Comparing Massive MIMO at Sub-6 GHz and Millimeter Waveusers.ece.utexas.edu/~rheath/presentations/2015/...signal outage important no yes cell size macro or micro pico penetration loss

(c) 2015 Robert W Heath Jr. WHAT STARTS HERE CHANGES THE WORLD

Robert W. Heath Jr., Ph.D., P.E.

Wireless Networking and Communications Group Department of Electrical and Computer Engineering

The University of Texas at Austin Join work with Tianyang Bai

www.profheath.org

Comparing Massive MIMO at Sub-6 GHz and Millimeter Wave

This material is based upon work supported in part by the National Science Foundation under Grant No. NSF-CCF-1218338 and NSF-CCF-1319556, as well was a gift from Huawei Technologies.

http://www.profheath.org

WHAT STARTS HERE CHANGES THE WORLD(c) 2015 Robert W Heath Jr.

Why massive MIMO at sub-6 GHz frequencies?

(c) 2015 Robert W. Heath Jr.

3

64 antennas or more @ BS Fading and noise become minor

with large arraysTDD avoids significant feedback overheads

Simple signal processing becomes near-optimal,with large arrays

Out-of-cell interference reduceddue to asymptotic orthogonality

of channels

Large antenna arrays serving tens of usersto increase cell throughput

Why Massive MIMO at sub-6 GHz?

Large antenna arrays increase cell throughput at sub-6 GHz


Why massive MIMO at mmWave frequencies?


5

256 antennas or more @ BS

Exploit channel sparsity to reduce training overhead

Out-of-cell interference reduceddue to directional transmission

and blockage

Increase cell throughput with large bandwidth at mmWave

Why massive MIMO at mmWave?

Large numbers of antennas are critical for mmWave

MmWave requires directivity gain from large arraysto overcome high path loss and noise


Comparingsub-6 GHz and mmWave massive MIMO

in terms of coverage and capacity


7

[And11] J. G. Andrews, F. Baccelli, and R. K. Ganti, "A Tractable Approach to Coverage and Rate in Cellular Networks", IEEE Transactions on Communications, November 2011.[Hae13] M. Haenggi, Stochastic Geometry for Wireless Networks, Cambridge Press 2013.[Mar10] T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov., 2010.[Bai15] T. Bai and R. W. Heath, Jr., “Massive MIMO: millimeter wave or lower frequencies?”, preprint, April 2015.

performance analyzed for a typical user

large

infinite

small

Approach for comparisonLarge network with randomly deployed BSs

Use stochastic geometry to analyze SINR and rate distributions

Poisson point process to model BS locations

Use certain soft-core point process for scheduled users’ locations

Consider a large number of antennas at BSsTDD based massive MIMO w/ matched filtering

Differentiating features incorporated into spatial correlation models

Infinity of base stations and antennas creates challenges

scheduled users

base station


8

sub-6 GHz massive mmWave massivebeamforming digital analog or hybrid

number of simul. users more than 10 up to 4network deployment low density higher density or hotspot

signal outage important no yescell size macro or micro pico

penetration loss some possibly highblockage sensitivity low highsmall-scale fading Rayleigh Nakagamin or non-fadingspatial correlation less morechannel sparsity less more

orientation sensitivity low highbackhaul wired or out-of-band inband

Some differentiating features


9

sub-6 GHz mmWave

bandwidth ~100 MHz 500 GHz @28 GHz2 GHz @E-Band

small-scale fading correlated with high rank correlated with low rank, varies with LOS or NLOS

large-scale fading distant dependent pathloss distant dependent with random blockage model and total outage

network deployment low BS density high BS density

UE array configuration single antenna directional antenna with gain

# users served simultaneously

higher (10 or more) few (limited by beamforming)

Differences incorporated in the analysis

[Bai15] T. Bai and R. W. Heath, Jr., “Massive MIMO: millimeter wave or lower frequencies?”, preprint, April 2015.


