1 Mis-modeling & Mis-correction of Mutual Coupling in an Antenna Array – A Case Study in the Context of Direction Finding Using a Linear Array of Identical Dipoles Yue Ivan WU College of Computer Science, Sichuan University, Chengdu, Sichuan, 610065, China ivan.wuyue@ieee.org Gerald Pacaba ARADA, Wai-Yip TAM, Kainam Thomas WONG Department of Electronic & Information Engineering, Hong Kong Polytechnic University, Hong Kong gerald.arada@connect.polyu.hk, wai.yip.tam@polyu.edu.hk, ktwong@ieee.org Abstract—In an array of antennas, the inter-antenna elec- tromagnetic mutual coupling, unless properly corrected, would degrade an antenna array’s performance in direction finding. In the special case of a uniformly spaced linear array of iden- tical antennas, Azarbar, Dadashzadeh & Bakshi have suggested discarding the antennas’ collected data at both ends of the linear array, on the assumption that all middle antennas experience near-identical mutual coupling, as each middle antenna would have many antennas on either side. The antennas whose data will be discarded are called the “auxiliary” antennas. While Azarbar, Dadashzadeh & Bakshi modeled the mutual coupling matrix as Toeplitz and banded, this key assumption is invalidated by simulations using the “method of moments” (as realized in the software “EMCoS Antenna VLab”). Using such more realistic values for the mutual coupling matrix for a uniform linear array (ULA) of identical dipoles, instead of the idealistic assumptions of a Toeplitz banded mutual coupling matrix, the method in Azarbar, Dadashzadeh & Bakshi’s paper is found here to perform very poorly. Index Terms—antenna array mutual coupling, array signal processing, direction-of-arrival estimation, antenna arrays, signal processing antennas, electromagnetic coupling. I. I NTRODUCTION Matrix Pencil is a “direct data domain” technique that implements non-statistical treatment on the data samples and originally found application in determining system’s poles [1]. Unlike MUSIC [2] and ESPRIT [3], the Matrix Pencil method a) does not need estimation of the correlation matrix, veer- ing away from extensive computation. b) requires only single snap shot from the array, thereby saving on memory storage. c) handles non-stationary or fast-fading environment easily and signals need not to be uncorrelated or incoherent. d) could discriminate closely spaced sources. A number of techniques have been implemented as variation to the matrix pencil method and ESPRIT in order to mitigate mutual coupling in [4]–[7]. These papers also advance the idea of discarding the data collected by antennas at both ends of the linear array. This method treats those antennas as “auxiliary” or “dummy” antennas. The remaining antennas in the “mid- array” would then supposedly be sufficiently similar in their mutual impedance. However, [4], [6]–[10] all make a key assumption that the mutual coupling matrix (not the impedance matrix) is banded symmetric Toeplitz. This foundational presumption is altogether invalid, as will be shown in this paper’s succeeding sections. Indeed, this paper will show how the algorithm in [4] would fail entirely when affronted with the mutual coupling data generated from the “EMCoS VLab” software. A similar case study [11] was also done where the mutual coupling matrix from VLab was fed to the mid-array ESPRIT algorithm [6] using a 7-element uniform linear array of iden- tical half-wave dipoles. II. UNIFORM LINEAR ARRAY’ S DATA MODEL WITHOUT ELECTROMAGNETIC COUPLING Consider K narrowband plane-waves s k (t) with wavelength λ from direction-of-arrival (DOA) θ k respectively, impinging upon M identical antennas lying along the x-axis. The anten- nas are z-oriented and uniformly spaced by Δ. s k (t) would then experience a complex phase-shift, e j 2π xm λ sin θk at the mth antenna with respect to an assumptive antenna at the x- coordinate’s origin. At time t, let an M × 1 vector represent the entire array’s