Antenna Measurement Concept Exploiting Echoes Based on Frequency Diversity Mouad Djedidi, Florian Monsef, Andrea Cozza Departement de Recherche en Electromagnetisme LSS, UMR8506, Univ. Paris-Sud, SUPELEC, CNRS 91192 Gif-sur-Yvette, France mouad.djedidi@lss.supelec.fr Abstract—Current antenna measurement techniques are based on the underlying idea that echoes generated by nearby structures should be avoided. Indeed, the absence of echoes allows a precise measurement of the line-of-sight radiation of the antenna under test (AUT), via mechanical rotation to span some or all spatial directions until the radiation pattern is formed. In this paper, this idea is challenged by introducing an alternative test approach that generates controlled echoes and use them as a useful source of information. Preliminary results are presented and it is shown how frequency diversity can be fruitfully used to retrieve the free space radiation pattern. A special care is given to the conditioning of the mathematical problem. Accordingly, it is shown how the different parameters involved in the set-up influence the feasibility of the technique. The proposed technique is expected to lead to a faster characterization of the AUT, as the need for mechanical rotation is cut down. I. I NTRODUCTION Antenna radiation pattern (ARP) measurements can be classified into two categories, depending on whether near- field or far-field techniques are performed [1]. Although these techniques are not exposed to the same non-idealities they both share a common paradigm: avoiding echoes. Indeed, spurious error signals from absorbers and other structures in the mea- surement set-up can significantly decrease the measurement accuracy in standard antenna measurement configurations. This explains that in practice, when unintentional echoes affect measurement, techniques to limit their effects are applied [2]. To reduce the risk of dealing with echoes, ARP measure- ment take place in anechoic indoor environments. This kind of environments are effective and well adapted for characterizing antennas with high resolution, but at the expense of facilities needing constraining test volumes and absorber foams whose cost and maintenance have to be taken into account. Moreover, although some facilities are based on multi-probe systems [3], mechanical displacement is a serious drawback in terms of characterization speed. In the present paper we will present an alternative technique in a non-anechoic environment. The technique is based on an environment where echoes are controlled in order to speed up ARP measurement. It goes against the common paradigm banning and regarding echoes as spurious signals. In section 2 we will firstly present the concept behind this off-the-beaten- track technique. In section 3 we model the concept, and in section 4 we study conditions to insure its robustness. II. PRESENTATION OF THE CONCEPT An ARP is a far field concept. It describes the spatial distribution of the radiated energy in the far field where the pattern does not depend on the distance separating the measurement point from the antenna. The far field criterion is met for distances greater than the Fraunhofer distance, given by [4]: D F raunhof er = 2D 2 λ , (1) where D is the maximum linear dimension of the radiating antenna, and λ is the wavelength. Under this condition, the antenna under test (AUT) is considered as a point source, and the electric field it radiates is given by [5]: ~ E(r)= G(r, ω) ~ F (θ, φ), (2) where ~ F (θ,φ) stands for the radiation pattern, with θ and φ being the elevation and azimuth angles respectively, and G(r, ω) is the free space Green’s function, which in its 3D general form is given by [6]: G(r, ω)= e -jkr 4πr . (3) The Green’s function describes the magnitude r -1 depen- dence, r being the distance separating the measurement point from the antenna, as well as the field phase which in addition to r, is a function of the working frequency ω, where ω = k×c, k being the wavenumber, and c the speed of light. In the 2D case, the field dies off as r -1/2 instead of r -1 . In order to perform ARP measurements, standard techniques try to emulate far field conditions, essentially characterized by the absence of echoes. The common principle is to measure the AUT line of sight radiation in some or all spatial directions via mechanical rotation of the antenna or the probe system [7]. This idea is challenged here by proposing an ARP measurement concept that uses controlled echoes in order to span a number of angles in one acquisition without the need for mechanical rotation. The proposed set up is as follows. The AUT and the probe are placed between two parallel metal plates on a common 2D plane, namely the x-y plane, as shown in Fig. 1.