## 1. Introduction

[2] In Digital Filter Design, different windowing techniques are used to reduce the oscillatory behavior in the causal FIR filter obtained by truncating the impulse response coefficients of the corresponding ideal filter. This behavior is referred to as the Gibbs phenomenon [*Mitra*, 1998]. The most commonly used windows are the Hanning, Hamming, Blackman, Chebyshev, and Kaiser windows. Among these, only Chebyshev and Kaiser windows provide control over the filter's ripple, since the sidelobe levels of their Fourier transform are adjustable. The coefficients of Chebyshev windows are related to Chebyshev polynomials, and those of Kaiser windows to modified Bessel functions of order zero.

[3] The linear antenna array with excitation equal to the coefficients of a Chebyshev window is the famous Chebyshev array. Chebyshev arrays have the important property of providing sidelobes of equal magnitude in their radiation patterns. They are optimum in the sense that for a specified sidelobe level they have the smallest beam width, and for a specified beam width they produce the lowest sidelobe level. However, they suffer from directivity saturation when the number of elements becomes large [*Mailloux*, 1994]. These properties are also shared by the Chebyshev planar arrays, which are described in *Tseng and Cheng* [1968].

[4] If the Kaiser window coefficients are taken as the excitations of a linear array's elements, the resulting array has a much higher directivity than the corresponding Chebyshev array at the cost of a slightly broader beam width, and a radiation pattern that does not have a constant sidelobe level, but a controllable maximal sidelobe level. In our paper, we exploit this observation and extend it to the case of planar arrays. The proposed arrays, the Bessel planar arrays, have radiation patterns close in shape to those of uniform planar arrays, but the maximal sidelobe levels are adjustable. In fact, uniform planar arrays are a special case of the proposed arrays, as will be clarified in later sections. Moreover, the Bessel planar arrays provide directivities much higher than those of Chebyshev planar arrays with the same numbers of elements, same size, and same sidelobe level, when the number of elements is high. The beam width is slightly broader than that of the optimal Chebyshev array.

[5] In Section 2, planar arrays are reviewed briefly, the Bessel planar arrays are formulated, equations of their current excitations are given, and methods for controlling the sidelobe level and estimating the half-power beam width of the proposed arrays are described. Examples are given in Section 3 to illustrate the features of the Bessel planar arrays and to compare them to the Chebyshev planar arrays. They will also be compared to some numerically synthesized high-performance planar arrays. Summarizing and concluding remarks are given in Section 4.