coverage and capacity analysis of mmwave cellular...
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Coverage and Capacity Analysis of mmWave Cellular Systems
Robert W. Heath Jr. The University of Texas at Austin
Joint work with Tianyang Bai
www.profheath.orgSaturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Why mmWave for Cellular?
Microwave
3 GHz 300 GHz
2
28 GHz 38-49 GHz 70-90 GHz300 MHz
Huge amount of spectrum available in mmWave bands*Cellular systems live with limited microwave spectrum ~ 600MHz
29GHz possibly available in 23GHz, LMDS, 38, 40, 46, 47, 49, and E-band
Technology advances make mmWave possibleSilicon-based technology enables low-cost highly-packed mmWave RFIC**
Hybrid precoding solves RF limitations
Commercial products already available (or soon) for PAN and LAN
1G-4G cellular 5G cellular
m i l l i m e t e r w a v e
* Z. Pi,, and F. Khan. "An introduction to millimeter-wave mobile broadband systems." IEEE Communications Magazine, vol. 49, no. 6, pp.101-107, Jun. 2011.** T.S. Rappaport, J. N. Murdock, and F. Gutierrez. "State of the art in 60-GHz integrated circuits and systems for wireless communications." Proceedings of the IEEE, vol. 99, no. 8, pp:1390-1436, 2011
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Smaller wavelength means smaller captured energy at antenna3GHz->30GHz gives 20dB extra path loss due to aperture
Larger bandwidth means higher noise power and lower SNR50MHz -> 500MHz bandwidth gives 10dB extra noise power
The Need for Gain
3
Solution: Exploit array gain from large antenna arrays
microwave noise bandwidth
mmWave noise bandwidth
microwave aperture
mmWave aperture
TXRX
�2
4⇡
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Antenna Arrays are Important
4
Narrow beams are a new feature of mmWaveReduces fading, multi-path, and interference
Implemented in analog due to hardware constraints
Baseband Processing
~100 antennas
Baseband Processing
antennas are small (mm)
highly directional MIMO transmission
used at TX and RX
Arrays will change system design principles
O. El Ayach, S. Abu-Surra, S. Rajagopal, Z. Pi, and R. W. Heath, Jr., `` Spatially Sparse Precoding in Millimeter Wave MIMO Systems,'' submitted to IEEE Trans. on Wireless, May 2013. Available on ArXiv.
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Different Propagation Behavior
Buildings block Line-of-sight (LOS) pathsmmWave signal suffer from high penetration losses
Reflections can establish non-LOS linksBest non-LOS links still tens of dB weaker than LOS signals
Different characteristics for LOS & non-LOSPath loss exponent is around 2 for LOS, and 4 for non-LOS
5
Line-of-sight linkReflection
Blockages
Signal blocked by buildings
Need to distinguish between LOS and non-LOS paths
T. S. Rappaport, et al. , "Millimeter Wave Mobile Communications for 5G Cellular: It Will Work!." IEEE Access, vol.1, no.1, pp.335-349, 2013
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Challenges of mmWave Analysis
6
LOS & non-LOS linksDirectional Beamforming (BF)
How to including beamforming + blockages in mmWave cellular analysis?
Need to incorporate directional beamformingRX and TX communicate via main lobes to achieve array gain
Steering directions at interfering BSs are random
Need to distinguish LOS and non-LOS pathsDramatically different characteristics in LOS & non-LOS channels
Better characterize blockages
Saturday, June 15, 13
Stochastic Geometry for mmWave Cellular
System Analysis
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Stochastic Geometry for Cellular
Stochastic geometry is a tool for analyzing microwave cellularReasonable fit with real deployments
Closed form solutions for coverage probability available
Provides a system-wide performance characterization
8
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.T. X. Brown, "Cellular performance bounds via shotgun cellular systems," IEEE JSAC, vol.18, no.11, pp.2443,2455, Nov. 2000.
base station locations distributed (usually) as a
Poisson point process (PPP)performance analyzed for a typical user
Need to incorporate LOS/non-LOS links and directional antennas
Baccelli
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Poisson Point Processes
Poisson point process (PPP): the simplest point process# of points is a Poisson variable with mean λS
Given N points in certain area, locations independent
Useful results like Campbell’s Theorem & Displacement Theorem apply
Assigning each point an i.i.d. random variable forms a marked PPP
9
14
Fig. 7. .
