This paper deals with the joint design of Multiple-Input Multiple-Output (MIMO) radar transmit waveform and receive filter to enhance multiple targets detectability in the presence of signal-dependent (clutter) and independent disturbance. The worst-case Signal-to-Interference-Noise-Ratio (SINR) over multiple targets is explicitly maximized. To ensure hardware compatibility and the coexistence between MIMO radar and other wireless systems, constant modulus and spectral restrictions on the waveform are incorporated in our design. A max-min non-convex optimization problem emerges as a function of the transmit waveform, which we solve via a novel polynomial-time iterative procedure that involves solving a sequence of convex problems with constraints that evolve with every iteration. We provide analytical guarantees of monotonic cost function improvement with proof of convergence to a solution that satisfies the KarushKuhnTucker (KKT) conditions. By simulating challenging practical scenarios, we evaluate the proposed algorithm against the state-of-the-art methods in terms of the achieved SINR value and the computational complexity.