Block-Based Transceivers With Minimum Redundancy

The standard design of multicarrier and single-carrier employing frequency-domain equalization transceivers requires, at least, L elements of redundancy, where L stands for the channel order. The redundancy eliminates the inherent interblock interference (IBI), which is part of all block-based transceivers, and turns the channel matrix circulant. The spectral decomposition of the circulant channel matrix through the discrete Fourier transform (DFT) allows the use of superfast algorithms for both the design of zero-forcing (ZF) and minimum mean squared error (MMSE) equalizers, and the equalization of received signals. However, it is well known that the minimum redundancy for IBI-free designs of block-based transceivers is [L/2] . This paper proposes practical ZF and MMSE solutions by using DFT, inverse DFT, and diagonal matrices. In particular, it is shown that, for some particular mild constraints on the channel model, the new designs may have similar bit error rate performance when compared to the standard ones, while keeping the same asymptotic complexity for the equalization process, that is, O(n log₂ n) numerical operations. The key feature of the proposed transceivers is their higher throughput.