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Lattice Structures of Precoders Maximizing the Minimum Distance in Linear Channels

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Author

Summary, in English

This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders.

Publishing year

2015

Language

English

Pages

908-916

Publication/Series

IEEE Transactions on Information Theory

Volume

61

Issue

2

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • MIMO
  • modulation
  • lattices

Status

Published

ISBN/ISSN/Other

  • ISSN: 0018-9448