Abstract
In radar applications, it is known that with a sparse array of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas, we can construct a virtual array of size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) using fourth-order coarrays and cumulants. Such a result is valid when the sources are not Gaussian. In this paper, we consider the estimation of angles of arrival (AoA) for mmWave channels using fourth-order coarrays. An mmWave system usually has a large number of antennas but few RF chains, which restricts the effective antenna size. The angle estimation problems of mmWave and radar systems are similar, but there are differences. In particular, in the problem formulation of angle estimation for mmWave systems, we have path gains instead of source symbols. The path gains in mmWave channels are typically modeled as Gaussian random variables. We show that the critical non-Gaussian assumption for using fourth-order coarrays can be circumvented by using a submatrix of a banded Toeplitz matrix for analog combining. The combiner can be designed so that the conditions for applying fourth-order coarrays are satisfied asymptotically. A virtual array of size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) can be constructed when there are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> RF chains.
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