Energy-ecient resource allocation in C-RANs with temporal and QoS constraints 1

Energy-ecient resource allocation in C-RANs with

temporal and QoS constraints

S. D'Oro 1_{, L. DaSilva}2_{, M. Marota}3_{, S. Palazzo} 1

1_{University of Catania, Italy,}2_{CONNECT, Trinity College Dublin, Ireland,} 3_{Federal University of Rio Grande do Sul, Brazil}

Outline

1 Outline 2 Scenario

3 The Problem

4 Problem Formulation 5 Optimal Oine Solution 6 Simulation Results 7 Conclusions

The considered network

C-RAN system with a set H of radio remote heads (RRHs) A virtually centralized baseband unit (BBU) pool

Multiple users served through downlink communications time-slotted communications

Modeling the RRHs

RRHs:

equipped with multiple antennas

transmit on a set S of available channels power constrained

connected to the BBU pool through high-performance optical bers

exploit both Joint Transmission (JT) and Coordinated Multi-Point (CoMP) communications

Modeling the Users

Users:

equipped with single-antenna transceivers receive data on a single channel

submit service requests with temporal and a minimum QoS requirements

Modeling the BBU pool

BBU pool:

where signal processing, user scheduling and power control/allocation is performed

The considered problem

Our goal

To nd an optimal joint user scheduling and power control policy that meets all users' requirements and satises system's constraints within a given nite horizon T

Problem Formulation

Let R be the set of the requests For each request r ∈ R we have:

r = n, t0_r, δr, γr, mr, Gr

where

n: the requesting user

t0_r ∈ T = {1, 2, . . . , T }: the starting time of the request δr: the duration of the temporal window

γr: the minimum SINR level requirement

mr: the amount of computational resources needed for signal

processing

Problem Formulation (cont'd)

Let Pj be the maximum transmission power for RRH j ∈ H

Let prjs(t) ∈ [0, Pj]be the transmission power of j on

subcarrier s at time slot t w.r.t. request r

Let yj(t) ∈ {0, 1}be the RRH activation indicator

The SINR is dened as follows: SINRrs(t) = P j∈Hprjs(t)grjs σ2₊P j∈H P r0_∈R,r0_6=rp_r0_js(t)g_r0_js (1)

Power Consumption Model at the RRH side

Each RRH j ∈ H produces transmission and activation power costs

Transmission power consumption C_jT X(p(t)) =X

r∈R

X

s∈S

prjs(t) (2)

Activation power consumption C_jA(y(t)) = yj(t)  P_j(ON)+ P_j(F) (3) where p(t) = (prjs(t))_{r∈R,j∈H,s∈S} y(t) = (yj(t))_j∈H,

Power Consumption Model at the BBU side

Let ars(t) ∈ {0, 1}be the request allocation variable of

request r on channel s

Each scheduled request r ∈ R produces a processing power cost

Processing power consumption C_rB(a(t)) = P(BBU)(mr)

X

s∈S

ars(t) (4)

where

P(BBU)(mr): the power consumption due to the utilization of

mr resources in the BBU pool

A weighted power consumption model

The weighted power consumption at time-slot t is C(a(t), p(t), y(t)) = CT X(p(t)) | {z } Transmission + ωRCA(y(t)) | {z } Activation + ωBCB(a(t)) | {z } Processing where CT X(p(t)) =P j∈HC T X j (p(t)) CB(a(t)) =P r∈RC B r(a(t)) CA(y(t)) =P j∈HC A j (y(t))

A weighted power consumption model (cont'd)

The weighted overall power consumption of the system is

C(a, p, y) =X t∈T C(a(t), p(t), y(t)) (5) where p = (p(t))_t∈T a = (a(t))_t∈T y = (y(t))_t∈T

