Ressource Allocation Schemes for D2D Communicationsd2d-4-5g.gforge.inria.fr/Workshop-June2016/slides/MohamadAsaad.pdf · Ressource Allocation Schemes for D2D Communications ... I

Ressource Allocation Schemes for D2D Communications

Mohamad AssaadLaboratoire des Signaux et Systèmes (L2S), CentraleSupélec, Gif sur Yvette, France.

Indo-french Workshop on D2D Communications in 5G and IoT Networks - June 2016

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General Introduction Hetnets - D2D with Non real Time Data

Outline

General Introduction

Hetnets - D2D with Non real Time Data

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Outline



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I Future 5G networks must support the 1000-fold increase in traffic demandI New physical layer techniques, e.g. Massive MIMO, Millimeter wave (mmWave)I New network architectureI Local caching of popular video traffic at devices and RAN edgeI Network topologyI Device-to-Device (D2D) communications

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Figure: Wireless network

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Resource Allocation in Wireless Networks

I Resource Allocation improves the network performanceI Resources: slots, channels, power, beamformers,...I Hetnets architecture (small cells, macro cells, D2D)I Existence/Non-existence of a central entity that can handle the allocation (e.g.

D2D) and the amount of information exchange (signaling) between transmitters.I Connectivity of the nodes (e.g. D2D communication).I Services: voice, video streaming, interactive games, smart maps, ...I Typical Utility functions: throughput, outage, packet error rate, transmit power,...I Availability of the system state information (e.g. CSI).I Low signaling overhead, low complexity solutions

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Example of System Model

Figure: System Model

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Existing Formulations of the Beamforming AllocationProblem

I Usually we define a continuous and nondecreasing function fi,j w.r.t. SINR (e.g.Log(1 + Λi,j ))

I The utility of the network is g(f1,1, ..., fi,j , ...

)where g is continuous and

nondecreasing w.r.t to each fi,jI Two main issues: complexity and signaling overhead (centralized/decentralized)

maxwi,j ∀i,j

g(f1,1, ..., fi,j , ...

)(1)

s.t . h(Λ1,1, ...,Λi,j , ...

)≤ 0

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Existing Formulations of the Beamforming AllocationProblem

I Examples:I Sum or weighted sum:

∑i,j fi,j (Λi,j )

I Proportional Fairness:∑

i,j log(fi,j (Λi,j )

)I MaxMin Fairness: maxwi,j ∀i,j mini,j fi,j (Λi,j )

I Constraint h(Λ1,1, ...,Λi,j , ...

)≤ 0

I ΛDLi,j ≥ γi,j ∀i, j : Not convex (but can be reformulated)

I∑

j wHi,j wi,j ≤ P i

max : convex

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Complexity of Optimization Problems

I Constraint ΛDLi,j ≥ γi,j ∀i, j ; utility:

∑i,j wH

i,j wi,j

I Constraint∑

j wHi,j wi,j ≤ P i

max ; Other utility functions

Table: Complexity

Objective function MIMO Single AntennaWeighted Sum NP-hard NP-hard

Proportional Fairness NP-hard Convex

MaxMin Fair Quasi-Convex Quasi-Convex

Harmonic Mean NP-hard Convex

Sum Power Convex Linear

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Some referencesI M. Bengtsson, B. Ottersten, "Optimal Downlink Beamforming Using Semidefinite

Optimization," Proc. Allerton, 1999.I A. Wiesel, Y. Eldar, and S. Shamai, "Linear precoding via conic optimization for

fixed MIMO receivers," IEEE Trans. on Signal Processing, 2006.I W. Yu and T. Lan, "Transmitter optimization for the multi-antenna downlink with

per-antenna power constraints," IEEE Trans. on Signal Processing, 2007.I E. Bjornson and E. Jorswieck, Optimal Resource Allocation in Coordinated

Multi-Cell Systems, Foundations and Trends in Communications and InformationTheory, 2013.

I Liu, Y.-F., Dai, Y.-H. and Luo, Z.-Q., "Coordinated Beamforming for MISOInterference Channel: Complexity Analysis and Efficient Algorithms," Acceptedfor publication in IEEE Transactions on Signal Processing, November 2010.

