distributed beamforming and cooperative communications … · distributed beamforming and...

Distributed Beamforming and CooperativeCommunications for Next Generation Wireless

Broadband Systems

Hamid Jafarkhani

Center for Pervasive Communications and ComputingUniversity of California, Irvine

http://newport.eecs.uci.edu/∼hamidj/

Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems1 / 64

Outline

Trends in wireless communication technologies

Cooperative Communications

Beamforming

Distributed (network) beamforming

Distributed beamformnig with quantized feedback

Distributed beamforming in relay-interference networks withquantized feedback

Conclusions


Characteristics of D2D Networks

Very large number of nodes (Trillion ?)I Sensor networks are used more oftenI Body area networks are gaining more attention

Self organized and autonomously operated

Operating through different domains (wireless and wired)seamlessly

Low latency

Low power


Beyond 4G

4Gs Peak Service Rate RequirementsI 100 Mb/s (high mobility)I 1 Gb/s (low mobility)

Other important factorsI Spectral efficiency enhancementI ServicesI Quality of experienceI Energy efficiency


Connectivity

Data rate at the edge of a cell is worse than the data rate at thecenter (10 times)

1

Interference at the edge of a cell is moreConnectivity is application dependent (content-aware networking)

I Connected for voiceI Not connected for video


Mobile traffic

The number of mobile-connected devices exceeded the worldspopulation in 2014 (it will be 11.5 Billion in 2019)

Total mobile traffic was 30 Exabytes in 2014 (the entire Internettraffic was 1 Exabyte in 2000)

Mobile video traffic was 55% of the mobile traffic in 2014 (72%in 2019)

The top 1% of mobile data subscribers generated 18% mobiledata traffic in 2014 (top 20% generated 85%)

4G users generate 10 times more traffic (6% of users, 40% oftraffic)

Globally, 46% of total mobile data traffic was offloaded ontoWi-Fi or Femto cell


Landscape in 2025

Billions of (trillion?) devicesI Today: more than a billion wireless subscribers

100 times growth in mobile trafficI more users & more traffic per user

10 times increase in device density10 times less power consumption (Bits/Joule)

I Today: Internet/Telecom infrastructure consumes 3% of the worldsenergy

Same connectivity everywhere (edge vs center)


4G Technologies

MIMOI Space-time coding, beamforming, precoding

Coordinated Multi-Point (CoMP)I Coordinated beamformingI Joint processing

Inter-Cell Interference Coordination (ICIC)I Macro cells, Micro-Pico cells, Femto cells

Higher order QAM


MIMO

Multiple antennas can be utilized toI Increase the throughput (Higher capacity)I Improve the reliability (Diversity)

......

Transmitter Receiver

......


Feedback

Closed loop system


Coordinated Multi-Point

Coherently coordinating the transmission and reception amongmultiple base stations

1


ICIC (Heterogeneous Networks)

Offloading: traffic from dual-mode devices over Wi-Fi andsmall-cell networks

45% of the total mobile data traffic from all mobile-connecteddevices is offloaded


Sources of Interference in HetNet

Large number of created cell boundaries

The adhoc nature of femto cell deployment

Power difference between nodes

Strong local signal of a femto cell can become interference for alocal user who is not subscribed to the femto cell


Need for a paradigm shift

Current wireless networks include many users and many datatransmitted simultaneously, but we allocate independentresources through routing, scheduling, · · · to send A’s messageto B without interference

What if we literally allow simultaneous transmission?

Point-to-Point =⇒ Many-to-Many

Competition =⇒ Cooperation


Many to many

Transmitter-1

Transmitter-2

Receiver-1

Receiver-2


Many to many with cooperation

......

...

...

...

...

...

+

+

Transm

itter 1

Transm

itter K

Receiv

er1

Receiv

erL

Relay1

Relay2

RelayR−1

RelayR


MIMO advantages

......


Multiplexing gain

Diversity

Array gain

Interference cancellation


Diversity and array gain

0 2 4 6 8 10 12 14 16 18 2010

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Bit

Err

or R

ate

(BE

R)

Signal−to−Noise Ratio (SNR), (dB)

Performance of a wireless communication system

Diversity gain = 2

Diversity gain = 4

Diversity gain = 4,and more array gain


Relay networks

......

