A major challenge in wideband spectrum sensing, in cognitive radio system for example, is the requirement of a high sampling rate which may exceed today's best analog-to-digital converters (ADCs) front-end bandwidths. Compressive sampling is an attractive way to reduce the sampling rate. The modulated wideband converter (MWC) proposed recently is one of the most successful compressive sampling hardware architectures, but it has high hardware complexity owing to its parallel channels structure. In this paper, we design a single channel sub-Nyquist sampling scheme to bring substantial savings in terms of not only sampling rate but also hardware complexity, and we also present a wideband power spectrum sensing and reconstruction method for bandlimited wide-sense stationary (WSS) signals. The total sampling rate is only one channel rate of the MWC's. We evaluate the performance of the sensing model by computing the probability of detecting signal occupancy in terms of the signal-to-noise ratio (SNR) and other practical parameters. Simulation results underline the promising performance of proposed approach.