  Reservoir computation models form a subclass of recurrent neural networks
with fixed non-trainable input and dynamic coupling weights. Only the static
readout from the state space (reservoir) is trainable, thus avoiding the known
problems with propagation of gradient information backwards through time.
Reservoir models have been successfully applied in a variety of tasks and were
shown to be universal approximators of time-invariant fading memory dynamic
filters under various settings. Simple cycle reservoirs (SCR) have been
suggested as severely restricted reservoir architecture, with equal weight ring
connectivity of the reservoir units and input-to-reservoir weights of binary
nature with the same absolute value. Such architectures are well suited for
hardware implementations without performance degradation in many practical
tasks. In this contribution, we rigorously study the expressive power of SCR in
the complex domain and show that they are capable of universal approximation of
any unrestricted linear reservoir system (with continuous readout) and hence
any time-invariant fading memory filter over uniformly bounded input streams.
