Introduction to Radar Basics - MATLAB Simulations for Radar Systems Design - page 22

Define the time it takes the radar to scan a volume defined by the solid angle
as the scan time . The time on target can then be expressed in terms of Ω T sc

as T sc

T sc
Ω

T sc
n B

------- θ a θ e

T i = ------- =

(1.65)

Assume that during a single scan only one pulse per beam per PRI illuminates
the target. It follows that

T i = T

and, thus, Eq. (1.64) can be written as

P av G 2 λ 2 σ
4( 3 kT e FLR 4

------------------------------------- T sc
Ω

------- θ a θ e

SNR =

(1.66)

Substituting Eqs. (1.40) and (1.42) into Eq. (1.66) and collecting terms yield
the search radar equation (based on a single pulse per beam per PRI) as

----------------------------- T sc
Ω

P av A e σ
4π kT e FLR 4

-------

SNR = (1.67)

The quantity in Eq. (1.67) is known as the power aperture product. In
practice, the power aperture product is widely used to categorize the radarÓs
ability to fulfill its search mission. Normally, a power aperture product is com-
puted to meet a predetermined SNR and radar cross section for a given search
volume defined by

P av A

. Ω

As a special case, assume a radar using a circular aperture (antenna) with
diameter . The 3-dB antenna beamwidth is D θ 3 dB

λ
----

θ 3 dB ≈

(1.68)

and when aperture tapering is used, . Substituting Eq. (1.68)

θ 3 dB ≈ 1.25λ D ⁄

into Eq. (1.62) yields

D 2
λ 2

------ Ω

n B = (1.69)

For this case, the scan time is related to the time-on-target by T sc

T sc λ 2
D 2 Ω

T sc
n B

T i = ------- = -------------- (1.70)

Substitute Eq. (1.70) into Eq. (1.64) to get

------------------------------------- T sc λ 2
D 2 Ω

P av G 2 λ 2 σ
4( 3 R 4 kT e FL

SNR = -------------- (1.71)