  Recently we demonstrated experimentally that microwave oscillators based on
the time delay feedback provided by traveling spin waves could operate as
reservoir computers. In the present paper, we extend this concept by adding the
feature of time multiplexing made available by the large propagation
times/distances of traveling spin waves. The system utilizes the nonlinear
behavior of propagating magnetostatic surface spin waves in a yttrium-iron
garnet thin film and the time delay inherent in the active ring configuration
to process time dependent data streams. Higher reservoir dimensionality is
obtained through the time-multiplexing method, emulating "virtual" neurons as
temporally separated spin-wave pulses circulating in the active ring below the
auto-oscillation threshold. To demonstrate the efficacy of the concept, the
active ring reservoir computer is evaluated on the short-term memory and parity
check benchmark tasks, and the physical system parameters are tuned to optimize
performance. By incorporating a reference line to mix the input signal directly
onto the active ring output, both the amplitude and phase nonlinearity of the
spin waves can be exploited, resulting in significant improvement on the
nonlinear parity check task. We also find that the fading memory capacity of
the system can be easily tuned by controlling the active ring gain. Finally, we
show that the addition of a second spin-wave delay line configured to transmit
backward volume spin waves can partly compensate dispersive pulse broadening
and enhance the fading memory capacity of the active ring.
