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

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


Wireless propagation


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


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


The promise with large antenna arrays

Better cellular network with heterogenous demand (objects andpeople)


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!


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!


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


Our contributions






Our contributions






Plan

Why large antenna arrays?

Channel models for MIMO large antenna arrays

Noncoherent schemes

Transmission and detection schemes

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


Fading models












Fading models












Fading models












Fading models












Fading models












Fading models












Fading models












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



Main assumptions




and


...

User 1

User 2

Base station

PathBeam

hm =1√L

L∑p=1


λ

Implications


• As L→∞, h ∼ CN (0, I)

⇒ IID Rayleigh fading



Main assumptions




and


...

User 1

User 2

Base station

PathBeam

hm =1√L

L∑p=1


λ

Implications


• As L→∞, h ∼ CN (0, I) ⇒ IID Rayleigh fading


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




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




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




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


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


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


Quantifying coherence time

IdeaWhen N →∞, becomes possible to track θ,G


0

5

10

15

20

25

30

35

Am

plit

ude

Time 0, 8 antennas

DFT(h) for N = 8


0

100

200

300

400

Am

plit

ude


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


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


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


Thus ...

Coherence times can be large for large antenna arrays

Rest of the talk ...How do we exploit that?


Thus ...

Coherence times can be large for large antenna arrays

Rest of the talk ...How do we exploit that?


Plan



Noncoherent schemes


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


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


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


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?


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


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)


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


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




Prob

(∣∣∣∣‖y‖2N− ‖x‖2 − σ2

∣∣∣∣ < d.= e−NIx(d)

)

Design criterion








Prob

(∣∣∣∣‖y‖2N− ‖x‖2 − σ2

∣∣∣∣ < d.= e−NIx(d)

)

Design criterion






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


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


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


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


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


0

100

200

300

400

Am

plit

ude



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


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


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


Plan



Noncoherent schemes


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



Why noncoherent?


• Simpler design









Why noncoherent?


• Simpler design









Why noncoherent?


• Simpler design









Why noncoherent?


• Simpler design








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


Plan



Noncoherent schemes


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


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


The end

Thank you for your attention!

Documents

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