A Modulation Based on Symbol Mapping on Hypersphere

Abstract

In general modulations, symbols are designed in two-dimensional Euclidean space, which is equivalent to the I-Q signal space, based on the quadrature modulation. The typical modulation schemes are phase shift keying (PSK) and quadrature amplitude modulation (QAM). Their symbols are designed to maximum the minimum Euclidean distance between the symbols under the condition of the constant average signal power. In this article, I explain the symbol design schemes in K-dimensional Euclidean space. In particular, I show three designs for the symbols on the K-1-sphere. It is possible to make the minimum distance between symbols longer than that of quadrature PSK (QPSK) and reduce E_b/N₀ required to achieve a BER. I explain the availability of hypersphere modulation in wireless communication systems.