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 )