...

Transm

itter R

eceiver

Relay1

Relay2

RelayR−1

RelayR

1


Cooperative strategies

Amplify and forward

Decode and forward

Coded cooperation

Compress/estimate and forward

Distributed space-time coding

· · ·


Amplify and forward

A simple and easy to implement protocol:I The relay amplifies its received signal t by a factor a.I a may depend on channel states, etc.


Decode and forward

In general s 6= s (decoding errors).I Good performance especially when the source-to-relay channel is good.


Distributed space-time coding

One can generate a space-time code using multiple distributed relays.I No need for CSI at relays, full spatial diversity, usually with simple

decoding.

......

... +

Transm

itter R

eceiver

s y

Relay1

Relay2

RelayR−1

RelayR

r1 t1

r2 t2

rR−1 tR−1

rR tR

f1

f2

fR−1

fR

g1

g2

gR−1

gR

1

s =[s1 · · · sT

]Tri = fis + ν i yi =

∑Ri=1 giti + w

ti = Ai ri + Bi ri


Properties ofdistributed space-time codes

Full diversity

Simple decoding

Simple relaying (linear codewords)

Scale-free: If some of the relays do not exist, the codestill works and provides the highest possible diversity.


Distributed beamforming

What if we know all the channel information at therelays as well?

Separate short-term power constraints on relays.

Adaptive Relay Power Control


Distributed beamforming

......

... +

Transm

itter R

eceiver

s y

Relay1

Relay2

RelayR−1

RelayR

r1 t1

r2 t2

rR−1 tR−1

rR tR

f1

f2

fR−1

fR

g1

g2

gR−1

gR

1

ti = xi ri = αiejθi ri .

Power constraint on each relay Pi .


MIMO beamforming

xi = αiejθi with αi = |hi |

‖h‖ , θi = − arg(hi).


MIMO beamforming withperfect feedback

Scalar coding and 1-dimensional beamforming is optimal.

Beamforming provides the maximum array gain and full diversity.

Tx

Rx

BeamTx

Rx


MIMO channel with feedback

......


Feedback

Closed loop system


Importance of limited feedback

About 30% of the traffic is feedback:I Physical locationI Channel state information (CSI)I RTS/CTS, ACK and other signalingI · · ·

Role of feedbackI BeamformingI PrecodingI Power/rate controlI Collision controlI Routing and schedulingI Resource management/allocationI · · ·


Channel feedback quality

If the feedback quality drops too low, thebeamforming scheme should gradually fall back to thenon-beamformed scheme.

Perfect Channel Feedback =⇒ Beamforming

No Channel Feedback =⇒ Space-Time Coding

What shall we do in between?


High quality feedback links

Diversity Gain Array Gain

Space-time Coding M 1

Perfect beamforming M M

Quantized beamforming M M − (M − 1)2−r

M−1

To achieve the full CSIT, perfect beamforming results, do we reallyneed r =∞ bits of feedback?

Is there a similar analysis for distributed beamforming, i.e., for relaynetworks?


Block diagram of a quantizedbeamforming system

Transmitter

Receiver

Inputbits

Baseband singledata stream

Use the codewordto transmit

Codebook

ChannelEstimation

FeedbackChannel

Select thebest codeword

Codebook

DecoderDecoded

bits

1


Outage probability as an example

h


The M-antenna transmitter wishes to communicate with data rate ρand has a power constraint P. The channel state is h ∈ CM .

The transmitter sends sx?√P.

I s ∈ C is a unit-energy Gaussian symbol.I x ∈ CM is a unit-norm beamforming vector.

Maximum reliable communication rate log2(1 + |〈x,h〉|2P).1 P-normalized SNR |〈x,h〉|2 < α , 2ρ−1

P : Outage.2 |〈x,h〉|2 ≥ α: No outage.


