The echo data can be modeled as the product of the Toeplitz matrix and reflectivity of the observed scene. The row of the Toeplitz matrix is the time-shift of the transmitted signal. Since, it is difficult to vertify whether the Toeplitz matrix satisfis the reconstruct condition of sparse microwave imaging (such as, restricted isometry property), analyzing the performance of the transmitted signal in sparse microwave imaging is a problem. RIPless, a new progress in sparse signal processing, shows if the row of the matrix is an i.i.d. random vector drawn from a distribution, and this distribution satisfies certain conditions, then one can faithfully recover approximately sparse signals from a minimal number of measurements. Toeplitz matrix satisfies RIPless. In this paper, we first introduce the construction of measurement matrix in sparse microwave imaging. Then the relationship of pulse duration, bandwidth and waveform type and the number of measurements in sparse microwave imaging is analyzed. At last simulation results show that the effectiveness of proposed method.