Space: The Final Frontier
Andrea Goldsmith
Stanford University
Joint work with Y. Chang, R. Dabora, D. Gunduz, I. Maric, Y. Xie
DAWN ARO MURI Program Review
U.C. Santa Cruz
Oct 5, 2009
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
In MIMO MANETs
 Application
 Network
Throughput
(T*,Dv*,Dl*)
Delay
 Access
 Link
Diversity
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)
TX1
RX1
Y4=X1+X2+X3+Z4
X1
relay
Y3=X1+X2+Z3
TX2
X3= f(Y3)
X2
Y5=X1+X2+X3+Z5
RX2
 Relaying strategies:
 Relay can forward all or part of the messages


Much room for innovation
Relay can forward interference

To help subtract it out
Achievable Rates
encoder 1
dest1
R2  I ( X 2 , X 3 ; Y2 | X 1 )
relay
encoder 2
R1  I ( X 1 ; Y1 | X 2 , X 3 )
dest2
R1  R2  I ( X 1 , X 2 , X 3 ; Y1 )
R1  R2  I ( X 1 , X 2 , X 3 ; Y2 )
R2  I ( X 2 ; Y3 | X 3 )
for any distribution p(p(x1)p(x2,x3)p(y1,y2|x1,x2,x3)
• 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
Beneficial to forward both
interference and message
New Outer Bound via a Genie
W1
W2
Y1
X1
X2
X3
relay
Y1g
Y1g= d1X1 +d2X2 + drX3 +d3Z1 +d4Z1’
Y2
 Parameters chosen so RX1 obtains less noisy information
about W2 then RX2:
Y 1  h21 X 1  X 2  h23 X 3  Z e
Y2  h21 X 1  X 2  h23 X 3  Z 2
where
var(Ze)≤var(Z2)
→ Receiver 1 can decode (W1,W2)
Currently extending to
MIMO multihop networks
Extension to MIMO and Multihop
 Open Questions
 Which nodes should cooperate
 What (partial) interference should be forwarded
 How should interference be cancelled: spatially or via detection
 The questions apply to ad-hoc and cellular infrastructures
Cognitive Radio Paradigms
Cognitive radios sense environment to
support new users without hurting legacy users
 Underlay
 Cognitive 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
 Overlay
 Cognitive radios overhear and enhance
noncognitive radio transmissions
Knowledge
and
Complexity
Capacity of Cognitive MIMO Networks
NCRX
NCR
RX1
NCTX
NCRX
NCRX
CR
RX2
CTX
CRX
• 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
Achievable rates (2 users)
• For MISO secondary users,
beamforming is optimal
• Maximum achievable rate obtained by solving
• Closed-form relationship between primary/secondary user rates.
3.6
3.4
3.2
Rs
3
2.8
2.6
2.4
2.2
2
0.4
0.6
0.8
1
1.2
Rp
1.4
1.6
1.8
2
MIMO cognitive users (2 Users)
Propose two (suboptimal) cognitive strategies
D-SVD
Precode based on SVD of
cognitive user’s channel
P-SVD
Pp  5, g  0.374
Pp  15, g  0.374
Project cognitive user’s
channel onto null space
between CTX and NCRX, then
perform SVD on projection
Pp  5, g  0.707
Pp  15, g  0.707
Multi-user Cognitive MIMO Networks
• 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.
