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© Robert W. Heath Jr. (2015)

Analysis of massive MIMO networks using stochastic geometry

Tianyang Bai and Robert W. Heath Jr.

Wireless Networking and Communications Group

Department of Electrical and Computer Engineering

The University of Texas at Austin

http://www.profheath.org

Funded by the NSF under Grant No. NSF-CCF-1218338 and a gift from Huawei

© Robert W. Heath Jr. (2015)

2

Cellular communication

Distributions of base stations in a major UK city*

(1 mile by 0.5 mile area)

* Data taken from sitefinder.ofcom.org.uk

Base station

Illustration of a cell in cellular networks

User

Uplink Downlink

To network

Irregular base station locations motivate the applications of stochastic geometry

© Robert W. Heath Jr. (2015)

More spectrum Millimeter wave spectrum

More base stations Network densification

More spectrum efficiency Multiple antennas (MIMO)

3

5G cellular networks – achieving 1000x better

This talk

Other work

© Robert W. Heath Jr. (2015)

7

Massive MIMO concept

* T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov. 2011

**X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, “Massive MIMO in real propagation environments,” To appear in IEEE Trans. Wireless Commun., 2015

Potential for better area spectral efficiency with massive MIMO

> 64 antennas 1 to 8 antennas

1 or 2 uses sharing same resources 10 to 30 users sharing same resources

Conventional cell Massive MIMO cell

MIMO (multiple-input multiple-output) a type of wireless

system with multiple antennas at transmitter and receiver

© Robert W. Heath Jr. (2015)

Massive MIMO: multi-user MIMO with lots of base station antennas*

Allows more users per cell simultaneously served

Analyses show large gains in sum cell rate using massive MIMO

Real measurements w/ prototyping confirm theory**

7

Three-stage TDD mode (1): uplink training

Users:

Send pilots to the base stations

* T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov. 2011

Base stations:

Estimate channels based on

training

Uplink training

Pilot contamination

Channel estimation polluted by pilot contamination

Assume perfect synchronization Assume full pilot reuse

© Robert W. Heath Jr. (2015)

Massive MIMO: multi-user MIMO with lots of base station antennas*

Allows more users per cell simultaneously served

Analyses show large gains in sum cell rate using massive MIMO

Real measurements w/ prototyping confirm theory**

7

Three-stage TDD mode (2): uplink data

Users:

Send data to base stations

* T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov. 2011

Base stations:

Matched filtering combining

based on

channel estimates

Uplink data

Simple matched filter receive combining based on channel estimate

© Robert W. Heath Jr. (2015)

Massive MIMO: multi-user MIMO with lots of base station antennas*

Allows more users per cell simultaneously served

Analyses show large gains in sum cell rate using massive MIMO

Real measurements w/ prototyping confirm theory**

7

Three-stage TDD mode (3): downlink data

Users:

Decode received signals

Base stations:

Beamforming based on channel

estimates

Downlink data

Simple matched filter transmit beamforming based on channel

estimates

© Robert W. Heath Jr. (2015)

Fading and noise become minor with large arrays [Ignore noise in analysis]

TDD (time-division multiplexing) avoids downlink training overhead [Include pilot contamination]

Simple signal processing becomes near-optimal, with large arrays [Assume simple beamforming]

Large antenna arrays serve more users to increase cell throughput [Compare sum rate w/ small cells]

Advantages of massive MIMO & implications

8

Out-of-cell interference reduced due to asymptotic orthogonality of channels [Show SIR convergence]

© Robert W. Heath Jr. (2015)

Modeling cellular system performance

using stochastic geometry

© Robert W. Heath Jr. (2015)

Stochastic geometry in cellular systems

10

Desired signal

Serving BS

Typical user Interference link

Stochastic geometry allows for simple characterizations of SINR distributions

Desired signal power

Interference from PPP interferers

Modeling base stations locations as Poisson point process

T. X Brown, ``Practical Cellular Performance Bounds via Shotgun Cellular System,'' IEEE JSAC, Nov. 2000.

M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti, “ Stochastic geometry and random graph for the analysis and design of wireless networks”,

IEEEJSAC 09

J. G. Andrews, F. Baccelli, and R. K. Ganti, “ A tractable approach to coverage and rate in cellular networks”, IEEE TCOM 2011.

H. S. Dhillon, R. K. Ganti, F. Baccelli, and J. G. Andrews, “ Modeling and analysis of K-tier downlink heterogeneous cellular networks”, IEEE JSAC, 2012

Thermal noise

(often ignored)

& many more…

© Robert W. Heath Jr. (2015)

11

Who* cares about antennas anyway?

Diversity

Changes fading distribution

Multiplexing

Multivariate performance measures

Interference cancelation

Changes received interference

Beamforming

Changes caused interference

* why should non-engineers care at all about antennas

© Robert W. Heath Jr. (2015)

Challenges of analyzing massive MIMO

13

Does not directly extend to massive MIMO

X

Single user per cell Multiple user per cell

Single base station antenna Massive base station antennas

Rayleigh fading Correlated fading MIMO channel

No channel estimation Pilot contamination

Mainly focus on downlink Analyze both uplink and downlink

© Robert W. Heath Jr. (2015)

Related work on massive MIMO w/ SG

Asymptotic analysis using stochastic geometry [1]

Derived distribution for asymptotic SIR with infinite BS antennas

Considered IID fading channel, not include correlations

Assumed BSs distributed as PPP marked with fixed-circles as cells

Nearby cells in the model may heavily overlap (not allowed in reality)

Concluded same SIR distributions in UL/DL (not matched to simulations)

Scaling law between user and BS antennas [2]

BS antennas linearly scale with users to maintain mean interference

The distribution of SIR is a more relevant performance metric

14

Need advanced system model for massive MIMO analysis

[1] P. Madhusudhanan, X. Li, Y. Liu, and T. Brown, “Stochastic geometric modeling and interference analysis for massive MIMO systems,” Proc.of WiOpt, 2013

[2] N. Liang, W. Zhang, and C. Shen, “An uplink interference analysis for massive MIMO systems with MRC and ZF receivers,” Proc. of WCNC, 2015.

© Robert W. Heath Jr. (2015)

Massive MIMO system model

© Robert W. Heath Jr. (2015)

16

Proposed system model

Each BS has M antennas serving K users

Base stations distributed as a PPP

: n-th base station : k-th scheduled user in n-th cell

Scheduled user

Unscheduled user

Need to characterize scheduled users’ distributions

Users uniformly distributed w/ high density

(each BS has at least K associated users)

© Robert W. Heath Jr. (2015)

Scheduled users’ distribution

Locations of scheduled users are

correlated and do not form a PPP [1,2]

Correlations prevent the exact analysis

of UL SIR distributions

17 [1] H. El Sawy and E. Hossain, “On stochastic geometry modeling of cellular uplink transmission with truncated channel inversion power control” IEEE TCOM, 2014

[2] S. Singh, X. Zhang, and J. Andrews, “ Joint rate and SINR coverage analysis for decoupled uplink-downlink biased cell association in HetNet,” Arxiv, 2014

1st scheduled user

2nd scheduled user

Base station

Locations of scheduled users are

correlated and do not form a PPP

Non-PPP users’ distributions make exact analysis difficult

Presence of a “red” user in one cell

prevents those of the other red

© Robert