Page 228 - Fundamentals of Radar Signal Processing

the modulation may be intrapulse (applied to individual pulses), interpulse

(applied across the pulses of a multipulse waveform), or both. Phase
modulation can be biphase (two possible states) or polyphase (more than two
phase states); frequency modulation can be linear or nonlinear. Intrapulse
amplitude modulation may be used, but usually is not.
The choice of waveform directly determines or is a major contributor to
several fundamental radar system performance metrics. These include the

signal-to-noise ratio (SNR) χ, the range resolution ΔR, the Doppler (velocity)
resolution ΔF (Δv), ambiguities in range and Doppler, range and Doppler
D
sidelobes, and range-Doppler coupling. These metrics are determined by such
waveform attributes as the pulse duration, bandwidth, amplitude, and phase or
frequency modulation. While all of these metrics are discussed, the primary
emphasis is on SNR, range resolution, and Doppler resolution because these are
the most fundamental drivers in choosing the waveform. As an example, the

simple pulse of Fig. 4.1a has a duration of τ seconds and an amplitude of A
volts. The SNR will prove to be proportional to the waveform energy, which is
the product A τ of its power and duration. The range resolution of cτ/2 is
2
proportional to the pulse duration. It will be shown shortly that both the
waveform bandwidth and the Doppler resolution of the simple pulse are

inversely proportional to the pulse length.
Two classic references on radar waveforms are Cook and Bernfeld (1993)
and Rihaczek (1996). Most radar system books cover the fundamentals of radar
waveforms (e.g., Nathanson, 1991; Peebles, 1998). A complete modern
reference on radar waveforms is Levanon and Mozeson (2004), while good
brief surveys of basic and advanced waveforms are in Keel (2010) and Keel
and Baden (2012), respectively. In addition to covering the mainstream

waveforms such as pulse bursts and LFM, this text covers the many
developments in phase codes in recent decades. Another new text that focuses
more on advanced waveforms and emerging applications is Gini et al. (2012).

4.2 The Waveform Matched Filter

4.2.1 The Matched Filter
So far, it has been implicitly assumed that the overall frequency response of the
radar receiver is a bandpass characteristic with a bandwidth equal to or greater
than that of the transmitted signal. Equivalently, once the carrier is demodulated

out, the effective frequency response is a lowpass filter with a bandwidth equal
to that of the complex envelope. It will be shown in Chap. 6 that detection
performance improves with increasing SNR. Thus, it is reasonable to ask what
overall receiver frequency response H(Ω) will maximize the SNR.
To answer this question, note that the spectrum of the receiver output, y(t),