Abstract: ‍ ‍Radar embedded communication （REC） is a low probability of intercept （LPI） communication method that enables radar and communication to share the spectrum. It completes convert communication by embedding a low-power communication waveform in a high-power radar backscatter echo. By optimizing the power exponent a of the eigenvalue matrix of the shaped water filling （SWF） waveform， this paper proposed the SWF waveform with variable power exponent of the eigenvalue matrix， namely SWF-a waveform. This paper deduced the processing gain of cooperative receiver and intercept receiver and gain advantage for SWF-a waveform， and theoretically analyzed its communication reliability， LPI performance and comprehensive performance. Finally， taking SWF-0.25， SWF and SWF-0.75 waveforms as examples， the simulation experiments were carried out. The experimental results are consistent with the theoretical analysis results， which shows that the different requirements of REC waveform performance can be met through the optimization of eigenvalue matrix power exponent. Specifically， the communication reliability can be improved by appropriately reducing the parameter a， while the LPI performance or the comprehensive performance can be improved by appropriately increasing the parameter a. However， for the synchronous improvement of LPI performance and communication reliability， it is difficult to have both by selecting parameter a.