Page 59 - Fundamentals of Radar Signal Processing

valued sinusoid Acos[ωn] and w[n] is real-valued zero mean white Gaussian

noise of variance , the peak SIR would be the same but the average SIR
would be because the average power of a real cosine or sine function of
2
amplitude A is A /2.
A variation is the “energy SIR,” defined as the ratio of the total energy E =
s
2
Σ |s[n]| in the signal s[n] divided by the average noise power:

(1.24)

The proportionality between E and A depends on the signal shape. For a
s
rectangular pulse or a complex exponential of amplitude A and duration N
samples, it is just E = N · A . It can be seen in Chap. 6 that when matched filters
2
s
are used, the peak SIR at the filter output is the energy SIR of the original signal.
SIR affects detection, tracking, and imaging performance in different ways.
In general, detection performance improves with SIR in the sense that P D
increases for a given P as SIR increases. For instance, it will be seen in Chap.
FA
6 that for one particular model of the target behavior and detection algorithm, P D
is related to P according to
FA

(1.25)

which shows that P → 1 as χ → ∞ for fixed P . As another example, the limit
D
FA
on precision (standard deviation of repeated measurements) due to additive
noise of typical estimators of range, angle, frequency, or phase tends to decrease

as ; this behavior will be demonstrated in Chap. 9. In radar imaging (Chap.
8), SIR directly affects the contrast or dynamic range (ratio of reflectivity of
brightest to dimmest visible features) of the image. These considerations make it
essential to maximize the SIR of radar data, and many radar signal processing
operations discussed in this text have as their primary goal increasing the SIR.

The ways in which this is done will be discussed along with each technique.

1.4.2 Resolution
The closely related concepts of resolution and a resolution cell will arise
frequently. Two equal-strength scatterers are considered to be resolved if they
produce two separately identifiable signals at the system output, as opposed to
6
combining into a single undifferentiated output. The idea of resolution is
applied in range, cross-range, Doppler shift or velocity, and angle of arrival.
Two scatterers can simultaneously be resolved in one dimension, say range, and
be unresolved in another, perhaps velocity.
Figure 1.14 illustrates the concept of resolution, in this case in frequency.