On efficient non-coherent detection of Grassmannian constellations

In this paper we derive analytic expressions for the boundaries of the search region of a recently proposed efficient detector for non-coherent reception of Grassmannian constellations. These boundaries are designed to ensure that the restriction of the detection search space to the enclosed region does not incur significant performance degradation. In addition, we show that the cardinality of the set of candidate constellation points, that is the number of constellation points that lie within the search space, approaches one at least as fast as the inverse of the square root of the received signal SNR.