SBL-based data-aided channel estimation for spatially evolving STTC MIMO systems

In this paper, a spatially sparse representation of the multiple-input multiple-output (MIMO) channel matrix is considered in terms of the overcomplete spatial signature dictionary comprising of the basis signature matrices which correspond to the various directional cosines at the transmit and receive antenna arrays. Further, the spatial evolution of the MIMO channel matrices is suitably captured by modeling the sparse weight vector corresponding to the significant directional cosines as a first order auto-regressive model. Towards this end, the sparse Bayesian learning (SBL) framework is employed to develop a novel pilot-based channel estimation scheme for space-time trellis coded (STTC) MIMO systems based on a time-varying spatially sparse representation of the MIMO channel. Subsequently, an enhanced data-aided channel estimation scheme is also developed by utilizing the expectation-maximization (EM) framework, which culminates in an optimal Kalman filter and smoother (KFS)-based minimum mean squared error channel estimate in the E-step followed by a modified path metric-based trellis decoder in the M-step. Additionally, the Bayesian Cramér-Rao bounds (BCRBs) corresponding to the proposed SBL-based channel estimation schemes are also developed. Finally, simulation results are presented to illustrate the superior performance of the proposed techniques and validate the analytical bounds.