Problem Statement

(A) : min a,p,y C(a, p, y) s.t. X t∈T X s∈S ars(t) = 1, ∀r ∈ R (6) X r∈R X s∈S prjs(t) ≤ yj(t)Pj, ∀j ∈ H, ∀t ∈ T (7) X r∈R X s∈S mrars(t) ≤ M, ∀t ∈ T (8) SINRrs(t) ≥ γrars(t), ∀s ∈ S, ∀r ∈ R, ∀t ∈ T (9) X t /∈[t0 r,t0r+δr] X s∈S ars(t) = 0, ∀r ∈ R (10) X t /∈[t0 r,t0r+δr] X s∈S X j∈H prjs(t) = 0, ∀r ∈ R (11) ars(t) ∈ {0, 1}, ∀r ∈ R, ∀s ∈ S, t ∈ [t0r, t0r+ δr] (12) yj(t) ∈ {0, 1}, ∀j ∈ H, ∀t ∈ T (13)

A discussion on Problem (A)

Problem (A) is a Mixed-Integer Non-Linear Problem (MINLP) It is easy to prove that it is NP-hard

It is dynamic

The proposed DP-based solution

Let us consider time-slot t and a given (a(t), y(t))

C(a(t), p(t), y(t)) = CT X(p(t)) | {z } Need to be calculated + ωRCA(y(t)) | {z } Fixed + ωBCB(a(t)) | {z } Fixed

The proposed DP-based solution

The problem reduces to nd a power allocation policy that minimizes the transmission power consumption

Ψ(a(t), y(t)) = min

p(t) X r∈R∗_(a(t)) X s∈S∗ r(a(t)) X j∈H∗_(y(t)) prjs(t) s.t. X r∈R∗_(a(t)) X s∈S∗ r(a(t)) prjs(t) ≤ Pj, ∀j ∈ H∗(y(t)) SINRrs(t) ≥ γr, ∀s ∈ Sr∗(a(t)), ∀r ∈ R ∗ (a(t)) where R∗_{(a(t)) = {r ∈ R(t) :}P s∈Sars= 1} S_r∗(a(t)) = {s ∈ S : ars= 1, r ∈ R∗(a(t))} H∗(y(t)) = {j ∈ H : yj(t) = 1}

An LP formulation

Ψ(a(t), y(t)) is obtianed by solving a Linear Programming (LP) problem

It can be solved eciently (e.g., polynomial time) through simplex or interior point methods

Writing the Bellman's Equation

Let us consider time-slot t and a given (a(t), y(t)) J (R(t), t) = min

a(t),y(t) Ψ(a(t), y(t)) + ωR

CA(y(t)) + ωBCB(a(t)) + J (R(t + 1), t + 1) s.t. T X τ =t X s∈S ars(τ ) = 1, ∀r ∈ R(t) X r∈R(t) X s∈S mrars(t) ≤ M ars(t) ∈ {0, 1}, ∀r ∈ R(t), ∀s ∈ S yj(t) ∈ {0, 1}, ∀j ∈ H X s∈S ars(t) = 0, ∀r /∈ R(t)

Simulation Results

Transmission rate, [kHz]

0 20 40 60 80 100 120 140

Weighted Power Consumption, [W]

0 1 2 3 4 5 6 7 R=10, w_r=0.1 R=20, w_r=0.1 R=10, w r=1 R=20, w r=1

Complexity of the proposed solution

The original problem is combinatorial and has exponential complexity

The proposed solution has complexity O(T OP(S + 1)R2R+H)

Still exponential Perfect knowledge

Some considerations

If (a(t), y(t)) is given, the problem is LP

We aim at nding a good heuristic for (a(t), y(t)) Intuition:

1 Interference increases the power consumption 2 JT and CoMP increase the power consumption

3 Using the same RRH to serve many users simultaneously is

power-ecient

4 Users with better channel conditions and loose QoS

Proposed Online Greedy Approach

1 We activate those RRHs that serves the highest number of

requests while consuming the minimum amount of power

2 We build an -orthogonal scheduling policy (a⊥_{ (t), y}⊥_(t))

such that interference is zero (or bounded by a small )

3 We use the residual power on each RRH to schedule requests

through JT and CoMP

4 We obtain the nal greedy scheduling policy (aG(t), yG(t))

5 We solve Ψ(aG_{(t), y}G_(t)) to obtain the power control policy

Conclusions

Optimal solutions for the joint power control and scheduling problem with QoS and temporal constraints can be designed However, it is NP-hard

Future Work

Complete the design of the heuristic

Simulation campaigns based on real datasets and settings Derive a theoretical bound w.r.t. the heuristic algorithm (if possible)

Thank you!

Thank you for your attention!!