Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from...
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![Page 1: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/1.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Noncoherent Communicationswith Large Antenna Arrays
Mainak ChowdhuryJoint work with: Alexandros Manolakos, Andrea Goldsmith,
Felipe Gomez-Cuba and Elza Erkip
Stanford University
September 29, 2016
![Page 2: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/2.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Wireless propagation
![Page 3: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/3.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
The promise of large antenna arrays
What is an antenna array?
Group of antennas receiv-ing/transmitting signals simul-taneously wavefront
wavelength/2
Benefits• Signal becomes stronger and less
uncertain• Fading and noise vanish [Marzetta, 2010]
• Beams are directed and steerable
• Used for precise imaging and trackingNote large gain alonga particular direction
![Page 4: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/4.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
The promise of large antenna arrays
What is an antenna array?
Group of antennas receiv-ing/transmitting signals simul-taneously wavefront
wavelength/2
Benefits• Signal becomes stronger and less
uncertain• Fading and noise vanish [Marzetta, 2010]
• Beams are directed and steerable
• Used for precise imaging and trackingNote large gain alonga particular direction
![Page 5: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/5.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
The promise with large antenna arrays
Better cellular network with heterogenous demand (objects andpeople)
![Page 6: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/6.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Challenges with large arrays in communication systems
antenna array baseband unitfronthaul
• Space constraints
• Number of radio frequency (RF) front ends is large
• Channel state information (CSI) needs to be acquired fast
• CSI needs to go through rate limited (fronthaul) links
Number of antennas doesn’t scaleeasily!
![Page 7: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/7.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Challenges with large arrays in communication systems
antenna array baseband unitfronthaul
• Space constraints
• Number of radio frequency (RF) front ends is large
• Channel state information (CSI) needs to be acquired fast
• CSI needs to go through rate limited (fronthaul) links
Number of antennas doesn’t scaleeasily!
![Page 8: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/8.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our contributions
In large antenna arrays:
• Fading channel models need to be rethought⇒ Coherence time and antenna correlation are different
• Many benefits also possible with noncoherent schemes⇒ Schemes with slowly changing statistics of the channel
• Simple transmission and detection works well⇒ ON-OFF keying, one-shot detectors
![Page 9: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/9.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our contributions
In large antenna arrays:
• Fading channel models need to be rethought⇒ Coherence time and antenna correlation are different
• Many benefits also possible with noncoherent schemes⇒ Schemes with slowly changing statistics of the channel
• Simple transmission and detection works well⇒ ON-OFF keying, one-shot detectors
![Page 10: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/10.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our contributions
In large antenna arrays:
• Fading channel models need to be rethought⇒ Coherence time and antenna correlation are different
• Many benefits also possible with noncoherent schemes⇒ Schemes with slowly changing statistics of the channel
• Simple transmission and detection works well⇒ ON-OFF keying, one-shot detectors
![Page 11: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/11.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Plan
Why large antenna arrays?
Channel models for MIMO large antenna arrays
Noncoherent schemes
Transmission and detection schemes
Conclusions
![Page 12: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/12.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 13: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/13.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 14: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/14.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 15: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/15.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 16: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/16.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 17: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/17.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 18: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/18.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 19: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/19.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Fading models
Channel from user equipment (UE) to mth antenna element is hm
Models for single antenna systems
• Statistical fading models (distribution on hm)
• Ray tracing models
Models for multi antenna systems
• Independent and identically distributed (IID) fading models
• Actual antennas not IID ⇒ modeling antenna correlation
Models for a single time varying channel
• Characterize joint distribution of hm(t), hm(t+ τ)
• Coherence time Tc implies hm(t) ≈ hm(t+ τ) for τ < Tc
![Page 20: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/20.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our analysis: starting point
Main assumptions
• Number of antennas N colocated
• UE b leads to L rays (or paths)
• Each ray has gain Gb,p = 1√L
and
angle of arrival θb,p
...
