A method for decoding data symbols modulated with a corresponding codeword from a constellation set of codewords expands the constellation set of codewords with a set of basis functions to produce a basis-expanded constellation set and projects projecting a received modulated data symbol onto orthogonal complements of the basis expanded constellation set to obtain a set of distance metric of a generalized likelihood ratio test (GLRT) for each codeword of the constellation set. The set of basis functions includes a Fourier exponential basis function in a frequency domain, a Legendre polynomial basis function in a time domain, and a Fourier-Legendre product basis function in the frequency domain. The method selects a codeword corresponding to a minimal distance metric or a maximal correlation metric and decodes the data symbol from the received modulated data symbol using the codeword.