Coverage in Dense Millimeter Wave Cellular Networks
Tianyang Bai and Robert W. Heath Jr. The University of Texas at Austin
www.profheath.org
(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 possible Silicon-based technology enables low-cost highly-packed mmWave RFIC**
Commercial products already available (or soon) for PAN and LAN
Already deployed for backhaul in commercial products
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
(c) Robert W. Heath Jr. 2013
Antenna Arrays are Important
�3
Narrow beams are a new feature of mmWave Reduces 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
(c) Robert W. Heath Jr. 2013
Sensitivity to Blockages
Signal and interference may be either LOS or NLOS
Users may connect to a further unblocked base station
Strong interferers may blocked
�4
Need to include propagation models in the analysis
T. Bai, V. Desai, and R. W. Heath Jr. “Millimeter Wave Cellular Channel Models for System Evaluation,” to appear in the Proc. of ICIN, Hawaii, Feb. 2014.
LOS channel Path loss exponent 2
NLOS channel Path loss exponent 4
Additional loss
(c) Robert W. Heath Jr. 2013
Contributions
�5
LOS & non-LOS linksDirectional Beamforming (BF)
Incorporate beamforming & LOS/NLOS into coverage analysis RX and TX communicate via steered directional beams
Steering directions at interfering BSs are random
Paths may be LOS or NLOS depending on blockage density
!
Approach is to leverage stochastic geometric analysis of cellular Extends work by [AndrewsGantiBaccelli2011] to include mmWave features
Extends our work [BaiHeath2013] with simplified expressions for dense networks
System Model
(c) Robert W. Heath Jr. 2013
Stochastic Geometry for Cellular
Stochastic geometry is a tool for analyzing microwave cellular Reasonable fit with real deployments
Closed form solutions for coverage probability available
Provides a system-wide performance characterization
�7
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 as a Poisson point
process (PPP)performance analyzed for a typical user
Need to incorporate LOS/non-LOS links and directional antennas
Baccelli
(c) Robert W. Heath Jr. 2013
Accounting for Beamforming
Each base station is marked with a directional antenna Antenna directions of interferers are uniformly distributed
Use “sector” pattern in analysis for simplicity Antenna pattern fully characterized by , M and m
�8
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✓ Main lobe beamwidth
Main lobe array gain M
Back lobe gain m
✓
✓
(c) Robert W. Heath Jr. 2013
Incorporating Blockages
Use random shape theory to model buildings Model random buildings as a rectangular 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
�9
Boolean scheme of rectangles K: # 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.
(c) Robert W. Heath Jr. 2013
15
Fig. 8. .
Proposed mmWave Model
Use stochastic geometry to model BSs as marked PPP Model the steering directions as independent marks of the BSs
Use random shape theory to model buildings Model the building as rectangle Boolean schemes
Different path loss exponents for LOS and NLOS paths
�10
PPP Interfering BSs
Serving BS
Buildings
Typical User
Reflections
(c) Robert W. Heath Jr. 2013
Different path loss model for LOS and nonLOS links Line-of-sight with probability : average LOS range is
!
!
LOS path Loss in dB:
Non-LOS path loss in dB:
28GHz system: let C=70 dB, K=10 dB
General small scale fading No fading case: small scaling fading is minor in mmWave [RapSun]
Link budget Tx antenna input power: 30dBm
Signal bandwidth: 500 MHz (Noise: -87 dBm)
Noise figure: 5dB
System Parameters
�11
e��R
PL2 = C +K + 40 logR(m)
PL1 = C + 20 logR(m)
h
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
b̂k = (N !)1N bk
lim⇢!1
SINRp.= 0
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt
� =2⌘([L] + [W ])
⇡[W ][L]
1/�The fraction of land covered by buildings
Average building length and width
Coverage Results
(c) Robert W. Heath Jr. 2013
SINR Expressions
�13
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 =
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)} ,
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)} ,
(c) Robert W. Heath Jr. 2013
Coverage Probability of mmWaveTheorem1 [mmWave Coverage probability] The coverage probability can be computed as
!!!where
,
! ,
.
�14
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
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
T. Bai and R. W. Heath Jr., ``Coverage analysis of millimeter cellular networks with blockage effects (invited)", to appear in Proc. of IEEE GlobalSIP, Austin, TX, Dec. 2013.
(c) Robert W. Heath Jr. 2013
Dense Network Analysis (1/3)
Good coverage requires dense BS deployments LOS BSs exist with high probability in dense networks
Noise and NLOS interference become much weaker than LOS interf.
Theorem 1 sometimes inefficient to compute The underlying reason is that LOS region is very irregular
Need to simplify expressions in Theorem 1
�15
LOS Region of the typical user
LOS BS
Typical User
Approximate LOS region & neglect NLOS contributions
Equivalent LOS ball
(c) Robert W. Heath Jr. 2013
Derive approximate bounds on SINR distribution in dense network Approximate LOS region as a ball with equal average size
Ignore noise, approximate LOS fading with high order gamma distribution
Use Alzer’s inequality to further simplify to single-finite integral
Provides approximate upper and lower bounds on SINR
Can be extended to other LOS exponents
Dense Network Analysis (2/3)
�16
Theorem 2 [Coverage probability with dense BSs] In dense networks with a LOS path loss exponent of 2
where and are constants determined by RX and TX antenna patterns.
ak bk
How accurate is the approximations?
