Modulated wideband converter system offers an under- sampling method aiming at the issue that sparse wideband signals require high sampling rates. In this paper, we propose a multi-bit pseudo-random measurement matrices construction method based on discrete chaotic sequences since Bernoulli random measurement matrix currently used in an MWC system is difficult to be implemented by hardware. Simulation results show that an MWC system can still perform sub-Nyquist sampling and achieve exact recovery with overwhelming probability while adopting the proposed pseudo-random sequences as measurement matrices. Thus our method is able to save system resources greatly on condition that the reconstruction performance hardly changes compared with Bernoulli matrix.