For the case that the direction of the reflected signal from desired target in the presence of clutter is uncertain

a robust joint design of transmit waveform and receive filter for MIMO radar is proposed. Under the condition of the transmit power constraint for each transmit element

a Max-min optimal model about the output SINR within the uncertainty set is designed using transmit weighting matrix. On this basis

the sequential optimization method

semi-definite relaxation and Charnes-Cooper transform are used to transform the joint optimization problem

which is non-convex

into two convex sub-problems about transmit waveform and receive filter

respectively. And through iteration optimization procedure

the optimized covariance matrixes of transmit waveform and receive filter are obtained. Finally

the desired transmit weighting matrix and receive filter are synthesized via the randomization method with the optimized covariance matrixes. Theoretical analysis and demonstration about the computation complexity and the convergence of the proposed method are given. The proposed method can improve the robustness and reduce the computational burden with the same transmit power constraint of each antenna. And the efficiency and validity of the proposed method are verified by the simulation results.