Page 290 - Fundamentals of Radar Signal Processing

rate at the edges with a constant pulse amplitude so as to spend less time in each

spectral interval near the band edges, or both. The technique using variable
sweep rates is referred to as nonlinear FM (NLFM).
The amplitude modulation technique implies operating the power amplifier
at less than full power over the pulse length. This requires more complicated
transmitter control but, more importantly, results in a pulse with less than the
maximum possible energy for the given pulse length. This technique is not

discussed further in this book; see Levanon and Mozeson (2004) for more
information.
Two methods that have been proposed for NLFM waveform design are the
principle of stationary phase method and empirical techniques. The PSP
technique is used to design a temporal phase function from a prototype spectral
amplitude function; the instantaneous frequency function is then obtained from
the temporal phase. Examples of using this technique for deriving NLFM

waveforms from common window functions such as Hamming or Taylor
functions are given in Keel and Baden (2012).
One empirically developed design gives the instantaneous frequency
function as (Price, 1979)

(4.121)

The term β t/τ represents a linear FM component, while the term involving β is
L
C
designed to achieve a result that approximates a Chebyshev-shaped (constant
sidelobe level) spectrum. Since F(t) = (1/2π)(dθ(t)/dt), integrating and scaling
i
this instantaneous frequency function gives the required phase modulation

(4.122)

Figure 4.37 illustrates the behavior of the resulting nonlinear FM
waveform for the case where β τ = 50 and β τ = 20. The waveform is sampled
C
L
at 10 times the bandwidth of the linear term, T = 1/10β . The instantaneous
s
L
frequency (part a of the figure) is nearly linear in the center of the pulse but
sweeps much more rapidly near the pulse edges. This reduces the spectral
density at the pulse edge, resulting in the spectrum shown in part c, which has a
window-like tapered shape instead of the usual nearly square LFM spectrum.
The resulting matched filter output, shown in part d, has most of its sidelobes
between –48 and –51 dB with the first sidelobe at –29 dB. In contrast, Fig. 4.38
illustrates the spectrum of the same waveform with β set to zero. This results in
C
a linear FM waveform with the usual nearly square spectrum. These two figures