Kumar Vijay Mishra

Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D ≥ 2) off-the-grid frequencies

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in [1] to recover 1-dimensional spectrally sparse signal. However, in spite of existing research efforts [2], it was still an open problem how to formulate an equivalent positive semidefinite program for atomic norm minimization in recovering signals with d-dimensional (d ≥ 2) off-the-grid frequencies. In this paper, we settle this problem by proposing equivalent semidefinite programming formulations of atomic norm minimization to recover signals with d-dimensional (d ≥ 2) off-the-grid frequencies.

Spectral Super-Resolution With Prior Knowledge

We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is often known. The prior information might be simply knowing precisely some signal frequencies or the likelihood of a particular frequency component in the signal. We devise a general semidefinite program to recover these frequencies using theories of positive trigonometric polynomials. Our theoretical analysis shows that, given sufficient prior information, perfect signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies. Numerical experiments demonstrate great performance enhancements using our method. We show that the nominal resolution necessary for the grid-free results can be improved if prior information is suitably employed.

Scientific and engineering overview of the NASA Dual-Frequency Dual-Polarized Doppler Radar (D3R) system for GPM Ground Validation

As an integral part of Global Precipitation Measurement (GPM) mission, Ground Validation (GV) program proposes to establish an independent global cross-validation process to characterize errors and quantify uncertainties in the precipitation measurements of the GPM program. A ground-based Dual-Frequency Dual-Polarized Doppler Radar (D3R) that will provide measurements at the two broadly separated frequencies (Ku- and Ka-band) is currently being developed to enable GPM ground validation, enhance understanding of the microphysical interpretation of precipitation and facilitate improvement of retrieval algorithms. The first generation D3R design will comprise of two separate co-aligned single-frequency antenna units mounted on a common pedestal with dual-frequency dual-polarized solid-state transmitter. This paper describes the salient features of this radar, the system concept and its engineering design challenges.

Compressed sensing applied to weather radar

We propose an innovative meteorological radar, which uses reduced number of spatiotemporal samples without compromising the accuracy of target information. Our approach extends recent research on compressed sensing (CS) for radar remote sensing of hard point scatterers to volumetric targets. The previously published CS-based radar techniques are not applicable for sampling weather since the precipitation echoes lack sparsity in both range-time and Doppler domains. We propose an alternative approach by adopting the latest advances in matrix completion algorithms to demonstrate the sparse sensing of weather echoes. We use Iowa X-band Polarimetric (XPOL) radar data to test and illustrate our algorithms.

Signal analysis and modeling of wind turbine clutter in weather radars

Lately, the continuing expansion of wind energy industry has led to the installation of several wind farms which are often in the vicinity of the weather radars. This is a source of growing concern for the weather radar community since wind turbines interfere with the normal operation of the weather radars. The wind turbine tower can drive the receivers into saturation and the Doppler shift from the moving blades can introduce errors in the estimation of wind speed, reflectivity and rainfall rates. The radar cross-section of the wind turbines has a large temporal and spatial variation which poses additional difficulties for traditional clutter filtering algorithms. This paper presents a first-order theoretical model of the radar signature of a wind turbine that can be helpful in deducing its unique features to be incorporated in filtering out the wind turbine clutter. A comparison with the observations from an S-band radar is made later in the paper.

Performance of time delay estimation in a cognitive radar

A cognitive radar adapts the transmit waveform in response to changes in the radar and target environment. In this work, we analyze the recently proposed sub-Nyquist cognitive radar wherein the total transmit power in a multi-band cognitive waveform remains the same as its full-band conventional counterpart. For such a system, we derive lower bounds on the mean-squared-error (MSE) of a single-target time delay estimate. We formulate a procedure to select the optimal bands, and recommend distribution of the total power in different bands to enhance the accuracy of delay estimation. In particular, using Cramér-Rao bounds, we show that equi-width subbands in cognitive radar always have better delay estimation than the conventional radar. Further analysis using Ziv-Zakai bound reveals that cognitive radar performs well in low signal-to-noise (SNR) regions.

Deployment and Performance Analyses of High-Resolution Iowa XPOL Radar System during the NASA IFloodS Campaign

AbstractThis article presents the data collected and analyzed using the University of Iowa’s X-band polarimetric (XPOL) radars that were part of the spring 2013 hydrology-oriented Iowa Flood Studies (IFloodS) field campaign, sponsored by NASA’s Global Precipitation Measurement (GPM) Ground Validation (GV) program. The four mobile radars have full scanning capabilities that provide quantitative estimation of the rainfall at high temporal and spatial resolutions over experimental watersheds. IFloodS was the first extensive test of the XPOL radars, and the XPOL radars demonstrated their field worthiness during this campaign with 46 days of nearly uninterrupted, remotely monitored, and controlled operations. This paper presents detailed postcampaign analyses of the high-resolution, research-quality data that the XPOL radars collected. The XPOL dual-polarimetric products and rainfall are compared with data from other instruments for selected diverse meteorological events at high spatiotemporal resolutions from...

Block Iterative Reweighted Algorithms for Super-Resolution of Spectrally Sparse Signals

We propose novel algorithms that enhance the performance of recovering unknown continuous-valued frequencies from undersampled signals. Our iterative reweighted frequency recovery algorithms employ the support knowledge gained from earlier steps of our algorithms as block prior information to enhance frequency recovery. Our methods improve the performance of the atomic norm minimization which is a useful heuristic in recovering continuous-valued frequency contents. Numerical results demonstrate that our block iterative reweighted methods provide both better recovery performance and faster speed than other known methods.

Off-the-grid spectral compressed sensing with prior information

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In this paper, we extend off-the-grid CS to applications where some prior information about spectrally sparse signal is known. We specifically consider cases where a few contributing frequencies or poles, but not their amplitudes or phases, are known a priori. Our results show that equipping off-the-grid CS with the known-poles algorithm can increase the probability of recovering all the frequency components.

Waveform considerations for dual-polarization Doppler weather radar with solid-state transmitters

Adequate sensitivity of weather radars using low-powered solid-state transmitter is achieved by using pulse compression waveforms. However, pulse compression waveforms have drawbacks of blind zone and range side lobes. In this paper, we present a methodology to address the major challenges in designing the waveforms for an X-band dual polarization Doppler radar operating with a solid-state transmitter. Here, frequency diversity wideband waveforms are proposed to mitigate low sensitivity of solid-state transmitters and the range eclipsing problem associated with pulse compression. An analysis of the performance of pulse compression using mismatched compression filters is reported. The performance of the proposed system is also quantified using signal and system simulations.