## 3 Interference Suppression through Beamforming Techniques
### Deterministic Null Generation  
The first proposal to limit the likelihood of the performance worsening due to interferences consists of estimating the DoA of main sources and generating deterministic nulls in the estimated angles. The first step is to select the RD cells of a maximum return due to interferences. For this purpose, as an ECA filtering was applied in the first processing stage, the first non-zero Doppler row is selected. In this case, we start from positive Doppler values and, taking into account the selected integration time of 500 ms, the first selected value is 2 Hz. According to beamforming theory, N-1 nulls can be generated using an array of N elements citeVanTrees. Taking this into consideration, the N-1 greater peaks of the CAFs intensities along the range dimension for the selected Doppler of 2 Hz are determined. The value of the RD map along all the ranges for the selected Doppler are plotted and the peaks are selected for each antenna. The selected peaks of N elements are combined and the N-1 peaks of maximum level are selected, ensuring that they have different interference sources, i.e., they are reasonably spaced in range. Figure 8: RD maps of different CPIs showing the variance in interference sources through the acquisition time. The DoA estimation can be achieved in different ways, each of them with its advantages and drawbacks. An estimation through monopulse techniques can be performed via amplitude comparison, forming sum and difference beams from the array elements, or through phase comparison (interferometry). These techniques are fast and involve low computational cost, but they can only estimate the DoA within the half-power beam-width, so they are not appropriate, bearing in mind the scenario knowledge that suggests that interferences can come from the back part of the array if they are caused by the wind farms. The selected technique for estimating DoA is through beam scanning in all possible directions of the azimuth plane following a discrete grid in steps of \(1^{\circ}\): a beam steered to each direction is generated, and the power received in the evaluated RD cell is calculated for each beam and the direction associated with the beam generating the peak of power is assigned as the angle of that interference source. This technique for estimating DoA involves a high computational load, as each RD cell must be evaluated in all the set of beams by applying the corresponding weights in each case. One problem with this technique is that generating beams steered to directions outside the visible margin of the array causes the appearance of grating lobes that involve ambiguity in DoA estimation. Once the angles of the interferences are known, the optimum weights \(w_{o}\) for generating a zero-order null in the desired direction \(\phi_{n}\), for \(n=1,\cdots,(N-1)\), are calculated following Equation (4), with \(v_{k}(\varphi_{n})\) being the steering vector of the array for the null constraints \(C=[v_{k}(\phi_{1})\vdots v_{k}(\phi_{2})\cdots v_{k}(\phi_{N})]\) and \(w_{d}\) the weights for achieving a desired pattern; for example beam steering, prior to null generation [28]. \[w_{o}^{H}=w_{d}^{H}(I_{N}-C[C^{H}C]^{-1}C^{H}) \tag{4}\]  
Figure 9 shows how most of the interference sources found previously in CPI 13 are rejected by applying the deterministic null proposal. However, observing the cumulative maxima of RD for all 158 CPIs after null generation (Figure 9(a)), it can be determined that the power of the targets has also been reduced, i.e., targets' trajectories are less appreciable above noise background level. This decrease in targets' power is caused by the deviation of the direction of the beam with respect to the desired one due to null generation in the vicinity of beam steering, as well as the decrease in directivity due to beam broadening (Figure 9(b)). The patterns have been represented by employing the simulated pattern of an isolated antenna for all the elements, i.e., coupling effects between antennas in the array formation are not considered.