Antenna steering orientations as marks of the
BS PPP
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Blockages in mmWave
Use random shape theory to model buildingsModel random buildings as rectangle Boolean scheme
Buildings distributed as PPP with independent sizes & orientations
Compute the LOS probability based on the building model# of blockages on a link is a Poisson random variable
The LOS probability that no blockage on a link of length R is
10
Boolean scheme of rectanglesK: # of blockages on a link
Randomly located buildings
e��R
LOS: K=0non-LOS
K>0
Tianyang Bai and R. W. Heath, Jr., ``Using Random Shape Theory to Model Blockage in Random Cellular Networks,'' Proc. of the International Conf. on Signal Processing and Communications, Bangalore, India, July 22-25, 2012.
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Directional Transmission at the BS
Each base station is marked with a directional antennaAntenna directions of interferers are uniformly distributed
Use “sector” pattern in analysis for simplicityEquivalent to uniform linear array of antennas with spacing
11
1
Summary of Cellular Millimeter Wave Channels
I. MEASUREMENT RESULTS
−3 −2 −1 0 1 2 30
1
2
3
4
5
6
7
8
9
10
Angel in Rad
Ante
nna
Gai
n
Exact antenna pattern"Sector" approximation
Fig. 1.
Sector antenna approximation
Half-Power BW✓
Nt �/2
Main lobe beamwidth:
Main lobe array gain:M = Nt
Front-back ratio:
Back lobe gain:
3
✓ = 2arcsin
✓2.782
⇡Nt
◆
FBR = sin
✓3⇡
2Nt
◆
m = Nt ⇥ FBR
3
✓ = 2arcsin
✓2.782
⇡Nt
◆
FBR = sin
✓3⇡
2Nt
◆
m = Nt ⇥ FBR
3
✓ = 2arcsin
✓2.782
⇡Nt
◆
FBR = sin
✓3⇡
2Nt
◆
m = Nt ⇥ FBR
# antennas
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
15
Fig. 8. .
Proposed mmWave Model
Use stochastic geometry to model BSs as marked PPPModel the steering directions as independent marks of the BSs
Use random shape theory to model buildingsModel the building as rectangle Boolean schemes
Different path loss exponents for LOS and non-LOS paths
12
PPP Interfering BSs
Serving BS
Buildings
Typical User
Reflections
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
System Parameters Different path loss model for LOS and nonLOS links
Line-of-sight with probability
LOS path Loss in dB:
Non-LOS path loss in dB:
28Ghz system: let C=50 dB, K=10 dB
General small scale fadingNo fading case: small scaling fading is minor in mmWave [RapSun]
Link budgetTx antenna input power: 30dBm
Signal bandwidth: 500 MHz (Noise: -87 dBm)
Noise figure: 5dB
13
e��R
PL2 = C +K + 40 logR(m)
PL1 = C + 20 logR(m)
h
Saturday, June 15, 13
Results on Coverage
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Coverage Analysis
15
where
7
P(SINR > T ) =
Z 1
�1
Z 1
0
E[e�tP
k
Lk |L⇤
= x ]fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt,
E[e�tP
k
Lk |L⇤
= x ] = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i,
Li = r↵i
i ,
L⇤= max
i{Li} ,
SINR =
MrMtH0`(r0)
N0/Pt +P
k>0 AkBkHk`(rk),
`(x) =
8<
:Cx�2 w. p. e��x
C Kx�4 w. p. 1� e
��x,
Ak =
8<
:Mt w. p. ✓t
2⇡
mt w. p. 1� ✓t2⇡
,
Bk =
8<
:Mr w. p. ✓r
2⇡
mr w. p. 1� ✓r2⇡
,
H0`(r0) = min
k>0{Hk`(rk)} ,
7
P(SINR > T ) =
Z 1
�1
Z 1
0
E[e�tP
k
Lk |L⇤
= x ]fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt,
E[e�tP
k
Lk |L⇤
= x ] = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i,
Li = r↵i
i ,
L⇤= max
i{Li} ,
SINR =
MrMtH0`(r0)
N0/Pt +P
k>0 AkBkHk`(rk),
`(x) =
8<
:Cx�2 w. p. e��x
C Kx�4 w. p. 1� e
��x.