SINR and rate analytical model


Sub-6 GHz massive MIMO model

11

M antennas at BS

Single antenna at MS

TDD massive MIMO with perfect synchronization and full reuse of pilotsChannel estimation polluted by pilot contaminations

Maximum ratio combining in UL and match-filtering beamforming in DL

Correlated small-scale fading channel modelApply general assumptions for covariance matrices of small-scale fading

Works for IID fading, ULA with continuous angle spread, exponential correlation, [Hoy13]…

Bounded log-distance model (w/ single exponent) for large-scale path loss[Mar10] T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov., 2010.[Hoy13] J. Hoydis et al, “Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?” IEEE JSAC, Feb, 2013


Interfering BS

Associated BS

Buildings

Typical ReceiverNLOS BS

LOS BS

MmWave massive MIMO model

Sectored model for UE beamforming Blockage+outage model for LOS/ NLOS

LOS/NLOS determined by LOS prob. function

UEs receive no signal from BSs outside outage ball

Apply deterministic vector for LOS channel vectors

NLOS channels have same parameters as sub-6GHz

12

Directional Antenna at MS

Sectored beamforming pattern model @ UE

Main lobe beamwidth

Main lobe array gainBack lobe gain

25

thinned Poisson point process with intensity function �u(x) = �b1(L(|X0 � x|) > �

x

), where

L(|X0 � x|) represents the path loss from x to X0, �x

is an IID random variable with the same

distribution as �

(1)00 , and the indicator function 1(L(|X0 � x|) > �

x

) is intended to ensure that

any other cell user has smaller path loss to its own base station than the tagged base station.

Further, the path loss in the tagged link �

(k)00 is assumed to be independent from the distribution

of the other users in N

(k)u . In addition, for k 6= k

0, the processes N

(k)u and N

(k0)u are assumed to

be independent.

qθ Q

Fig. 1. Sectored antenna model to simplify the beamforming pattern at the mobile station.

Mmwave handsets will use antenna arrays to perform directional beamforming. To simplify the

analysis, we make the following assumption on the beamforming pattern at the mobile stations.

Assumption 11 (MS beamforming): The antenna array at the mobile station is simplified as a

single directional antenna, and the actual antenna pattern is further approximated by the sectored

antenna pattern. As shown in Fig. 1, in the sectored antenna model, the directivity gain within

the main lobe ✓ is assumed to be a constant Q, while all angles outside the main lobe have the

constant side lobe gain q. The sectored antenna model has already been used in the analysis of

mmWave cellular and ad hoc networks [19], [64]. Furthermore, we assume the directions of the

mobile station antennas are adjusted to maximize the desired link signals once the base station

association is completed, and we ignore the alignment errors of users’ beamforming, as the

mobile station are often assumed to have wider main lobes. In the analysis, besides the typical

user, the antenna directions of all the other mobile stations are assumed to be independently and

uniformly distributed in space. Let D(k)``

be the directivity gain of the mobile station Y

(k)`

0 to base

February 23, 2015 DRAFT

Outage ball

M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, “ Millimeter Wave Channel Modeling and Cellular Capacity Evaluation,” IEEE JSAC, 2014.T. Bai, R. Vaze, and R. W Heath, Jr., “ Analysis of Blockage Effects on Urban Cellular Networks”, IEEE Trans. Wireless, 2014.

BSs in outage


Summary of analytical results

13

Uplink and downlink SINR distributions are decoupled

SINR expression CCDF of SINR

Asymptoticsub-6GHz uplink

Asymptoticsub-6GHz downlink

Non Asymptotic sub-6 GHz uplink

AsymptoticmmWave uplink

AsymptoticmmWave downlink

2

¯h(k)`` = h(k)

`` +

X

`0 6=`

h(k)``0

SIRU =

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

SIRD =

|h(1)⇤00 f (1)0 |2

Pk 6=1 |h

(k)⇤00 f (k)0 |2 +

PKk=1

P`>0 |h

(1)⇤`0 f (k)` |2 + ⇢�1

D

f (k)` =

¯h(k)``

||¯h(k)`` ||

SIRUp.!

⇣�(1)00

⌘2

P6̀=0

⇣�(1)0`

⌘2 (1)

P(SIRU > T ) ⇡ 1� e

�(

↵�1T )

1/↵

(2)

lim

M!1SIRD

p.! �(1)200P

`6=0 �(1)2`0

(3)

min

✓1,

↵ sin(⇡/↵)

⇡T 1/↵

◆(4)

⇣�(1)00

⌘2

P` 6=0

⇣�(1)0`

⌘2 (5)

P(SIRU > T ) ⇡ 1� e

�(

↵�1T )

1/↵

(6)

�(1)200P

` 6=0 �(1)2`0

(7)

min

✓1,

↵ sin(⇡/↵)

⇡T 1/↵

◆(8)

2

¯h(k)`` = h(k)

`` +

X

`0 6=`

h(k)``0

SIRU =

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

SIRD =

|h(1)⇤00 f (1)0 |2

Pk 6=1 |h

(k)⇤00 f (k)0 |2 +

PKk=1

P`>0 |h

(1)⇤`0 f (k)` |2 + ⇢�1

D

f (k)` =

¯h(k)``

||¯h(k)`` ||

SIRUp.!

