### Abstract

In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT). With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

Original language | English |
---|---|

Pages (from-to) | 222-230 |

Number of pages | 9 |

Journal | Journal of Communications and Networks |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Networks and Communications

### Cite this

*Journal of Communications and Networks*,

*12*(3), 222-230. https://doi.org/10.1109/JCN.2010.6388450

}

*Journal of Communications and Networks*, vol. 12, no. 3, pp. 222-230. https://doi.org/10.1109/JCN.2010.6388450

**Sum rate approximation of zero-forcing beamforming with semi-orthogonal user selection.** / Yang, Janghoon; Jang, Seunghun; Kim, Dong Ku.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sum rate approximation of zero-forcing beamforming with semi-orthogonal user selection

AU - Yang, Janghoon

AU - Jang, Seunghun

AU - Kim, Dong Ku

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT). With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

AB - In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT). With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

UR - http://www.scopus.com/inward/record.url?scp=77954478738&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954478738&partnerID=8YFLogxK

U2 - 10.1109/JCN.2010.6388450

DO - 10.1109/JCN.2010.6388450

M3 - Article

AN - SCOPUS:77954478738

VL - 12

SP - 222

EP - 230

JO - Journal of Communications and Networks

JF - Journal of Communications and Networks

SN - 1229-2370

IS - 3

ER -