I Shi, Q.J., Razaviyayn, M., He, C. and Luo, Z.-Q., "An Iteratively Weighted MMSEApproach to Distributed Sum-Utility Maximization for a MIMO InterferingBroadcast Channel," IEEE Transactions on Signal Processing, 2011.

I N. Ul Hassan and M. Assaad, "Low Complexity Margin adaptive resourceallocation in Downlink MIMO-OFDMA systems," IEEE Transactions on WirelessCommunications, July 2009.

I etc...

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Outline



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Energy Efficient Beamforming Allocation 1

I Hetnets architectureI Delay tolerant traffic (flexibility to dynamically allocate resources over the fading

channel states)I Decentralized Solution (Lyapunov Optimization)I Simple online solutions based only on the current knowledge of the system stateI Only local knowledge of CSI is requiredI Does not require a-priori the knowledge of the statistics of the random processes

in the systemI Joint design of feedback and beamforming

1S. Lakshminaryana, M. Assaad and M. Debbah, "Energy Efficient Cross LayerDesign in MIMO Systems," in IEEE JSAC, Special issue on Hetnets, 33 (10), pp.2087-2103, Oct. 2015.

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Problem Formulation

I The transmission power by each transmitterPi [t] =

∑Kj=1 wH

i,j [t]wi,j [t], i = 1, . . . ,N.

I The optimization problem is to minimize the time average power subject to timeaverage QoS constraint

min limT→∞

1T

T−1∑t=0

E[ N∑

i=1

Pi [t]]

(2)

s.t . limT→∞

1T

T−1∑t=0

E[γi,j [t]

]≥ λi,j , ∀i, j (3)

K∑j=1

wHi,j [t]wi,j [t] ≤ Ppeak ∀i, t (4)

where Ppeak is the peak power

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Static Problem

I Static Problem

min∑i,j

wHi,j wi,j (5)

s.t .|wH

i,j hi,i,j |2∑(n,k)6=(i,j)

|wHn,k hn,i,j |2 + σ2

≥ γi,j , ∀i, j (6)

(7)

where γi,j is the instantaneous target SINR of UTi,j .

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Lyapunov Optimization

I Suboptimal solution using Lyapunov optimization approach 2.I Lyapunov vs. MDP base approachI Nonconvex static problems but can be solved using SDPI The complexity of our solution is at most O(N ∗ N3

t ). (usually O(N + N2t )3.5 for

SDP)I Our solution is distributed (based on local CSI)I The transmitters have to exchange the virtual queues (signaling overhead «

CSIs)

Main ResultOptimality gap: O(C1/V ); Delay: O(V )

2M. Neely, Stochastic Network Optimization with Application to Communication andQueueing Systems. Morgan & Claypool, 2010.

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Lyapunov Optimization - More detailsI The QoS metric which we denote by γi,j [t] is

γi,j [t] = |wHi,j [t]hi,i,j [t]|2 − νi,j

∑(n,k)6=(i,j)

|wHn,k [t]hn,i,j [t]|2 (8)

I Virtual queue evolves as follows Qi,j [t + 1] = max(Qi,j [t]− µi,j [t], 0

)+ Ai,j [t]

where Ai,j [t] = νi,j∑

(n,k)6=(i,j)

|wHn,k [t]hn,i,j [t]|2 + λi,j and µi,j [t] = |wH

i,j [t]hi,i,j [t]|2

Figure: Virtual queue

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Queue ModelI Let Q(t) a discrete time queueing system with K queues.I For each queue i , ai (t) and ri (t) denote the arrival and departure processesI Arrivals occur at the end of slot tI The Q(t) process evolves according to the following discrete time dynamic:

Qi (t + 1) = [Qi (t)− ri (t)]+ + ai (t) (9)

I The time average expected arrival process satisfiesI There exists 0 < λi <∞ such that

limt→∞

1t

t−1∑τ=0

E (ai (τ)) = λi (10)

I There exists 0 < Amax <∞ such that ∀ t

Ea2i (t)|Ω[t] ≤ Amax (11)

I Ω[t] represents all events (or the history) up to time tI Similar assumptions for the departure process ri (t) (ri (t) ≤ rmax ).