⇣�(1)00

⌘2

P`6=0

⇣�(1)0`

⌘2 (1)

P(SIRU > T ) ⇡ 1� e

�(

↵�1T )

1/↵

(2)

lim

M!1SIRD

p.! �(1)200P

`6=0 �(1)2`0

(3)

min

✓1,

↵ sin(⇡/↵)

⇡T 1/↵

◆(4)

⇣�(1)00

⌘2

P` 6=0

⇣�(1)0`

⌘2 (5)

P(SIRU > T ) ⇡ 1� e

�(

↵�1T )

1/↵

(6)

�(1)200P

` 6=0 �(1)2`0

(7)

min

✓1,

↵ sin(⇡/↵)

⇡T 1/↵

◆(8)

3

min

✓1,

↵ sin(⇡/↵)

⇡T 1/↵

◆(8)

�(1)200 /a(1)0P

6̀=0 �(1)2`0 /a(1)`

(9)

a(k)` =

P`0 �

(k)``0 .

2

¯h(k)`` = h(k)

`` +

X

`0 6=`

h(k)``0

SIRU =

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

SIRD =

|h(1)⇤00 f (1)0 |2

Pk 6=1 |h

(k)⇤00 f (k)0 |2 +

PKk=1

P`>0 |h

(1)⇤`0 f (k)` |2 + ⇢�1

D

f (k)` =

¯h(k)``

||¯h(k)`` ||

SIRUp.!

⇣�(1)00

⌘2

P6̀=0

⇣�(1)0`

⌘2 (1)

P(SIRU > T ) ⇡ 1� e

�(

↵�1T )

1/↵

(2)

lim

M!1SIRD

p.! �(1)200P

`6=0 �(1)2`0

(3)

min

✓1,

↵ sin(⇡/↵)

⇡T 1/↵

◆(4)

⇣�(1)00

⌘2

P` 6=0

⇣�(1)0`

⌘2 (5)

P(SIRU > T ) ⇡ 1� e

�(

↵�1T )

1/↵

(6)

�(1)200P

` 6=0 �(1)2`0

(7)

Asymptotic SIR limited by pilot contamination

4

P(SIR > T ) ⇡NX

n=1

✓N

n

◆(�1)

n+1

Z 1

0

e

�a1t↵�a2tdt (11)

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

Q2�(1)200 /a(1)0P

`6=0 D(1)2`0 �(1)2

`0 /a(1)`

SINRULp.! Q2�(1)2

00P`6=0 D

(1)20` �(1)2

0`

(12)

ANX

n=1

✓N

n

◆(�1)

n ⇥Z 1

0

e

�Wn(T,t)�Vn(T,t)�⌅(t)⌅(dt)

ANX

n=1

✓N

n

◆(�1)

n

Z 1

0

e

�Zn(T,t)�⌅(t)⌅(dt)

4

P(SIR > T ) ⇡NX

n=1

✓N

n

◆(�1)

n+1

Z 1

0

e

�a1t↵�a2tdt (11)

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

Q2�(1)200 /a(1)0P

`6=0 D(1)2`0 �(1)2

`0 /a(1)`

Q2�(1)200P

` 6=0 D(1)20` �(1)2

0`

(12)

ANX

n=1

✓N

n

◆(�1)

n ⇥Z 1

0

e


ANX

n=1

✓N

n

◆(�1)

n

Z 1

0

e

�Zn(T,t)�⌅(t)⌅(dt)

4

P(SIR > T ) ⇡NX

n=1

✓N

n

◆(�1)

n+1

Z 1

0

e

�a1t↵�a2tdt (11)

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

Q2�(1)200 /a(1)0P

`6=0 D(1)2`0 �(1)2

`0 /a(1)`

Q2�(1)200P

` 6=0 D(1)20` �(1)2

0`

(12)

ANX

n=1

✓N

n

◆(�1)

n ⇥Z 1

0

e


ANX

n=1

✓N

n

◆(�1)

n

Z 1

0

e

�Zn(T,t)�⌅(t)⌅(dt)

4

P(SIR > T ) ⇡NX

n=1

✓N

n

◆(�1)

n+1

Z 1

0

e

�a1t↵�a2tdt (11)

