Transcript Sparse Array

Sparse Array
Geometry
Mr. Ahmed El-makadema
Professor A.K Brown
• The purpose of this work is to evaluate the
possible application of sparse arrays to the mid
frequency SKA aperture array concept
• The approach is to compute the performance of
various array geometries assuming a fixed
number of elements (1000 chosen for
convenience )
• A maximum scan angle of 45 degrees is
assumed and a “crossed dipole type” element.
At this stage mutual coupling has been ignored
Element pattern assumed
Regular Grid Arrays
• Must be spaced adequately to give us maximum
effective area at the highest frequency.
• This is achieved when there are no grating lobes
appearing in real space at the top frequency.
• However this means a low effective area at the
low frequencies for the same number of
elements.
• More effective area is gained at the low
frequency by increasing the separation.
• At high frequencies performance then drops due
to grating lobes.
A typical regular grid
Effective area vs. freq (regular
grid) at boresight
Effective area vs. freq (regular
grid) at 45 degrees
• We note that the effective area does not
behave smoothly with frequency due to
energy occurring inside grating lobes at
higher frequencies where the grid
separation is large in terms of wavelength
Random Grid
• Elements are placed randomly on a defined area
such that any two elements cannot be closer
than a specific desired distance (minimum
separation).
• The aim is to gain more effective area at the low
frequency while trying to maintain a good side
lobe control. This is due to the random effect
used to average out the power contained in the
grating lobes
• This effect will smooth out the effective area
curve.
Typical random grid
Effective area vs. freq (Random
Grid) at boresight
Effective area vs. freq (Random
Grid) at 45 degrees
Maximum effective area
• If effective area of one element is A, then one would
expected that the maximum possible effective area to be
achieved from N elements is N*A.
• However in a narrow band optimally spaced array the
effective area is larger than N*A
• On the other hand in broad band array environment this
is not true since geometry and spacing between
elements effects the array factor and therefore effective
area might be less or more that N*A throughout the
band.
• Another way of representing the random array behaviour
is to plot it as a function of spacing for different
frequencies.
Effective area vs. minimum separation at
boresight
Effective area vs. minimum separation at
45 degrees scan
Optimum design
• In the two previous figures one can see where
the optimum design point that would achieve the
highest effective area for each frequency.
• This could be useful in choosing the optimum
minimum separation to achieve the maximum
effective area at the band of interest
• Side lobe level and radiation pattern needs to be
examined for performance
Peak Side lobe at boresight
Peak Side lobe at 45 degrees
Example Pattern at boresight for random array
Same example pattern for random array with 45 degrees scan
Future work
• This approach could be useful in optimizing the broad band array
performance
• This can be achieved by selecting an optimally spaced regular array
for the top frequency and a randomly sparse array for the low
frequencies.
• Apply specific thinning methods for more side lobe control
• We note that the increase of side lobe level has two major effects,
one is on sky noise and the other is on the dynamic range of the
system. Both these are currently being investigated.
• Sparse techniques allows maximum sensitivity at lower frequencies
for a given number of elements at the cost of higher side lobes and
sensitivity reduction at the higher frequencies. Therefore the
optimum design will probably be a combination of sparse and fully
filled arrays. (note: this was reflected in the draft SKA specifications
discussed at SKA2007 )