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This paper presents a unifying framework for designing a joint channel-estimation-and-data-detection (CE/DD) scheme and space-time block code (STBC) that improves the performances in a multiple-input-multiple-output (MIMO) slow flat Rayleigh fading channel. Modeling the channel using the continuous-fading model, a matrix state-space model, which naturally represents the temporal and spatial dimensions of a MIMO system, is introduced. A consistent and novel matrix CE/DD scheme is developed using a matrix Kalman filter and a matrix normalized-innovations-based maximum-likelihood detector. In MIMO CE/DD in multiplicative fading, symmetric STBCs (S-STBCs) cause isometric data sequences, which lead to a detection error floor. Motivated by the minimization of the probability of error, two asymmetric STBCs are introduced to be used with these S-STBCs to mitigate isometry. To further improve detection performance, a self-matching STBC (SM-STBC), which mitigates isometry using asymmetry, improves estimation performance using training, and improves detection performance by adapting its code properties, is introduced. This SM-STBC generalizes a limited version that was previously proposed. A comprehensive analysis, which is supported by some simulation studies, indicates that the proposed framework of transceiver and STBC designs offers excellent detection performance.