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

Q2�(1)200 /a(1)0P

`6=0 D(1)2`0 �(1)2

`0 /a(1)`

Q2�(1)200P

` 6=0 D(1)20` �(1)2

0`

(12)

ANX

n=1

✓N

n

◆(�1)

n ⇥Z 1

0

e


ANX

n=1

✓N

n

◆(�1)

n

Z 1

0

e

�Zn(T,t)�⌅(t)⌅(dt)

4

P(SIR > T ) ⇡NX

n=1

✓N

n

◆(�1)

n+1

Z 1

0

e

�a1t↵�a2tdt (11)

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

Q2�(1)200 /a(1)0P

`6=0 D(1)2`0 �(1)2

`0 /a(1)`

Q2�(1)200P

` 6=0 D(1)20` �(1)2

0`

(12)

ANX

n=1

✓N

n

◆(�1)

n ⇥Z 1

0

e


ANX

n=1

✓N

n

◆(�1)

n

Z 1

0

e

�Zn(T,t)�⌅(t)⌅(dt)

4

P(SIR > T ) ⇡NX

n=1

✓N

n

◆(�1)

n+1

Z 1

0

e

�a1t↵�a2tdt (11)

|¯h(1)⇤00 h(1)

00 |2Pk 6=1 |¯h

(1)⇤00 h(k)

00 |2 +PK

k=1

P`>0 |¯h

(1)⇤00 h(k)

0` |2 + |¯h(1)⇤00 nu|2

Q2�(1)200 /a(1)0P

`6=0 D(1)2`0 �(1)2

`0 /a(1)`

Q2�(1)200P

` 6=0 D(1)20` �(1)2

0`

(12)

ANX

n=1

✓N

n

◆(�1)

n ⇥Z 1

0

e


ANX

n=1

✓N

n

◆(�1)

n

Z 1

0

e

�Zn(T,t)�⌅(t)⌅(dt)

[Bai15] T. Bai and R. W. Heath, Jr., “Massive MIMO: millimeter wave or lower frequencies?”, preprint, April 2015.

Scaling law derived from non-asymptotic SINR

Tight bound for 200+ antennas in dense mmWave


Numerical results


−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

SIR threshold in dBC

CD

F of

SIR

(K,M,ρ)=(5,32,0)(K,M,ρ)=(10,131,0)(K,M,ρ)=(5,32,0.8)(K,M,ρ)=(10,152,0.8)

Sub-6 GHz SINR simulations

15

scaling exponent s = ↵

2

(1� ✏) + ✏. The expression of scalingexponent s is from a linear fit between the cases of ✏ = 0 and✏ = 1, where s =

↵

2

with ✏ = 0, and s = 1 with ✏ = 1.Though a conjecture, the proposed scaling law is shown to

be a good match through extensive simulations.Last, we can apply the SIR results to compute the achievable

rate. Let the average achievable spectrum efficiency at a typicaluser be ⇠ = log

2

(1 + min{SIR, Tmax

}) , where T

max

is aSINR distortion threshold determined by the limiting factorslike non-linearity in the radio frequency front-end. By [12],given the SIR distribution P(SIR > T ), the average achievablerate can be computed as E [⇠] = ln 2

RT

max

0

P(SINR>t)

1+t

dt.

IV. NUMERICAL RESULTS

In this section, we verify our analytical results with numer-ical simulations. As a general setup of Monte Carlo simula-tions, we assume the user density is 60 times the base stationdensity, and the base stations randomly pick K out of theassociated users to serve in a resource block. In the simulation,the average inter-site distance between base stations is 300meters.

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

SINR threshold in dB

CC

DF

of S

INR

M=102

M=103

M=104

M=∞

Fig. 1. Convergence to the asymptotic SIR. In the simulations, we assume↵ = 4, K = 10, and ✏ = 0. The asymptotic curve is drawn based onTheorem 1.

Asymptotic SIR distribution: In Fig. 1, we show theconvergence of uplink SIR to its asymptotic equivalence. Weassume IID fading channel in the simulations. Numericalresults show that more than 10

4 antennas are required toapproach the performance in the asymptotic regime.

