Memoryless block transceivers with minimum redundancy based on Hartley transforms

This paper proposes real linear transceivers employing minimum redundancy, unlike the standard block transceivers that require, at least, L elements of redundancy, where L   is the channel order. In all block-based systems, there is an inherent interblock interference (IBI) that can be eliminated by inserting redundancy. For transceivers based on the discrete Fourier transform (DFT), the redundancy induces a circulant channel matrix, allowing superfast implementations. Although it has been known for some time that the minimum redundancy for IBI-free designs of block transceivers is ⌈L/2⌉⌈L/2⌉, only recently practical DFT-based solutions using minimum redundancy were proposed. However, the extension of these solutions to real transforms, such as the discrete Hartley transform (DHT), is not straightforward. The only known solution imposes a symmetry on the channel model that is unlikely to be met in practice. This paper proposes transceivers with practical zero-forcing (ZF) and minimum mean-squared error (MMSE) receivers using DHT, diagonal, and antidiagonal matrices. The resulting systems are asymptotically as simple as orthogonal frequency-division multiplex (OFDM) and single-carrier with frequency-domain (SC-FD) equalization transceivers. In addition, they do not enforce constraints on the channel model. Several computer simulations indicate the higher throughput of the proposals as compared to the standard solutions.