Pulse Compression - MATLAB Simulations for Radar Systems Design - page 234

P t τ′ G 2 λ 2 σ
4( 3 R 4 kT e FL

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

(5.5)

where P t is peak power, τ′ is pulsewidth, G is antenna gain, σ is target RCS,

R is range, k is BoltzmanÓs constant, T e is effective noise temperature, F is

noise figure, and L is total radar losses.

Pulse compression radars transmit relatively long pulses (with modulation)
and process the radar echo into very short pulses (compressed). One can view
the transmitted pulse as being composed of a series of very short subpulses
(duty is 100%), where the width of each subpulse is equal to the desired com-
pressed pulsewidth. Denote the compressed pulsewidth as

τ c . Thus, for an

individual subpulse, Eq. (5.5) can be written as

P t τ c G 2 λ 2 σ
4( 3 R 4 kT e FL

( SNR ) τ c = ------------------------------------

(5.6)

The SNR for the uncompressed pulse is then derived from Eq. (5.6) as

=( ) G 2 λ 2 σ
4( 3 R 4 kT e FL

P t τ′ n τ c

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

(5.7)

where is the number of subpulses. Equation (5.7) is denoted as the radar
equation with pulse compression.

n

Observation of Eqs. (5.5) and (5.7) indicates the following (note that both
equations have the same form): For a given set of radar parameters, and as long
as the transmitted pulse remains unchanged, the SNR is also unchanged
regardless of the signal bandwidth. More precisely, when pulse compression is
used, the detection range is maintained while the range resolution is drastically
improved by keeping the pulsewidth unchanged and by increasing the band-
width. Remember that range resolution is proportional to the inverse of the sig-
nal bandwidth,

∆ Rc 2 B = ⁄ (5.8)

5.3. LFM Pulse Compression
Linear FM pulse compression is accomplished by adding frequency modula-
tion to a long pulse at transmission, and by using a matched filter receiver in
order to compress the received signal. As a result, the matched filter output is
compressed by a factor , where is the pulsewidth and is the
bandwidth. Thus, by using long pulses and wideband LFM modulation large
compression ratios can be achieved.

ξ = B τ' τ' B