Variable-length feedback

Quantizer q := {xn, En, bn}I .

h

Find n with h ∈ En

Transmitter

Uses xn = q(h)

Receiver

Feed back bn

Channel: h ∼ CN(0, IM).

Quantized beamforming vector: q(h) ∈ CM with ‖q(h)‖ = 1.

{bn}I ⊂ {ε, 0, 1, 00, 01, . . .}.We are in outage if |〈q(h),h〉|2 < α.

Minimize the outage prob. P(|〈q(h),h〉|2 < α) s.t. R(q) ≤ r .

The best outage probability is out? = P(‖h‖2 < α).


Fixed-length designs

A fixed-length quantizer that is optimal forcodebook B:

qB(h) = arg maxx∈B|〈x,h〉|2.

How to design a good codebook:I Distribute the reproduction vectors

“uniformly” on the unit-norm complexhypersphere: Grassmannian codebooks,etc.

outf (r) ∼ out? + CαM

eα 2−r

M−1 [Mukkavilli et al.,

2003]

x1

x2

x3

x4

‖h‖ = 1

‖h‖ = ∞

1


Variable-length designs - Take 1

Try: Fixed-length codecells +variable-length code. Does not work.

Then, is outv (r) ∼ outf (r) > out??

No, we can do much better.outv (r0) = out? at finite r0.

x1

x2

x3

x4

‖h‖ = 1

‖h‖ = ∞

1


Optimal variable-length designs

The best outage prob. with codebook B:

P(maxx∈B|〈x,h〉|2 < α)

Fixed-length quantizer: qB(h) = arg maxx∈B |〈x,h〉|2Overkill

Unavoidable outage:I Consider an h with |〈x,h〉|2 < α, ∀x ∈ B.

Does it matter which vector I choose?

More than one “good” vector:I Consider an h with |〈x,h〉|2 ≥ α and |〈y,h〉|2 ≥ α, x, y ∈ B.

Does it matter which one of x and y I choose?


Optimal variable-length designs

Given codebook {x0, x1, . . . , } design the encoding regions:

E?0 = {h : x0 does not result in outage or

all the vectors x0, x1, . . . result in outage}.E?1 = {h : x1 does not result in outage but

x0 results in outage}.E?2 = {h : x2 does not result in outage but

x0 and x1 result in outage}.E?3 = {h : x3 does not result in outage but

x0, x1 and x2 result in outage}.and so on..

The quantizer q? := {xn, E?n , ·} is optimal for {xn}.


Geometric interpretation

‖h‖ =√α

‖h‖ = ∞

‖h‖ = 1

x−x

|〈x,h〉|2 < α

|〈x,h〉|2 ≥ α|〈x,h〉|2 ≥ α

1

x0

x1x3

x2

E⋆0

E⋆0

E⋆0

E⋆1

E⋆1

E⋆2

E⋆2

E⋆3

E⋆3

E?0 = {h : |〈x0,h〉|2 ≥ α or |〈xi ,h〉|2 < α, ∀i}.E?n = {h : |〈xn,h〉|2 ≥ α} − (E?0 ∪ · · · ∪ E?n−1), n ≥ 1.


Results

Theorem

The minimum (Full-CSIT) outage probability is achievable with rater0 , e−α[α + C (α2 + αt)].

Recall α = 2ρ−1P .

r0 → 0 as r0 ∈ α + o(α) for α→ 0 (High transmission power).

r0 → 0 for α→∞ (Low transmission power).

Achieving the performance of the full-CSIT system with a finitefeedback rate is possible!


Example: 2× 1 system

R(q⋆F)

OUT(open)

OUT(q⋆F)

OUT(Full)

P (dB)

Outage

probab

ilityor

Feedbackrate

10

1

10−1

10−2

10−3

10−4

10−5

10−6

−10 −5 0 5 10 15 20 25 30


Distributed beamforming withperfect feedback

......

... +

Transm

itter R

eceiver

s y

Relay1

Relay2

RelayR−1

RelayR

r1 t1

r2 t2

rR−1 tR−1

rR tR

f1

f2

fR−1

fR

g1

g2

gR−1

gR

1

ti = xi ri = αiejθi ri .


