## 1 Introduction
Therefore, a suitable trade-off should be found between the attenuation of the misleading cross-terms and the TF energy concentration of the signal components. A meaningful solution to deal with this trade-off for the TF distributions is the reassignment method [16, 17, 18], which is a point-wise transformation of regular TFRs; it works by relocating the values of a TFR from the geometrical center of the analysis window to the center of gravity, which is more representative of the localization of the TF energy distribution. In this way, the reassignment method smooths out oscillating cross-terms while squeezing localized terms, which spread over the TF plane; and the TF energy density components are relocated to the position causing the signal features. The main feature of the reassigned TF distribution is that it provides good TF localization properties. Since the spectrogram is a typical type of cross-term-free representation of Cohen's class, in this paper, a modified version of the spectrogram based on the reassignment in the TF plane has been applied in interference detection for GNSS receivers in the jamming scenarios. The reassigned spectrogram allows improving the TF resolution to provide a readable and localized distribution in the TF domain. This results in a squeezed representation with sharp TF energy concentration, which presents no cross-terms in the TF plane. The motivation of this paper is to design a novel TF distribution for the removal of the serious cross-terms and the enhancement of TF resolution, which is suitable to be used in interference detection for GNSS receivers. Therefore, in this paper, a novel TF analysis method by adopting a reassigned spectrogram has been proposed in interference detection for GNSS receivers. To the best of our knowledge, this interference detection technique based on the reassigned spectrogram in the interference detection units for GNSS receivers is new. The performance of the proposed method has been deeply evaluated in comparison to the existing TF analysis approaches. Different localization properties and cross-term effects in the TF plane have been well investigated and compared among the aforementioned TF distributions adopted in interference detection for GNSS receivers. In addition, the acquisition performances in the presence and absence of interference mitigation units in GNSS receivers have been studied. In this paper, the interference is mitigated by using a notch filter, which is implemented by an impulse response filter (IIR) based on the interference instantaneous frequency estimated by the proposed reassigned spectrogram method. The interference mitigation performance has been evaluated in terms of the receiver operating characteristic (ROC) or the ROC curve by means of Monte Carlo simulations [19, 20, 21]. The ROC curve is a graphical plot of the sensitivity, plotting the behaviors of the detection probability \(P_{d}\) versus the false alarm probability \(P_{fa}\) or, equivalently, of the missed detection probability \(P_{m}\) versus the false alarm probability \(P_{fa}\) of a binary classifier system as its discrimination threshold is varied. Therefore, the ROC curve can be used to completely characterize the acquisition performance, which provides a statistical characterization of the acquisition performance allowing comparative analysis for different algorithms. Among all of the different classes of interfering signals, a constant amplitude linearly-modulated sweep interference (chirp disturbance) has been shown to have severe impacts on the quality of the received GNSS signal [6,10,22]. Therefore, in this paper, such an interference has been employed as a test bench for the the proposed TF analysis method. In order to prove the effectiveness of the proposed reassigned spectrogram in interference detection for GNSS receivers, an experiment has been accomplished in the GPS L1 signal, which is characterized in additive white Gaussian noise (AWGN) corrupted by chirp interference.