  Adaptive control is a control method that has an adaptation mechanism that
reacts to model uncertainties. The control method is used to realized
synchronization of a new chaotic system in a unidirectional master-slave
topology. The master chaotic system and the slave system are adopted as
transmitter and receiver, respectively for the purpose of secure
communications. Both analog and digital designs are realized. The digital
system is a cycle and bit accurate design having a system rate of $450MHz$. The
design is targeted at an Artix-7 Nexys 4 FPGA. The transmitters are accordingly
modulated by analog signals and fixed-point signals of different resolutions,
sampling and frequencies. Although the adaptive controller tends to react on
introduction of a modulating signal, we show that with a special detection
mechanism or filtering including exponential smoothing, the choice of which
depends on the nature of the modulating signal, it is possible to recover the
modulating signal at the receiver. Moreover, chaos-based spectrum-spectrum
communication systems are realized based on adaptive synchronization of the new
chaotic system. Furthermore, in order to ascertain the robustness of the
adaptive controller, the modulated signal is transmitted via an awgn channel
and the probability of error and bit-error-rate (BER) computed by sweeping
across sets of SNR and noise power values in a Monte Carlo simulation. It turns
out that the probabilities of error or error rates are reasonably low for
effective communication through mediums with certain noise conditions. Hence,
the adaptive controlled communication system can be robust.
