Sub-Nyquist SAR via Quadrature Compressive Sampling with Independent Measurements

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.