Three-dimensional equalization for the 3-D QAM system with strength reduction

Recently, the 3-D CAP system was introduced as a modification to the conventional 2-D CAP. This paper makes two contributions in the context of the 3-D CAP system. First, the QAM equivalent for the three-dimensional case is introduced by extending the 2-D complex notation into a 3-D vector notation. The definition is a modification of the well known quaternions. Second, the 3-D QAM filtering is redefined using algorithmic strength reduction to reduce the overall complexity by about one third with marginal degradation. The 3-D QAM system using 9 filters performs almost exactly as the 3-D CAP. Further complexity reduction is achieved by exploiting filtering reduction at the expense of only one dB of receiver SNR degradation.