A subspace theory for differential chaos-shift keying

In this brief, we introduce a subspace theory for differential chaos-shift keying (DCSK) systems. We show that DCSK systems operate by transmission of chaotic signals residing in a low-dimensional subspace. The subspace formalism of DCSK schemes leads to the derivation of useful subspace detectors that can be applied to decode the DCSK signal for various types of channels. Closed form expressions for the bit error rate is derived for an M-ary FM-version of DCSK, under the assumption of orthogonal subspace generating vectors. Numerical simulations demonstrate that the proposed subspace detector in general outperforms the conventional correlation detector for DCSK