Minimum BER Block-Based Precoder Design for Zero-Forcing Equalization: An Oblique Projection Framework

This work devises a minimum bit error rate (BER) block-based precoder used in block transmission systems with the proposed cascaded zero-forcing (ZF) equalizer. 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 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 block-based precoder, such that the BER is minimized, 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 performance to previous works for cases with sufficient redundancy, but also allows their results to be extended to the cases of insufficient redundancy.