the AIC to generate an array of incomplete measurements. Then, an extended number of correlated measurements is constructed by adding up subsets of the incomplete measurements selected in a specific manner. Due to the inherent special structure of the method, the complexity of the sampling device is unchanged, while the signal recovery performance is significantly improved. The validity of the proposed method is justified through theoretical analysis. Simulation results also verify the effectiveness of the proposed segmented compressed sampling method.

Decimated least mean squares for frequency sparse channel estimation

The standard least mean squares (LMS) parameter estimation method does not assume any special structure for the parameters being estimated. However, when additional knowledge about the system is available, the performance of LMS can be improved by appropriate modification of the algorithm. We develop such modifications for the case of estimating frequency sparse channels. Such modifications provide either better performance or less complexity when compared to the standard LMS algorithm. Decimated LMS and zero attracting decimated LMS are the two methods proposed in this paper. Simulation results are also provided to compare the performance of the proposed algorithms to the standard LMS and other sparsity aware modifications of LMS.

Empirical risk minimization-based analysis of segmented compressed sampling

A new segmented compressed sampling (CS) method for analog-to-information conversion (AIC) has been proposed in our recent work. Its essence is to collect a larger number of samples (although correlated) than the number of parallel branches of mixers and integrators in the AIC devise. The objective of this paper is to prove that the additional samples obtained based on the proposed segmented CS method lead to improved signal recovery quality. The study is performed based on the empirical risk minimization recovery method, but the least absolute shrinkage and selection operator algorithm can also be viewed as a particular realization of the empirical risk minimization method.

Correlation-Based UWB Radar for Thin Layer Resolution

Liquid level measurement and material identification with ultrawideband (UWB) free-space radar is considered in this letter. Traditional level measurement methods cannot distinguish between overlapping pulses, and their accuracy in identifying thin layers of material is limited by the width of the pulse used. A thin layer resolution algorithm is introduced to estimate the amplitudes of overlapping pulses, which in turn increases the accuracy in thin layer identification. The proposed thin layer resolution algorithm is shown to outperform spectral estimation methods such as multiple signal classification (MUSIC). A complete test setup was developed in laboratory, and the proposed signal processing method was tested on measurement data. The thin layer resolution method can recognize a 1-cm top layer of oil that corresponds to an overlapping of 66% between the first two reflected pulses.