Signal Outage Optimized Beamforming for MISO TWDP Fading Channels - International Symposium on Personal, Indoor and Mobile Radio Communications Bologna, ItalyStefan Schwarz Sept. 12, 2018
Dependable Wireless Connectivity for the Society in Motion
Motivation
− Two dominant specular components with random relative phase
− Diffuse background scattering
• Larger probability of deep fades than Rayleigh fading
⇒ Must be considered in reliable system design!
Slide 2 / 17
Contents
System Model – MISO TWDP Fading
x
NLOS
x
x
x
f
azi
m
u
th
h = h1 + h2 + hd ,
hd ∼ NC ( 0, 2σ2
ji hi
hi = 1 √ Nt
System Model – MISO TWDP Fading
x
NLOS
x
x
x
f
azi
m
u
th
h = h1 + h2 + hd ,
hd ∼ NC ( 0, 2σ2
ji hi
hi = 1 √ Nt
Beamforming over MISO TWDP Channels
• Effective beamformed channel
jψ2 + hHd f Zd
d
Vi e jψi := hHi f,
Vi = √ γi
hHi f ,
fTWDP(r) = 1
K = V 2
2
Slide 5 / 17
Beamforming over MISO TWDP Channels
• Effective beamformed channel
jψ2 + hHd f Zd
d
Vi e jψi := hHi f,
Vi = √ γi
hHi f ,
fTWDP(r) = 1
K = V 2
2
Slide 5 / 17
Beamforming over MISO TWDP Channels
• Effective beamformed channel
jψ2 + hHd f Zd
d
Vi e jψi := hHi f,
Vi = √ γi
hHi f ,
fTWDP(r) = 1
K = V 2
2
Slide 5 / 17
TWDP Fading Illustration
TWDP Fading Illustration
rst specular component
TWDP Fading Illustration
rst specular component
TWDP Fading Illustration
rst specular component
TWDP Fading Illustration
!rst specular component
Contents
Outage-Optimized Beamforming
P {r ≤ rmin} ,
0 fTWDP(r)dr
• Alternative: evaluation of the CDF requires a single integral of a Marcum Q-function
⇒ Obviously non-convex and global optimization is not feasible
• Considered approach: local gradient optimization
∇fPout = 1
• ∇f fRice(r ;K(1 + cos δ)) can be calculated in closed-form
• However, only numerical integration is possible
Slide 8 / 17
Outage-Optimized Beamforming
P {r ≤ rmin} ,
0 fTWDP(r)dr
• Alternative: evaluation of the CDF requires a single integral of a Marcum Q-function
⇒ Obviously non-convex and global optimization is not feasible
• Considered approach: local gradient optimization
∇fPout = 1
• ∇f fRice(r ;K(1 + cos δ)) can be calculated in closed-form
• However, only numerical integration is possible
Slide 8 / 17
Outage-Optimized Beamforming – Illustration
!rst specular component
Outage-Optimized Beamforming – Illustration
Outage-Optimized Beamforming – Upper Bound and Approximation
PDF of diuse
Outage-Optimized Beamforming – Upper Bound and Approximation
PDF of diuse
Contents
Outage-Probability, Upper Bound and Approximation
1050-5-10-15-20
100
10-1
10-2
10-3
10-4
• Equally strong specular components V 2 1 = V 2
2 = 1 and diffuse component σ2 d = 1
Slide 12 / 17
Outage-Optimized Beamforming – Approximation vs. Accurate Gradient
1086420-2-4-6-8-10 Signal power threshold [dB]
Si gn
al o
ut ag
e pr
ob ab
ili ty
• Nt = 4 transmit antennas, equal macroscopic pathloss γ1 = γ2 = 2
• Averaging over random angles θi , phases i and diffuse channels hd
Slide 13 / 17
Outage-Optimized Beamforming – Comparison to MRT and ZF
1086420-2-4-6-8-10 Signal power threshold [dB]
Si gn
al o
ut ag
e pr
ob ab
100
10-1
10-2
10-3
• MRT over stronger specular component, ZF of weaker specular component
Slide 14 / 17
Outage-Optimized Beamforming – Comparison to MRT and ZF
1086420-2-4-6-8-10 Signal power threshold [dB]
Si gn
al o
ut ag
e pr
ob ab
Í1 = 3, Í2 = 1
• MRT over stronger specular component, ZF of weaker specular component
Slide 14 / 17
Contents
Conclusions
Summary:
• It has been observed in several mmWave measurement campaigns
• It potentially causes fading that is even worse than Rayleigh fading!
• Outage-optimal beamforming for TWDP fading is complicated
Future Work:
• Multi-user beamforming under TWDP fading
Slide 16 / 17
Conclusions
Summary:
• It has been observed in several mmWave measurement campaigns
• It potentially causes fading that is even worse than Rayleigh fading!
• Outage-optimal beamforming for TWDP fading is complicated
Future Work:
• Multi-user beamforming under TWDP fading
Slide 16 / 17
Stefan Schwarz Sept. 12, 2018
Dependable Wireless Connectivity for the Society in Motion
Motivation
x-axis
y-axis
fridge
• Better than Rician: Modelling millimetre wave channels as Two-Wave with Diffuse Power E. Zochmann et.al. under review at EURASIP JWCN
• Rician vs. two-wave with diffuse power (TWDP) fading statistics
Slide 1 / 1
Motivation
x-axis
y-axis
fridge
• Better than Rician: Modelling millimetre wave channels as Two-Wave with Diffuse Power E. Zochmann et.al. under review at EURASIP JWCN
• Rician vs. two-wave with diffuse power (TWDP) fading statistics
Slide 1 / 1