User 1
User 2
Base station
PathBeam
hm =1√L
L∑p=1
ejφb,p+j2πmsin(θb,p)
λ
Implications
• For a finite L, there exists antenna correlations
• As L→∞, h ∼ CN (0, I)
⇒ IID Rayleigh fading
![Page 21: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/21.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our analysis: starting point
Main assumptions
• Number of antennas N colocated
• UE b leads to L rays (or paths)
• Each ray has gain Gb,p = 1√L
and
angle of arrival θb,p
...
User 1
User 2
Base station
PathBeam
hm =1√L
L∑p=1
ejφb,p+j2πmsin(θb,p)
λ
Implications
• For a finite L, there exists antenna correlations
• As L→∞, h ∼ CN (0, I)
⇒ IID Rayleigh fading
![Page 22: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/22.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our analysis: starting point
Main assumptions
• Number of antennas N colocated
• UE b leads to L rays (or paths)
• Each ray has gain Gb,p = 1√L
and
angle of arrival θb,p
...
User 1
User 2
Base station
PathBeam
hm =1√L
L∑p=1
ejφb,p+j2πmsin(θb,p)
λ
Implications
• For a finite L, there exists antenna correlations
• As L→∞, h ∼ CN (0, I) ⇒ IID Rayleigh fading
![Page 23: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/23.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Coherence time as a function of N
Factφb,p[t] changes much faster than Gb,p[t] or θb,p[t] (10× to 1000×)
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
0
1
2
3
4
5
6
Ang
leof
arriv
al
θ1,1 variation with time
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
0
1
2
3
4
5
6
Inst
anta
neou
sph
ase
φ1,1 variation with time
![Page 24: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/24.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Coherence time as a function of N
Factφb,p[t] changes much faster than Gb,p[t] or θb,p[t] (10× to 1000×)
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
0
1
2
3
4
5
6
Ang
leof
arriv
al
θ1,1 variation with time
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
0
1
2
3
4
5
6
Inst
anta
neou
sph
ase
φ1,1 variation with time
![Page 25: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/25.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Coherence time as a function of N
Factφb,p[t] changes much faster than Gb,p[t] or θb,p[t] (10× to 1000×)
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
0
1
2
3
4
5
Am
plitu
deof
chan
nelc
oeffi
cien
t
Channel coefficient amplitude evolution in time
Element 1Element 2
|h1| and |h2| variation
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
−4
−3
−2
−1
0
1
2
3
4
Pha
seof
chan
nelc
oeffi
cien
t
Channel coefficient phase evolution in time
Element 1Element 2
Phase variation
![Page 26: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/26.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Coherence time as a function of N
Factφb,p[t] changes much faster than Gb,p[t] or θb,p[t] (10× to 1000×)
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
0
1
2
3
4
5
Am
plitu
deof
chan
nelc
oeffi
cien
t
Channel coefficient amplitude evolution in time
Element 1Element 2
|h1| and |h2| variation
0.00 0.02 0.04 0.06 0.08 0.10
Time (s)
−4
−3
−2
−1
0
1
2
3
4
Pha
seof
chan
nelc
oeffi
cien
t
Channel coefficient phase evolution in time
Element 1Element 2
Phase variation
hm changes much faster than spatial parameters θ or G
![Page 27: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/27.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Quantifying coherence time
IdeaWhen N →∞, becomes possible to track θ,G
3 2 1 0 1 2 3Angle in the beamspace
0
5
10
15
20
25
30
35
Am
plit
ude
Time 0, 8 antennas
DFT(h) for N = 8
3 2 1 0 1 2 3Angle in the beamspace
0
100
200
300
400
Am
plit
ude
Time 0, 256 antennas
DFT(h) for N = 256
DFT(h) =
{1√N
N−1∑n=0
hne−j2πkn/N
}N−1k=0
Coherence time of r = |∑n hnωn|2 can be much larger
![Page 28: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/28.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Quantifying coherence time
IdeaWhen N →∞, becomes possible to track θ,G
3 2 1 0 1 2 3Angle in the beamspace
0
5
10
15
20
25
30
35
Am
plit
ude
Time 0, 8 antennas
DFT(h) for N = 8
3 2 1 0 1 2 3Angle in the beamspace
0
100
200
300
400
Am
plit
ude
Time 0, 256 antennas
DFT(h) for N = 256
DFT(h) =
{1√N
N−1∑n=0
hne−j2πkn/N
}N−1k=0
Coherence time of r =|∑i hn|2N can be much larger
![Page 29: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/29.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Quantifying coherence time Tc
IdeaFor any time series r(t), look at Ar(t, τ) = E[r(t)r(t+ τ)]
τ
Ar(0, τ)
3 dB
Tc
0
1
![Page 30: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/30.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Autocorrelation function plots for different values of N
0 5 · 10−2 0.1 0.15 0.2
0.5
0.6
0.7
0.8
0.9
1
τ
|Ar(0,τ)/A
r(0,0)|
N = 1N = 2N = 4N = 32
Note that coherence time increases for increasing N
![Page 31: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/31.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Thus ...
