Pulse-Doppler Signal Processing with Quadrature Compressive Sampling

Quadrature compressive sampling (QuadCS) is a newly introduced sub-Nyquist sampling for acquiring inphase and quadrature (I/Q) components of radio-frequency signals. For applications to pulse-Doppler radars, the QuadCS outputs can be arranged in 2-dimensional data similar to that by Nyquist sampling. This paper develops a compressive sampling pulse-Doppler (CoSaPD) processing scheme from the sub-Nyquist samples. The CoSaPD scheme follows Doppler estimation/detection and range estimation and is conducted on the sub-Nyquist samples without recovering the Nyquist samples. The Doppler estimation is realized through spectrum analyzer as in classic processing. The detection is done on the Doppler bin data. The range estimation is performed through sparse recovery algorithms on the detected targets and thus the computational load is reduced. The detection threshold can be set at a low value for improving detection probability and then the introduced false targets are removed in the range estimation stage through inherent detection characteristic in the recovery algorithms. Simulation results confirm our findings. The CoSaPD scheme with the data at one eighth the Nyquist rate and for SNR above -25dB can achieve performance of the classic processing with Nyquist samples.Comment: 37 pages, 18 figure

A General and Yet Efficient Scheme for Sub-Nyquist Radar Processing

We study the target parameter estimation for sub-Nyquist pulse-Doppler radar. Several past works have addressed this problem but either have low estimation accuracy for off-grid targets, take large computation load, or lack versatility for analog-to-information conversion (AIC) systems. To overcome these difficulties, we present a general and efficient estimation scheme. The scheme first formulates a general model in the sense that it is applicable to all AICs regardless of whether the targets are on or off the grids. The estimation of Doppler shifts and delays is performed sequentially, in which the Doppler estimation is formulated into a spatial spectrum estimation problem and the delay estimation is decomposed into a series of compressive parameter estimation problems with each corresponding to an estimated Doppler shift. By the sequential and decomposed processing, the computational complexity is substantially reduced, and by the parametric estimation techniques, the high accurate estimation is obtained. Theoretical analyses and numerical experiments show the effectiveness and the correctness of the proposed scheme.Comment: 13 pages, 3 figure

Gridless Quadrature Compressive Sampling with Interpolated Array Technique

Quadrature compressive sampling (QuadCS) is a sub-Nyquist sampling scheme for acquiring in-phase and quadrature (I/Q) components in radar. In this scheme, the received intermediate frequency (IF) signals are expressed as a linear combination of time-delayed and scaled replicas of the transmitted waveforms. For sparse IF signals on discrete grids of time-delay space, the QuadCS can efficiently reconstruct the I/Q components from sub-Nyquist samples. In practice, the signals are characterized by a set of unknown time-delay parameters in a continuous space. Then conventional sparse signal reconstruction will deteriorate the QuadCS reconstruction performance. This paper focuses on the reconstruction of the I/Q components with continuous delay parameters. A parametric spectrum-matched dictionary is defined, which sparsely describes the IF signals in the frequency domain by delay parameters and gain coefficients, and the QuadCS system is reexamined under the new dictionary. With the inherent structure of the QuadCS system, it is found that the estimation of delay parameters can be decoupled from that of sparse gain coefficients, yielding a beamspace direction-of-arrival (DOA) estimation formulation with a time-varying beamforming matrix. Then an interpolated beamspace DOA method is developed to perform the DOA estimation. An optimal interpolated array is established and sufficient conditions to guarantee the successful estimation of the delay parameters are derived. With the estimated delays, the gain coefficients can be conveniently determined by solving a linear least-squares problem. Extensive simulations demonstrate the superior performance of the proposed algorithm in reconstructing the sparse signals with continuous delay parameters.Comment: 34 pages, 11 figure

Segment-Sliding Reconstruction of Pulsed Radar Echoes with Sub-Nyquist Sampling

It has been shown that analog-to-information con- version (AIC) is an efficient scheme to perform sub-Nyquist sampling of pulsed radar echoes. However, it is often impractical, if not infeasible, to reconstruct full-range Nyquist samples because of huge storage and computational load requirements. Based on the analyses of AIC measurement system, this paper develops a novel segment-sliding reconstruction (SegSR) scheme to effectively reconstruct the Nyquist samples. The SegSR per- forms segment-by-segment reconstruction in a sliding mode and can be implemented in real-time. An important characteristic that distinguish the proposed SegSR from the existing methods is that the measurement matrix in each segment satisfies the restricted isometry property (RIP) condition. Partial support in the previous segment can be incorporated into the estimation of the Nyquist samples in the current segment. The effect of interference intro- duced from adjacent segments is theoretically analyzed, and it is revealed that the interference consists of two interference levels having different impacts to the signal reconstruction performance. With these observations, a two-step orthogonal matching pursuit (OMP) procedure is proposed for segment reconstruction, which takes into account different interference levels and partially known support of the previous segment. The proposed SegSR achieves nearly optimal reconstruction performance with a signi- ficant reduction of computational loads and storage requirements. Theoretical analyses and simulations verify its effectiveness.Comment: 13 pages, 10 figure

Gridless Parameter Estimation for One-Bit MIMO Radar with Time-Varying Thresholds

We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varying threshold in the temporal domain and employs compressive sensing in the spatial and Doppler domains. The goals are to significantly reduce the hardware cost, energy consumption, and amount of stored data. The joint angle and Doppler frequency estimations from noisy one-bit data are studied. By showing that the effect of noise on one-bit sampling is equivalent to that of sparse impulsive perturbations, we formulate the one-bit $\ell_1$-regularized atomic-norm minimization (1b-ANM-L1) problem to achieve gridless parameter estimation with high accuracy. We also develop an iterative method for solving the 1b-ANM-L1 problem via the alternating direction method of multipliers. The Cram$\acute{\text{e}}$r-Rao bound (CRB) of the 1b-MIMO radar is analyzed, and the analytical performance of one-bit sampling with two different threshold strategies is discussed. Numerical experiments are presented to show that the 1b-MIMO radar can achieve high-resolution parameter estimation with a largely reduced amount of data.Comment: 31 pages, 12 figure