Page 276 - Fundamentals of Radar Signal Processing

higher energy, given the same transmitted power) by the factor βτ.

4.6.4 Range-Doppler Coupling
The skew in the ambiguity function for the LFM pulse gives rise to an interesting
phenomenon. Consider the AF of Eq. (4.98). The peak of this sinc-like function
will occur when

(4.105)

That is, when there is a Doppler mismatch the peak of the matched filter output
will not occur at t = 0 as desired. Instead, it will be shifted by an amount

proportional to the Doppler shift. Because the target range will be estimated
based on the time of occurrence of this peak, a Doppler mismatch will induce an
error in measuring range. The corresponding range error will be

(4.106)

The amplitude of the peak will also be reduced by the factor (1 –|t|/τ) = (1 –
F /β). Figure 4.29 illustrates the skewed ridge of the LFM ambiguity function
D
and the relationship between Doppler shift and range measurement error.

FIGURE 4.29 Illustration of the effect of range-Doppler coupling on apparent
target range.

While an incorrect range measurement is certainly undesirable, range-
Doppler coupling is a useful phenomenon in some systems. A simple pulse with

duration τ will have a Doppler Rayleigh resolution of 1/τ Hz; targets with
Doppler mismatches approaching this value or larger will produce a greatly