Abstract
This paper presents an efficient sampling system for the acquisition of synthetic aperture radar (SAR) data at sub-Nyquist rate. The system adopts a quadrature compressive sampling architecture, which uses modulation, filtering, sampling and digital quadrature demodulation to produce sub-Nyquist or compressive measurements. In the sequential transmit-receive procedure of SAR, the analog echoes are modulated by random binary chipping sequences to inject randomness into the measurement projection, and the chipping sequences are independent from one observation to another. As a result, the system generates a sequence of independent structured measurement matrices, and then the resulting sensing matrix has better restricted isometry property, as proved by theoretical analysis. As a standard recovery problem in compressive sensing, image formation from the sub-Nyquist measurements has significantly improved performance, which in turn promotes low sampling/data rate. Moreover, the resulting sensing matrix has structures suitable for fast matrix-vector products, based on which we provide a first-order fast image formation algorithm. The performance of the proposed sampling system is assessed by synthetic and real data sets. Simulation results suggest that the proposed system is a valid candidate for sub-Nyquist SAR.
Highlights
Synthetic aperture radar (SAR) is an imaging radar mounted on a moving platform
We assume that the SAR operates in stripmap mode and the transmitted pulses are linear frequency modulated (LFM); chirp scaling algorithm (CSA) can be used to obtain the SAR image, which can be described in a compact form as XCSA = (H3 ◦ Fr∗ (H2 ◦ Fr (H1 ◦ YFa))) F∗a
The proposed system is based on the quadrature compressive sampling (QuadCS), which is easy to insert randomness into the sensing matrix
Summary
Synthetic aperture radar (SAR) is an imaging radar mounted on a moving platform. As the platform moves, electromagnetic waves are sequentially transmitted to illuminate an area and the backscattered echoes are collected by the radar receiver to form raw data for subsequent digital processing. For all Na observations, where l is the index of azimuth position, yl and nl are vectors denoting the Nyquist samples of SAR echo and the sub-Nyquist measurements of observation noise, respectively, and Φl is the measurement matrix resulting from the sampling system. As mentioned above, Xampling has been exploited for sub-Nyquist SAR [4], where a fixed measurement matrix is taken to sample radar echoes for all observations, i.e., the measurement matrices Φl for l = 1, · · · , Na are the same. It is important to note that the proposed QuadCS system does not put further burden on hardware implementation because the independence of chipping sequences can be set beforehand by maximal-length linear feedback shift registers (MLFSR) with a set of unique initial seeds Another contribution of this paper is the development of a fast sparse imaging algorithm for the proposed sub-Nyquist SAR system. The symbols ⊗ and ◦ denote the Kronecker product and the Hadamard product, respectively
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