Impact of fading correlations: We plot the SIR distribu-tions with IID fading and correlated fading in in Fig. 2. Notethat ⇢ = 0 represents IID fading, and ⇢ = 0.8 indicates highfading correlations. We study the scaling law by choosing thebaseline case as (K,M) = (4, 16); when doubling K from 4to 8, the required numbers of antennas M to maintain the SIRare computed by the proposed scaling law, which is verified bythe simulations. The impact of correlations can be summarizedas follows: (i) correlations in fading degrade the SIR coveragein massive MIMO networks, as fixing M and K, the CCDF

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SIR threshold in dB

CC

DF

of S

IR

Simu: (K,M,ρ)=(4,16,0.8)Analy: (K,M,ρ)=(4,16,0.8)Simu: (K,M,ρ)=(8,88,0.8)Simu: (K,M,ρ)=(4,16,0)Analy: (K,M,ρ)=(4,16,0)Simu: (K,M,ρ)=(8,67,0)

Fig. 2. SIR distributions with correlated fading. We assume ✏ = 0, and↵ = 4. The analytical curves are drawn using N = 5 terms, based onTheorem 2 and its corollary.

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SIR threhold in dB

CC

DF

of S

IR

(K,M,ε)=(5,32,0)(K,M,ε)=(10,131,0)(K,M,ε)=(5,32,0.5)(K,M,ε)=(10,92,0.5)(K,M,ε)=(5,32,1)(K,M,ε)=(10,64,1)

Fig. 3. SIR distributions with fractional channel inversion. We assume ↵ = 4,and IID fading channel. Note that ✏ = 1 is for full channel inversion, and✏ = 0 for no inversion.

of SIR decreases with ⇢; (ii) the correlations requires moreantennas to maintain the uplink SIR when increasing thenumber of scheduled users.

Impact of fractional channel inversion: We examinethe impact of fractional channel inversion in Fig. 4. In thesimulations, we choose (K,M) = (4, 16) as the baselinecurve, and use the scaling law in Conjecture 3 to computeM when K = 10. The proposed scaling law is shown to beaccurate in the simulations. Numerical results also show that alarge channel inversion fraction ✏ improves the SIR coveragein the low SIR regime at the expense of sacrificing the highSIR coverage. Intuitively speaking, channel inversion improvesthe cell edge user coverage by trading off the performance ofthe other users.

Verification with hexagonal grid model: We verify thescaling law derived from stochastic geometry with the hexag-onal grid model. In the simulations, we use a layout of 19

Asymptotic UL SINR result(IID fading, K=10, ) ↵ = 4

Require >10,000 antennas to approach asymptotic

@ sub-6 GHz

Non-asymptotic UL SIR result( , no power inversion,

19-cell hexagonal model)

Correlations in fading reduce SIR

↵ = 4

If doubling users>4x antennas needed to maintain UL SIR

K: Scheduled User per cellM: # of BS antennas : correlation coefficient of fading⇢

K↵/2 ⇠ (M + 2� � 1)

Scaling law to maintain UL SIR

mean square of the eigenvalues of fading covariance matrices


MmWave sensitivity to base station density

16

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


CC

DF

of S

INR

M=64M=256M=1024M=∞Analy:M=∞

(a) Downlink SINR in dense networks.

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7


CC

DF

of S

INR

M=200M=2000M=20000M=∞

(b) Downlink SINR in sparse networks.

Fig. 2. Downlink mmWave SINR distributions with different base stationdensities. We assume ISD = 100 m in (a), and ISD = 400 m in (b). Theanalytical curve in (a) is drawn based on Corollary 2.1.

TABLE ICOMPARISON OF ACHIEVABLE RATES

Carrier 2 GHz 28 GHz 28 GHzAvg. ISD (m) 500 100 400

Training overhead 20% 14% 14%Bandwidth (MHz) 100 500 500

Rate per user (Mbps) 52.8 1791.0 436.5Users per cell 14 4 4

Cell throughput (Mbps) 740.0 7164.0 1745.8

V. CONCLUSIONS

In this paper, we analyzed the asymptotic SINR distributionin mmWave massive MIMO networks by incorporated keyfeatures of mmWave systems, including the sensitivity toblockages and directional beamforming at mobile stations,into the analytical framework. We provided the asymptoticequivalences for both the uplink and downlink SINR in alarge-scale network with Poisson distributed base stations, andderived approximation expressions to compute their distribu-tions. The accuracy of the analytical expressions were verifiedby numerical simulations. The numerical results showed thatmmWave massive MIMO requires a high base station densityto achieve good SINR coverage. Moreover, the comparison

with massive MIMO systems at lower frequencies showed thepromising gain of mmWave massive MIMO over conventionalmassive MIMO in cell throughput. For future work, it wouldbe interesting to incorporate mmWave hardware constraints,such as hybrid beamforming and one-bit A/D converter [8].

