Page 22 - Radar Technology Encyclopedia

12 ambiguity, doppler ambiguity functions for typical waveforms

Doppler ambiguity is absent, by definition, when a high tion of unwanted clutter.” The function was first introduced
pulse repetition frequency (PRF) waveform is used, although by Woodward. SAL
this solution leads to ambiguous range measurement (range Ref.: IEEE (1993), p. 31; Woodward (1953); Skolnik (1980), pp. 411–420;
ambiguity). SAL Nathanson (1990), pp. 283–301; Sloka (1970), pp. 45–61.
Ref.: Long (1992), p. 98. Ambiguity functions for typical waveforms. There are
Phase ambiguity is the result of the periodic nature of a sinu- three general classes of ambiguity function: the knife-edge
soidal wave, and sometimes of the inability to determine the (ridge), the bed of spikes (nails), and the thumbtack ambigu-
quadrant in which a given signal lies. Quadrant ambiguities in ity function. Ambiguity functions for several common radar
phase measuring can be resolved, for example, by using waveforms are given in Table A1, and two-dimensional dia-
coherent in-phase/quadrature detection of the received signal. grams of these ambiguity functions are given in Figs. A24
SAL through A30.
The following notations are introduced: f is the wave-
Ref.: Currie (1987), p. 499. 0
form carrier frequency; t is the transmitted pulse width; t is
e
Range ambiguity is the result of the periodic structure of a
the effective duration of the waveform (equal to t for a rect-
transmitted pulse train. If the pulse repetition interval is t , angular transmitted pulse); B is the frequency excursion for a
r
and measured time delay from transmission to the received
chirp waveform during time t; K is the compression ratio:
w
target echo pulse is t , the target range is normally taken to be 2 2
d
t
R = t c/2, where c is the velocity of light. However, the tar- ---------------------------- and t = ----------------------------
t
e
0
e
d
e
get may actually be at a range R = R + iR = (t + it )c/2, B = ò G f () df e ò A () dt
¥
¥
4
2
d
0
r
u
t
where R is the apparent range at which target is detected, and – ¥ – ¥ m
0
i is any positive integer. Target echoes received from an ear- are Woodward functions; A (t) is the amplitude modulation
m
lier pulse transmission are called multiple-time-around ech- function; and G( f ) is the energy spectrum. SAL
oes. They can be distinguished from unambiguous echoes if Ref.: Skolnik (1970), Ch. 3; Sloka (1970), pp. 40–43.
the radar operates with varying PRF or completely eliminated
if it is operated at low PRF where, by definition, the maxi- f f
mum range at which targets are expected is less than the
unambiguous range R = c/2f , where f is the pulse repetition 20 dB
u
r
r
12 dB
frequency. The upper bound on the PRF to provide unambig- 6 dB
uous range measurement is called the range-ambiguity limit. 3 dB
SAL
Ref.: Skolnik (1980), p. 53; Cantafio (1989), p. 127. t t
Range-doppler ambiguity refers to the joint range and dop-
pler ambiguity in pulsed-doppler radar due to effects of range
and doppler ambiguities. This case applies by definition to the
medium PRF mode of operation. The choice of proper PRF
Figure A24 Two-dimensional ambiguity diagram of a single
and waveform (e.g., noiselike waveforms or bursts at differ-
Gaussian pulse. (a) long pulse; (b) short pulse. The contours
ent PRFs) can be helpful when unambiguous target location
indicate levels relative to the central response.
in both range and velocity is required. SAL
Ref.: Nathanson (1990), pp. 306–310.
AMBIGUITY FUNCTION. The ambiguity function is “the f
2
squared magnitude |c(t , f )| of the function that describes
d
d
the response of a radar receiver to targets displaced in range
(time delay, t ) and doppler frequency, f , from a reference 20 dB
d
d
12 dB
2
position, where the function |c(0, 0)| is normalized to unity. 6 dB
Mathematically, 3 dB
t
¥
c t , f ) = ò ut () u * t + t ) exp j2pf t ) td
(
(
(
d d d d
– ¥
where u(t) is the transmitted envelope waveform, suitably
normalized, positive t indicates a target beyond the reference
delay, and positive f indicates an incoming target. Used to Figure A25 Ambiguity function of a rectangular pulse.
d
examine the suitability of radar waveforms for achieving
accuracy, resolution, freedom from ambiguities, and reduc-