Page 52 - Fundamentals of Radar Signal Processing

considering the antenna in its receive, rather than transmit mode. Suppose the

leftmost element is taken as a reference point, there are N elements in the array,
and the elements are isotropic (unity gain for all θ). The signal in branch n is
weighted with the complex weight a . For an incoming electric field E exp(jΩt)
0
n
at the reference element, the total output voltage E can easily be shown to be
(Stutzman and Thiele, 1998; Skolnik, 2001)

(1.13)

This is similar in form to the discrete Fourier transform (DFT) of the weight
sequence {a }. Like the aperture antenna, the antenna pattern of the linear array
n
thus involves a Fourier transform, this time of the weight sequence (which
determines the current distribution in the antenna). For the case where all the a n
= 1, the pattern is the familiar “aliased sinc” function, whose magnitude is

(1.14)

This function is very similar to that of Eq. (1.8) and Fig. 1.6. If the number of
elements N is reasonably large (nine or more) and the product Nd is considered
to be the total aperture size D, the 3-dB beamwidth is 0.89λ/D, and the first
sidelobe is 13.2 dB below the mainlobe peak; both numbers are the same as
those of the uniformly illuminated aperture antenna. Of course, by varying the

amplitudes of the weights a , it is possible to reduce the sidelobes at the
n
expense of a broader mainlobe. The phase center is at the center of the array.
Actual array elements are not isotropic radiators. A simple model often
used as a first-order approximation to a typical element pattern E (θ) is
el

(1.15)

The right-hand side of Eq. (1.13) is then called the array factor AF(θ), and the
composite radiation pattern becomes

(1.16)

Because the cosine function is slowly varying in θ, the beamwidth and first
sidelobe level are not greatly changed by including the element pattern for
signals arriving at angles near broadside (near θ = 0°). The element pattern does
reduce distant sidelobes, thereby reducing sensitivity to waves impinging on the