ACKNOWLEDGEMENT

This paper is based upon work supported by the NationalScience Foundation under Grants No. 1218338 and 1319556.

REFERENCES

[1] E. Larsson, O. Edfors, F. Tufvesson, and T. Marzetta, “Massive MIMOfor next generation wireless systems,” IEEE Communications Magazine,vol. 52, no. 2, pp. 186–195, Feb. 2014.

[2] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, and P. Popovski,“Five disruptive technology directions for 5G,” IEEE CommunicationsMagazine, vol. 52, no. 2, pp. 74–80, February 2014.

[3] L. Lu, G. Li, A. Swindlehurst, A. Ashikhmin, and R. Zhang, “Anoverview of massive MIMO: Benefits and challenges,” IEEE J. Sel.Topics Signal Process., vol. 8, no. 5, pp. 742–758, Oct. 2014.

[4] T. Marzetta, “Noncooperative cellular wireless with unlimited numbersof base station antennas,” IEEE Trans. Wireless Commun., vol. 9, no. 11,pp. 3590–3600, Nov. 2010.

[5] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile broad-band systems,” IEEE Communications Magazine, vol. 49, no. 6, pp.101–107, June 2011.

[6] T. Rappaport et al., “Millimeter wave mobile communications for 5Gcellular: It will work!” IEEE Access, vol. 1, pp. 335–349, 2013.

[7] A. Swindlehurst, E. Ayanoglu, P. Heydari, and F. Capolino, “Millimeter-wave massive MIMO: the next wireless revolution?” CommunicationsMagazine, IEEE, vol. 52, no. 9, pp. 56–62, September 2014.

[8] A. Alkhateeb, J. Mo, N. Gonzalez-Prelcic, and R. Heath, “MIMOprecoding and combining solutions for millimeter-wave systems,” IEEECommunications Magazine, vol. 52, no. 12, pp. 122–131, Dec. 2014.

[9] J. Andrews et al., “A tractable approach to coverage and rate in cellularnetworks,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, 2011.

[10] P. Madhusudhanan, X. Li, Y. Liu, and T. Brown, “Stochastic geometricmodeling and interference analysis for massive MIMO systems,” inProc.of Modeling Optimization in Mobile, Ad Hoc Wireless Networks(WiOpt),, May 2013, pp. 15–22.

[11] T. Bai and R. W. Heath Jr., “Asymptotic coverage probability and ratein massive MIMO networks,” in Proc. of IEEE Global Conf. on Signaland Information Processing (GlobalSIP), Dec. 2014.

[12] T. Bai and R. Heath Jr., “Coverage and rate analysis for millimeter-wavecellular networks,” IEEE Trans. Wireless Commun., vol. 14, no. 2, pp.1100–1114, Feb. 2015.

[13] T. Bai, A. Alkhateeb, and R. W. Heath Jr, “Coverage and capacity inmillimeter wave cellular networks,” IEEE Commun. Mag., Sep. 2014.

[14] T. Bai, R. Vaze, and R. W. Heath Jr., “Analysis of blockage effects onurban cellular networks,” IEEE Trans.Wireless Commun., vol. 13, no. 9,pp. 5070–5083, Sep. 2014.

[15] 3GPP TR 36.814, “Further advancements for E-UTRA physical layeraspects (Release 9),” Mar. 2010.

[16] M. Akdeniz, Y. Liu, M. Samimi, S. Sun, S. Rangan, T. Rappaport,and E. Erkip, “Millimeter wave channel modeling and cellular capacityevaluation,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1164–1179,June 2014.

[17] A. Goldsmith, Wireless Communications. Cambridge University Press,2005.

[18] H. Q. Ngo, E. Larsson, and T. Marzetta, “Aspects of favorable propaga-tion in massive MIMO,” in Proc. of European Signal Processing Conf.(EUSIPCO), Sep. 2014, pp. 76–80.

[19] A. Adhikary, J. Nam, J.-Y. Ahn, and G. Caire, “Joint spatial division andmultiplexing: The large-scale array regime,” IEEE Trans. on InformationTheory, vol. 59, no. 10, pp. 6441–6463, Oct. 2013.

[20] T. Bai and R. W. Heath Jr., “Massive MIMO: Millimeter wave or lowerfrequencies?” Preprint, Feb. 2015.

[21] Z. Pi and F. Khan, “A millimeter-wave massive MIMO system for nextgeneration mobile broadband,” in Proc. of the Forty Sixth Asilomar Conf.on Signals, Systems and Computers (ASILOMAR), 2012, pp. 693–698.

