Spectral reconstruction of signals from periodic nonuniform subsampling based on a Nyquist folding scheme

Abstract

Periodic nonuniform sampling occurs in many applications, and the Nyquist folding receiver (NYFR) is an efficient, low complexity, and broadband spectrum sensing architecture. In this paper, we first derive that the radio frequency (RF) sample clock function of NYFR is periodic nonuniform. Then, the classical results of periodic nonuniform sampling are applied to NYFR. We extend the spectral reconstruction algorithm of time series decomposed model to the subsampling case by using the spectrum characteristics of NYFR. The subsampling case is common for broadband spectrum surveillance. Finally, we take example for a LFM signal under large bandwidth to verify the proposed algorithm and compare the spectral reconstruction algorithm with orthogonal matching pursuit (OMP) algorithm.

Analysis of Sampling Aperture Impact on Nyquist Folding Receiver Output

“…1, the LO modulation using the SFM can be expressed as θ(t) = z θ sin (2π f θ t), where z θ = T θ ∆F is the modulation coefficient, T θ = 1/ f θ is the LO modulation period, f θ is the modulation frequency and ∆F is the bandwidth of the LO modulation [6], [9]. The average frequency of the RF sample clock is f s1 that equals the bandwidth of NZ when the input is complex, and the cut-off frequency of F( f ) is f s = f s1 [5]. After the mixing and the interpolation filtering, the input signal spreading in the wide frequency space is folded into 0, f s , which realizes the ultra-wideband receiving.…”

“…where j = √ −1, k ∈ Z, * means convolution. Under the simplified condition, p(t) contains no aperture and the sample pulse template p(t) = δ(t), where δ(•) is the Dirichlet function [5], [6]. However, in the practical situation, p(t) contains an and p(t) can be expressed as a rectangular function [8]…”

“…Unlike the typical receiving architecture, the Nyquist folding receiver (NYFR) is a novel ultra-wideband receiving structure that can overcome the limitations of ADC sample rate [3]- [5]. The NYFR only uses a local oscillator (LO) and an ADC to realize wideband receiving, which means its receiving resource is small.…”

“…Recently, the studies of the NYFR mainly focus on the receiving model and the corresponding signal processing [3], [4]. These studies are based on the simplified condition, which means the aperture of the non-uniform sample pulse train is not considered [5], [6]. In practice, the aperture of the sample pulse train is inevitable when it is generated from the LO, which implies the sample pulse has a width [7], [8].…”

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.…”