Cross-Layer Design of MIMO Wireless Networks

Andrea GoldsmithStanford University

DAWN ARO MURI Program Review

U.C. Santa CruzOct 5, 2009

Joint work with Y. Chang, R. Dabora, D. Gunduz, I. Maric, Y. Xie

Space: The Final Frontier

Introduction

Multiple antennas add a new degree of freedom in MIMO wireless network design

MIMO increases capacity as well as tradeoff regions available to higher protocol layers

We investigate capacity, performance regions, and cross-layer design to optimize tradeoffs

Crosslayer Protocol Design

ApplicationNetworkAccessLink

Throughput

Delay

Diversity

(T*,Dv*,Dl*)

In MIMO MANETs

Results will lead to optimal layering and insight into layer interfaces

Technical Approach•Capacity via cooperation: Investigate strategies where node cooperation exploits degrees of freedom from multiple antennas

• Capacity with cognition: Extend overlay cognitive techniques to exploit MIMO

• Diversity-multiplexing-delay tradeoffs: Investigate these tradeoffs for multihop MIMO networks.

• End-to-end performance optimization: Optimize end-to-end performance in MIMO MANETs using joint source/channel coding and wireless network utility maximization (WNUM)

Cooperation in MIMO Wireless Networks

Many possible cooperation strategies:Virtual MIMO , generalized relaying and

interference forwarding, one-shot/iterative conferencing, others

“Easy” to extend virtual MIMO to MIMO nodes

Impact of extra antennas on other techniques unclear

Practical issues: Overhead, forming groups, dynamics, synch,…

Generalized Relaying (SISO)

Relaying strategies: Relay can forward all or part of the messages

Much room for innovation Relay can forward interference

To help subtract it out

TX1

TX2

relay

RX2

RX1X1

X2

Y3=X1+X2+Z3

Y4=X1+X2+X3+Z4

Y5=X1+X2+X3+Z5

X3= f(Y3)

Achievable Rates

)|;();,,();,,(

)|;,(),|;(

3322

232121

132121

12322

32111

XYXIRYXXXIRRYXXXIRR

XYXXIRXXYXIR

• The strategy to achieve these rates is: - Single-user encoding at the encoder 1 to send W1

- Decode/forward at encoder 2 and the relay to send message W2

• This region equals the capacity region when the interference is strong and the channel is degraded

for any distribution p(p(x1)p(x2,x3)p(y1,y2|x1,x2,x3)

dest1

dest2

encoder 1

encoder 2

relay

Beneficial to forward bothinterference and message

New Outer Bound via a Genie

Parameters chosen so RX1 obtains less noisy information about W2 then RX2:

1W

2Wrelay

Y1g

Y1

Y2

X1

Y1g= d1X1 +d2X2 + drX3 +d3Z1 +d4Z1’

232321212

32321211

ZXhXXhYZXhXXhY e

where var(Ze)≤var(Z2)

X2

X3

→ Receiver 1 can decode (W1,W2)

Currently extending to MIMO multihop networks

Extension to MIMO and Multihop

Open QuestionsWhich nodes should cooperateWhat (partial) interference should be forwardedHow should interference be cancelled: spatially or via detectionThe questions apply to ad-hoc and cellular infrastructures

Cognitive Radio Paradigms

UnderlayCognitive radios constrained to cause minimal interference to

noncognitive radios

Interweave (Dynamic Spectrum Access)Cognitive radios find and exploit spectral holes to avoid interfering

with noncognitive radios

OverlayCognitive radios overhear and enhance noncognitive radio

transmissions Knowledgeand

Complexity

Cognitive radios sense environment to support new users without hurting legacy users

Capacity of Cognitive MIMO Networks

• Coexistence conditions:• Noncognitive user unaware of secondary users• Cognitive user doesn’t impact rate of noncognitive user

• Encoding rule for the cognitive encoder:• Generates codeword for primary user message • Generates codeword for its message using dirty paper coding• Two codewords superimposed to form final codeword

NCTX

CTX

NCRX

NCRX

NCRX

CRX

RX1

RX2CR

NCR

Achievable rates (2 users)• For MISO secondary users, beamforming is optimal • Maximum achievable rate obtained by solving

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

Rp

Rs

• Closed-form relationship between primary/secondary user rates.

