### Abstract

Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power, largely induced by various space-time processing techniques, make it highly challenging to quantitatively characterize the performance of multi-antenna networks. In this paper, using tools from stochastic geometry, a unified framework is developed for the analysis of such networks. The major results are two innovative representations of the coverage probability, which make the analysis of multi-antenna networks almost as tractable as the single-antenna case. One is expressed as an ℓ1-induced norm of a Toeplitz matrix, and the other is given in a finite sum form. With a compact representation, the former incorporates many existing analytical results on single- and multi-antenna networks as special cases, and leads to tractable expressions for evaluating the coverage probability in both ad hoc and cellular networks. While the latter is more complicated for numerical evaluation, it helps analytically gain key design insights. In particular, it helps prove that the coverage probability of ad hoc networks is a monotonically decreasing convex function of the transmitter density and that there exists a peak value of the coverage improvement when increasing the number of transmit antennas. On the other hand, in multi-antenna cellular networks, it is shown that the coverage probability is independent of the transmitter density and that the outage probability decreases exponentially as the number of transmit antennas increases.

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

Journal | IEEE Transactions on Wireless Communications |

DOIs | |

Publication status | Accepted/In press - 1 Jan 2018 |

Externally published | Yes |

### Fingerprint

### Keywords

- Ad hoc networks
- Analytical models
- Cellular networks
- Coverage probability
- Fading channels
- Interference
- MIMO
- performance analysis
- stochastic geometry
- Transmitters
- Wireless networks
- wireless networks

### ASJC Scopus subject areas

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

### Cite this

*IEEE Transactions on Wireless Communications*. https://doi.org/10.1109/TWC.2018.2873301

**A Unified Framework for the Tractable Analysis of Multi-Antenna Wireless Networks.** / Yu, Xianghao; Li, Chang; Zhang, Jun; Haenggi, Martin; Letaief, Khaled.

Research output: Contribution to journal › Article

*IEEE Transactions on Wireless Communications*. https://doi.org/10.1109/TWC.2018.2873301

}

TY - JOUR

T1 - A Unified Framework for the Tractable Analysis of Multi-Antenna Wireless Networks

AU - Yu, Xianghao

AU - Li, Chang

AU - Zhang, Jun

AU - Haenggi, Martin

AU - Letaief, Khaled

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power, largely induced by various space-time processing techniques, make it highly challenging to quantitatively characterize the performance of multi-antenna networks. In this paper, using tools from stochastic geometry, a unified framework is developed for the analysis of such networks. The major results are two innovative representations of the coverage probability, which make the analysis of multi-antenna networks almost as tractable as the single-antenna case. One is expressed as an ℓ1-induced norm of a Toeplitz matrix, and the other is given in a finite sum form. With a compact representation, the former incorporates many existing analytical results on single- and multi-antenna networks as special cases, and leads to tractable expressions for evaluating the coverage probability in both ad hoc and cellular networks. While the latter is more complicated for numerical evaluation, it helps analytically gain key design insights. In particular, it helps prove that the coverage probability of ad hoc networks is a monotonically decreasing convex function of the transmitter density and that there exists a peak value of the coverage improvement when increasing the number of transmit antennas. On the other hand, in multi-antenna cellular networks, it is shown that the coverage probability is independent of the transmitter density and that the outage probability decreases exponentially as the number of transmit antennas increases.

AB - Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power, largely induced by various space-time processing techniques, make it highly challenging to quantitatively characterize the performance of multi-antenna networks. In this paper, using tools from stochastic geometry, a unified framework is developed for the analysis of such networks. The major results are two innovative representations of the coverage probability, which make the analysis of multi-antenna networks almost as tractable as the single-antenna case. One is expressed as an ℓ1-induced norm of a Toeplitz matrix, and the other is given in a finite sum form. With a compact representation, the former incorporates many existing analytical results on single- and multi-antenna networks as special cases, and leads to tractable expressions for evaluating the coverage probability in both ad hoc and cellular networks. While the latter is more complicated for numerical evaluation, it helps analytically gain key design insights. In particular, it helps prove that the coverage probability of ad hoc networks is a monotonically decreasing convex function of the transmitter density and that there exists a peak value of the coverage improvement when increasing the number of transmit antennas. On the other hand, in multi-antenna cellular networks, it is shown that the coverage probability is independent of the transmitter density and that the outage probability decreases exponentially as the number of transmit antennas increases.

KW - Ad hoc networks

KW - Analytical models

KW - Cellular networks

KW - Coverage probability

KW - Fading channels

KW - Interference

KW - MIMO

KW - performance analysis

KW - stochastic geometry

KW - Transmitters

KW - Wireless networks

KW - wireless networks

UR - http://www.scopus.com/inward/record.url?scp=85055020777&partnerID=8YFLogxK

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U2 - 10.1109/TWC.2018.2873301

DO - 10.1109/TWC.2018.2873301

M3 - Article

JO - IEEE Transactions on Wireless Communications

JF - IEEE Transactions on Wireless Communications

SN - 1536-1276

ER -