Page 23 - Radar Technology Encyclopedia

ambiguity functions for typical waveforms cross-ambiguity function 13

f
f

20 dB
1
12 dB
6 dB 1/t r 3 nt r
3 dB t
t
1.15
2 pB

2 t

Figure A26 Ambiguity function of an LFM Gaussian pulse. Figure A30 Ambiguity function of a train of rectangular

f
3 dB The bed of spikes [nails] ambiguity function applies to peri-
6 dB
12 dB odic pulse trains. The internal structure of its components
20 dB depends on the waveform of individual pulses in the train.
The response regions for this waveform appear equally
t spaced in the delay-doppler plane (Fig. A31). SAL
Ref.: Skolnik (1980), p. 418.

c
| (t , f )| 2
d d

Figure A27 Ambiguity function of an LFM rectangular pulse. f d
2
c (t , f )
d
d

t t
d
t t
n
Figure A28 Ambiguity function of a PSK pulse. Figure A31 Bed of nails ambiguity function (after Skolnik,
1980, Fig. 11.13, p. 419).

The cross-ambiguity function is a description of radar
f
receiver response when the receiver filter is mismatched to
(2- 3) t
the transmit waveform:
1 1
3 t ¥ 2
3nt r 2
(
(
(
c t f , ) = ò ut () v * t + t ) exp j2pf t ) dt
d
d
d
d
t
– ¥
where the variable u refers to the waveform properties and v
1/t
r
to the mismatched filter. SAL
(2- 3) tn r t r Ref.: Rihaczek (1969), pp. 153–157; Nathanson (1990) p. 286.
2
Figure A29 Ambiguity function of a train of Gaussian pulses
(after Sloka, 1970).