Comparison of Lattice Search Techniques for Nonlinear Precoding


Georgios Psaltopoulos, Michael Joham, and Wolfgang Utschick


International ITG - IEEE Workshop on Smart Antennas, WSA 2006, Ulm, Germany, Mar. 2006.

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We introduce a new theoretical framework which comprises linear precoding, Tomlinson-Harashima precoding (THP), and vector precoding (VP). Whereas linear precoding generates the transmit signal by linearly transforming the data signal, THP and VP linearly transform the superposition of the data signal and a signal obtained by a search in a lattice. We observe that THP is constrained VP, i.e., the search in the lattice is constrained. Moreover, we are able to develop a new precoding scheme, scaled vector precoding (SVP), whose diversity order lies between the diversity orders of THP and VP. By including lattice reduction in SVP, we end up with a generalization of Babai’s nearest-plane algorithm. Our simulations reveal that lattice reduction and also the new SVP are advantageous for the zero-forcing variants of nonlinear precoding. However, the improvement of THP based on the minimum mean square error criterion by lattice reduction and/or SVP is modest.


MIMO, MMSE, ZF, THP, VP, LLL, Tomlinson-Harashima Precoding, Vector Precoding, Lattice Reduction, nearest-plane, rounding-off, Babai, flat fading.

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