The Radar Ambiguity Function - MATLAB Simulations for Radar Systems Design - page 204

As one would expect, high PRF pulse trains (i.e., small ) lead to extreme
uncertainty in range, while low PRF pulse trains have extreme ambiguity in
Doppler. Medium PRF pulse trains have moderate ambiguity in both range and
Doppler, which can be overcome by using multiple PRFs. It is possible to
avoid ambiguities caused by pulse trains and still have reasonable independent
control on both range and Doppler accuracies by using a single modulated
pulse with a time-bandwidth product that is much larger than unity. Fig. 4.12
shows the ambiguity contour plot associated with an LFM waveform. In this
case, is the pulsewidth and is the pulse bandwidth. The exact plots can be
obtained using the function Ðlfm_ambg.mÑ .

T

τ′ B

frequency

time

1 τ′ ⁄

⁄
Figure 4.12. Ambiguity contour plot associated with an up-chirp LFM
waveform. For an exact plot see Fig. 4.5b.

1 B

4.4. Digital Coded Waveforms

In this section we will briefly discuss the digital coded waveform. We will
determine the waveform range and Doppler characteristics on the basis of its
autocorrelation function, since in the absence of noise, the output of the
matched filter is proportional to the code autocorrelation.

4.4.1. Frequency Coding (Costas Codes)

Construction of Costas codes can be understood from the construction pro-
cess of Stepped Frequency Waveforms (SFW) described in Chapter 3 . In SFW,
a relatively long pulse of length τ′ is divided into N subpulses, each of width

τ 1 ( τ′ = N τ 1 ). Each group of N

∆ f

subpulses is called a burst. Within each burst

the frequency is increased by from one subpulse to the next. The overall

burst bandwidth is N ∆ f . More precisely,