Previous studies have demonstrated that many existing communication systems can be formulated within a unified multirate filterbank transceiver model. A redundant block transmission system implemented via this unified multirate filterbank transceiver model is usually known as a multiple-input-multiple-output (MIMO) system in literature. This dissertation devises an optimum linear block-based precoder and the corresponding equalizer for MIMO systems over perfect reconstruction (PR) channels by exploiting the proposed oblique projection framework. Particularly, two main criteria of interest in a digital communication link with limited transmission power are investigated, namely, average bit error rate (BER) minimization and mutual information rate maximization. The study framework is developed as follows. For a block-based precoder, a received signal model is formulated for the two redundancy schemes, viz., trailing-zeros (TZ) and cyclic-prefix (CP). By exploiting the property of oblique projection, a cascaded equalizer for block transmission systems (i.e., MIMO systems) is proposed and implemented with a scheme, in which the inter-block interference (IBI) is completely eliminated by the oblique projection and followed by a matrix degree of freedom for inter-symbol interference (ISI) equalization. With the available channel state information at the transmitter side, the matrix for ISI equalization of the cascaded equalizer is utilized to design an optimum linear block-based precoder, such that the BER is minimized (or the mutual information rate is maximized), subject to the ISI-free and the transmission power constraints. Accordingly, the cascaded equalizer with the ISI-free constraint yields a cascaded ZF equalizer. Theoretical derivations and simulation results confirm that the proposed framework not only retains identical BER and information rate performances to previous works for cases with sufficient redundancy, but also allows their results to be extended to the cases of insufficient redundancy.