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Queue StabilityDefinitionA discrete time process Q(t) is rate stable if

limt→∞

1t

Q(t) = 0 w .p.1

I

DefinitionA discrete time process Q(t) is mean rate stable if

limt→∞

1tE [Q(t)] = 0

I

DefinitionA discrete time process Q(t) is strongly stable if

limt→∞

sup1t

t∑τ=1

E [Q(τ)] <∞

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Lyapunov Optimization - More detailsI The notion of strong stability of the virtual queue is given as

∑i,j Qi,j [t] <∞.

I Strong stability of the queues implies

Ai,j [t]− µi,j [t]] ≤ 0 ∀i, j. (12)

I Virtual Queue stability implies that the time average constraint is satisfiedI Modified optimization problem - Minimize energy expenditure subject to virtual

queue-stability

Figure: Virtual queue

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Lyapunov Optimization - More details

I V (Q[t]) = 12∑

i,j (Qi,j [t])2. The Lyapunov function is a scalar measure of theaggregate queue-lengths in the system. We define the one-step conditionalLyapunov drift as

∆(Q[t]) = E[

V (Q[t + 1]))− V (Q[t])|Q[t]]

(13)

I Lyapunov Optimization [Neely2006] - If there exist constants B > 0,ε > 0,V > 0such that for all timeslots t we have,

∆(Q[t]) + VE[∑

i Pi (t)|Q[t]]≤ B − ε

∑i,j Qi,j (t) + VPinf

I Time average energy expenditure is bounded distance from Pinf

I Allows us to consider the result of queuing stability and performance optimizationusing a single drift analysis.

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Lyapunov Optimization - Decentralized Solution

I Each BS must solve the optimization problem given by

maxw

∑j

wHi,j Ai,j wi,j (14)

s.t .∑

j

wHi,j wi,j ≤ Ppeak.

where the matrix Ai,j = Qi,j Hi,i,j −∑

(n,k)6=(i,j)

νn,k Qn,k Hi,n,k − V I and

Hi,n,k = hi,n,k hHi,n,k .

I

Popti,j =

Ppeak if j = j∗and λmax(Ai,j∗ ) > 00 else.

(15)

j∗ = arg maxj λmax(Ai,j ).

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Lyapunov Optimization - Decentralized SolutionI The transmitters have to exchange the queue-length informationI No CSI exchange required

Figure: Decentralized Solution

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Lyapunov Optimization - Decentralized SolutionI The virtual queue is strongly stable and for any V ≥ 0, the time average

queue-length satisfies∑

i,j Qopti,j [t] ≤ C1+VNKPpeak

εand the time average energy

expenditure yields,∑N

i=1 Popti [t] ≤ Pinf + C1

V .

Figure: Decentralized Solution

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Delayed Queues

I The transmitters exchange the queue-length information with a delay of τ <∞time slots.

I Each transmitter i knows Qi,j [t] ∀j and Qn,k [t − τ ], ∀n 6= i, k .

Main ResultOptimality gap: O((C1 + C2)/V ); Delay: O(V )

LemmaThere exists a 0 ≤ C2 <∞ independent of the current queue-length Qi,j [t], ∀i, j suchthat, ∑

i,j

Tr(Ai,j [t]Wopti,j [t]) ≤

∑i,j

Tr(Ai,j [t]Wdeli,j [t]) + C2 ∀t . (16)

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Numerical Result I

2 4 6 8 10

−5

0

5

Target SINR (dB)

Dow

nlin

kPo

wer

Instant. ConstraintAvg. constraint, V = 200Avg. constraint, V = 400Avg. constraint, V = 600Avg. constraint, V = 800

Figure: each transmitter is connected to two UTs, Nt = 5,

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Numerical Results II

10 12 14 16 180

1

2

3

·104

Target QoS (dB)

Avg

.Q

ueue

-Len

gth

Nt = 2Nt = 4Nt = 6Nt = 8

Figure: V = 100.

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Numerical Results III

Figure: Achieved time average SINR Vs target QoS, each transmitter is connected totwo UTs, Nt =5.

