Joint radar and communication (RadCom) systems have been proposed to achieve the spectrum sharing between radar and communication in recent years. However, the joint RadCom systems cause the clutter modulation and the performance degradation of both radar and communication. As a consequence, it's very critical to improve the performance of both radar and communication when designing joint RadCom systems. Firstly, this paper designs the constant modulus dual function waveforms for spatial modulation based joint RadCom systems. In order to solve the nonsmooth and nonconvex optimization problem, we propose a method based on alternating direction method of multipliers (ADMM) to obtain a suboptimal solution. Secondly, this paper analyses the effect of beampattern variation on clutter modulation for spatial modulation based joint RadCom systems. Besides, this paper considers the design of robust doppler filter for joint RadCom systems when the receive temporal steering vector is mismatched to the desired temporal steering vector. This paper aims to maximize the worst signal-to-interference-plus-noise-ratio (SINR) of the doppler filter in the specific doppler interval under the similarity constraint and constant white noise gain constraint. In order to solve the nonconvex optimization problem, we relax the original optimization problem to a semidefinite programming (SDP), which is convex and can be solved using off-the-shelf optimization solvers. What's more, the rank-one decomposition method is utilized to synthesize the weight vector of the proposed robust doppler filter. Finally, lots of simulation results are presented to show the robustness of the designed doppler filter.