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


CC

DF

of S

INR

M=64M=256M=1024M=∞Analy:M=∞

(a) Downlink SINR in dense networks.

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7


CC

DF

of S

INR

M=200M=2000M=20000M=∞

(b) Downlink SINR in sparse networks.

Fig. 2. Downlink mmWave SINR distributions with different base stationdensities. We assume ISD = 100 m in (a), and ISD = 400 m in (b). Theanalytical curve in (a) is drawn based on Corollary 2.1.

TABLE ICOMPARISON OF ACHIEVABLE RATES

Carrier 2 GHz 28 GHz 28 GHzAvg. ISD (m) 500 100 400

Training overhead 20% 14% 14%Bandwidth (MHz) 100 500 500

Rate per user (Mbps) 52.8 1791.0 436.5Users per cell 14 4 4

Cell throughput (Mbps) 740.0 7164.0 1745.8

V. CONCLUSIONS

In this paper, we analyzed the asymptotic SINR distributionin mmWave massive MIMO networks by incorporated keyfeatures of mmWave systems, including the sensitivity toblockages and directional beamforming at mobile stations,into the analytical framework. We provided the asymptoticequivalences for both the uplink and downlink SINR in alarge-scale network with Poisson distributed base stations, andderived approximation expressions to compute their distribu-tions. The accuracy of the analytical expressions were verifiedby numerical simulations. The numerical results showed thatmmWave massive MIMO requires a high base station densityto achieve good SINR coverage. Moreover, the comparison

with massive MIMO systems at lower frequencies showed thepromising gain of mmWave massive MIMO over conventionalmassive MIMO in cell throughput. For future work, it wouldbe interesting to incorporate mmWave hardware constraints,such as hybrid beamforming and one-bit A/D converter [8].

ACKNOWLEDGEMENT

This paper is based upon work supported by the NationalScience Foundation under Grants No. 1218338 and 1319556.

REFERENCES

[1] E. Larsson, O. Edfors, F. Tufvesson, and T. Marzetta, “Massive MIMOfor next generation wireless systems,” IEEE Communications Magazine,vol. 52, no. 2, pp. 186–195, Feb. 2014.

[2] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, and P. Popovski,“Five disruptive technology directions for 5G,” IEEE CommunicationsMagazine, vol. 52, no. 2, pp. 74–80, February 2014.

[3] L. Lu, G. Li, A. Swindlehurst, A. Ashikhmin, and R. Zhang, “Anoverview of massive MIMO: Benefits and challenges,” IEEE J. Sel.Topics Signal Process., vol. 8, no. 5, pp. 742–758, Oct. 2014.

[4] T. Marzetta, “Noncooperative cellular wireless with unlimited numbersof base station antennas,” IEEE Trans. Wireless Commun., vol. 9, no. 11,pp. 3590–3600, Nov. 2010.

[5] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile broad-band systems,” IEEE Communications Magazine, vol. 49, no. 6, pp.101–107, June 2011.

[6] T. Rappaport et al., “Millimeter wave mobile communications for 5Gcellular: It will work!” IEEE Access, vol. 1, pp. 335–349, 2013.

[7] A. Swindlehurst, E. Ayanoglu, P. Heydari, and F. Capolino, “Millimeter-wave massive MIMO: the next wireless revolution?” CommunicationsMagazine, IEEE, vol. 52, no. 9, pp. 56–62, September 2014.

[8] A. Alkhateeb, J. Mo, N. Gonzalez-Prelcic, and R. Heath, “MIMOprecoding and combining solutions for millimeter-wave systems,” IEEECommunications Magazine, vol. 52, no. 12, pp. 122–131, Dec. 2014.

[9] J. Andrews et al., “A tractable approach to coverage and rate in cellularnetworks,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, 2011.

[10] P. Madhusudhanan, X. Li, Y. Liu, and T. Brown, “Stochastic geometricmodeling and interference analysis for massive MIMO systems,” inProc.of Modeling Optimization in Mobile, Ad Hoc Wireless Networks(WiOpt),, May 2013, pp. 15–22.

[11] T. Bai and R. W. Heath Jr., “Asymptotic coverage probability and ratein massive MIMO networks,” in Proc. of IEEE Global Conf. on Signaland Information Processing (GlobalSIP), Dec. 2014.

[12] T. Bai and R. Heath Jr., “Coverage and rate analysis for millimeter-wavecellular networks,” IEEE Trans. Wireless Commun., vol. 14, no. 2, pp.1100–1114, Feb. 2015.

