# Planar Array Diagnostic Tool for Millimeter-Wave Wireless Communication Systems
## 5 Simulations and Analysis  
Assessing the performance of the BCS algorithm, we consider an RA with \(N=316\) with Taylor taper and peak sidelobe level of \(-25\) dB. Assuming a complete failure (\(h=0\)), the given percentage of failed elements is \(\Phi=4\%\). To determine the detection error numerically, the index of detection can be expressed as  
\[\zeta=100\times\frac{\sum_{n=1}^{N}\left|\mathrm{Y}_{n}-\hat{\mathrm{Y}}_{n} \right|^{2}}{\sum_{n=1}^{N}\left|\mathrm{Y}_{n}\right|^{2}}, \tag{18}\]  
where \(\mathrm{Y}_{n}\) and \(\hat{\mathrm{Y}}_{n}\), \(n=1,\ldots,N\), are the real and predicted failure entries of vector \(\underline{\mathrm{Y}}\). The uniformly sampled (\(k=316\) samples) far-field radiation pattern is within (\(u,v\)) space, with the signal-to-noise ratio \(SNR=30\) dB. The configuration of the AUT is presented in Figure 4, while the excitation coefficients \(\beta_{n}\) of the failed array are equally shown. Figure 5 shows \(\hat{\mathrm{Y}}_{n}\) of the failure vector estimated via the proposed technique. As expected, there is good correlation between the location and the number of the real and predicted failed elements. Accuracy of the estimation was ascertained by a very small index of detection figure of \(\zeta=3.83\ \times\ 10^{-3}\). Figure 3: Flowchart of the proposed Bayesian compressive sensing (BCS) procedure. To analyze the impact on performance metrics of the technique of the noise on far-field patterns, we ranged the SNR between 0 dB and 100 dB. Figure 6 shows the obtained result. The estimation error \(\zeta\) is high for low SNRs irrespective of failed element percentage. Also, for higher SNR, the robustness of the approach increases, which shows that the best performances are attained at \(\Phi=3\%\). The impact of the percentage of failed elements on the performance of the method proposed was also assessed by varying the percentage of the failed elements from \(\Phi=2\%\) to \(\Phi=20\%\) (see Figure 7). Expectedly, the performance metrics of the approach reduced for a higher percentage of failed elements, even for very low noise levels. Conversely, the approach achieved a degree acceptable accuracy until about 10% of damaged elements at any SNR. This result validates the efficiency of the BCS technique in the diagnosis of sparse failures in arrays. Figure 4: Normalized array excitation of the array under test (AUT). Figure 5: Normalized array excitation with estimated failure vector \(\underline{\hat{Y}}\) and location and amplitude of entries. _Example Using Full-Wave Simulation Set-Up_  
A \(10~{}\times~{}10\) microstrip patch antenna array with an aperture size of \(31~{}\times 31\) mm\({}^{2}\) operating at 28.9 GHz was designed, as shown in Figure 8. We designed and computed the radiation pattern and S-parameter (Figure 9) of the antenna using full-wave three-dimensional (3D) EM software Ansys HFSS v. 17. The elements were uniformly spaced along the \(x\) and \(y\) directions. Each element had an excitation port. Practically, measurements are made impure by noise; hence, a Gaussian noise \(n\) was added to the data on both radiation patterns as \(y_{n}^{q}=~{}y^{q}+n^{q}\), with \(q=\{r,d\}\). The noise level was determined by signal-to-noise ratio (SNR) defined from the maximum received field magnitude fitting the dynamic measurement range. The noise was estimated as  
\[n^{q}=\frac{\mathcal{N}(0,1)+j\mathcal{N}(0,\,1)}{\sqrt{2}}~{}max|y^{q}|~{} \times~{}10^{-SNR_{dB}/20}, \tag{19}\]  
Figure 6: Detection index against signal-to-noise ratio (SNR) for different failure percentages. Figure 7: Detection index against failure rate for various SNRs. where \(\mathcal{N}(0,1)\) is a Gaussian random vector of mean 0 and standard deviation 1. The faulty elements cause low gain, high sidelobe level, wider beamwidth, lower front-to-back ratio, and a boresight pointing error. The effects are shown in Figure 9b.