## 1. Introduction

[2] The actual performance of any antenna is affected by the operating environment, which may cause pattern distortion, loss of signal due to blockage, multipath interference and interantenna coupling. Furthermore, on-site power density maps are needed to predict radiation hazards. As a consequence, in order to effectively design and install an array, an accurate and efficient modeling of its interaction with the surrounding environment is important. The relevant analysis requires an effective description of the radiated field in both the near and the far zones. However, the application of a full wave method frequently results in an overwhelming computational burden because of the very large electrical size of the antenna under investigation and because of the surrounding complex platform. This suggests to resort to high-frequency methods. In the present case, it is assumed that the current on the antenna is not significantly perturbed by the presence of the platform; then, the environment effects are introduced by means of asymptotic techniques, such as the uniform theory of diffraction (UTD) or the physical optics (PO). In this framework, the radiation from array antennas may be described in terms of rays emanating from individual array elements, or from small subarrays with well defined phase centers. However, this approach becomes highly inefficient for very large arrays because of the huge number of rays. A more convenient strategy consists in collectively representing the array radiation as the superimposition of continuous truncated Floquet wave (FW) distributions, defined over the entire aperture of the array [*Ishimaru et al.*, 1985; *Carin and Felsen*, 1992]. This approach has been proven to be very effective for the analysis of rectangular arrays [*Capolino et al.*, 2000a, 2000b, 2000c; *Maci et al.*, 2001]. However, for more irregularly contoured arrays, the number of ray contributions increases and an intrinsic ambiguity occurs in the definition of diffracting edges and vertices. In order to overcome this limitation, an alternative approach has been proposed by *Martini et al.* [2003]. It basically consists of reconstructing the field radiated by the planar array as the superimposition of the asymptotically dominant contributions from the constitutive parallel line arrays. These contributions are conical FWs truncated at their relevant shadow boundaries, spherical diffracted waves arising from the array tips and transition contributions across the FW shadow boundaries [*Capolino and Felsen*, 2002]. *Martini et al.* [2003] showed that this approach yields very accurate results when uniform amplitude line arrays are considered; however, the extension to the case of tapered arrays is not straightforward, since the strong localization of the dominant contributions leads to inaccuracies when the observation points approaches the far field region. A slowly varying tapering can be accommodated by weighting the conical wave and the two diffracted spherical waves by the value of the tapering function at the stationary phase point and at the endpoints, respectively. The accuracy can be improved by introducing in the asymptotic representation higher-order terms, related to the derivatives of the tapering function and to slope diffraction effects, as shown by *Mariottini et al.* [2005] for the strip array case. However, although the introduction of few terms is satisfactory for describing the field radiated in the vicinity of the array, this asymptotic approximation gradually fails as the observation point moves from the Fraunhofer to the Fresnel zone. There, the asymptotic ray description needs to be replaced by a more conventional FFT numerical representation of the radiated field.

[3] Different procedures, based on a Fourier transform rigorous decomposition of the tapering function into a set of uniform amplitude, phased excitations, have been proposed for both planar [*Nepa et al.*, 1999] and line [*Cicchetti et al.*, 2003] arrays. Although these representations exhibit a high flexibility, the number of uniform excitations required to accurately represent the radiated field depends on the array size and tapering. This partially nullifies the benefits deriving from the use of the Floquet wave concept.

[4] An alternative solution to provide a uniform description from the near to the far region, limiting at the same time the number of ray contributions, is presented in this paper. While previous approaches rely on a mathematical transform to precisely represent the current distribution in terms of exponential functions, the expansion employed in this work is directly defined to provide an accurate estimate of the radiation integral. To this end, the asymptotically dominant characteristics of the integrand function are conveniently reconstructed by approximating the tapering along the line array through a proper superposition of a few equiamplitude, linearly phased excitations, whose number is small (seven at most) and completely independent of the array size and tapering. In particular, these excitations are linearly combined to match the actual tapering function and its derivative at the endpoints and at the stationary phase point of the spatial integral along the line. Also, an additional constraint is imposed on the approximated tapering function in order to match the area subtended to the line array. This adaptive asymptotic procedure is able to uniformly cover the region ranging from the near to the far field zone. Once the field from each tapered array has been obtained, the planar array radiation is calculated by superimposing the line arrays dominant contributions. This leads to a limited number of conical and spherical rays emanating from points located on the array surface and on the actual contour of the array, respectively.

[5] It is worth pointing out that the present approach can also be employed to describe the scattering from a periodic arrangement of elements illuminated by a plane wave. Furthermore, it can be applied to speed up the computation of the field radiated by a current distribution calculated with a numerical method. Finally, by exploiting the concepts presented by *Civi et al.* [2000], *Neto et al.* [2000a, 2000b], and *Cucini et al.* [2003], the proposed field representation can be used as a basic constituent for an efficient full wave analysis of large phased-array antennas.

[6] The problem is formulated in section 2. The high-frequency representation of the radiation from a linear tapered phased array is derived in section 3. In section 4, it is shown how these results can be employed to build up the radiation from the planar array. Finally, some representative numerical results are presented in section 5, and conclusions are drawn in section 5.