Optimal mask operation 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 demodulations in general transform domains 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 an optimal multiplication in an optimal Hermitian transform domain for performing the optimal mask operation. The joint design of the mask coefficients and the Hermitian transform matrix is formulated as a least squares optimization problem subject to the Hermitian condition.