Optimal Joint Design of Hermitian Transform Matrix and Corresponding Mask Coefficients for Multi-Digital Demodulation Systems

Nowadays, signals are transmitted using different digital modulation systems according to different channel conditions. Different digital modulation systems transmit signals using different frequency bands. To demodulate the signals and decode the corresponding digital symbols, different filters with different frequency bands are employed. This paper explores the possibility of performing the digital demodulation in a general energy preserved transform domain instead of in the conventional frequency domain. In particular, instead of performing the multiplication in the frequency domain for performing the conventional filtering, this paper proposes to perform the multiplication in an optimal Hermitian transform domain for performing the optimal mask operation. The joint design of the Hermitian transform matrix and the corresponding mask coefficients is formulated as a least squares optimization problem subject to the Hermitian condition. This is actually a complex-valued quadratic matrix equality constrained least squares optimization problem. A condition on an optimal solution is derived via a singular value decomposition approach. Based on the derived condition, an iterative approach is proposed for finding the solution of the optimization problem. Computer numerical simulation results show that our proposed approach outperforms the conventional filtering approach.