Cayley Differential Unitary Space-Time Codes

One method for communicating wih multiple antennas is to differentially encode the transmitted date using unitary matrices at the transmitter, and to differentially decode without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Although this basic principle is well understook, it is not known how to generate good-performing constellations of unitary matrics, for any number of transmit and receive antennas and for any rate. This is especially true at high rates where the constellations must be rapidly encoded and decoded. We propse a class of Cayley codes that works with any number of antennas, and have efficient encoding and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skew-Hermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an information-theoretic design criterion based on either successive nulling/cancelling or sphere decoding. Simulation show that the Cayley codes allow efficient and effective high-rate data transmission in multi-antenna communication systems without knowing the channel.