Distributed beamformingproblem formulation

Optimize the received SNR:

maxx

|〈f,Ax〉|2P0

1 + ‖Ax‖2 = maxy

P0|〈c, y〉|21 + ‖y‖2 ,

where f =[f1 · · · fR

]H, and A = diag

{g1√P1√

1+|f1|2P0· · · gR

√PR√

1+|fR |2P0

}.

Total power constraint:‖x‖2 ≤ 1.

1

Individual power constraint:‖x‖∞ ≤ 1 (|xi | ≤ 1, ∀i).

1


Comparing MIMO &distributed beamforming

Differences:

IAntennas can share power in MIMO (total powerconstraint), ‖x‖2 ≤ 1.

1

I Antennas know the transmitted signals perfectly in MIMO.

Consequences:

IIndividual (separate) power constraints, ‖x‖∞ ≤ 1.This results in a non-convex optimazation problem.

1

I Distributed solutions.


Distributed solution

An analytical closed-form solution exists despite the non-convex nature

of the optimization problem.

Properties of the optimal solution:I The optimal xi is not binary.I At least one relay uses its full power.I The optimal xi depends on all the channels, not just the ith relay’s

channels.I The optimal beamforming coefficient can be calculated using

1 A global parameter (fed back by the receiver), and2 A local parameter (calculated using the relay’s own channels).


Simulation results:2 Relays (BPSK)

10 12 14 16 18 20 22 24

10−4

10−3

10−2

10−1

Power (dB)

Blo

ck e

rror

rat

e

Alamouti DSTCNetwork beamformingBest relay selectionAF without power control


Simulation results:3 Relays (BPSK)

6 8 10 12 14 16 1810

−4

10−3

10−2

10−1

Power (dB)

Blo

ck e

rror

rat

e

AF without power controlNetwork beamformingBest relay selection


Relay networks withquantized feedback

......

... +

Transm

itter R

eceiver

s y

Relay1

Relay2

RelayR−1

RelayR

t1 u1

t2 u2

tR−1 uR−1

tR uR

f1

f2

fR−1

fR

g1

g2

gR−1

gR

B feedback bits

1


Distributed beamforming withlimited feedback

Each relay has B bits of partial CSI provided by thereceiver.

The feedback channel is error-free and delay-free.

The information each relay receives from the feedbackis the same.

Common codebook: C = {x1, . . . , xM}, containsM = 2B beamforming vectors.


Main results

Maximal diversity with the relay selection scheme

The relay selection scheme achieves the full diversity order R forB = dlog2 Re.In general, the diversity order min(2B ,R) is achievable with quantizedfeedback.

SNR/Capacity loss with quantized feedback

Both the ergodic capacity loss and the SNR loss with quantizedfeedback decays at least exponentially with the number of feedbackbits B,

E[SNR/Capacity loss] ≤ C2− B

2(R−1) .


Simulation results

2 relays, Selection2 relays, 1 bit2 relays, 2 bits2 relays, 4 bits2 relays, ∞ bits

0 2 4 6 8 10 12 14 16 18 20 22 24 2610

−5

10−4

10−3

10−2

10−1

P (dB)

BE

R

4 relays, Selection4 relays, 2 bits4 relays, 4 bits4 relays, 8 bits4 relays, ∞ bits


A natural generalization

......

...

...

...

...

...

+

+

Transm

itter 1

Transm

itter K

Receiv

er1

Receiv

erL

Relay1

Relay2

RelayR−1

RelayR

How to deal with (wanted or unwanted) interference while preservingcooperative diversity benefits?


Beamforming in relay-interferencenetworks

......

...

...

...

...

...

+

+

Transm

itter 1

Transm

itter K

Receiv

er1

Receiv

erL

Relay1

Relay2

RelayR−1

RelayR

K transmitters, R relays in parallel, L receivers.

Each node has a single antenna in half-duplex mode.

Quasi-static channel model.


CSI knowledge

......

...

...

...

...

...

