Hypercomplex OFDM schemes for cross-polarized antennas

This paper presents orthogonal frequency-division multiplexing (OFDM) schemes for wireless communications using quaternions and hypercomplex commutative algebras. Although there is no simple or common definition for hypercomplex Fourier transform, it is shown that the 1-D function quaternion Fourier transform is well appropriated for the OFDM schemes. This 1-D function transform also applies with success for the hypercomplex commutative algebras. The important quaternion shift property necessary in OFDM as guard interval to combat ISI also applies appropriately to these schemes. Transmitter and receiver schemes were simulated using MIMO wireless links by means of cross-polarized antennas. Quaternion simulations suggest that the performance of the modulation schemes, concerning the bit error rate versus E_b/N₀, is independent of the Fourier transform axis for narrowband and orthogonal channels. For non flat fading or non orthogonal channels, the Cayley-Dickson´s composition form must be taken in consideration. Another new interesting result shown at this paper is the performance equivalence of the quaternion OFDM with the hypercomplex commutative algebras OFDM.