Page 207 - Fundamentals of Radar Signal Processing

The 3-dB beam-width of an aperture antenna is of the form (Balanis, 2005)

(3.31)

For the uniformly illuminated case, k = 0.89. Combining Eqs. (3.30) and (3.31)
gives

(3.32)

For k = 0.89, this gives a Nyquist sampling rate of 0.56 times the 3-dB
beamwidth, or 1.8 samples per 3-dB beamwidth. In practice, many systems
sample in angle at approximately one sample per 3-dB beamwidth. The search
space is then undersampled in angle, at least according to the Nyquist criterion.

While derived for the uniformly illuminated aperture, these results apply to
all aperture antennas. For a finite aperture of size D, different antenna patterns
(for instance, with lower sidelobes at the expense of a wider mainlobe) are
obtained by changing the aperture illumination function, typically by tapering it
in a manner similar to windowing operations in signal processing. The Fourier

transform of these antenna power patterns will still be the autocorrelation of the
corresponding illumination function. Since the illumination function still has
finite support, its autocorrelation will still be limited to a width of 2α in s, as
shown in Fig. 3.17; only the detailed shape of the function will change. Thus,
Eq. (3.32) applies for any finite aperture antenna. The difference is that the
factor k will be different for different illumination functions. Lower sidelobe
antennas will have values of k in the range of approximately 1.4 to 2.0, giving
corresponding Nyquist sampling rates on the order of 2.8 to four samples per 3-

dB beamwidth for low sidelobe antennas.
For a rotating radar, the angular sampling rate of Eq. (3.31) implies a
lower bound on PRF. Suppose the rate of rotation is Ω radians per second. In
0
order that successive pulses be transmitted in directions differing by no more
than the T of (3.31), the PRI and PRF must satisfy
θ

(3.33)

Equations (3.33) and (3.9) illustrate a conflict between volume coverage

and search rate in a rotating search radar. For a given antenna design, θ and k
3
are fixed. Then, increasing the sweep rate Ω will increase the volume search
0
rate, but will also require an increased PRF; but a higher PRF reduces the