Determinant Criterion Optimizing Linear Subspace Projector for Burst Orthogonal STC CPM Modulation in MIMO Channel

We consider a general burst block orthogonal space- time coded CPM modulation in MIMO slowly fading Rayleigh channel. The modulated signal has multidimensional constellation waveforms. The optimal receiver must perform a multidimensional matched filtering on its front-end. This operation is highly demanding on the processing computational resources. We derive sub-optimal complexity reducing receiver linear preprocessor which reduces the dimensionality of the signal. We analytically derive the optimal linear projector matrix for several cases of the free trellis path and its termination. The determinant optimization is shown to lead to an eigenvector problem solution. It is a two-fold joint optimization problem with 2 mutually coupled domains (similar to a decoding in a parametric channel) with number of solution options with generally high complexity. We adopt simplified approach decoupling this 2 domains. As an example, we apply the procedure for a particular case of one-dimensional subspace projector and Burst Alamouti coded MSK modulation as a special case of STC CPM modulation.