Cognitive MIMO network
with multiple primary users
Achievable rates with
two primary users
Diversity-Multiplexing Tradeoffs in MIMO
 Use antennas for multiplexing:
High-Rate
Quantizer
ST Code
High Rate
Decoder
Error Prone
 Use antennas for diversity
Low-Rate
Quantizer
ST Code
High
Diversity
Decoder
Low Pe
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
log Pe ( SNR )
lim
 d
SNR 
log SNR
R(SNR)
lim
r
SNR  log SNR
‡Zheng/Tse
2002
d (r)  (m  r)(n  r)
*
Optimizing Diversity vs. Multiplexing
 Closed-form solution at high SNR
log D T (Q, SNR,  )
lim
 d * ( r * )
SNR 
log SNR
 Optimal d*(r*) diversity/multiplexing point minimizes DT
 For nonasymptotic regime,
 Use optimization
DT
d*(r*)
DMT in MIMO Multihop Networks
•Quasi-static Rayleigh fading channel
Yi 
SNR
H i X i  Wi
Mi
•Channel state known only at the receivers
DMT for Full-duplex Relays
 The relay can receive and transmit simultaneously
 The DMT for (M1,M2,M3) full-duplex system is
d M1M 2 M 3 (r )  min{d M1M 2 (r ), d M 2 M 3 (r )}
 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
Dynamic Decode-and-Forward in Half-duplex
 In half-duplex system, TX and RX must share time
 DDF introduced by Azarian et al. (IT’05) to optimize this
sharing
 Relay 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
DMT of (4,1,3) half-duplex relay channel
4
3.5
d
4,1
(r)
Diversity gain, d(r)
3
2.5
d
1,3
(r)
2
dDDF(r)
1.5
d
1
(r), a=0.5
fDF
d
(r)
vDF
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Multiplexing gain, (r)
0.7
0.8
0.9
1
DMT of (2,2,2) half-duplex relay channel
4
3.5
Diversity gain, d(r)
3
2.5
d2,2(r)
2
dvDF(r)
1.5
dDDF(r)
1
0.5
0
0
0.2
0.4
0.6
0.8
1
1.2
Multiplexing gain, (r)
1.4
1.6
1.8
2
Multiple Relay Networks
• 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
End to End Distortion
 Use antennas for multiplexing:
High-Rate
Quantizer
ST Code
High Rate
Decoder
DMT of (2,2,2) half-duplex relay channel
4
3.5
 Use antennas for diversity
Diversity gain, d(r)
3
2.5
d2,2(r)
2
dvDF(r)
1.5
dDDF(r)
1
0.5
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Multiplexing gain, (r)
Low-Rate
Quantizer
ST Code
High
Diversity
Decoder
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 E2E
ARQ 1
Infinite
Queue
Delay:k1
D
H1
ARQ 3
ARQ 2
Delay:k2
Delay:k3
R
H2
R
H3
D
DMDT for MIMO Relay Networks
 Mi antennas on ith node
 End-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 delay
ARQ L1
ARQ L2
ARQ L3
Infinite
Queue
Delay:k1
Messages
Poisson rate
mu
D
H1
Delay:k2
Delay:k3
R
H2
R
H3
D
Messages
Received
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
Point-to-point (4,2)
 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
2 hop (4,2, 2)
 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
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 Distortion
 Source rate: bR bits per source sample
 Channel rate: R bits per channel use
 Expected end-to-end distortion:
E[ D]  (1  Pout ( R, SNR) D(bR)  Pout ( R, SNR)
 At high SNR
 Source distortion D(R)=2-R
 R=rlog(SNR)
 PoutSNR-d(r)
 E[D] SNR-(br) +SNR-d(r)
 E[D] minimized for br=d(r)
 Use optimization at moderate SNR
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 strategy
 Optimize power allocation across layers
Distortion Results
 Broadcasting layered source codes hits upper bound for MISO/SIMO
 For MIMO, we can achieve the upper bound with 1 bit of feedback
 Complex systems don’t have closed-form solns; need optimization (NUM)
Interference in End-to-End Distortion
 Interference exploitation at the physical layer improves end-
to-end distortion
 We have proved a separation theorem for a class of
interference channels
 Separate source and channel coding optimal
 We found the operating point on the DMT multihop region
for minimal distortion
 Under delay constraints, optimization needed
 Investigating new notions of capacity, distortion, and
separation optimality
 Incorporate notions of outage and expectation in capacity and
end-to-end distortion
 Future work will apply these notions to MIMO multihop
networks
Summary and Open Questions
 MIMO 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
Throughput
 Open questions in MIMO MANET design
(T*,Dv*,Dl*)
Delay
 How to best use limited feedback
 Cross-layer design for cognitive MIMO nodes
 Protocol layering, separation, and interfaces
Diversity