Page 210 - Fundamentals of Radar Signal Processing

mismatches; the DC component is the direct result of the individual channel DC
offsets.
Recall that the phase function exp[jθ(t)] can represent phase modulation of
the radar waveform, the effect of the environment on the waveform (such as a
phase shift due to spatial Doppler), or both. In the case of a spatial Doppler
phase shift, θ (t) on the mth pulse will be of the form ω m for some normalized
D
Doppler radian frequency ω . The image component will then have a phase shift
D
of the form –ω m. Thus, over a series of M pulses, the mismatches will give
D
rise to a false signal at the negative of each actual Doppler frequency component
in addition to the desired signal. Furthermore, the DC component is equivalent
to a false signal at a Doppler shift of zero, i.e., clutter or a stationary target.
As another example, suppose θ (t) represents the intentional quadratic
2
phase modulation used to construct a linear FM chirp signal, θ (t) = αt (see
Chap. 4 for details). Then the image component will have a phase modulation of
2
–αt , which represents a linear frequency modulation (FM) signal with a slope
opposite to the transmitted pulse. This signal will not be properly compressed
by the matched filter, instead causing an apparent increase in the noise floor
(Sinsky and Wang, 1974).

To judge the significance of the gain and phase mismatch errors, consider
the ratio P of the power in the image component relative to that in the desired
r
component. From Eq. (3.36), this is

(3.37)

Figure 3.19 illustrates the value of P as a function of the phase and amplitude
r
imbalance.