International Journal of Antennas and Propagation

Volume 2018, Article ID 2521953, 6 pages

https://doi.org/10.1155/2018/2521953

## Main Lobe Control of a Beam Tilting Antenna Array Laid on a Deformable Surface

^{1}Department of Information Engineering, University of Padova, Padova, Italy^{2}Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 4ET, UK

Correspondence should be addressed to Giulia Mansutti; moc.liamg@ittusnam.ailuig

Received 30 October 2017; Revised 10 January 2018; Accepted 11 February 2018; Published 19 April 2018

Academic Editor: Xianming Qing

Copyright © 2018 Giulia Mansutti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The projection method (PM) is a simple and low-cost pattern recovery technique that already proved its effectiveness in retrieving the radiation properties of different types of arrays that change shape in time. However, when dealing with deformable beam-tilting arrays, this method requires to compute new compensating phase shifts *every time* that the main lobe is steered, since these shifts depend on *both* the deformation geometry *and* the steering angle. This tight requirement causes additional signal processing and complicates the prediction of the array behavior, especially if the deformation geometry is not a priori known: this can be an issue since the PM is mainly used for *simple and low-cost systems*. In this letter, we propose a simplification of this technique for beam-tilting arrays that requires only basic signal processing. In fact the phase shifts that we use are the sum of two components: one can be directly extracted from strain sensor data that measure surface deformation and the other one can be precomputed according to basic antenna theory. The effectiveness of our approach has been tested on two antennas: a 4 × 4 array (trough full-wave simulations and measurements) and on an 8 × 8 array (trough full-wave simulations) placed on a doubly wedge-shaped surface with a beam tilt up to 40 degrees.

#### 1. Introduction

Recently many wireless communication systems have raised the need of developing antenna arrays capable of adapting to surfaces that change shape in time: this can be the case of simple wearable devices that monitor health and fitness parameters and that are placed on body parts that move and bend (e.g., wrists, ankles, and knees). The main issue related to the design of this type of antennas consists in the control of the radiation pattern that results significantly altered as a consequence of the array deformation. In order to overcome this problem, many different pattern recovery approaches can be adopted, from very accurate and expensive ones to cheaper and simpler ones. We will focus on this second class of techniques that is particularly appealing for simple and cheap wearable devices whose main requirement is to keep the product cost as low as possible.

Among these pattern recovery techniques, a popular one is the projection method (PM) that exploits only strain sensors and phase shifters to retrieve the main radiation properties of deformable arrays [1], thus avoiding the use of extensive signal processing, narrow-band correction algorithms, and potentially complex sensor networks that are instead required by more accurate and expensive solutions (e.g., mechanical [2] and electrical [3, 4] compensation). The projection method effectiveness was thoroughly studied for many types of antennas, as, for example, 1 × 4 and 1 × 6 linear arrays placed on surfaces that change shape in time [5–7] and planar arrays subject to cylindrical [8], spherical [9], and asymmetrical [10] surface deformations. All the aforementioned works adopt the PM in order to recover the pattern of *broadside* arrays, but a common requirement when dealing with phased arrays is to dynamically steer the main lobe towards different desired directions. Some works dealt also with this issue: for example, in [11], the effectiveness of the PM is evaluated for a beam-tilting linear 1 × 5 array placed on a wedge-shaped deformable surface.

The main issue of the PM when applied to beam-tilting arrays is related to the fact that it requires the correcting phase shifts to be a function of *both* the surface deformation *and* the main lobe direction. This is because the phase shifts introduced in the elements have two purposes in this case: *compensating* the array deformation and *steering* the beam towards a desired direction. Therefore, it can be seen how the PM is formulated in order to *tilt* the beam of an array taking into account (i.e., compensating) the array deformation; it is not used to retrieve the pattern of a deformed array whose main lobe has *already* been tilted towards a specific direction. This fact complicates the overall system since the phase compensation in this case cannot be simply extracted by the strain sensor data that measure the geometrical deformation (unless this is a priori known): an additional signal processing step is required in order to *project* the array elements onto a new reference plane *every time* that the beam is tilted towards a different direction. In [11], this was not an issue since the deformation geometry was quite simple and a priori known, and therefore, also the analytical relation that linked the phase shifts to the geometrical deformation and to the tilting angles was a priori given, but as soon as the deformation becomes slightly more complex (as the one we present here) and/or a priori *unknown*, the computation of the correcting phase shifts becomes cumbersome. This is because the shifts cannot be directly computed from the strain sensor data anymore, because a new *analytical* relation between surface deformation and the direction of maximum and compensating phase shifts must be formulated for *each* main lobe direction and for *each* possible geometrical deformation.

Since we are assuming that this type of arrays is used for simple and cheap devices, we are interested in keeping the overall system complexity and the cost as low as possible. Therefore, we decided to express the correcting phase shifts as the sum of two independent terms: one related to the geometrical deformation and one related to the main lobe direction. Doing so, it is possible to simplify the system reducing the amount of signal processing required: in fact, the first term can be directly extracted from strain sensor data that measure surface deformation, while the second component can be easily precomputed through basic antenna theory.

As we will show in the next sections, this approach allowed us to recover the main radiation properties of a doubly wedge-deformed planar array when its beam is tilted up to 40°.

#### 2. Theoretical Framework

In order to explain and test our approach, we consider a 4 × 4 planar array, whose elements are patch microstrip antennas resonating at 2*.*48 GHz. We will refer to array rows and columns as those sets of elements sharing, respectively, the same *y*- or *x*-coordinate (refer to Figure 1 for axes orientation). The array is placed on a surface which is subject to a doubly wedge-like geometrical deformation as depicted in Figure 1: the first and last rows of the array are tilted of *θ _{w}* degrees. As a consequence of the surface deformation, the array radiation pattern is distorted (as it will be shown in the followings), that is, the main lobe decreases in gain, and shifts in direction. We will focus only on this particular geometrical deformation as we assume that the array beam is tilted faster than the speed at which the deformation changes shape: this scenario makes it easier to test the validity of our approach.