[13] T. Bai, A. Alkhateeb, and R. W. Heath Jr, “Coverage and capacity inmillimeter wave cellular networks,” IEEE Commun. Mag., Sep. 2014.

[14] T. Bai, R. Vaze, and R. W. Heath Jr., “Analysis of blockage effects onurban cellular networks,” IEEE Trans.Wireless Commun., vol. 13, no. 9,pp. 5070–5083, Sep. 2014.

[15] 3GPP TR 36.814, “Further advancements for E-UTRA physical layeraspects (Release 9),” Mar. 2010.

[16] M. Akdeniz, Y. Liu, M. Samimi, S. Sun, S. Rangan, T. Rappaport,and E. Erkip, “Millimeter wave channel modeling and cellular capacityevaluation,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1164–1179,June 2014.

[17] A. Goldsmith, Wireless Communications. Cambridge University Press,2005.

[18] H. Q. Ngo, E. Larsson, and T. Marzetta, “Aspects of favorable propaga-tion in massive MIMO,” in Proc. of European Signal Processing Conf.(EUSIPCO), Sep. 2014, pp. 76–80.

[19] A. Adhikary, J. Nam, J.-Y. Ahn, and G. Caire, “Joint spatial division andmultiplexing: The large-scale array regime,” IEEE Trans. on InformationTheory, vol. 59, no. 10, pp. 6441–6463, Oct. 2013.

[20] T. Bai and R. W. Heath Jr., “Massive MIMO: Millimeter wave or lowerfrequencies?” Preprint, Feb. 2015.

[21] Z. Pi and F. Khan, “A millimeter-wave massive MIMO system for nextgeneration mobile broadband,” in Proc. of the Forty Sixth Asilomar Conf.on Signals, Systems and Computers (ASILOMAR), 2012, pp. 693–698.

Carrier frequency: 28 GHzBandwidth:500 MHzUE: 2-by-2 UPABS: ULA of M antennasBlockage parameter: NYU model in [1](Avg. LOS 70 m,no signal > 200 m)TX power:UL: 20 dBmDL: 30 dBmNo UE beamforming

MmWave massive requires dense BS deployments

[1]M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, “ Millimeter Wave Channel Modeling and Cellular Capacity Evaluation,” IEEE JSAC, 2014.

Dense DL mmWave (ISD=200 m) Sparse DL mmWave (ISD=400 m)

Converges fast to asymptoticwhen BSs dense

Converges slow to asymptoticdue to high noise powerrelative to NLOS signals

Sparse network subject to severe outage

Good coverage achieved with dense BSs


Rate comparison setting

17

Carrier freq. 2 GHz 28 GHz 73 GHz

bandwidth 100 MHz Varies Varies

# of scheduled user per cell

10 4 1

# of base stationantennas

8X8 16X16 40X40

# of UE antennas 1 2X2 5X5

TX power (DL/ UL) 46/ 20 dBm 30/ 20 dBm 30/ 20 dBm

1. We vary the bandwidth of mmWave systems in the simulations2. We assume the same amount of overhead for all systems3. Use the parameters in the blockage model from [1] based on NYU measurements

[1] M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, “ Millimeter Wave Channel Modeling and Cellular Capacity Evaluation,” IEEE JSAC, 2014.

Keep the same aperture in 28 and 73 GHz


Comparison of average cell throughput

18MmWave outperforms in cell throughput when densely deployed

Inter-site distance in meters

Mm

Wav

e ba

ndw

idth

in M

Hz

Gai

n ov

er 2

GH

z in

cel

l thr

ough

put

(in

dB)

73 GHz Cell throughputGain for mmWave

0

28 GHz Cell throughput

Large gain with dense BSs deployment

10

-10

5

-5

Inter-site distance in meters2GHz setup: bandwidth fixed as 100 MHz, while ISD varies

“Black” in heatmap indicates same cell throughput

in mmWave and 2 GHz

100 m in ISD = 128 BS/ km2

200 m in ISD = 32 BS/ km2

Poor cell throughput due to severe outage

in sparse mmWave networkGain for sub-6 GHz


Conclusions

Go Massive @ mmWave if network dense

@ lower frequencies if network sparsequestions?

Comparing Massive MIMO at Sub-6 GHz and Millimeter Waveusers.ece.utexas.edu/~rheath/presentations/2015/...signal outage important no yes cell size macro or micro pico penetration loss

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