Coherence times can be large for large antenna arrays
Rest of the talk ...How do we exploit that?
![Page 32: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/32.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Thus ...
Coherence times can be large for large antenna arrays
Rest of the talk ...How do we exploit that?
![Page 33: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/33.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Plan
Why large antenna arrays?
Channel models for MIMO large antenna arrays
Noncoherent schemes
Transmission and detection schemes
Conclusions
![Page 34: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/34.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Main assumptions
Fast changing channel unknown, slow fading channel known
Slow changing information depends on the number of multipathcomponents L
• When L large, statistics of the channel known• energy σ2
h for Rayleigh fading• line of sight (LOS) and non-LOS energy for Rician fading
• For small L, the spatial parameters (θ and G) are known
...
User 1
User 2
Base station
PathBeam
![Page 35: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/35.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Related (prior) work
Noncoherent capacity
Capacity when the channel realization is unknown at thetransmitter and the receiver
• Capacity/bounds with knowledge only of channel statistics
• Characterization of noncoherent capacity achievingdistributions
• Error-exponent optimal distributions for channels
We focus instead on the one shot communication problem
![Page 36: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/36.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Related (prior) work
Noncoherent capacity
Capacity when the channel realization is unknown at thetransmitter and the receiver
• Capacity/bounds with knowledge only of channel statistics
• Characterization of noncoherent capacity achievingdistributions
• Error-exponent optimal distributions for channels
We focus instead on the one shot communication problem
![Page 37: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/37.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
The one-shot problem
• Base station has an N element linear antenna array
• User equipments (UEs) have 1 antenna each
Uplink (single antenna UEs to base station)
y =∑i
hixi + ν...
User 1
User 2
Downlink (base station to UEs)
y = hTi x + ν ...
User 1
User 2
Objective
How do we choose transmissions, and how do we detect them?
![Page 38: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/38.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
The one-shot problem
• Base station has an N element linear antenna array
• User equipments (UEs) have 1 antenna each
Uplink (single antenna UEs to base station)
y =∑i
hixi + ν...
User 1
User 2
Downlink (base station to UEs)
y = hTi x + ν ...
