As the most promising technology in wireless communications, massive multiple-input multiple-output (MIMO) faces a significant challenge in practical implementation because of the high complexity and cost involved in deploying a separate front-end circuit for each antenna. In this paper, we apply the compressive sampling technique to reduce the number of required front-end circuits in the analog domain and the computational complexity in the digital domain. Unlike the commonly adopted random projections, we exploit the a priori probability distribution of the user positions to optimize the compressive sampling strategy, so as to maximize the mutual information between the compressed measurements and the direction-of-arrival (DOA) of user signals. With the optimized compressive sampling strategy, we further propose a compressive sampling Capon spatial spectrum estimator for DOA estimation. In addition, the user signal power is estimated by solving a compressed measurement covariance matrix fitting problem. Furthermore, the user signal waveforms are estimated from a robust adaptive beamformer through the reconstruction of an interference-plus-noise compressed covariance matrix. Simulation results clearly demonstrate the performance advantages of the proposed techniques for user signal parameter estimation as compared to existing techniques.