ITLinQ: A New Approach for Spectrum Sharing in Device-to-Device Networks

Salman Avestimehr

In collaboration with Navid Naderializadeh

ITA 2/10/14

D2D Communication •  Device-to-Device (D2D) communication is expected

to play a key role in future wireless networks •  Will be the backbone for

Ø  Communication Ø  Control and Sensing Ø  Proximal Interaction

Key Bottleneck (at PHY) •  Interference control (or spectrum sharing) and coordination

•  Main issues as the network becomes large and complex

How to Deal with the Interference?

Fully-coordinated Cellular-type Fully Distributed WiFi-type

Hard to implement in Practice! Degraded Performance for large number of users

Another Approach …

• Rely on a small level of coordination for scheduling links

Ø Use a “conflict graph” to describe when interference among a set of users is “low enough”

Ø Schedule a set of non-conflicting users at each time Ø Treat the interference among them as noise

• Two key challenges Ø How to define the conflict graph? Ø How to design a scheduler with minimal coordination?

How to define the conflict graph? •  Two common approaches

1.  “Geometric”: •  Comparing Interference-to-noise ratio (INR) to a

fixed threshold •  If INR between two users is below threshold, they

are considered non-conflicting (i.e., independent)

•  In a path-loss fading, this corresponds to a “fixed distance-guard”

Criteria: INR ≤ γIS

•  “Qualcomm’s FlashLinQ”: •  Comparing Signal-to-interference ratio (SIR) to a

fixed threshold •  If SIR between two users is above threshold, they

are considered non-conflicting (i.e., independent)

•  In a path-loss fading, this corresponds to an “adaptive distance guard”

Criteria: SIR ≥ γ

How to define the conflict graph?

* X. Wu, S. Tavildar, S. Shakkottai, T. Richardson, J. Li, R. Laroia, and A. Jovicic, “FlashLinQ: A Synchronous Distributed Scheduler for Peer-to-Peer Ad Hoc Networks,” IEEE/ACM Transactions on Networking, vol. 21, no. 4, pp. 1215-1228, Aug. 2013.

FlashLinQ

Metric: SIR ≥ γ

A theoretically-justified criteria?

How to define the conflict graph?

Geometric

Metric: INR ≤ γ

Why not, for example, p

SNRINR

� �

Our proposal: Information-Theoretic Conflict Graph

A set of users in a wireless network form an information-theoretic independent set (ITIS) (i.e., are non-conflicting), if

Ø  treating interference as noise (TIN) is information-theoretically optimal for the sub-network created by them

Condition for Optimality of TIN •  Question: Under what condition, power control and

treating interference as noise (TIN) is optimal? •  Not  much  is  known  about  its  op2mality  (except  for  some  

symmetric  and  very  low  interference  regimes)!  •  TIN  region  is  hard  to  analyze  analy2cally  

•  Includes  a  (hard)  op2miza2on  problem  for  power  control  (e.g.  Foschini-­‐Milijanic  1993,  Tan-­‐Chiang-­‐Srikant  2013)  

•  Can  be  characterized  through  solving  a  sequence  of  GP’s  (Mahdavi  et  al  2008)    

•  Non-­‐explicit  and  non-­‐convex  region  in  general  •  Very  few  general  bounds  on  the  capacity  region  of  K-­‐user  IC  

     Theorem:  In  a  K-­‐user  interference  channel,  if  

 Ø TIN  achieves  the  capacity  region  within  a  constant  gap  of  log2(3K)  bits,  Ø TIN  region  is  approximated  by  a  polyhedron.  

•  In  words,  the  condi2on  is  

Optimality  condition  for  TIN  

T1#

T2#

TK#

R1#

R2#

RK#

↵11

↵21

“at  each  user,  the  desired  channel  strength  is  at  least  the  sum  of  the  strengths  of  the    strongest  interference  from  this  user  and  the  strongest  interference  to  this  user”  

*C.  Geng,  N.  Naderializadeh,  A.  S.  Aves2mehr,  and  S.  A.  Jafar  “On  the  Op2mality  of  Trea2ng  Interference  as  Noise”,  submi\ed  to  IT.  

SNRi � max

j:j 6=iINRji ⇥max

j:j 6=iINRij , 8i 2 {1, 2, . . . ,K}

     Theorem:  In  a  K-­‐user  interference  channel,  if  

 Ø TIN  achieves  the  capacity  region  within  a  constant  gap  of  log2(3K)  bits,  Ø TIN  region  is  approximated  by  a  polyhedron.  