+

+

Transm

itter 1

Transm

itter K

Receiv

er1

Receiv

erL

s1

sK

v1

vL

Relay1

Relay2

RelayR−1

RelayR

t1 u1

t2 u2

tR−1 uR−1

tRuR

f11f12

f1,R−1

f1R

fK1

fK2

fK,R−1

fKR

g11g21

gR−1,1

gR1

g1L

g2L

gR−1,L

gRL

B feedbackbits

The rth relay knows fir .

Receiver ` knows all fir and gr`.

Each relay and receiver has B bits of partial CSI provided by feedback.


How to provide the feedback?

......

...

...

...

...

...

+

+

Transm

itter 1

Transm

itter K

Receiv

er1

Receiv

erL

s1

sK

v1

vL

Relay1

Relay2

RelayR−1

RelayR

t1 u1

t2 u2

tR−1 uR−1

tRuR

f11f12

f1,R−1

f1R

fK1

fK2

fK,R−1

fKR

g11g21

gR−1,1

gR1

g1L

g2L

gR−1,L

gRL

B feedbackbits

Two quantization schemes:I Global quantizationI Local quantization


Maximal achievable diversityTake - 1

Claim: The maximal achievable diversity in the interference-network isR regardless of the relay operation (AF or DF) or the quality of thefeedback.

The claim is true but incomplete.


Diversity measures

Generalized Diversity

Suppose that NER(Q) =C

Pd1(logP)d2. Then,

d1 is the first-order diversity.

d2 is the second-order diversity.

The overall diversity is the tuple (d1, d2).


Visualizing second-order diversity

Two hypothetical wireless communication schemes:

P (dB)

Pe

Pe =4P 2

Pe =log2 PP 2

5 10 15 20 25 3010−6

10−5

10−4

10−3

10−2

10−1

100

The red scheme with Pe = log2 PP2 has diversity (2,−2).

The blue scheme with Pe = 4P2 has diversity (2, 0).

The error probability with the red scheme “decays much slower”


Maximal achievable diversityTake - 2

Claim: The maximal achievable diversity in the interference-network is Rregardless of the relay operation (AF or DF) or the quality of the feedback.

Refined claim:

Diversity Bounds

The maximal diversity in the relay-interference network isI For amplify-and-forward relays:

F (R, 0) if K = 1 (no-interference scenario).F (R,−R) if K > 1 (interference scenario).

I For decode-and-forward relays:F (R, 0) for any K .

Interference results in a second-order diversity loss for AF.


Main diversity results

Maximum

Diversity

AF DF

K = 1 (R, 0) (R, 0)

K > 1 (R,−R) (R, 0)

Diversity with different quantization strategies

1 Fixed-length Global quantizers achieve the optimal diversity gain withdlog2 Re bits of global feedback per channel state.

2 Fixed-length local quantizers achieve the optimal first-order diversitygain, but they incur a second-order diversity loss of R.

3 Variable-length local quantizers are diversity-optimal. The averagenumber of feedback bits per receiver vanishes as P →∞.

Relay-selection-based quantizers can achieve the optimal diversity gains.


Main Results

How to deal with (wanted or unwanted) interference while preservingcooperative diversity benefits?

Broadest sense: Network beamforming with distributed quantization.I DF relays achieve full diversity. AF achieves full first-order diversity.I In any case, feedback overhead is extremely low at high power.

Specific relaying method: Choice depends on the system resourcesand the amount of complexity one can tolerate (DF vs AF).


Main Results forRelay-Interference Networks

Traditional diversity definitions may not be good enough to comparethe asymptotic reliability of different communication systems.

Despite interference, multi-user relay networks can provide the samediversity as single-user networks.

In terms of diversity, relay selection is an optimal codebook usingquantized feedback information.

Very low-rate CSI quantizers exist that achieve full diversityasymptotically with zero feedback rate.


Conclusions

Tremendous challenges need to be addressed to satisfy the demandsof future wireless communication networks.

There is a need for paradigm shifts

Point-to-Point =⇒ Many-to-Many

Competition =⇒ Cooperation

The optimal design of feedback systems is a crucial component ofcurrent and future communication systems

Source coding theory plays an important role in the design offeedback systems


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