# Reduction of Phase Shifters in Planar Phased Arrays Using Novel Random Subarray Techniques
## 1 Introduction  
Phased antenna arrays provide enhanced performance and flexibility compared to traditional single-element antennas, with the capability of steering and shaping their radiation patterns by combining multiple individual antenna elements [1]. This allows transmitting and receive signals in specific directions, which makes them a crucial component of modern communication systems. Planar phased arrays are currently used in a broad spectrum of beamforming applications, due to their ability to steer a beam in both azimuth and elevation planes, which makes this technology suitable for 5G and satellite applications [2, 3]. Furthermore, there are applications that require almost a free redirection of the mainlobe radiant energy, such as in automotive radars and landing systems [4].  
The reduction of phase shifters in the array is an important consideration in antenna design, given that phase shifters directly affect the cost, complexity, and power consumption of the system. One approach involves exploiting the spatial properties of the antenna array to achieve beamforming. This can be achieved by using subarrays [5, 6, 7, 8], where each subarray consists of a group of antennas with a single phase shifter. Proper configuration of the subarrays allows reducing the number of phase shifters, while maintaining beamforming capabilities and achieving a complementary reduction in the side lobe level (SLL).  
Previous works on the subject suggested different design techniques for planar phased arrays, such as the ones mentioned in [9, 10, 11], where distinct strategic arrangements of antenna elements into subarrays are presented. The subarrays are depicted as tiles thatform diverse geometric figures, which in some cases form a unique pattern of design. As mentioned in [12], an exhaustive methodology is used to generate various planar array designs based on the replication of geometric patterns of subarrays, which reduces the quantity of solutions in the search space. Although this approach considerably reduces the number of phase shifters in the system, there is limited scanning of the mainlobe in the elevation plane.  
There have been many techniques based on subarrays in previous works, although more research is required to generate better techniques that achieve phased antenna systems with lower complexity and maintaining the desired radiation features. This paper presents a novel method for the design of phased planar antenna arrays to reduce the number of phase shifters used in the antenna system. This method consists of creating fusions of subarrays to generate random sequences that construct the best feeding network configuration with previously defined radiation characteristics for planar antenna arrays.  
The techniques presented in this work can result in a reduction of up to 70% in the number of phase shifters used by the array system with respect to the conventional case of one phase shifter per antenna element. The obtained solution allows scanning the mainlobe at \(\theta=-40^{\circ}\) elevation with a range of scanning of \([-75^{\circ}\leq\phi\leq~{}75^{\circ}]\) in the azimuth plane, while maintaining a side lobe level below \(-10\) dB and achieving a reduction of 62% in the number of phase shifters. This methodology may be of interest for antenna designers in order to set appropriate design compromises between the number of control ports and radiation performance.