Abstract
Modern radar and communication systems require the detection and parameter estimation of signal under a broadband radio frequency (RF) environment. The Nyquist folding receiver (NYFR) is an efficient analog-to-information (A2I) architecture. It can use the compressive sensing (CS) techniques to break the limitations of the analog-to-digital converter (ADC). This paper demonstrates the restricted isometry property (RIP) of the NYFR deterministically by applying the Gershgorin circle theory. And, the NYFR suffers a poor RIP for the broadband signal, which will lead the conventional CS algorithms to be invalid. So, we derive the Fourier spectrum of the broadband signal, which covered multiple Nyquist zones and received by the NYFR. Then, the broadband signal can be regarded as the block-sparse signal. And, the block CS algorithms are applied for recovering the signal based on the analysis of the block-RIP. Finally, the simulation experiments demonstrate the validity of the findings.
Highlights
Electronic warfare (EW) plays a leading role in most conflicts for future war, and the receiver is the core
We demonstrate the restricted isometry property (RIP) of the Nyquist folding receiver (NYFR) deterministically by applying the Gershgorin circle theory
The NYFR suffers a poor RIP for the broadband signal, which will lead the conventional compressive sensing (CS) algorithms to be invalid
Summary
Electronic warfare (EW) plays a leading role in most conflicts for future war, and the receiver is the core. Reference [1] discusses the CS framework of the NYFR and the signal reconstruction with single-frequency applying the orthogonal matching pursuit algorithm (OMP). Reference [15] uses various techniques for demonstrating RIP deterministically including the Gershgorin circle theory. We demonstrate the RIP of the NYFR deterministically by applying the Gershgorin circle theory. The broadband signal covers multiple Nyquist zones received by the NYFR, and we present its Fourier spectrum. We demonstrate the block-RIP of the NYFR deterministically by using the property that the Toeplitz matrix satisfies the RIP.
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