The RIP and block-RIP analysis of Nyquist folding receiver for recovering signals

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.

Nyquist Zone Index and Chirp Rate Estimation of LFM Signal Intercepted by Nyquist Folding Receiver Based on Random Sample Consensus and Fractional Fourier Transform

“…In the literature, there are many studies focused on the LFM signal intercepted by the conventional receiver, such as fractional Fourier transform (FrFT) [14], Radon-ambiguity transform [15], and combined Wigner–Hough transform [16,17]. Nevertheless, there are fewer methods on the NYFR, and most research on the NYFR is based on CS methods [18,19,20]. Since the NYFR output contains the added local oscillator (LO) modulation, its signal processing is more complex compared to conventional receivers.…”

Parameter Estimation of SAR Signal Based on SVD for the Nyquist Folding Receiver

“…Conventional processing algorithms can be introduced to the NYFR to deal with intercepted SAR signals and avoid computationally expensive reconstruction. However, existing research on the NYFR have mainly focused on CS methods [ 12 , 13 , 14 ], and algorithms of signal parameter estimation for the NYFR output signal still require further research due to its special signal type. In conventional NYFR utilizing sinusoidal frequency modulation (SFM) LOS, the intercepted LFM signal will be converted into LFM/SFM hybrid modulated signal.…”

Estimation of both Nyquist zone index and code rate for BPSK radar signal intercepted by Nyquist folding receiver

“…The NZ information is called NZ index and it is unknown under the non‐cooperative receiving condition. Therefore, the NYFR output signal is a hybrid modulated signal [6, 8]. In order to process the NYFR output easier, the synchronous NYFR structure with a simplified LOS has been designed [9].…”