We consider the problem of multiple-target estimation using a colocated multiple-input multiple-output (MIMO) radar system. We employ sparse modeling to estimate the unknown target parameters (delay, Doppler) using a MIMO radar system that transmits frequency-hopping waveforms. We formulate the measurement model using a block sparse representation. We adaptively design the transmit waveform parameters (frequencies, amplitudes) to improve the estimation performance. Firstly, we derive analytical expressions for the correlations between the different blocks of columns of the sensing matrix. Using these expressions, we compute the block coherence measure of the dictionary. We use this measure to optimally design the sensing matrix by selecting the hopping frequencies for all the transmitters. Secondly, we adaptively design the amplitudes of the transmitted waveforms during each hopping interval to improve the estimation performance. To perform this amplitude design, we initialize it by transmitting constant-modulus waveforms of the selected frequencies to estimate the radar cross section (RCS) values of all the targets. Next, we make use of these RCS estimates to optimally select the waveform amplitudes. We demonstrate the performance improvement due to the optimal design of waveform parameters using numerical simulations. Further, we employ compressive sensing to conduct accurate estimation from far fewer samples than the Nyquist rate.