Abstract: The existing radar estimation waveform design methods mostly concentrate on the frequency domain in presence of signal dependent clutter, which leads to the missing of waveform phase information. Then the estimation performance will decline when the waveform is transformed into time domain. To solve this problem, while considering the nonlinear characteristics of the amplifier, we propose a low peak-to-average power ratio (PAR) estimation waveform design method. Firstly, an optimization model is established based on the maximum mutual information criterion. Secondly, an approximate waveform matrix is obtained by relaxing the nonconvex problem into a convex problem based on the sequence linear programming method. Finally, the proposed waveform matrix which satisfies the Toeplitz matrix structure is obtained by approximating the former waveform matrix, then the optimal vector solution of waveform can be extracted. Compared with the existing method, the proposed method has better estimation performance without adding additional computation.