Modelling D2D Communications in Cellular Access Networks via Coupled

Processors

Christian Vitale Institute IMDEA Networks and Univ. Carlos III de Madrid Vincenzo Mancuso Institute IMDEA Networks Gianluca Rizzo HES SO Valais

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Outline

• Overview In-band Underlay D2D • Our contributions:

– A new model for D2D communications: Coupled Processor – How to study a D2D Coupled Processor model – Sufficient conditions for stability D2D transmitters – Effects of D2D transmissions on cellular transmitters – Proportional Fair assignment of resources to D2D transmitters

• Future developments

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D2D Communications

• D2D: Device to Device communications – Info among two device in proximity do not traverse any eNBs

but is directly exchanged

• D2D scope: – Content Distribution – Offloading cellular infrastructure – Increase efficiency spectrum use – …

• No standardization yet – LTE Release 12 will contain D2D transmissions too

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In-band Underlay D2D

• D2D transmitters reuse Resource Blocks (RBs) assigned to cellular transmitters (mutual interference)

• Complex modeling and performance evaluation

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Analysed In-band Underlay D2D • D2D – Uplink channel • eNB schedules D2D transmissions too • Cellular transmission scheduling:

– Equal Time • Cellular transmitters in saturation • D2D scheduling approach (FlashLinQ[1] like):

– Scheduling happens every RB, or blocks of RBs (when SC-FDMA)

– D2D transmitters with traffic to serve are randomly ordered and scheduled if:

• Interference to and from the concurrent cellular transmission is under a given threshold

• Interference to and from the already scheduled D2D transmissions is under a given threshold

[1] Wu, Xinzhou, et al. "FlashLinQ: A synchronous distributed scheduler for peer-to-peer ad hoc networks." IEEE/ACM Transactions on Networking

(TON) 21.4 (2013): 1215-1228.

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A Coupled Processor Model for D2D communications

• The Modulation Coding Scheme used by each transmitter is univocally determined by the set of active transmitters in the same RB

• Coupled processor – Queueing system. Service rate at each time t univocally depends from the set of

not empty queues • CPS can mimic the network behavior

∑+=

≠>−

>−

activej

ij

ii

ijR

Ri PN

PSINR

|

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A Coupled Processor Model for D2D communications(2)

• CPS model details: – A queue per D2D transmitter – System state I: set of not empty queues – Service rate at each queue determined by I

• Average throughput achieved by the corresponding D2D transmitter d when the set of transmitters is I

where pu is the probability of cellular transmitter u to be scheduled; Io one of the possible ordering of I; is the throughput of d under ordering Io and cellular transmitter u

|!|)(

)(I

IRpIR OI o

ud

ud∑

=

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Coupled Processor Stability • Find sufficient conditions for stability of CP is as

difficult as for D2D system • Evaluation is done through simpler upper bounding

systems, i.e., simpler systems which stability implies the stability of a CP[2]

[2] C. Vitale, G. Rizzo, and B. Rengarajan. Performance Bounds in Coupled Processor Systems, 2013. Available at http://publications.hevs.ch/index.php/attachments/single/665

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Sufficient condition for stability in D2D system

• Arrivals considered are leaky bucket constrained {𝞺,𝞼}

• Stability is studied through introduced upper bounding networks and basic Network Calculus results

Union over the upper bounding networks GPS nodes

capacity given the network

Maximum “absorbed” capacity given the network

Minimum capacity, saturation

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Sufficient condition for stability D2D system: Results

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Effects on Cellular transmissions • Previously cellular transmitters were considered in

saturation: – Cellular transmitters are active in every system state I

• To evaluate effects on cellular transmitters, a new CP model is studied

• Given the demands of the D2D transmitters, maximum stable rate for the cellular transmitter is evaluated

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Effects on Cellular transmissions: Results

• In all scenarios previously simulated, from position A to position B, analytical and simulated stable rates for cellular transmitters are compared

• Highest average underestimation of real simulated maximum achievable rate in position B – Average underestimation: 11.18%

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Proportional Fairness • Objective: maximize a proportional Fairness measure

picking stable long term rates for the D2D transmitters – Can be implemented at the application level through leaky bucket

shapers

where dO is a particular order of mapping D2D transmitters-> stages upper

bounding networks

STABILITY REGION

ARRIVALS LIMIT

PROPORTIONAL FAIRNESS

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Proportional Fairness-Brute Force • Per-network optimization:

– Big-M transformation

– Branch and Bound over introduced binary variables

– Concave Optimization ->Unique solution

• Evaluation over each possible mapping D2D transmitters GPS nodes upper bounding networks

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Proportional Fairness-Heuristic • Per-network approximation:

– Branch and bound stopped when current solution not far than 𝟄% than the optimum (𝟄=10)

• Selected set of analyzed networks – Small set of starting networks

• For each starting network, D2D transmitters are assigned from top to bottom proportionally to the inverse of the weight

The highest is the weight the best the interference is modelled

– From each starting network, all networks achieved swapping two D2D transmitters into the upper bounding networks are evaluated

– Such operation is repeated up to a local maximum

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Proportional Fairness Results

• Utility Brute Force vs. Heuristic and Simulation optimized system vs. simulations – Utility is sensibly improved – Simulations of optimized system gets analytical optimization results – Heuristic very close to brute force

• Complexity

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Conclusions

• First analytical evaluation of performances underlay D2D transmissions – Sufficient condition for stability D2D transmission queues – Quantification effects D2D transmission over cellular transmission – Simple and effective proportional fairness scheme for D2D

transmissions

• Next step: – Statistical characterization of stability of D2D system