User 1
User 2
Short answerDepends heavily on channel characteristics and N
![Page 39: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/39.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Channel models considered in the next few slides
• Narrowband IID Rayleigh fading models• Uplink• Downlink
• Wideband IID fading model• Uplink• Downlink
• Ray tracing models (uplink and downlink)
![Page 40: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/40.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Narrowband IID Rayleigh fading uplink
ObservationIn the uplink,
y ∼ f(‖y‖2,x)
Discussions
• One-shot detection performance depends only on the receivedenergy ‖y‖2
• As N increases, ‖y‖2N con-
verges to ‖x‖2 + σ2 almostsurely
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00
50
100
150
200
250
300
350n = 100
• At detector use threshold energy detection
![Page 41: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/41.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Optimizing transmit constellations
IdeaThe width of the histogram can be derived from the rate functionIx(d) which satisfies
Prob
(∣∣∣∣‖y‖2N− ‖x‖2 − σ2
∣∣∣∣ < d.= e−NIx(d)
)
Design criterion
Choose {x} and thresholds to minimize probability of error ormaximize minx Ix(detection threshold width for x)
Capacity scaling result
For a large N, and a fixed number of users, the rate scales asΘ(log(N)) with a vanishing probability of error
Knowing the channel h does not improve capacity scaling
![Page 42: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/42.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Optimizing transmit constellations
IdeaThe width of the histogram can be derived from the rate functionIx(d) which satisfies
Prob
(∣∣∣∣‖y‖2N− ‖x‖2 − σ2
∣∣∣∣ < d.= e−NIx(d)
)
Design criterion
Choose {x} and thresholds to minimize probability of error ormaximize minx Ix(detection threshold width for x)
Capacity scaling result
For a large N, and a fixed number of users, the rate scales asΘ(log(N)) with a vanishing probability of error
Knowing the channel h does not improve capacity scaling
![Page 43: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/43.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Optimizing transmit constellations
IdeaThe width of the histogram can be derived from the rate functionIx(d) which satisfies
Prob
(∣∣∣∣‖y‖2N− ‖x‖2 − σ2
∣∣∣∣ < d.= e−NIx(d)
)
Design criterion
Choose {x} and thresholds to minimize probability of error ormaximize minx Ix(detection threshold width for x)
Capacity scaling result
For a large N, and a fixed number of users, the rate scales asΘ(log(N)) with a vanishing probability of error
Knowing the channel h does not improve capacity scaling
![Page 44: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/44.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Narrowband IID Rayleigh fading downlink
Observationy = hTx + ν ∼ CN (0, σ2 + P ), independent of N
ResultUnder an average transmit power constraint ‖x‖2 ≤ P, increasingN does not improve detection performance
With IID fading, adding antennas does not help in the downlink
![Page 45: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/45.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Narrowband IID Rayleigh fading downlink
Observationy = hTx + ν ∼ CN (0, σ2 + P ), independent of N
ResultUnder an average transmit power constraint ‖x‖2 ≤ P, increasingN does not improve detection performance
With IID fading, adding antennas does not help in the downlink
![Page 46: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/46.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Wideband IID Rayleigh fading uplink
Setting
B parallel narrowband channels (frequency bins) under total powerconstraint P
bin 0 bin 1 bin 3 bin B. . .
Results
• If B is fixed and N →∞, rates Θ(log2(N)) achievable
• If B →∞ and N fixed, rates proportional to Θ(1) achievable
• Joint scaling : if B = N ε,• for 0 < ε < 0.5, rates close to Θ(B log2(N)) achievable• for ε > 0.5, rates cannot be better than Θ(N0.5)
Too much channel uncertainty for ε > 0.5,bandwidth limited below ε < 0.5
![Page 47: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/47.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Wideband IID Rayleigh fading uplink
Setting
B parallel narrowband channels (frequency bins) under total powerconstraint P
bin 0 bin 1 bin 3 bin B. . .
Results
• If B is fixed and N →∞, rates Θ(log2(N)) achievable
• If B →∞ and N fixed, rates proportional to Θ(1) achievable
• Joint scaling : if B = N ε,• for 0 < ε < 0.5, rates close to Θ(B log2(N)) achievable• for ε > 0.5, rates cannot be better than Θ(N0.5)
Too much channel uncertainty for ε > 0.5,bandwidth limited below ε < 0.5
![Page 48: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/48.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Beyond IID: ray tracing models
Ray tracing with finite number of multipath components
• For a large enough N, no noise or interuser interference
• For a finite N, may experience significant interference
3 2 1 0 1 2 3Angle in the beamspace
0
100
200
300
400
Am
plit
ude
Time 0, 256 antennas
![Page 49: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/49.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Beyond IID: ray tracing models
Ray tracing with finite number of multipath components
• For a large enough N, no noise or interuser interference
• For a finite N, may experience significant interference
Reasons for performance degradation
• Outage: Two rays closer than ∆ from each other causedestructive or constructive interference
• Inter-path interference (IPI): Rays or paths not in outagealso interfere
• Additive receiver noise
Objective
Study number of users B supported with a vanishing outage andgood detection error performance
![Page 50: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/50.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our result
TheoremFor both uplink and downlink, if the number of users B = o(
√N)
then one can choose ∆ with a vanishing outage probability andwith a non-outage diversity gain same as the one with a single user
Diversity gain definition
limN→∞
− log(Probability of error)
N
With a slowly growing number of users, multiuser interferencevanishes even if fast fading not known
![Page 51: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/51.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Our result
TheoremFor both uplink and downlink, if the number of users B = o(
√N)
then one can choose ∆ with a vanishing outage probability andwith a non-outage diversity gain same as the one with a single user
Diversity gain definition
limN→∞
− log(Probability of error)
N
With a slowly growing number of users, multiuser interferencevanishes even if fast fading not known
![Page 52: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/52.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Plan
Why large antenna arrays?
