In a transmit method, a set of data eigenvectors that are based on a Prometheus Orthonormal Set (PONS) code construction and orthogonal to each other are stored, wherein the data eigenvectors are mapped to unique multi-bit words. A pilot sequence representing a pilot eigenvector that is based on the PONS code construction and orthogonal to each of the data eigenvectors is generated. Input data are grouped into multi-bit words and data eigenvectors among the data eigenvectors are selected based on the multi-bit words. A spread data sequence including the selected data eigenvectors and that is synchronized to the pilot sequence is generated. An acoustic signal including the synchronized pilot sequence and the spread data sequence is generated. The acoustic signal is transmitted.