# Planar Array Diagnostic Tool for Millimeter-Wave Wireless Communication Systems
## 1 Introduction
This is why sparse recovery-based methods require fewer measurement numbers and provide faster antenna array diagnosis. Recently, compressive sensing emerged rapidly as a potential technique for solving sparse recovery problems [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. Within this context, the appropriateness of compressive sensing in addressing the array diagnosis problem was examined in References [3; 12; 14; 16; 18; 21]. Evidently, faulty element distribution in array configurations in practice were found to be highly sparse because it accounts for small non-null entries in the excitation vector of the transmit/receive modules. Beginning from that hypothesis, \(\ell_{1}\)-norm minimization mechanism was applied successfully to detect failures in planar arrays using a small number of near-field [9] or far-field [14] measurements. Conversely, deterministic compressive sparse techniques require a \"measurement matrix\" to comply with the restricted isometric property (RIP) condition, for which the estimation of large matrices remains an open challenge [3; 14; 21]. An alternative is the probabilistic compressive sensing approach reported in Reference [21] to diagnose linear arrays from far-field measurements. However, most of these techniques were not tested experimentally. In this work, the problem of antenna element excitation level was not examined; however, we estimated field distribution on the array aperture. This helps us identify the modifications of aperture field distribution as a result of factors that cannot be quantified by simple failure of elements, such as different reflections of the array and its feed. The problem faced in getting more information about the AUT is the larger number of unknowns. However, in sparse recovery methods, the required number of measurements increases slowly and logarithmically with the number of unknowns [10; 11; 12; 13]. Hence, the field reconstruction scheme benefits more in sparse recovery-based mechanisms. Different sparse recovery algorithms used to conduct antenna array diagnosis were unveiled [14] and compared to the traditional BPA and MMA. In particular, total variation (TV) norm, mixed \(\ell_{1}/\ell_{2}\) norm, and minimization of the \(\ell_{1}\) norm were used to proffer solutions to the resulting inversion issues. From the field reconstructed on the antenna aperture, [PERSON] et al. [20] acquired a good antenna diagnosis. The approach was applied to far-field simulation data generated from a 100-element antenna array. The performance of the diagnosis was evaluated and compared to the two standard techniques (BPA and MMA) under different conditions. The approaches were also applied to far-field measurement data of an antenna array with failure to justify the practical applicability of the proposed schemes. Although there were many more works on sparse recovery methods in applied electromagnetics and microwaves involving the diagnosis processes of antenna arrays [13; 14], experimental data, which are fundamental for testing any procedure, were reported in few of them. In References [15; 16; 17; 18; 19; 20], differential scenarios with sparse recovery algorithms were employed to perform antenna diagnosis and retrieve element excitations. Reference [21] proposed a joint scheme for adaptive diagnosis of antenna arrays using communication signal fusion (radar-communication scheme) and the echoes of probe signals received at the same antenna. This method equally solved the antenna diagnosis problem at low signal-to-noise ratios (SNRs) to ensure optimal performance of smart sensors in wireless sensor networks. Also, Reference [22] attempted array diagnosis in millimeter waves using compressive sensing. This work considered both full and partial blockage, which occurs from a plethora of particles (such as ice, water droplets, salt, and dirt) and the technique jointly computed the locations of the blocked elements, and the induced phase-shifts and induced attenuation provided the prior knowledge of the angles of departure/arrival.