### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 453-456 |

Number of pages | 4 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Volume | 4 |

State | Published - Jan 1 1998 |

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### Cite this

**Three-dimensional equalization for the 3-D QAM system with strength reduction.** / Shalash, Ahmed F.; Parhi, Keshab K.

Research output: Contribution to journal › Article

*Proceedings - IEEE International Symposium on Circuits and Systems*, vol. 4, pp. 453-456.

}

TY - JOUR

T1 - Three-dimensional equalization for the 3-D QAM system with strength reduction

AU - Shalash, Ahmed F.

AU - Parhi, Keshab K

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031622520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031622520&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 453

EP - 456

JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

SN - 0271-4310

ER -