  Multiple-input multiple-output (MIMO) has become a key technology for
contemporary wireless communication systems. For typical MIMO systems, antenna
arrays are separated by half of the signal wavelength, which are termed
collocated arrays. In this paper, we ask the following question: For future
wireless communication systems, is it possible to achieve better performance
than collocated arrays by using sparse arrays, whose element spacing is larger
than half wavelength? The answer to this question is not immediately clear
since while sparse arrays may achieve narrower beam for the main lobe, they
also generate undesired grating lobes. In this paper, we show that the answer
to the above question is affirmative. To this end, we first provide an
insightful explanation by investigating the key properties of beam patterns of
sparse and collocated arrays, together with the typical distribution of spatial
angle difference \Delta, which all critically impact the inter-user
interference (IUI). In particular, we show that sparse arrays are less likely
to experience severe IUI than collocated arrays, since the probability of
\Delta typically reduces with the increasing of |\Delta|. This naturally helps
to reject those higher-order grating lobes of sparse arrays, especially when
users are densely located. Then we provide a rigorous derivation of the
achievable data rate for sparse and collocated arrays, and derive the condition
under which sparse arrays strictly outperform collocated counterparts. Finally,
numerical results are provided to validate our theoretical studies.
