Innovative parallel equalizer design for continuous phase modulation systems

In this paper, we propose a new parallel structure of the linear frequency-domain equalization approach for continuous phase modulated (CPM) signals. Since CPM is a nonlinear modulation technique, the corresponding equalizer design is mathematically intractable. However, it is possible to decompose any CPM signal into a sum of linearly modulated signals through Laurent decomposition. By utilizing Laurent decomposition, the nonlinear nature of CPM is manifested by the mapping of the input symbols onto the “pseudo-coefficients”. This enables us to establish a time-domain polyphase matrix signal model, which can characterize various block-based CPM systems. Such a polyphase matrix model can yield a linear equalizer as its matrix inverse. Moreover, we propose a matrix inverse approximation algorithm to design the equalizers for CPM systems in a parallel paradigm. The algorithmic complexity for the optimal equalizer design is thus significantly reduced. Monte Carlo simulations are taken in compliance with the wireless personal-area network (WPAN) standard. Two primary equalizers, namely minimum-mean-square-error (MMSE) and zero-forcing (ZF) equalizers, are adopted therein. Simulation results demonstrate that our proposed new parallel MMSE/ZF equalizer would lead to a slightly worse bit-error-rate performance than the conventional MMSE/ZF equalizer. Nevertheless, the former scheme would reduce a lot of computational complexity compared to the latter method.