Most existing space-time coding schemes assume time-invariant fading channe
ls and offer antenna diversity gains relying on accurate channel estimates
at the receiver. Recent single differential space-time block coding schemes
forego channel estimation but are less effective in rapidly fading environ
ments. Based on a diagonal unitary matrix group, a novel double differentia
l space-time block coding approach is derived in this paper for time-select
ive fading channels. Without estimating the channels at the receiver, infor
mation symbols are recovered with antenna diversity gains regardless of fre
quency offsets. The resulting transceiver has very low complexity and is ap
plicable to an arbitrary number of transmit and receive antennas. Approxima
tely optimal space-time codes are also designed to minimize bit error rate.
System performance is evaluated both analytically and with simulations.