Page 294 - Fundamentals of Radar Signal Processing

4.8 The Stepped Frequency Waveform
The LFM waveform increases resolution well beyond that of a simple pulse by

sweeping the instantaneous frequency over the desired range β within the pulse.
This technique is very effective and very common but does have drawbacks in
some systems, particularly those using very large bandwidths on the order of
hundreds of megahertz or more. First, the transmitter hardware must be capable
of generating the LFM sweep. Second, all of the analog components must be
able to support an instantaneous bandwidth of β Hz without introducing

distortion. Even if stretch processing is used, the same is true of the receiver
components up to and including the dechirp mixer and reference oscillator.
A second issue arises in systems using phase-steered array antennas.
Recall from Chap. 1 that the antenna pattern of a phase-steered array antenna is
determined primarily by the array factor where d is the element spacing and the
{a } are the complex weights on each subarray output. The antenna is steered to
n
a particular look direction θ by setting the steering weights a according to 7
n
0

(4.123)

(4.124)

The magnitudes of the weights are chosen to provide the desired sidelobe level.
E(θ) will exhibit a peak at θ = θ ; for example, if|a |≡ 1, E(θ) will be an asinc
0
n
function with its peak at θ . Note that the phases of the required weights {a } are
n
0
a function of the wavelength λ. If an LFM pulse is transmitted, the effective
wavelength changes during the pulse sweep. If the system is wideband, this
wavelength change will be significant and the value of θ at which E(θ) peaks
will change as well. That is, the antenna look direction will actually change
during the LFM sweep (see Prob. 18). This undesired frequency steering effect
is an additional source of SNR loss.
Stepped frequency waveforms are an alternative technique for obtaining a
large bandwidth and thus fine range resolution without requiring intrapulse

frequency modulation. A stepped frequency waveform is a pulse burst
waveform. Each pulse in the burst is a simple, constant-frequency pulse;
however, the RF is changed from one pulse to the next. The most common
stepped frequency waveform employs a linear frequency stepping pattern,
where the RF of each pulse is increased by ΔF Hz from the preceding pulse.

Factoring out the starting RF gives the following baseband waveform