Multidimensional Signal Constellations for Voiceband Data Transmission

Abstract

A significant improvement in noise immunity can be achieved for digital transmission over band-limited channels by the use of multidimensional signal constellations. Conventional 16-point QAM signaling, such as that used in many digital transmission systems, is a two-dimensional modulation scheme where in each signaling interval a group of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> bits is used to determine the amplitudes of the in-phase and quadrature dimension or coordinate, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N/2</tex> bits are conveyed per dimension. In a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2M</tex> -dimensional QAM system, a group of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MN</tex> bits is used to determine the in-phase and quadrature ampllitudes for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> consecutive, symbol intervals where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N/2</tex> bits are still conveyed by each dimension. It is the purpose of this paper to describe the basic theory and implementation for a particular 2 bits/dimension four-dimensional (two-symbol interval) encoding which readily lends itself to simple encoding and decoding. For this encoding, theory predicts a 1.2 dB gain in noise margin over conventional 16-point (two-dimensional) QAM signaling. Experimental results agreed with the theoretical predictions, and have demonstrated an order of magnitude reduction in block error rate. Extension to eight-dimensional signaling offers a theoretical gain of 2.4 dB over conventional 16-point QAM.