## 3 Proposed Mitigation Architecture for an RF Front-End
### Mitigation Architecture  
As shown in Figure 4, mitigation architecture can be divided into three steps including signal extraction, best delay searching and power residuals optimization, and nonlinearity compensation. Since the reason and method of step 3 have been introduced in Section 2, step 1 and step 2 will be discussed in this section. Let us begin with the process of step 1. Signals \(x(t)\) are first sampled and converted to digital baseband signals \(z(n)\). Subsequently, noise \(n_{z}(n)\) is obtained when the RF front-end is at the same working state of receiving \(z(n)\), such as the center frequency, passband bandwidth, system gain,  
Figure 4: Mitigation architecture. and attenuation. Then, a fast Fourier transform (FFT) is carried out to obtain the frequency spectra of \(z(n)\) and \(n_{z}(n)\). By substituting the power spectrum of \(z(n)\) for the noise power spectrum according to the set threshold, strong signals \(Z_{1}(k)\) and weak signals \(Z_{2}(k)\) in the frequency domain are separated from \(z(n)\), respectively. Finally, the waveforms of \(z_{1}(n)\) and \(z_{2}(n)\) in the time domain are available through IFFT. It is worth mentioning that this type of signal extraction saves both amplitudes and phases of the original signal and, hence, has the following benefits. In the literature [23; 27], FIRs are utilized. Suffering from imperfect performance of amplitude-frequency and phase-frequency response, there will be unwanted amplitude and phase changes in \(z_{1}(n)\) and \(z_{2}(n)\). This is inevitably harmful for best delay searching and nonlinear behavior model kernel calculation. In addition, compared with continually designing and changing multi-stopband/multi-passband digital filters with extremely high performance, in the proposed approach, only power threshold altering is needed. Therefore, this method is more likely to handle the situation of multiple signals with different power levels or wide ranges of bandwidth, which is apparently more flexible and convenient. In the rest of Section 3, step 2 is explained in detail including the choice of nonlinear behavior model for complex baseband signal in Section 3.1, the objective function establishment in Section 3.1, and the optimization solution in Section 3.2. The generalized Hammerstein model [24] is chosen to simulate the nonlinear behavior in the RF front-end. If the input is \(x(n)\), the expression is:  
\[ham(n)=\omega_{1}(n)*x(n)+\omega_{2}(n)*x^{2}(n)+\omega_{3}(n)*x^{3}(n)+... \tag{19}\]  
where \(\{\omega_{1}(n),\omega_{2}(n),\omega_{3}(n)\}\) are impulse responses taking memory effect into account for each order, and \(ham(n)\) is the output. Even-order nonlinear components are usually far away from others [18] in the spectrum, and even if the bandwidth of the RF front-end is extremely wide, proper circuit design methodologies [18; 36] can provide a high second-order intercept point where harmful effects resulting from the even-order nonlinearity are kept to a minimum. On the contrary, the odd-order nonlinearity appearing at the frequency near or inside the total frequency band of interest is hardly eliminated simply by some analog filters and, hence, more complicated to deal with. In the baseband, most nonlinearities belong to odd-order intermodulation components, and the third-order and fifth-order spectrum hyperplasia are much stronger than others. Therefore, Equation (19) is simplified to:  
\[ham(n)=\omega_{1}(n)*z_{1}(n)+\omega_{3}(n)*|z_{1}(n)|^{2}z_{1}(n)+\omega_{5  
The next step is to calculate the error signals between the outputs of the Hammerstein model \(ham(n)\) and the delayed weak signal \(z_{2}(n-\tau)\), while the power residual \(E(\omega,\tau)\) is regarded as the objective function to be minimized. Thus, \(E(\omega,\tau)\) is:  
\[E(\omega,\tau)=\sum_{n=1}^{N}|ham(n)-z_{2}(n-\tau)|^{2}=[U\omega-Z_{2}(\tau)]^ {H}[U\omega-Z_{2}(\tau)] \tag{24}\]  
where \(U^{T}=\left[ \begin{array}{cccc}u(1)&u(2)&...&u(N)\end{array} \right]\), \(Z_{2}(\tau)=\left[