Ak =
8<
:Mt w. p. ✓t
2⇡
mt w. p. 1� ✓t2⇡
,
Bk =
8<
:Mr w. p. ✓r
2⇡
mr w. p. 1� ✓r2⇡
,
H0`(r0) = min
k>0{Hk`(rk)} ,
Connecting to the strongest signal before BF
Array gain of the TX antenna
Array gain of the RX antenna
Path Loss of LOS or non-LOS
Serving BS and User connect via main lobe
Use stochastic geometry to compute SINR distribution
General small-scale fading
7
P(SINR > T ) =
Z 1
�1
Z 1
0
E[e�tP
k
Lk |L⇤
= x ]fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt,
E[e�tP
k
Lk |L⇤
= x ] = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i,
Li = r↵i
i ,
L⇤= max
i{Li} ,
SINR =
NrNtH0`(r0)
N0/Pt +P
k>0 AkBkHk`(rk),
`(x) =
8<
:Cx�2 w. p. e��x
C Kx�4 w. p. 1� e
��x.
Ak =
8<
:Nt w. p. ✓t
2⇡
NtFBRt w. p. 1� ✓t2⇡
,
Bk =
8<
:Nr w. p. ✓r
2⇡
NrFBRr w. p. 1� ✓r2⇡
,
H0`(r0) = min
k>0{Hk`(rk)} ,
7
P(SINR > T ) =
Z 1
�1
Z 1
0
E[e�tP
k
Lk |L⇤
= x ]fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt,
E[e�tP
k
Lk |L⇤
= x ] = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i,
Li = r↵i
i ,
L⇤= max
i{Li} ,
SINR =
NrNtH0`(r0)
N0/Pt +P
k>0 AkBkHk`(rk),
`(x) =
8<
:Cx�2 w. p. e��x
C Kx�4 w. p. 1� e
��x.
Ak =
8<
:Nt w. p. ✓t
2⇡
NtFBRt w. p. 1� ✓t2⇡
,
Bk =
8<
:Nr w. p. ✓r
2⇡
NrFBRr w. p. 1� ✓r2⇡
,
H0`(r0) = min
k>0{Hk`(rk)} ,
7
P(SINR > T ) =
Z 1
�1
Z 1
0
E[e�tP
k
Lk |L⇤
= x ]fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt,
E[e�tP
k
Lk |L⇤
= x ] = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i,
Li = r↵i
i ,
L⇤= max
i{Li} ,
SINR =
NrNtH0`(r0)
N0/Pt +P
k>0 AkBkHk`(rk),
`(x) =
8<
:Cx�2 w. p. e��x
C Kx�4 w. p. 1� e
��x.
Ak =
8<
:Nt w. p. ✓t
2⇡
NtFBRt w. p. 1� ✓t2⇡
,
Bk =
8<
:Nr w. p. ✓r
2⇡
NrFBRr w. p. 1� ✓r2⇡
,
H0`(r0) = min
k>0{Hk`(rk)} ,
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Coverage Probability of mmWaveMain Theorem [mmWave Coverage probability] The coverage probability can be computed as
where
,
,
.
