Aerospace and Electronic Systems Magazine May 2017 - 47
phases to reduce the instantaneous transmit peak power. Analogous to direct sequence spread spectrum technique, which reduces
the power spectral density of the transmitted signals, a series of
spoiled low-gain beams covering the desired surveillance region
are formed sequentially, rather than scanning the scenarios with a
high-gain transmit beam.
Figure 1 illustrates the LPI scheme by reducing the transmitted
peak power. Consider an M-element phased array. When a uniform
excitation is adopted, the fundamental far-field basis pattern can
be expressed as
a0
M 1
e
j
m
e jm ,
(1)
m0
where ψ = 2πd sin θ/λ, with d, θ, and λ being the element spacing,
spatial broadside angle, and carrier wavelength, respectively. The
set of phase shift values αm is chosen to create a low-gain, spoiled
beam pattern. Certainly, minimizing the beam pattern gain implies
that a broad beam can be generated. If αm = 0, Eq. (1) simplifies to
a general phased array beam pattern, providing a dominant mainlobe, with a high-gain-directed broadside to the array.
Additional low-gain basis patterns can be formed by applying a
linear-phase progression to the fundamental basis pattern in incre-
ments of γ = 2π/N for the first basis pattern, 2γ for the second basis
pattern, and so on. In doing so, we can obtain N basis patterns:
an (ψ ) =
M −1
e
jnγ
e jα m e jmψ ,
n = 0,1,..., N − 1.
(2)
m=0
These N steered versions of the fundamental pattern are linearly
independent and more importantly, the peak power radiated to any
direction is significantly reduced, while maintaining the same array performance as a traditional surveillance radar with a scanned
high-gain antenna. The N low-gain beams can then be weighted
and coherently combined to form an ensemble of the high-gain
beam toward the desired direction. Assuming the weight used for
the kth synthesized high-gain beam and nth low-gain basis beam
is wk,n, we then have
N −1
g k (ψ ) = wk , n an (ψ ) ,
n =0
k = 0,1,..., K − 1.
(3)
Note that once the set of basis patterns are formed, all K-steered
high-gain patterns can be synthesized at once.
In an actual system, the beamforming methodology can be
integrated with the radar waveform consisting of N consecutive
subpulses separated by the pulse repetition interval. Each subpulse
Figure 1.
Illustration of LPI transmission and receiver-processing schemes.
MAY 2017
IEEE A&E SYSTEMS MAGAZINE
47
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