Phased Array Scanning with Sequential Commands
Randy L. Haupt, Brian Thrall, Aaron Lyons, M. Bruce Davis, Robert Fitzgerald
Ball Aerospace
Westminster, CO, USA
Abstract—Phase shift commands to steer a phased array beam
are sent to the phase shifters sequentially. In a radar system, the
phase shifters simultaneously change when they receive a strobe
signal. In a communications phased array, the phase shifters can
either change simultaneously or sequentially as they receive the
commands. The sequential approach causes the beam to
gradually move from one position to another. This paper shows
this behavior and effects the element sequence.
I.
INTRODUCTION
Phased arrays steer the main beam of the antenna by
placing a linear phase shift across the elements. When the
signals from all the elements add in phase, then this coherent
addition results in a main beam peak [1].
Sequential phase shifting switches ones phase shifter at a
time in the array. If all phase shifters receive their steering
phase simultaneously, then the beam jumps from one steering
angle to another. If the phase shift commands are delivered
sequentially to the phase shifters, however, then the elements
do not receive their phase shifts at the same time.
Consequently, the main beam does not jump from one
direction to another, but morphs from one direction to another,
as will be now shown.
If the phase shifts are delivered first to element 1, then
element 2, …, finally to element N, then the aperture is split in
half with the left half of n elements receiving a linear phase
shift that steers the beam to , and the right half N-n elements
having a main beam that points to boresight.
When the beam is at θ1 , then only term A exists. Steering
the beam to θ 2 replaces term A with term B. If the phase shifts
are delivered to the elements starting with element 1 and going
in sequence to element N, then the array factor is a
superposition of a uniform array factor pointing at broadside
and a uniform array factor pointing the in steering direction.
III. EXAMPLES
Assume a linear array has 20 elements spaced λ / 2 apart
and the elements receive phase shift commands sequentially
from element 1 to element 20. The commands are separated by
a time Δts . Figure 1 shows a plot of the array factor starting
at broadside ( t = 0 ) and ending when the beam reaches the
desired steering angle at θ s = 45o , ( t = 20Δt s ). The main beam
at broadside gradually degrades, while the main beam at
θ s = 45o gradually emerges.
This paper presents the effects of sequential phase shifting
on the array factor of a linear array. Mutual coupling, element
patterns, phase shifter quantization, and bandwidth are ignored
in order to isolate the effects of changing one phase shifter at a
time.
II. BEAM STEERING WITH SEQUENTIAL COMMANDS
The array factor for an N-element uniform linear phased
array with sequential phase shifting is given by
AF =
where
sin ⎣⎡ n (ψ −ψ 1 ) / 2⎦⎤
+
sin ⎣⎡( N − n )(ψ −ψ 2 ) / 2 ⎦⎤
sin ⎡⎣(ψ −ψ 1 ) / 2 ⎤⎦
sin ⎡⎣(ψ −ψ 2 ) / 2 ⎤⎦
A
B
(1)
ψ m = kd sin θ m
k = 2π / wavelength
Figure 1. Array factor as a function of time when steering a 20
element array from 0o to 45o .
d = element spacing
The effects of sequential steering on the array factor
depend upon the difference between θ1 and θ 2 . Steering from
θ m = steer from θ1 to θ 2
0o to 2.5o keeps the peak of the main beam inside the 3 dB
978-1-4673-0462-7/12/$31.00 ©2012 IEEE
beamwidth of the broadside beam. Figure 2 is a plot of the
array factor after each phase shifter receives its steering
command. The broadside beam moves in the negative
θ direction while the new main beam at 2.5o begins to emerge.
The main beam at 0o eventually disappears leaving the main
beam at 2.5o . Figure 3 is a plot of the maximum directivity
and its location in θ as the beam is steered. This plot confirms
that the main beam starts moving in the negative θ direction
before moving to its final destination. Along the way, the peak
directivity decreases by 3 dB.
ordering of the phase shift commands. The beam wandering is
reduced at the expense of loss in directivity.
Figure 4. Location of main beam peak as a function of time.
Figure 2. Array factor as a function of time.
Figure 5. Location of main beam peak vs. angle as a function
of time when the element ordering is optimized.
IV. CONCLUSIONS
Figure 3. Location of main beam peak vs. angle as a function
of time.
Increasing the beam steering to θ s = 5.5o puts the steered
beam at the peak of the first sidelobe of the broadside
pattern.Error! Reference source not found. Figure 4 is a
plot of the maximum directivity and its location in θ as the
beam scans. The maximum directivity shifts from θ = 0o to
θ = −1o at the same time the directivity decreases before main
beam maximum jumps. It then slowly gains directivity as it
moves to the desired steering angle.
The beam wandering can be reduced by either randomizing
the order of the elements that receive the phase shifts or
optimizing the order. Figure 5 results from an optimized
The main beam of a phased array can be scanned by
sending the phase shifts to all the phase shifters, then changing
their phase simultaneously, or by sending the phase shifts one
at a time and changing the phase whenever the phase shifter
receives the command. A sequential phase shift, however,
results in the main beam traveling a path from its present
position to its desired new position with accompanying
sidelobe level distortions. The beam wandering can be
minimized by sending the phase steering commands in a
random or optimal non-sequential order.
REFERENCES
[1]
R. L Haupt, Antenna Arrays: A Computational Approach, New York,
Wiley, 2010.