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Lyapunov Optimization - Some References

I Junting Chen, Vincent K. N. Lau, "Large Deviation Delay Analysis ofQueue-Aware Multi-User MIMO Systems With Two-Timescale Mobile-DrivenFeedback," IEEE Transactions on Signal Processing 61(16): 4067-4076 (2013)

I M. Neely, Stochastic Network Optimization with Application to Communicationand Queueing Systems. Morgan & Claypool, 2010.

I Ying Cui, Vincent K. N. Lau, Edmund M. Yeh, "Delay Optimal BufferedDecode-and-Forward for Two-Hop Networks With Random Link Connectivity,"IEEE Transactions on Information Theory 61(1): 404-425 (2015)

I S. Lakshminaryana, M. Assaad and M. Debbah, "Energy Efficient Cross LayerDesign in MIMO Multi-cell Systems," to appear in IEEE JSAC, 2015.

I S. Lakshminarayana, M. Assaad and M. Debbah, "Energy Efficient Design inMIMO Multi- cell Systems with Time Average QoS Constraints", in IEEE SPAWC,June 2013.

I H. Shirani-Mehr, G. Caire, and M. J. Neely, "MIMO Downlink Scheduling withNon-Perfect Channel State Knowledge," IEEE Transactions on Communications,July 2010.

I etc...

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Queueing Stability in MIMO SystemsI A. Destounis, M. Assaad, M. Debbah and B. Sayadi, "Traffic-Aware Training and

Scheduling in MISO Downlink Systems," IEEE Transactions on InformationTheory, 61 (5), pp. 2574-2599, 2015.

I A. Destounis, M. Assaad, M. Debbah and B. Sayadi, "A Threshold-BasedApproach for Joint Active User Selection and Feedback in MISO DownlinkSystems," in proc. of IEEE ICC, London UK, June 2015.

I Kaibin Huang, Vincent K. N. Lau, "Stability and Delay of Zero-Forcing SDMAWith Limited Feedback," IEEE Transactions on Information Theory, 2012.

I M. Deghel, M. Assaad, and M. Debbah, "Queueing Stability and CSI Probing in aWireless Network with Interference Alignment in TDD Mode," in proc. of IEEEInternational Symposium on Information Theory (ISIT), HongKong, June 2015.

I Junting Chen, Vincent K. N. Lau, "Large Deviation Delay Analysis ofQueue-Aware Multi-User MIMO Systems With Two-Timescale Mobile-DrivenFeedback," IEEE Transactions on Signal Processing 61(16): 4067-4076 (2013)

I A. Destounis, M. Assaad, M. Debbah and B. Sayadi, "Traffic-Aware Training andScheduling for the 2-user MISO Broadcast Channel," in IEEE ISIT, 2014.

I Ying Cui, Vincent K. N. Lau, Edmund M. Yeh, "Delay Optimal BufferedDecode-and-Forward for Two-Hop Networks With Random Link Connectivity,"IEEE Transactions on Information Theory 61(1): 404-425 (2015)

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Queueing Stability in MIMO Systems

I N. Pappas, M. Kountouris, A. Ephremides, A. Traganitis, "Relay-assisted MultipleAccess with Full-duplex Multi-Packet Reception," IEEE Transactions on WirelessCommunications, July 2015

I I. E. Telatar and R. G. Gallager, "Combining queueing theory with informationtheory for multiaccess," IEEE Journal on Sel. Areas in Communications, vol. 13,Aug. 1995.

I E. Yeh, Multiaccess and Fading in Communication Networks. Ph.D. Thesis,EECS, MIT, 2001.

I E. M. Yeh and A. S. Cohen, "Throughput and delay optimal resource allocation inmultiaccess fading channels," in Proc. of IEEE Intl. Symposium on InformationTheory, June/July 2003.

I etc...

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End of the Talk

Thank you for listening!Questions??

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Ressource Allocation Schemes for D2D Communicationsd2d-4-5g.gforge.inria.fr/Workshop-June2016/slides/MohamadAsaad.pdf · Ressource Allocation Schemes for D2D Communications ... I