MIMO cognitive users (2 Users)Propose two (suboptimal) cognitive strategies

5, 0.374pP g 15, 0.374pP g

15, 0.707pP g 5, 0.707pP g

D-SVDPrecode based on SVD of cognitive user’s channel

P-SVDProject cognitive user’s channel onto null space between CTX and NCRX, then perform SVD on projection

Multi-user Cognitive MIMO Networks

Achievable rates with two primary users

Cognitive MIMO network with multiple primary users

• Extend analysis to multiple primary users• Assume each transmitter broadcasts to multiple users

• Primary receivers have one antenna • Secondary users are MISO.

• Main Result:• With appropriate power allocation among primary receivers, the

secondary users achieve their maximum possible rate.

Diversity-Multiplexing Tradeoffs in MIMOUse antennas for multiplexing:

Use antennas for diversity

High-RateQuantizer

ST CodeHigh Rate Decoder

Error Prone

Low Pe

Low-RateQuantizer

ST CodeHigh

DiversityDecoder

How should antennas be used?Depends on end-to-end metric.

DMT at High SNR‡

Define family of block codes {C(SNR)} of length T with rate R(SNR)~r log SNR

Define diversity and multiplexing gains asymptotically

rSNRlog

R(SNR)lim SNR

dSNRlog

)(P loglim e

SNRSNR

‡Zheng/Tse 2002

r)r)(n(m(r)d*

Optimizing Diversity vs. MultiplexingClosed-form solution at high SNR

Optimal d*(r*) diversity/multiplexing point minimizes DT

)r(dSNRlog

),,(D loglim **T

SNRQSNR

d*(r*)

DTFor nonasymptotic regime,

Use optimization

DMT in MIMO Multihop Networks

iiii

i WXHM

SNRY

• Quasi-static Rayleigh fading channel

• Channel state known only at the receivers

DMT for Full-duplex RelaysThe relay can receive and transmit simultaneously The DMT for (M1,M2,M3) full-duplex system is

The hop with the minimum diversity gain is the bottleneck

Achieved by decode-and-forward relaying with block Markov structure

Follows easily since DF achieves capacity

)}(),(min{)(3221321

rdrdrd MMMMMMM

Dynamic Decode-and-Forward in Half-duplexIn half-duplex system, TX and RX must share time DDF introduced by Azarian et al. (IT’05) to optimize this

sharingRelay listens until decoding complete, then transmit

DDF achieves the best known DMT for half-duplex relay channels, yet short of the upper bound

We show: Achieves optimal DMT in multi-hop relay channels

Not piece-wise linear, no general closed form expression

Can be cast into a convex optimization problem

Extended to multiple relays

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

Multiplexing gain, (r)

Div

ersi

ty g

ain,

d(r)

DMT of (4,1,3) half-duplex relay channel

d4,1(r)

d1,3(r)

dDDF(r)

dvDF(r)

dfDF(r), a=0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

Multiplexing gain, (r)

Div

ersi

ty g

ain,

d(r)

DMT of (2,2,2) half-duplex relay channel

d2,2(r)

dDDF(r)dvDF(r)

• Multiple full-duplex relays: • DMT dominated by hop with minimum diversity

gain.

• Multiple half-duplex relays: • Odd and even numbered relays transmit in turn. • DDF (with time limitation for successive hops) is

DMT optimal.• DMT dominated by 2 consecutive hops with min.

diversity gain

Multiple Relay Networks

End to End DistortionUse antennas for multiplexing:

Use antennas for diversity High-RateQuantizer

ST CodeHigh Rate Decoder

Low-RateQuantizer

ST CodeHigh

DiversityDecoder

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

Multiplexing gain, (r)

Div

ersi

ty g

ain,

d(r)

DMT of (2,2,2) half-duplex relay channel

d2,2(r)

dDDF(r)dvDF(r)

We optimize the point on the DMT tradeoff curve to minimize distortion

What about delay?• Retransmissions add time diversity at the cost of delay

• Extends DMT to diversity-multiplexing-delay tradeoff• ARQ can be done on each link and/or end-to-end. • The diversity-multiplexing-delay (DMDT) tradeoff has been characterized for point-to-point links:

•Want to extend this to multihop networks• End-to-end distortion can be optimized over the DMDT.