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
✓N
`
◆Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
b̂k = (N !)1N bk
lim⇢!1
SINRp.= 0
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
✓N
`
◆Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt
� =2⌘([L] + [W ])
⇡[W ][L]
R =1
ln(2)
Z C
0
Pc(T )
1 + TdT
(c) Robert W. Heath Jr. 2013
−10 −5 0 5 10 15 20 25 30 35 400.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SINR in dB
Cov
erag
e Pr
obab
ility
SimulationsUpper bound: N=5Lower bound: N=5Lower bound: N=3Lower bound: N=1
Fig. 1.
Dense Network Analysis(3/3)
Larger N (more terms) increases accuracy
N=5 terms generally provides acceptable accuracy
�17
Tx directivity gain: 20 dB Tx beamwidth: 30 degree Rx directivity gain: 10 dB Rx beamwidth: 90 degree Rc=100 m =141 m1/�
Becomes better as N increases
What is the design insight from coverage analysis?
(c) Robert W. Heath Jr. 2013
Insights for Dense Networks
Given antenna patterns, SINR only depends on
!
!The larger , the denser the BSs (and closer)
Increasing BS density need not improve SINR SINR goes to zero in a infinitely dense network
!Optimal BS density is finite
�18
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,⇢
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
b̂k = (N !)1N bk
lim⇢!1
SINRp.= 0
What is the optimal BS density in dense networks?
⇢
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
✓N
`
◆Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
b̂k = (N !)1N bk
lim⇢!1
SINRp.= 0
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
✓N
`
◆Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt
� =2⌘([L] + [W ])
⇡[W ][L]
R =1
ln(2)
Z C
0
Pc(T )
1 + TdT
(c) Robert W. Heath Jr. 2013
Finding Optimal BS Density
Exhaustive search optimal BS density using Theorem 2 Maximize the coverage probability given a target SINR
Much efficient than simulations with minor errors
Optimal cell radius is approximately 2/3 of the avg. LOS range.�19
20 40 60 80 100 120 140 160 180 200
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Average cell radius
Cov
erag
e Pr
obab
ility
with
T=1
0 dB
Exhuastive search using SimulationsExhaustive search using Theorem 2
Fig. 2.
Tx directivity gain: 20 dB Tx beamwidth: 30 degree Rx directivity gain: 10 dB Rx beamwidth: 10 dB Avg. LOS range: =141 m Target SINR: T=10 dB
1/�
Increasing BS density need not improve SINR
Optimal BS density is finite
(c) Robert W. Heath Jr. 2013
0 100 200 300 400 500 600 700 8000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Avg. Cell Radius Rc
Cov
erag
e Pr
obab
ility
SimulationsAnalytical Results
Fig. 7.
Finding Optimal BS Density
Exhaustive search optimal BS density using Theorem 2 Maximize the coverage probability given a target SINR
Much efficient than simulations with minor errors
Optimal cell radius is approximately 2/3 of the avg. LOS range.�20
Tx directivity gain: 20 dB Tx beamwidth: 30 degree Rx directivity gain: 10 dB Rx beamwidth: 10 dB Avg. LOS range: =141 m Target SINR: T=20 dB
1/�
Increasing BS density need not improve SINR
Optimal BS density is finite
Gap by ignoring NLOS and noise
(c) Robert W. Heath Jr. 2013(c) Robert W. Heath Jr. 2013
Given coverage probability, the achievable rate is
!
!
Microwave network 4X4 SU MIMO with bandwidth 50MHz: Spectrum efficiency is 4.56 bps/ Hz
Data rate is 228 Mbps (invariant with the cell size Rc)
mmWave network with bandwidth 500MHz:
Achievable Rate Analysis
�21
100m 200m
10 dB 2.76 Gbps 1.61 Gbps
20 dB 2.91Gbps 1.88 Gbps
Rc
mmWave achieves high gain in average rate
Tx beamforming Gain
Average cell radiusMTx beamwidth: 30 degree Rx directivity gain: 10 dB Rx beamwidth: 90 degree Avg. LOS range: =141 m1/�
Tempting file for making slidesTianyang Bai
I. INTRODUCTION
⇢ =Average size of LOS region
Average cell size
1
�
2⇡
�2
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt,
b̂k = (N !)1N bk
lim⇢!1
SINRp.= 0
P(SINR > T ) ⇡ ⇢e�⇢NX
n=1
(�1)n+1
Z 1
0
4Y
k=1
e⇢ak(e�nbkt�te�nbk)✓1� e�n⌘bkt
1� e�n⌘bk
◆n⇢akbkt
dt
� =2⌘([L] + [W ])
⇡[W ][L]
R =1
ln(2)
Z C
0
Pc(T )
1 + TdT
clipped by 6 bps/Hz (64QAM)
Conclusions
(c) Robert W. Heath Jr. 2013
Going Forward with mmWave
mmWave coverage probability and rate Need 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 abound Analog 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
Going away from cells to a more ad hoc configuration
�23