Pulse Compression - MATLAB Simulations for Radar Systems Design - page 233

noise PSD

B B

N 0 ⁄ 2

frequency

0

Figure 5.1. Input noise power.

where the factor of two is used to account for both negative and positive fre-
quency bands, as illustrated in Fig. 5.1. The average input signal power over a
pulse duration

τ' is

E
τ'

S i = ---

(5.2)

E is the signal energy. Consequently, the matched filter input SNR is given by

S i
N i

E
N 0 B τ'

( SNR ) i == ----- --------------

(5.3)

The output peak instantaneous SNR to the input SNR ratio is

SNR t ()
SNR

-------------------- = 2 B τ'

(5.4)

( ) i

The quantity is referred to as the Ðtime-bandwidth productÑ for a given
waveform or its corresponding matched filter. The factor by which the
output SNR is increased over that at the input is called the matched filter gain,
or simply the compression gain.

B τ'

B τ'

In general, the time-bandwidth product of an unmodulated pulse approaches
unity. The time-bandwidth product of a pulse can be made much greater than
unity by using frequency or phase modulation. If the radar receiver transfer
function is perfectly matched to that of the input waveform, then the compres-
sion gain is equal to . Clearly, the compression gain becomes smaller than
as the spectrum of the matched filter deviates from that of the input signal.

B τ'

B τ'

5.2. Radar Equation with Pulse Compression

The radar equation for a pulsed radar can be written as