16
P[SINR > T ]
4
P(SINR > T ) =
Z 1
�1
Z 1
0
U(x, t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i
⇤(x) = 2⇡�
0
@Z x
14
0
t�1� e
��t�dt+
Z px
0
te��tdt
1
A
⇤L(x) = 2⇡�
Z px
0
te��tdt
⇤NL(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt
fL⇤(x) = � d
dxe
�⇤(x)
Li = r↵i
i
L⇤= max
i{Li}
F =
1
SINR
E⇥e
�sF |L⇤= x
⇤= U(x, s)
E⇥e
�sF⇤=
Z 1
0
U(x, s)fL⇤(x)dx
4
P(SINR > T ) =
Z 1
�1
Z 1
0
U(x, t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i
⇤(x) = 2⇡�
0
@Z x
14
0
t�1� e
��t�dt+
Z px
0
te��tdt
1
A
⇤L(x) = 2⇡�
Z px
0
te��tdt
⇤NL(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt
fL⇤(x) = � d
dxe
�⇤(x)
Li = r↵i
i
L⇤= max
i{Li}
F =
1
SINR
E⇥e
�sF |L⇤= x
⇤= U(x, s)
E⇥e
�sF⇤=
Z 1
0
U(x, s)fL⇤(x)dx
4
P(SINR > T ) =
Z 1
�1
Z 1
0
U(x, t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i
⇤(x) = 2⇡�
0
@Z x
14
0
t�1� e
��t�dt+
Z px
0
te��tdt
1
A
⇤L(x) = 2⇡�
Z px
0
te��tdt
⇤NL(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt
fL⇤(x) = � d
dxe
�⇤(x)
Li = r↵i
i
L⇤= max
i{Li}
F =
1
SINR
E⇥e
�sF |L⇤= x
⇤= U(x, s)
E⇥e
�sF⇤=
Z 1
0
U(x, s)fL⇤(x)dx
Transform interference field into 1D space by Displacement Thm
4
P(SINR > T ) =
Z 1
�1
Z 1
0
U(x, t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤(du)
i
⇤(x) = 2⇡�Eh
"Z(
xh
K
)
0.25
0
t�1� e
��t�dt+
Z pxh
0
te��tdt
#
⇤L(x) = 2⇡�
Z px
0
te��tdt
⇤NL(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt
fL⇤(x) = � d
dxe
�⇤(x)
Li = r↵i
i
L⇤= max
i{Li}
F =
1
SINR
E⇥e
�sF |L⇤= x
⇤= U(x, s)
E⇥e
�sF⇤=
Z 1
0
U(x, s)fL⇤(x)dx
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
10
!10 !8 !6 !4 !2 0 2 4 6 8 100.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SINR Threshold
Co
ve
rag
e P
rob
ab
ilit
y
Nt=64, !=1.6o
Nt=32, !=3.2O
Nt=16, !=6.5o
Microwave: SU MIMO 4X4
Fig. 6.
Coverage Gain from Large Arrays
17
Mobile user 16 antennasBS density Rc=200 mBuildings cover 5% of the landAverage building size 15 m by 15 m
Large arrays provide better coverage probabilitythe more antennas, the smaller beamwidth, the larges array gain
Smaller beamwidth provides better coverage
mmWave coverage probability comparable to microwave
Gain from directional antenna array
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
10
!10 !8 !6 !4 !2 0 2 4 6 8 10
0.4
0.5
0.6
0.7
0.8
0.9
1
SINR Threshold
Co
ve
rag
e P
rob
ab
ilit
y
rc=50 m
rc=100 m
rc=200 m
rc=300 m
Microwave: 4X4 SU MIMO
Fig. 6.
Coverage Gain from Higher Density
18
Higher density can also increase coverage probabilityCoverage probability no longer invariant with BS density
Become interference-limited when coverage probability is good
32 antennas at BSBlockages covers 10% land
Noise-limited region due to high path loss
Interference-limited region
Gain over microwave
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
LOS & non-LOS Path Loss
Coverage probability differs in LOS and non-LOS regionNeed to incorporate blockage model & differentiate LOS and nonLOS
Non-LOS coverage probability generally provides a lower bound
Buildings may improve coverage by blocking more interference19
7
!10 !8 !6 !4 !2 0 2 4 6 8 100.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SINR Threshold
Co
ve
rag
e P
rob
ab
ilit
y
Proposed model
LOS path loss only
non!LOS path loss only
Fig. 2. .
