We propose and demonstrate a photonic compressive sensing (PCS) scheme for microwave signals using optical pulse random mixing, significantly enhancing both the compression ratio and operating frequency range. Unlike continuous-wave laser-based PCS systems, our approach mitigates the non-ideal characteristics of the pseudo-random binary sequence (PRBS), such as sloped edges and amplitude jitters, resulting in a more ideal compression process. Additionally, the high harmonic components of the optical pulses further facilitate wideband downconversion, improving the system's operating frequency range. In a proof-of-concept experiment, a dual-tone signal within the 4 GHz range is successfully recovered with a compression ratio of 20. Moreover, single-tone signals beyond the first Nyquist zone, at 7.17 GHz, 11.26 GHz, and 14.6 GHz, are effectively reconstructed with a compression ratio of 40. The proposed PCS system offers a simple, highly efficient solution for wideband spectrum identification, surpassing the performance of conventional continuous-wave-based PCS systems.