Introduction to Radar Basics - MATLAB Simulations for Radar Systems Design - page 21

adopted. A two-dimensional (2-D) fan beam search pattern is shown in
Fig.1.15a. In this case, the beamwidth is wide enough in elevation to cover the
desired search volume along that coordinate; however, it has to be steered in
azimuth. Figure 1.15b shows a stacked beam search pattern; here the beam has
to be steered in azimuth and elevation. This latter kind of search pattern is nor-
mally employed by phased array radars.

Search volumes are normally specified by a search solid angle in steradi-
ans. Define the radar search volume extent for both azimuth and elevation as
and

Ω

. Consequently, the search volume is computed as

Θ A Θ E

) 2

Ω A Θ E = ( ) ⁄ ( 57.296 steradians

(1.61)

where both and are given in degrees. The radar antenna beam-
width can be expressed in terms of its azimuth and elevation beamwidths

Θ A Θ E 3 dB

θ a

and , respectively. It follows that the antenna solid angle coverage is θ e θ a θ e

and, thus, the number of antenna beam positions required to cover a solid n B

angle is Ω

Ω

n B = --------------------------------------------

(1.62)

) 2 ( θ a θ e ) ⁄ ( 57.296

In order to develop the search radar equation, start with Eq. (1.56) which is
repeated here, for convenience, as Eq. (1.63)

P t G 2 λ 2 σ
4( 3 kT e BFLR 4

SNR = -----------------------------------------

(1.63)

Using the relations and , where is the PRI and is τ = 1 ⁄ B P t = P av T τ ⁄ T τ

the pulsewidth, yields

P av G 2 λ 2 στ
4( 3 kT e FLR 4

T
---

-------------------------------------

SNR =

(1.64)

(a)

(b)

Figure 1.15. (a) 2-D fan search pattern; (b) stacked search pattern.