32 antennas at BSsBlockages covers 10% landRc=100 m
Gain from blocking more interference
pure LOS (no buildings)
pure NLOS
proposed model
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
LOS & Reflection CoverageCorollary 1 [Coverage probability by LOS BSs]
The coverage probability provided by LOS BSs is
,
where
20
6
P(SINR > T ) =
Z 1
�1
Z 1
0
U1(x, t)U2(t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U2(s) = exp
Z 1
0
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤2(du)
i
U1(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤1(du)
i
⇤1(x) = 2⇡�
Z px
0
te��tdt
⇤2(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt
fL⇤(x) = � d
dxe
�⇤1(x)
6
P(SINR > T ) =
Z 1
�1
Z 1
0
U1(x, t)U2(t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U2(s) = exp
Z 1
0
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤2(du)
i,
U1(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤1(du)
i,
⇤1(x) = 2⇡�
Z px
0
te��tdt,
⇤2(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt,
fL⇤(x) = � d
dxe
�⇤1(x).
6
P(SINR > T ) =
Z 1
�1
Z 1
0
U1(x, t)U2(t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U2(s) = exp
Z 1
0
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤2(du)
i,
U1(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤1(du)
i,
⇤1(x) = 2⇡�
Z px
0
te��tdt,
⇤2(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt,
fL⇤(x) = � d
dxe
�⇤1(x).
6
P(SINR > T ) =
Z 1
�1
Z 1
0
U1(x, t)U2(t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U2(s) = exp
Z 1
0
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤2(du)
i,
U1(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤1(du)
i,
⇤1(x) = 2⇡�
Z px
0
te��tdt,
⇤2(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt,
fL⇤(x) = � d
dxe
�⇤1(x).
6
P(SINR > T ) =
Z 1
�1
Z 1
0
U1(x, t)U2(t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U2(s) = exp
Z 1
0
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤2(du)
i,
U1(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤1(du)
i,
⇤1(x) = 2⇡�
Z px
0
te��tdt,
⇤2(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt,
fL⇤(x) = � d
dxe
�⇤1(x).
6
P(SINR > T ) =
Z 1
�1
Z 1
0
U1(x, t)U2(t)fL⇤(x)
e
j2⇡t/T � 1
j2⇡tdxdt
U2(s) = exp
Z 1
0
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤2(du)
i,
U1(x, s) = exp
� sx
MrMt⇢+
Z 1
x
⇣ptpre
� sx
u
+ (1� pt)pre� sxmt
uMt+ pt(1� pr)e
� sxmruMr
+(1� pt)(1� pr)e� sxmtmr
uMrMt � 1
⌘⇤1(du)
i,
⇤1(x) = 2⇡�
Z px
0
te��tdt,
⇤2(x) = 2⇡�
Z(
x
K
)
1/4
0
t�1� e
��t�dt,
fL⇤(x) = � d
dxe
�⇤1(x).
Coverage probability by reflections derived in a similar way
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
10
!10 !8 !6 !4 !2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SINR Threshold
Co
ve
rag
e P
rob
ab
ilit
y
Overall coverage probability
Covergage probability by LOS BSs
Coverage probability by reflections
Fig. 6.
