Page 265 - Fundamentals of Radar Signal Processing

estimation performance requires a longer pulse. The two metrics are coupled in

this unfortunate way because there is effectively only one free parameter τ in the
design of the simple pulse waveform.
Pulse compression waveforms decouple energy and resolution. Recall that
a simple pulse has a Rayleigh bandwidth β = 1/τ Hz and a Rayleigh resolution in
time at the matched filter output of τ seconds. Thus, the time-bandwidth product
(BT product) of the simple pulse is τ(1/τ) = 1. A pulse compression waveform,

in contrast, has a bandwidth β that is much greater than 1/τ. Equivalently, it has a
duration τ much greater than that of a simple pulse with the same bandwidth, τ
1/β. Either condition is equivalent to stating that a pulse compression waveform
has a BT product βτ much greater than one.
Pulse compression waveforms are obtained by adding frequency or phase
modulation to a simple pulse. There are a vast number of pulse compression
waveforms in the literature. In this text, only the most commonly used types will

be described. These include linear frequency modulation, biphase codes, and
certain polyphase codes. Nonlinear FM will also be briefly introduced. Many
other waveforms are described in Levanon and Mozeson (2004) and Keel and
Baden (2012).

4.6.1 Linear Frequency Modulation
A linear frequency modulated waveform is defined by

(4.83)

The complex equivalent is

(4.84)

The instantaneous frequency in hertz of this waveform is the time derivative of
the phase function

(4.85)

This function is shown in Fig. 4.22, assuming β > 0. F(t) sweeps linearly across
i
a total bandwidth of β Hz during the τ-second pulse duration. The waveform x(t)
[Eq. (4.83), or the real part of Eq. (4.84)] is shown in Fig. 4.23 for βτ = 50. The
LFM waveform is often called a chirp waveform in analogy to the sound of an
acoustic sinusoid with a linearly changing frequency. When β is positive the

pulse is an upchirp; if β is negative it is a downchirp. The BT product of the