### Abstract

In this paper, we analyze the average sum rate of downlink multi-antenna systems with zero-forcing beamforming (ZFBF). In practical implementations, each antenna is equipped with its own power amplifier and is limited individually by linearity of the amplifier. Thus, this paper adopts a more realistic per-antenna power constraint instead of conventional sum-power constraint on transmit antennas. To this end, we first show that a distribution of the received signal-to-noise ratio (SNR) of the ZFBF scheme with per-antenna power constraint and equal-rate metric can be approximated as a minimum of chi-square random variables. Based on this result, we present an accurate formula of the average sum rate in a closed form. Furthermore, employing extreme value theory, an expression of the asymptotic average sum rate with large numbers of transmit antennas and users is derived from the limiting distribution of the received SNR. Simulation results verify the validity of our analysis even with not so large numbers of transmit antennas and users.

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

Article number | 6377481 |

Pages (from-to) | 228-236 |

Number of pages | 9 |

Journal | IEEE Transactions on Wireless Communications |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

### Fingerprint

### Keywords

- Broadcast channel
- per-antenna power constraints
- zero-forcing precoding

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Science Applications
- Applied Mathematics

### Cite this

*IEEE Transactions on Wireless Communications*,

*12*(1), 228-236. [6377481]. https://doi.org/10.1109/TWC.2012.120312.120332

**Zero-forcing beamforming in multiuser MISO downlink systems under per-antenna power constraint and equal-rate metric.** / Lee, Sang Rim; Kim, Jin Sung; Moon, Sung Hyun; Kong, Han Bae; Lee, Inkyu.

Research output: Contribution to journal › Article

*IEEE Transactions on Wireless Communications*, vol. 12, no. 1, 6377481, pp. 228-236. https://doi.org/10.1109/TWC.2012.120312.120332

}

TY - JOUR

T1 - Zero-forcing beamforming in multiuser MISO downlink systems under per-antenna power constraint and equal-rate metric

AU - Lee, Sang Rim

AU - Kim, Jin Sung

AU - Moon, Sung Hyun

AU - Kong, Han Bae

AU - Lee, Inkyu

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper, we analyze the average sum rate of downlink multi-antenna systems with zero-forcing beamforming (ZFBF). In practical implementations, each antenna is equipped with its own power amplifier and is limited individually by linearity of the amplifier. Thus, this paper adopts a more realistic per-antenna power constraint instead of conventional sum-power constraint on transmit antennas. To this end, we first show that a distribution of the received signal-to-noise ratio (SNR) of the ZFBF scheme with per-antenna power constraint and equal-rate metric can be approximated as a minimum of chi-square random variables. Based on this result, we present an accurate formula of the average sum rate in a closed form. Furthermore, employing extreme value theory, an expression of the asymptotic average sum rate with large numbers of transmit antennas and users is derived from the limiting distribution of the received SNR. Simulation results verify the validity of our analysis even with not so large numbers of transmit antennas and users.

AB - In this paper, we analyze the average sum rate of downlink multi-antenna systems with zero-forcing beamforming (ZFBF). In practical implementations, each antenna is equipped with its own power amplifier and is limited individually by linearity of the amplifier. Thus, this paper adopts a more realistic per-antenna power constraint instead of conventional sum-power constraint on transmit antennas. To this end, we first show that a distribution of the received signal-to-noise ratio (SNR) of the ZFBF scheme with per-antenna power constraint and equal-rate metric can be approximated as a minimum of chi-square random variables. Based on this result, we present an accurate formula of the average sum rate in a closed form. Furthermore, employing extreme value theory, an expression of the asymptotic average sum rate with large numbers of transmit antennas and users is derived from the limiting distribution of the received SNR. Simulation results verify the validity of our analysis even with not so large numbers of transmit antennas and users.

KW - Broadcast channel

KW - per-antenna power constraints

KW - zero-forcing precoding

UR - http://www.scopus.com/inward/record.url?scp=84873082961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873082961&partnerID=8YFLogxK

U2 - 10.1109/TWC.2012.120312.120332

DO - 10.1109/TWC.2012.120312.120332

M3 - Article

VL - 12

SP - 228

EP - 236

JO - IEEE Transactions on Wireless Communications

JF - IEEE Transactions on Wireless Communications

SN - 1536-1276

IS - 1

M1 - 6377481

ER -