# Planar Array Diagnostic Tool for Millimeter-Wave Wireless Communication Systems
## 1 Introduction
Reference [23] proposed a deterministic sampling strategy for failure detection in uniform linear arrays via compressed sensing or a sparse recovery approach. This is an extension of the Weyl formula which is basically used for prime  
Figure 1: _Ka_-band active antenna array formation which integrates multiple-input multiple-output (MIMO) and beamforming. numbers. The strategy obtained was good for nonprime number (i.e., valid for any number of array elements). This sampling approach is good for sparse electromagnetic (EM) problems encompassing Fourier matrices. Reference [24] gives a review of different capacities of sparse recovery by analyzing how compressive sensing can be applied to antenna array synthesis, diagnosis, and processing. Illustrations of a set of applicative examples were given, including direction-of-arrival estimation, along with present challenges and current trends in compressive sensing applications to the solution of innovative and traditional antenna array challenges. In general, compressive sensing generates few unknown numbers; however, it needs a comprehensive array model with exact knowledge of the radiating element patterns to produce useful results. The technique is sparse with respect to the whole array structure, and requires a priori information to recast it as the function of minimization of \(\ell_{1}\) norm. However, these techniques are applicable only if the relationships between the data and the unknowns satisfy the restricted isometry property (RIP). To overcome this challenge, the Bayesian compressive sensing (BCS) approach is adopted. This technique was explored in many electromagnetic problems, such as antenna design and synthesis [25; 26], microwave imaging [27; 28; 29; 30], and direction-of-arrival estimation [31; 32; 33]. It is employed in this paper to estimate the number, magnitude, and location of failures in antenna arrays from far-field measurements. The BCS approach was attempted to diagnose large linear arrays [11], and more recently, planar array configurations [34]; however, no experimental validation was reported. Hence, there is a need for a more reliable procedure tested experimentally and via simulation, because experiments are fundamental tests of any given procedure. Specifically, this work is an extension of that described in References [15; 16]. The BCS method is applied to both the simulated and measured far-field data of a millimeter-wave 100-element microstrip patch antenna array in which failures were added intentionally. A new regularization technique was unveiled and applied to field distribution in order to enhance the efficiency and reliability of antenna array diagnosis. The proposed BCS-based approach is a better choice due to its fast nature and robustness under different noise conditions. The key contributions of this paper are summarized as follows:  
1. The BCS technique was applied to diagnose a millimeter-wave planar array, and the result was compared with other approaches reported in the literature. 2. The procedure shows high effectiveness and reliability with fewer measurement points compared to the other methods, and is highly robust to additive noisy data. This was validated experimentally and via simulations. However, some boundary conditions were observed. The BCS-based approach detects diagnostic problems with few measurements, provided prior knowledge of the reference array radiation pattern, and the number of faults is relatively smaller than the array size. The remainder of this paper is arranged as follows: Section 2 contains the problem formulation of antenna array diagnosis. Section 3 presents compressed sparse recovery methods. Resolution via the BCS-based approach is given in Section 4. The numerical simulations are presented in Section 5. Diagnoses from experimental data are presented and discussed in Section 6. Finally, some conclusions are drawn in Section 7.