In this paper, we investigate optimal scheme to manage time scheduling of different modules including spectrum sensing, radio frequency (RF) energy harvesting (RFH) and ambient backscatter communication (ABCom) by maximizing data transmission rate in the internet of things (IoT). We first consider using spectrum sensing with energy detection techniques to detect high power ambient RF signals, and then performing RFH and ABCom with them. Specifically, to improve the spectrum sensing efficiency, compressive sensing is used to detect the wideband RF singals. We propose a joint optimization problem of optimizing time scheduling parameter and power allocation ratio, where power allocation ratio appears because REH and ABCom work at the same time. In addition, a method to find the threshold of spectrum sensing for backscatter communication by analyzing the outage probability of backscatter communication is proposed. Numerical results demonstrate that the optimal schemes with spectrum sensing are achieved with larger transmission rates. Compressive sensing based method is confirmed to be more efficient, and that the superiorities become more obvious with the increasing of the network operation time. Moreover, the optimal scheduling parameters and power allocation ratios are obtained. Also, simulations illustrate that the threshold of spectrum sensing for backscatter communication is obtained by analyzing the outage probability of backscatter communication.