Page 58 - Fundamentals of Radar Signal Processing

1.4 Common Threads in Radar Signal Processing
A radar system’s success or failure in detecting, tracking, and imaging objects

or features of interest in the environment is affected by various characteristics of
those objects, the environment, and the radar itself, and how they are reflected
in the received signals available for processing. Two of the most basic and
important signal quality metrics are the signal-to-interference ratio and the
resolution. Because of their importance, improving SIR and resolution is the
major goal of most of the basic radar signal processing discussed in this text.
While subsequent chapters discuss a wide variety of signal processing

techniques, there are a few basic ideas that underlie most of them. These include
coherent and noncoherent integration, target phase history modeling,
bandwidth expansion, and maximum likelihood estimation. The remainder of
this section gives a heuristic definition of SIR and resolution, and then
illustrates the simplest forms of integration, phase history modeling, and
bandwidth expansion and how they affect SIR and resolution. Maximum

likelihood estimation is deferred to Chap. 9 and App. A.

1.4.1 Signal-to-Interference Ratio and Integration
Consider a discrete-time signal x[n] consisting of the sum of a “desired signal”
s[n] and an interfering signal w[n]:

(1.22)

The discussion is identical for continuous time signals. The SIR χ of this
signal is the ratio of the power of the desired signal to that of the interference. If
s[n] is deterministic, the signal power is usually taken as the peak signal value,
and may therefore occur at a specific time t . In some deterministic cases, the
0
average signal power may be used instead. The interference is almost invariably
2
modeled as a random process, so that its power is the mean-square E{|w[n]| }.
If the interference is zero mean, as is very often the case, then the power also
equals the variance of the interference, . If the desired signal is also modeled
as a random process, then its power is also taken to be its mean-square or
variance.
As an example, let s[n] be a complex sinusoid Aexp[jωn] and let w[n] be
complex zero mean white Gaussian noise of variance . The SIR of their sum

x[n] is

(1.23)

In this case, the peak and average signal power are the same. If s[n] is a real-