General Introduction Fully Decentralized Allocation Future Work

Resource Allocation Challenges in FutureWireless Networks

Mohamad Assaad

Dept of Telecommunications, Supelec - France

Mar. 2014

General Introduction Fully Decentralized Allocation Future Work

Outline

1 General Introduction

2 Fully Decentralized Allocation

3 Future Work

General Introduction Fully Decentralized Allocation Future Work

General Introduction

Future 5G cellular networks must support the 1000-foldincrease in traffic demandNew physical layer techniques, e.g. Massive MIMO,Millimeter wave (mmWave)New network architecture: user centric architectureCloud RAN concept is also emergingLocal caching of popular video traffic at devices and RANedgeNetwork topologyDevice-to-Device (D2D) communications

General Introduction Fully Decentralized Allocation Future Work

General Introduction

Figure: Wireless network

General Introduction Fully Decentralized Allocation Future Work

Resource Allocation in Wireless Networks

Resource Allocation improves the network performanceResources: slots, channels, power, beamformers,...Services: voice, video streaming, interactive games, smartmaps, ...Typical Utility functions: throughput, outage, packet errorrate, transmit power,...Stability region

General Introduction Fully Decentralized Allocation Future Work

Resource Allocation in Wireless Networks

Computational complexity: NP hard, sub-optimalsolutions,...Physical layer (e.g. Massive MIMO): convex/non-convex,combinatorial, MINLP, ...optimization frameworksNon-existence of a central entity that can handle theallocation (e.g. D2D) and the amount of informationexchange (signaling) between transmitters. Mathematicaltools: stochastic game theory, distributed optimization,distributed learning, etc.Connectivity of the nodes (e.g. D2D communication).Network topology, high number of usersTraffic pattern and QoS/QoE: stochastic constraintsdepending on the service used (real time, streaming, ...).Availability of the system state information (e.g. CSI).

General Introduction Fully Decentralized Allocation Future Work

Fully Decentralized Allocation

General Introduction Fully Decentralized Allocation Future Work

Fully Decentralized Policies

Fully decentralized scenarioNo exchange of information between transmitters.Each transmitter exchanges information with its ownreceiverThe action (resource) is a scalarLow complexity algorithm

General Introduction Fully Decentralized Allocation Future Work

Nash Equilibrium Seeking [1]

Consider a network of n interacting nodes (e.g.interference)Each node has a reward to maximize. The decision ofeach node has an impact on the reward function of theother nodes.

supaj∈Aj

ESrj(S,aj ,a−j) j ∈ N (1)

where N := 1, . . . ,N is the set of nodes, Aj ⊆ R is theaction space of node j , S is the state space of the wholesystem, where S ⊆ CN×N and the node rewardrj : S ×

∏j ′∈N Aj ′ −→ R is a smooth function. The state

space S evolves ergodically such that ESrj(S,aj ,a−j) isalways finite.

General Introduction Fully Decentralized Allocation Future Work

Nash Equilibrium Seeking [1]

No exchange of information between the transmittersEach receiver sends to its own transmitter a numericalvalue (or estimation) of the rewardThe reward may have a complicated expression (e.g.outage probability, throughput...) : computing the gradientis hard!Each transmitter has always an information to send (fullbuffer)Extremum seeking has been studied in [2, 3, 4, 5, 6, 7]

General Introduction Fully Decentralized Allocation Future Work

NE Seeking [1]

Algorithm:

aj,k = aj,k + bj sin(Ωj tk + φj) (2)aj,k+1 = aj,k + λkzjbj sin(Ωj tk + φj)rj,k+1 (3)

Performance:

Main Result (Variable Learning Rate)

The learning algorithm converges almost surely to the followingODE (i.e. asymptotic pseudo-trajectory):

ddt

aj,t = zjbj sin(Ωj t + φj)ES[rj(S,at )] (4)

aj,t = aj,t + bj sin(Ωj t + φj) (5)

General Introduction Fully Decentralized Allocation Future Work

NE Seeking [1]

Let ∆t := ‖at − a∗‖ be the gap between the trajectory of theODE at at time t and the equilibrium point a∗.

