Optimization of adaptive signal processing algorithms for wireless communications is based on a model of the underlying propagation channel. In practice, this model is never known perfectly. For example, its parameters have to be estimated and are only known with significant errors.In this book, a systematic treatment of this practical design problem is provided for signal processing in the physical layer with multiple antennas. The design of robust signal processing algorithms is based on a description of the errors and the uncertainties in the system's model. It applies principles of modern estimation, optimization, and information theory. Tutorial introductions to relevant literature and mathematical foundations give the necessary background and context to the reader.The book provides detailed derivations and enlightening insights into the related technical problems covering the following topics in detail: An overview of the principles of training-based multiple-input multiple-output (MIMO) channel estimation. Robust minimax estimation of the wireless communication channel. Robust minimax prediction of the wireless communication channel based on the maximum Doppler frequency. Identification of channel and noise correlations (power delay profile, spatial and temporal correlations, spatial correlations of interference). Interpolation of band-limited autocovariance sequences. Robust linear and nonlinear precoding for the multi-user downlink with multiple antennas which is based on incomplete channel state information or channel correlations (performance measures, duality, robust Tomlinson-Harashima precoding, robust vector precoding, nonlinear beamforming).