Multiple transformation analysis for interference separation in TDCS

Various types of interference signals limit the practical application of transform domain communication systems (TDCSs) in the severe electromagnetic field, an orthogonal basis learning method of transformation analysis (OBL-TA) is proposed to effectively address the problem of obtaining an optimal transform domain based on sparse representation. Then, the sparse availability is utilized to obtain the optimal transformation analysis by the iterative methods, which yields the sparse representation for transform domain (SRTD) in unrestricted form. In addition, the iterative version of SRTD (I-SRTD) in unrestricted form is obtained by decomposing the SRTD problem into three sub-problems and each sub-problem is iteratively solved by learning the best orthogonal basis. Furthermore, orthogonal basis learning via cost function minimization process is conducted by stochastic descent, which is assured to converge to a local minimum at least. Finally, the optimal transformation analysis is developed by the effectiveness of different transform domains according to the accuracy of the sparse representation and an optimal transformation analysis separately (OPTAS) is applied to the synthesized signal forms with conic alternatives, dualization, and smoothing. Simulation results demonstrate that the superiorities of the proposed methods achieve the optimal recovery and separation more rapidly and accurately than conventional methods.