Linear Approximation of the Exponential Map with Application to Simplified Detection of Noncoherent Systems

We propose an approximated generalized likelihood ratio test (GLRT) for noncoherent systems which use constellations over the Grassmannian generated by the exponential map. By means of this approximation we succeeded in coping with the strong non-linearity introduced by the exponential map. The new simplified decoder, which implements the approximated GLRT, is in fact quasi-optimal with respect to the GLRT. We analyze the performance of the new decoder in terms of structure, complexity and error probability for uncoded and coded noncoherent constellations