Reflections Improve Coverage
Reflections can establish links in the shadowed areasWith dense blockages, most users are served by reflected links
Non-LOS links improve the coverage probability of mmWave
21
128 antennas at BSsBlockages covers 30% land(Heavy shadowing case)Rc=200 m
With dense blockages, a large fraction of users is non-LOS
Saturday, June 15, 13
Results on Rate
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Data Rate ComparisonGiven coverage probability, the achievable rate is
Microwave network 4X4 MU MIMO with bandwidth 50MHz: Spectrum efficiency is 4.95 bps/ Hz
Data rate is 248 Mbps (invariant with the cell size Rc)
mmWave network with bandwidth 500MHz:
23
3
A. Distribution of L0
Lemma 8: The probability density function (pdf) of L0 is fL0(x) = ⇤
0(x)(e)⇤x, where ⇤
0(x) =
d⇤(x)dx , ⇤(x) = ⇤1(x) + ⇤2(x), and
⇤1(x) = 2⇡�EH1
"Z pxH1
0
te��tdt
#, (3)
⇤2(x) = 2⇡�EH2
"Z pxH2
0
t�1� e
��t�dt
#. (4)
Remark 9: Note that if there is no fading in both LOS and non-LOS links, then
⇤1(x) = 2⇡�
Z px
0
te��tdt, (5)
⇤2(x) = 2⇡�
Z px
0
t�1� e
��t�dt. (6)
B. Laplace Transform of F
First, we compute the conditional Laplace transform of F, given that L0 = x, in the following
lemma.
Lemma 10: Given that L0 = x, the conditional Laplace transform of F is
E⇥e
�sF |L0 = x⇤= e
�sx
M⇢
exp
✓Z 1
x
⇣e
�Msx
u � 1
⌘ ✓
2⇡⇤(u)du
◆exp
✓Z 1
x
�e
�msx
u � 1
�2⇡ � ✓
2⇡⇤(u)du
◆
(7)The unconditional Laplace transform of F is
E⇥e
�sF⇤=
Z 1
0
E⇥e
�sF |L0 = x⇤fL0(x)dx (8)
C. Computation of Coverage probability
Using Parseval’s Theorem, we can obtain the coverage probability as
Pc(T ) = P(SINR > T ) (9)
= P(F < 1/T ) (10)
=
Z 1
0
E⇥e
�sF⇤e
j2⇡/T � 1
j2⇡dt (11)
D. Rate
As we did previously, the achievable rate ⌘ can be computed as
⌘ =
Z 1
0
Pc(T )
1 + TdT (12)
100m 200m
32 3.4Gbps 3.25Gbps
64 3.8Gbps 3.45Gbps
NtRc
mmWave achieves high gain in average rate
16 antenna at MSBlockages covers 10% land
# of antenna at BS
Average cell radius
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
7
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cell Throughput in Mbps
Rate
Co
vera
ge P
rob
ab
ilit
y
CoMP: Nt=4, 2 Users, 3 BSs/ Cluster
Massive MIMO: Nt=!
mmWave: Nt=64, R
c=100m
SU MIMO: 4X4
Fig. 3.
Cell Throughput Comparison
24
Gain from larger bandwidth
Gain from serving multiple users
mmWave can support much higher data rate
* for more information on this setup refer to: Robert W. Heath Jr., “ Role of MIMO Beyond LTE: Massive? Coordinated? mmWave?”, Workshop on Beyond 3GPP LTE-A ICC 2013.
Saturday, June 15, 13
Conclusions
Saturday, June 15, 13
(c) Robert W. Heath Jr. 2013
Going Forward with mmWave
mmWave coverage probability and rateNeed to include both LOS and Non-LOS conditions
Interference is reduced by directional antennas and blockages
Good rates and coverage can be achieved
Theoretical challenges aboundAnalog beamforming algorithms & hybrid beamforming
Channel estimation, exploiting sparsity, incorporating robustness
Multi-user beamforming algorithms and analysis
Microwave-overlaid mmWave system a.k.a. phantom cells
More advanced stochastic geometry models including multi-tier
26
Saturday, June 15, 13
Questions?Robert W. Heath Jr.
The University of Texas at Austin
www.profheath.org
See forthcoming book:
Millimeter Wave Wireless
Communication
Theodore Rappaport, Robert W. Heath Jr.,
Robert C. Daniels, and James N. Murdock
Saturday, June 15, 13