On the complexity distribution of sphere decoding
AuthorsDominik Seethaler, Joakim Jaldén, Christoph Studer, and Helmut Bölcskei
ReferenceIEEE Transactions on Information Theory, Vol. 57, No. 9, pp. 5754-5768, Sept. 2011
AbstractWe analyze the (computational) complexity distribution of sphere decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is fully determined by the inverse volume of the fundamental regions of the underlying lattice. Particularizing this result to NxM, N>=M, i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Pareto-type with tail exponent given by N-M+1. A more refined analysis reveals that the corresponding average complexity of SD is infinite for N = M and finite for N > M. Finally, for i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we analyze SD preprocessing techniques based on lattice-reduction (such as the LLL algorithm or layer-sorting according to the V-BLAST algorithm) and regularization. In particular, we show that lattice reduction does not improve the tail exponent of the complexity distribution while regularization results in a SD complexity distribution with tails that decrease faster than polynomial.
KeywordsClosest lattice point problem, complexity distribution, MIMO wireless, random lattices, sphere decoding
Download this document:
Copyright Notice: © 2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.