# Planar Array Failed Element(s) Radiation Pattern Correction: A Comparison
## 1 Introduction  
Phased array antennas are used to form directed signals that can be steered at the desired angle. Some specific applications of phased arrays include broadcasting, radar, optics, and space communication. The current trend in the telecommunication industry with Massive-Input-Massive-Output (MIMO) uses a large number of multiple antennas at the transmitter and receiver ends. Its base station is equipped with tens to hundreds of antennas in a single antenna array. The usage of phased arrays in space communication is also increasing [1].  
This large array distribution in a system increases the probability of more antenna system elements failing, and the failures are unavoidable [2]. The failed elements cause thearray to lose its symmetry, resulting in a distorted radiation pattern with increased sidelobe levels, weakening null depth and null shift [1]. This causes transmitters to waste energy and cause interference to other equipment by radiating signals in unwanted directions. While in receivers, the noise level is increased by receiving interfering signals. This will reduce the efficiency of the transmitter and the receiver.  
Research on failure elements in arrays has existed since the end of the 20 th century and the beginning of the 21 st century because of its continuous usage in various fields. Now it is regaining its attention due to its mass usages in wireless and communication systems and other fields. The need for failure correction techniques is still necessary.  
Replacing the failed element with a new element is not a possible solution for applications such as space platforms, where it is complex, time-consuming, and expensive. So, optimization-based far-field radiation pattern correction methods with remaining active elements in the array are being researched [3; 4; 5; 6].  
Recent research on correcting failed radiation patterns are with grey wolf optimizer hybridized with an interior point algorithm [7], Improved Particle Swarm Optimization with Wavelet Mutation [8], Particle Swarm Optimization (PSO) and Bacteria Foraging Optimization (BFO) [5], Whale Optimization Algorithm (WOA) and Chaotic Whale Optimization Algorithm (CWOA) [9], and Backtracking Search Optimization [10]. However, this research focuses on the linear array, which consists of a smaller number of elements in an array. Failed pattern correction with the planar array is limited. Some available research uses the Simulated Annealing Technique [11], Artificial Neural Network with Hopfield network [12], and Particle Swarm Optimization [13]. In study [11], the number of faulty elements in an array is very little, while the current communication systems have more probability of element failure in an array. Other than that, reference [13] has investigated a 5 \(\times\) 5 planar array with 2 to 20 element failures in the array.  
Most of the papers in the literature used a meta-heuristic search for restoring the radiation pattern. However, each method has its disadvantages, such as solutions converge prematurely, easily fall into a local optimum, and adequate parameter tuning [14]. An optimization algorithm developed varies case by case. Similarly, optimization methods developed for linear arrays and smaller array sizes will not be suitable for a large planar array.  
This paper compares four different optimization methods; simulated annealing (SA), genetic algorithm (GA), particle swarm optimization (PSO), and pattern search (PS) method, and proposes a method that is suitable for large planar array radiation pattern correction at the end of the paper. A failed radiation pattern is corrected by optimizing the weights of the remaining working elements in the array. The method will improve the overall efficiency of any system with a planar array and reduce the cost of repairing and replacing the failed element(s) in an array. This method also avoids near fields measurement, which involves complex processes and uses expensive equipment.