ARQ 1

DRD RARQ 2 ARQ 3

H1 H

2H3

Infinite QueueDelay:k1 Delay:k2 Delay:k3

ARQ E2E

DMDT for MIMO Relay NetworksMi antennas on ith nodeEnd-to-end ARQ: L max ARQ rounds, per hop Li max

ARQ rounds, sum Li = L.Delay sensitive data: end-to-end delay constraint k,

per hop ki delay constraint: sum ki = k.Messages: come and leave a node Poisson Process (in

equilibrium), exponential “service” time with mean Li Transmission outage has two causes

Used all ARQ rounds but still cannot decode Missing a deadline due to queueing and

transmission delayARQ L1

DRD R

ARQ L2 ARQ L3

H1 H

2H3

Messages Poisson rate mu

Messages Received

Infinite QueueDelay:k1 Delay:k2 Delay:k3

Optimal Multihop ARQ Transmission outage probability: P(ARQ error) + P(Delay > k) Finite but high SNR: P(ARQ error) use DMDT, P(Delay > k) derived

from stationary distribution of random delay Optimal ARQ and ki allocation that minimizes the transmission

outage probability Larger Li has smaller P(ARQ error) but larger P(Delay > k), vice

versa Quasi-convex optimization problem, global optimal solution can be

solved

Optimal ARQs For point-to-point MIMO (4,2), L =

10, SNR 20dB As deadline constraint is

relaxed, optimal ARQ converges to maximum allowable (L = 10)

Similar effect for (4,2,2) multihop MIMO relay network

Conclusion Under an end-to-end delay

constraint, using the maximum number of ARQ rounds L is not necessarily optimal

Contrasts with prior ARQ results without a delay constraint

Point-to-point (4,2)

2 hop (4,2, 2)

Open question: Is ARQ best use of 1 bit feedback

What about Interference Cancellation?

• Antennas can be used for multiplexing, diversity, or interference cancellation• Cancel M-1 interferers with M antennas

• What metric best captures the tradeoff?

Diversity/Multiplexing/SINR-1?

Minimizing End-to-End DistortionSource rate: bR bits per source sampleChannel rate: R bits per channel useExpected end-to-end distortion:

At high SNRSource distortion D(R)=2-R

R=rlog(SNR) PoutSNR-d(r)

E[D] SNR-(br) +SNR-d(r)

E[D] minimized for br=d(r)Use optimization at moderate SNR

),()(),(1(][ SNRRPbRDSNRRPDE outout

Layered Source Coding We extend these ideas to layered SCs

By prioritizing source bits, can reduce E[D]Use either a time-division or broadcast strategyOptimize power allocation across layers

Distortion Results

Broadcasting layered source codes hits upper bound for MISO/SIMOFor MIMO, we can achieve the upper bound with 1 bit of feedbackComplex systems don’t have closed-form solns; need optimization (NUM)

Interference in End-to-End DistortionInterference exploitation at the physical layer improves end-to-end

distortion

We have proved a separation theorem for a class of interference channelsSeparate source and channel coding optimal

We found the operating point on the DMT multihop region for minimal distortionUnder delay constraints, optimization needed

Investigating new notions of capacity, distortion, and separation optimalityIncorporate notions of outage and expectation in capacity and end-to-end

distortionFuture work will apply these notions to MIMO multihop networks

Summary and Open QuestionsMIMO improves MANET capacity as well as diversity-multiplexing-delay-

interference cancellation tradeoffs

Much room for innovation in generalized relaying and cognitive techniques for MIMO nodes

Capacity and tradeoff regions still largely uncharacterized

New tools for optimizing the tradeoff region operating point to maximize end-to-end performance metrics are needed

Open questions in MIMO MANET designHow to best use limited feedbackCross-layer design for cognitive MIMO nodesProtocol layering, separation, and interfaces

Throughput

Delay

Diversity

(T*,Dv*,Dl*)