•  In  words,  the  condi2on  is  

Optimality  condition  for  TIN  

“at  each  user,  the  desired  channel  strength  is  at  least  the  sum  of  the  strengths  of  the    strongest  interference  from  this  user  and  the  strongest  interference  to  this  user”  

SNRi � max

j:j 6=iINRji ⇥max

j:j 6=iINRij , 8i 2 {1, 2, . . . ,K}

Definition of ITIS and ITLinQ •  In a network of n users, S⊆{1,…,n} is called an information-

theoretic independent set (ITIS) if for any user i  ∈  S

•  Information-theoretic link scheduling (ITLinQ) •  Identify an ITIS and schedule the users in ITIS to transmit together •  Each destination treats all its incoming interference as noise

A Simpler Sufficient Condition …

•  S forms an ITIS if for any user i  ∈  S

FlashLinQ

Metric:

ITLinQ

Metric: p

SNRINR

� �

SNRINR

� �

Geometric

Metric: INR ≤ γ

How good is ITLinQ?

•  n source-destination pairs •  Sources located uniformly at random in a circle of radius R •  Each destination located within a distance rn=r0n-β  of its

corresponding source, β  >0 •  Channel gain at distance r is equal to h0r -α (path loss)

rn ∝  n-β

R

Capacity Analysis of ITLinQ •  Theorem*: In the described setting, when n→∞, ITLinQ can

almost-surely achieve a fraction λ of the capacity region within a gap of k bits, where

* N. Naderializadeh and A. S. Avestimehr, “ITLinQ: A New Approach for Spectrum Sharing in Device-to-Device Communication Systems”, submitted to IEEE JSAC Special Issue on 5G Wireless Communications

rn ∝  n-β

R

Comparison with Geometric approach

rn ∝  n-β

R

Closest AP-Selection Model •  All sources and destinations located randomly and

uniformly inside a circle of radius R

•  Each destination gets associated with its closest source

•  Corollary: In the above model, ITLinQ can achieve a

fraction of the capacity region ⇥(1pn

)

⇥(

pn) gain over the geometric approach

Proof Sketch of the Theorem

•  If the distance between sources in S⊆{1,…,n} is greater than dth,n, where then S is an ITIS.

•  Convert the network to information-theoretic conflict graph Gn •  Nodes: {1,…,n} •  Edges: i and j are connected if the

distance between Si and Sj is not greater than dth,n

•  Gn is a random geometric graph

•  ITLinQ can achieve 1/χ(Gn) fraction of capacity region

≤ dth,n

> dth,n

Comparing with FlashLinQ •  Links (S-D pairs) dropped uniformly in a 1km ×1km square •  Length of each link ~ u(0,40m)

•  Two-way training is used for estimating local channels at each node •  At each phase a (random) priority order is assigned to all links in the network •  Link j will be active in that phase if

1)  At destination j:

2)  At source j:

1km

Transmit power: 20 dBm Noise PSD: -174 dBm/Hz Channel model: ITU-1411 LoS Log-normal shadowing with 10 dB STD

pSNRj

INRij� 1, 8i < j

pSNRj

INRji� 1, 8i < j

Comparing with FlashLinQ •  Links (S-D pairs) dropped uniformly in a 1km ×1km square •  Length of each link ~ u(0,40m)

•  Two-way training is used for estimating local channels at each node •  At each phase a (random) priority order is assigned to all links in the network •  Link j will be active in that phase if

1)  At destination j:

2)  At source j:

1km

Transmit power: 20 dBm Noise PSD: -174 dBm/Hz Channel model: ITU-1411 LoS Log-normal shadowing with 10 dB STD

SNR⌘j

INRji� 1, 8i < j

SNR⌘j

INRij� 1, 8i < j

Comparison with FlashLinQ: Sum-rate

110% Gain

Comparison with FlashLinQ: Average Rate Distribution

Summary and Concluding Remarks •  Interference management and coordination is a key

bottleneck in D2D networks

•  We introduced ITLinQ •  We characterized a sufficient condition for optimality of treating

interference as noise •  We used this condition to define information-theoretic conflict

graphs for scheduling

•  Demonstrated significant gains over similar state-of-the-art schemes, such as FlashLinQ

•  Impact on utility maximization? •  An approach to jointly address Interference management

and coordination?

Questions?