Can Sparse Arrays Outperform Collocated Arrays for Future Wireless Communications?
Huizhi Wang, Yong Zeng
Abstract
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta$</tex> , 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta$</tex> typically reduces with the increasing of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\vert \Delta\vert$</tex> . 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.