## 1 Introduction
In addition to the above nonlinearity suppression methods by analog circuits, a great many methods [21; 22; 23; 24; 25; 26; 27] based on more flexible digital signal processing (DSP) have been published. In Reference [21], a modified post-distortion algorithm was proposed to mitigate nonlinearities in a broadband receiver which is far away from the original fundamental waves, as well as to corrupt the other sub-channels. This method succeeded in designing a broadband direct digitization RF receiver. However, it could hardly adapt to compensating intermodulation products since its signal extraction is unsuitable for the components inside or nearby the adjacent channel of strong signals. In Reference [22], a nonlinear behavior model of a baseband signal was designed to eliminate nonlinearities in an RF receiver. The objective signal was converted to a baseband and then centered at DC after rotation. Then, each distortion component and its frequency content function were calculated to form an output of a nonlinear model for compensation. Unfortunately, this method has an unwanted limitation in the number of input signals. In References [23; 24], a finite impulse response (FIR) band-pass/band-stop filter was formed according to the strong signals' frequency location and practical adaptive filtering-based learning algorithms were then proposed. Our previous work [27] suggested a blind identification criterion for minimizing the short-time energy of the nonlinear components in the frequency domain. However, suffering from the non-ideal frequency response characteristic of FIR, the methods mentioned above may hardly adapt to the situation where multiple unknown signals with different power levels exist simultaneously. Unfortunately, in most cases, this is exactly the electromagnetic environment in which the RF front-end of the sensor works. On the other hand, in-band group delay distortion, which introduces inter-symbol interference to the output signal, inevitably degrades the overall CR-WSN system performance. Many references [28; 29; 30; 31; 32; 33] have been presented up to now. Due to an analog circuit's lack of flexibility and applicability, strategies in DSP have become a trend. In Reference [34], the cumulative distribution function (CDF) of a given modulation signal was calculated and a measure of distortion of the in-band group delay was then constructed in the statistical domain, which could be optimized to obtain the equalizing filter coefficients. Nevertheless, this method cannot be utilized in the RF front-end in the sensor because the statistical characteristic of various modulation mode signals with different levels is hardly determined and, furthermore, the processing procedure of the proposed algorithm is too complicated to meet the requirement in the context of CRs. In addition, it is worth noting that even though non-constant group delay belongs to linear distortion, when it joins with the memory nonlinear effect, the system modeling of group delay compensation and nonlinearity mitigation in series cannot achieve the desired improvement any longer. Even worse, the equalizer could increase the memory depth of the nonlinear behavior model. According to the best knowledge of the author, in the existing state-of-the-art literature, few methods involving nonlinearity mitigation take group delay distortion compensation into account. In this paper, a simplified RF front-end model containing a low noise amplifier (LNA) and filter with a non-constant group delay in the passband is chosen as the object of analysis. Then, we emphasize how the group delay distortion brings a phase change to each frequency component at the output. Furthermore, in terms of the time domain, it can be interpreted as a delay between the strong signals producing nonlinearities and the weak signals including the nonlinear components and low signal-to-noise ratio (SNR) signals. Thereupon, the instantaneous power residual error can be regarded as a function of nonlinear model kernels and delay.