International Journal of Electrical and Computer Engineering (IJECE) Vol. 12, No. 2, April 2022, pp. 1732~1743 ISSN: 2088-8708, DOI: 10.11591/ijece.v12i2.pp1732-1743  1732 Journal homepage: http://ijece.iaescore.com Discrete interferences optimum beamformer in correlated signal and interfering noise Satyanand Singh 1 , Sajai Vir Singh 2 , Dinesh Yadav 3 , Sanjay Kumar Suman 4 , Bhagyalakshmi 5 , Ghanshyam Singh 6 1 School of Electrical and Electronics Engineering, Fiji National University, Suva, Fiji 2 Department of Electronics and Communication Engineering, Jaypee Institute of Information Technology, Noida, India 3 Department of Electronics and Communication Engineering, Manipal University Jaipur, Rajasthan, India. 4 Department Electronics and Communication, Bharat Institute of Engineering and Technology, Hyderabad, India 5 Department Electronics and Communication Engineering, Rajlakshmi Engineering College, Chennai, India 6 Department of Electronics and Communication Engineering, Malaviya National Institute of Technology Jaipur, Rajasthan, India Article Info ABSTRACT Article history: Received Nov 18, 2020 Revised Sep 7, 2021 Accepted Oct 2, 2021 This paper introduces a significant special situation where the noise is a collection of D-plane interference signals and the correlated noise of D+1 is less than the number of array components. An optimal beamforming processor based on the minimum variance distortionless response (MVDR) generates and combines appropriate statistics for the D+1 model. Instead of the original space of the N-dimensional problem, the interference signal subspace is reduced to D+1. Typical antenna arrays in many modern communication networks absorb waves generated from multiple point sources. An analytical formula was derived to improve the signal to interference and noise ratio (SINR) obtained from the steering errors of the two beamformers. The proposed MVDR processor-based beamforming does not enforce general constraints. Therefore, it can also be used in systems where the steering vector is compromised by gain. Simulation results show that the output of the proposed beamformer based on the MVDR processor is usually close to the ideal state within a wide range of signal-to-noise ratio and signal-to-interference ratio. The MVDR processor-based beamformer has been experimentally evaluated. The proposed processor-based MVDR system significantly improves performance for large interference white noise ratio (INR) in the sidelobe region and provide an appropriate beam pattern. Keywords: Direction of arrival Interference white noise ratio Minimum power distortion Minimum variance distortionless response Signal-to-interference and noise ratio This is an open access article under the CC BY-SA license. Corresponding Author: Satyanand Singh School of Electrical and Electronics Engineering, Fiji National University Samabula Fiji Lakeba Street Samabula, Suva, Fiji Email: Satyanand.singh@fnu.ac.fj 1. INTRODUCTION Beamformers are commonly used in a variety of applications of signal processing, such as voice amplification, radar, and wireless communication. In particular, one of the fundamental problems in array processing is the problem of measuring the signals of several transmitters using an antenna array. The Capon beamformer [1] has gained popularity in this context due to its high ability to refuse interference. Nevertheless, Capon beamformers also known as Van Trees minimum power distortionless response (MPDR) beamformers are still prone to steering errors [2]. Ward, Cox, and Kogon based on diagonal loading effect provides a comparison of several robust MPDR beamformers to correct model errors [3]. Wax et al. [4] performed a theoretical score reading of the signal-to-interference-plus-noise ratio (SINR), which is generalized (that is, not necessarily a diagonal) covariance matrix and the existence of random steering vector