> The thinned-array curse (sometimes, sparse-array curse) is a theorem in electromagnetic theory of antennas. It states that a transmitting antenna which is synthesized from a coherent phased array of smaller antenna apertures that are spaced apart will have a smaller minimum beam spot size, but the amount of power that is beamed into this main lobe is reduced by an exactly proportional amount, so that the total power density in the beam is constant

So you can transmit with a sparse array, but the power you can deliver with it (for a set synthetic aperture size) decreases with the degree of sparseness. No free lunch.