Channel models for MIMO large antenna arrays
Noncoherent schemes
Transmission and detection schemes
Conclusions
![Page 53: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/53.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Noncoherent transceivers
Why noncoherent?
• Do not have to track instantaneous phase/fast fading
• Simpler design
• Energy efficient
• Lower channel feedback rate requirements
Examples of noncoherent architectures
• Energy detectors
• Fourier transform
• Other unitary precoders/receiver shaping transforms notdependent on fast fading
![Page 54: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/54.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Noncoherent transceivers
Why noncoherent?
• Do not have to track instantaneous phase/fast fading
• Simpler design
• Energy efficient
• Lower channel feedback rate requirements
Examples of noncoherent architectures
• Energy detectors
• Fourier transform
• Other unitary precoders/receiver shaping transforms notdependent on fast fading
![Page 55: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/55.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Noncoherent transceivers
Why noncoherent?
• Do not have to track instantaneous phase/fast fading
• Simpler design
• Energy efficient
• Lower channel feedback rate requirements
Examples of noncoherent architectures
• Energy detectors
• Fourier transform
• Other unitary precoders/receiver shaping transforms notdependent on fast fading
![Page 56: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/56.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Noncoherent transceivers
Why noncoherent?
• Do not have to track instantaneous phase/fast fading
• Simpler design
• Energy efficient
• Lower channel feedback rate requirements
Examples of noncoherent architectures
• Energy detectors
• Fourier transform
• Other unitary precoders/receiver shaping transforms notdependent on fast fading
![Page 57: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/57.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Noncoherent transceivers
Why noncoherent?
• Do not have to track instantaneous phase/fast fading
• Simpler design
• Energy efficient
• Lower channel feedback rate requirements
Examples of noncoherent architectures
• Energy detectors
• Fourier transform
• Other unitary precoders/receiver shaping transforms notdependent on fast fading
![Page 58: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/58.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Benefits from noncoherent transceiver
antenna array baseband unitfronthaul (9 Gbps)
• Bit rate requirements• Fronthaul limits the number of antennas that can be supported
N ≤ 9 Gbps
2× bits per sample× bandwidth in hertz× no. of sectors≈ 5
• Noncoherent architectures are independent of the fronthaulrate limits
• Energy consumption• RF front ends for each antenna infeasible• Energy consumption for analog-to-digital converters high• Efficient architectures for energy detection or fixed precoders
![Page 59: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/59.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Plan
Why large antenna arrays?
Channel models for MIMO large antenna arrays
Noncoherent schemes
Transmission and detection schemes
Conclusions
![Page 60: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/60.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Conclusions
Noncoherent architectures promise benefits for large antennaarrays. We discussed how:
• channel fading is different
• noncoherent schemes are optimal according to various metrics
• noncoherent transceiver architectures are practical
TODO...Test theory on real implementations
![Page 61: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/61.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
Conclusions
Noncoherent architectures promise benefits for large antennaarrays. We discussed how:
• channel fading is different
• noncoherent schemes are optimal according to various metrics
• noncoherent transceiver architectures are practical
TODO...Test theory on real implementations
![Page 62: Noncoherent Communications with Large Antenna ArraysMainakch/Talks/Ieee_scv_talk.pdfChannel from user equipment (UE) to mthantenna element is h m Models for single antenna systems](https://reader034.fdocuments.net/reader034/viewer/2022042213/5eb73b235d401a71d561f393/html5/thumbnails/62.jpg)
Motivation Channel models Noncoherent schemes Transceiver architecture Conclusions
The end
Thank you for your attention!