Main Result (Exponential Stability)

There exist M,T > 0 and ε, bj such that, for all ε ∈ (0, ε) andbj ∈ (0, bj), if the initial gap is ∆0 := ‖a∗ − a0‖ (which is small)then for all time t ,

∆t ≤ y1,t (6)

where

y1,t := Me−Tt ∆0 + O(ε+ maxj

b3j ) (7)

General Introduction Fully Decentralized Allocation Future Work

Numerical Results [8]

Power control problem (two users)

ri(Hk ,pk ) = w log(1 +pi,k |hii,k |2

σ2 +∑

i ′ 6=i pi ′,k |hi ′i,k |2)− κpi,k

p1,0 and p2,0: initial pointshi,j is time varying, i.i.d. complex gaussianNoise variance σ2 = 1NE: p∗i = 3.9604 i ∈ (1,2)

General Introduction Fully Decentralized Allocation Future Work

Numerical Results [8]

Rx1Tx1h11

r1

Tx2

h21

Rx2

Tx1

h12

Tx2h22

r2

Transmitter Receiver 1

Transmitter Receiver 2

Figure: System model for two network each with transmit receive pair

General Introduction Fully Decentralized Allocation Future Work

Numerical Results [8]

0 500 1000 1500 2000 2500 30000

5

10

15

20

25

Time

Pow

er

Averaged

User1

User2

Figure: Power evolution (discrete time)

General Introduction Fully Decentralized Allocation Future Work

Randomized Policies

General Introduction Fully Decentralized Allocation Future Work

Randomized Policies

Stability regionSISO, MIMO : joint precoding and scheduling (queueaware)Joint resource allocation and channel feedback policies

General Introduction Fully Decentralized Allocation Future Work

Example [9]

Two user interference channel with single antenna per userand fading channel(R1,0), (r1,r2) and (0,R2)Symmetric environment (r1 =r2 =α)FCSMA

λ <α2

α + 1+

12(α + 1)

(8)

Joint traffic splitting and FCSMA

λ <α2

α + δ+

δ

2(α + δ)(9)

General Introduction Fully Decentralized Allocation Future Work

Future Work

Dense networksGlobal convergenceNetwork Stability and Feedback Design in Dense NetworksMassive MIMO and dense networks (TDD)Stability regionDecentralized stable solutions (joint precoding-scheduling)delay, QoS, QoE constraints

General Introduction Fully Decentralized Allocation Future Work

Last Slide

Thank youQuestions?

General Introduction Fully Decentralized Allocation Future Work

A. Hanif, T. Hamidou, M. Assaad, and D. Zeghlache, “Onthe convergence of a nash seeking algorithm withstochastic state dependent payoffs,” submitted to IEEETran. on Automatic Control, 2013.

P. Frihauf, M. Krstic, and T. Basar, “Nash equilibriumseeking in noncooperative games,” Automatic Control, IEEETransactions on, vol. 57, no. 5, pp. 1192 –1207, may 2012.

M. S. Stankovic and D. M. Stipanovic, “Extremum seekingunder stochastic noise and applications to mobile sensors,”Automatica, vol. 46, no. 8, pp. 1243–1251, Aug. 2010.[Online]. Available:http://dx.doi.org/10.1016/j.automatica.2010.05.005

M. Stankovic and D. Stipanovic, “Stochastic extremumseeking with applications to mobile sensor networks,” inAmerican Control Conference, 2009. ACC 09., june 2009,pp. 5622 –5627.

General Introduction Fully Decentralized Allocation Future Work

M. Stankovic, K. Johansson, and D. Stipanovic, “Distributedseeking of nash equilibria with applications to mobilesensor networks,” Automatic Control, IEEE Transactionson, vol. 57, no. 4, pp. 904 –919, april 2012.

S.-J. Liu and M. Krstic, “Stochastic averaging in continuoustime and its applications to extremum seeking,” AutomaticControl, IEEE Transactions on, vol. 55, no. 10, pp. 2235–2250, oct. 2010.

——, “Stochastic nash equilibrium seeking for games withgeneral nonlinear payoffs.” SIAM J. Control andOptimization, vol. 49, no. 4, pp. 1659–1679, 2011. [Online].Available: http://dblp.uni-trier.de/db/journals/siamco/siamco49.html#LiuK11

A. Hanif, T. Hamidou, M. Assaad, and D. Zeghlache,“Distributed stochastic learning for continuous powercontrol in wireless networks,” in IEEE SPAWC, june 2012.

General Introduction Fully Decentralized Allocation Future Work

S.Lakshminarayana, B.Li, M.Assaad, A.Eryilmaz, andM.Debbah, “A Fast- CSMA Based Distributed SchedulingAlgorithm under SINR Model,” in submitted to IEEEInternational Symposium on Information Theory (ISIT),Cambrigde, MA, USA, 2012.