funems 2013 talk

Green Joint User Scheduling and Power Control inDownlink Multi-Cell OFDMA Networks

L. Venturino1 C. Risi1 A. Zappone2 S. Buzzi1

1CNIT/ University of Cassino and Lazio Meridionale, Italy{l.venturino, chiara.risi, buzzi}@unicas.it

2Dresden University of Technology, GermanyCommunications Laboratory

[email protected]

July 3, 2013

Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA

The considered system: a downlink multi-cell OFDMAsystem

OBJECTIVE: Find user scheduling and power allocation policies tomaximize energy efficiency, assuming coordinated decisions by the BS


System Model

M coordinated access points employing N subcarriers and universalfrequency reuse

k(m, n) ∈ Bm is the user served by base station m on tone n

The discrete-time baseband signal received by user k(m, n) on tonen is given by

r[n]k(m,n) = H

[n]m,k(m,n)x

[n]m︸︷︷︸

useful data

+M∑

`=1, 6=m

H[n]`,k(m,n)x

[n]`︸︷︷︸

inter-cell interference

+ n[n]k(m,n)︸︷︷︸noise

. (1)


System Model (cont’d)

The signal-to-interference-plus-noise ratio (SINR) for base station mon tone n is written as

SINR[n]m =

p[n]m G

[n]m,k(m,n)

1 +M∑

`=1, 6=m

p[n]` G

[n]`,k(m,n)

(2)

with G[n]q,s , |H [n]

q,s |2/N [n]s

The corresponding achievable information rate (in bit/s) is given bythe Shannon’s formula

R[n]m = B log2

[1 + SINR[n]

m

](3)

where B is the bandwidth of each subcarrier.


Coordinated resource allocation

The coordinated base stations jointly determine 1) the set ofco-channel users on each tone and 2) the power allocation acrosssubcarriers so as to maximize the system energy efficiency

EE(p, k) ,M∑

m=1

N∑n=1

wk(m,n)R

[n]m

θ[n]m + p

[n]m

(4)

ws > 0 is a weight accounting for the priority

θ[n]m > 0 is the circuit power consumed by base station m on tone n

EE is unfortunately non-concave


Coordinated resource allocation (cont’d)

Observe that

EE(p, k) ≥

M∑m=1

N∑n=1

wk(m,n)R[n]m

B∑m=1

N∑n=1

(θ[n]m + p[n]

m

) , EE(p, k) , (5)

and consider arg max

p,kEE(p, k)

s.t. p[n]m ≤ Pm,max/N, ∀m, n

p[n]m ≥ 0, ∀m, n

k(m, n) ∈ Bm, ∀m, n

(6)



The problem is still non-convex. However....

for any given feasible power allocation p the solution to{arg max

kEE(p, k)

s.t. k(m, n) ∈ Bm, ∀m, n

is achieved at

k(m, n) = arg maxs∈Bm

ws log2

1 +p

[n]m G

[n]m,s

1 +M∑

`=1, 6=m

p[n]` G

[n]`,s

, (7)

e.g., each BS assigns each subcarrier to the user with the bestchannel



Next, since

log2(1 + z) ≥ α log2 z + β, with

α = z1+z , β = log2(1 + z)− z

1+z log2 z ,(8)

which is tight at z = z we have

EE(p, k) ≥

f (p,k)︷︸︸︷B

M∑m=1

N∑n=1

wk(m,n)

[α[n]m log2

(SINR[n]

m

)+ β[n]

m

]M∑

m=1

N∑n=1

(θ[n]m + p[n]

m

)︸︷︷︸

g(p)

= EELB(p, k)



Using the transformation q = lnp, f (exp{q}) and g(exp{q})become a concave and convex function of q, respectively.

The maximization of EELB(p, k) with respect to p can be thusrecast as a concave/convex fractional problem, which can beoptimally and efficiently solved by means of Dinkelbach’s algorithm.

W. Dinkelbach, On nonlinear fractional programming, Management Science,

vol. 13, no. 7, pp. 492 - 498, 1967.



Algorithm 1

1: Initialize Imax and set i = 02: Initialize p and compute k according to (7)

3: Set z[n]m = SINR[n]

m and compute α[n]m and β

[n]m as in (8), for m =

1, . . . ,M and n = 1, . . . ,N4: repeat5: Update p by solving the following non-linear fractional problem using

the Dinkelbach’s procedure (p = exp{q}):{arg max

qEELB(exp{q}, k)

s.t. exp{q[n]m } ≤ Pm,max/N, ∀m, n

(9)

6: Update k according to (7)

7: Set z[n]m = SINR[n]

m and update α[n]m and β

[n]m as in (8), for m =

1, . . . ,M and n = 1, . . . ,N8: Set i = i + 19: until convergence or i = Imax


Dinkelbach’s algorithm

Algorithm 2

1: Set ε > 0, π = 0, and FLAG = 02: repeat3: Update q by solving the following concave maximization problem:{

arg maxq

f (exp{q}, k)− πg(exp{q})

s.t. exp{q[n]m } ≤ Pm,max/N, ∀m, n

(10)

4: if f (exp{q}, k)− πg(exp{q}) < ε then5: FLAG = 16: else7: Set π = f (exp{q}, k)/g(exp{q})8: end if9: until FLAG = 0


The noise-limited scenario

In the noise-limited operating regime (wherein the intercellinterference is neglected) the objective function EE(p, k) is strictlypseudo-concave, which implies that any local maximum is a globalmaximum. In this case, the optimal solution to (6) can be found bydirectly applying Dinkelbach’s algorithm.

A pseudoconvex function is a function that behaves like a convex function with

respect to finding its local minima, but need not actually be convex. Informally,

a differentiable function is pseudoconvex if it is increasing in any direction

where it has a positive directional derivative.


The noise-limited scenario (cont’d)

Algorithm 3

1: Initialize Imax and set i = 02: Initialize p and compute k according to (7)3: repeat4: Update p by solving the following concave/linear fractional problem

using the Dinkelbach’s procedure:

arg max

p

B∑M

m=1

∑Nn=1 wk(m,n) log2

(1 + P

[n]m G

[n]m,k(m,n)

)∑M

m=1

∑Nn=1

(θ

[n]m + P

[n]m

)s.t. P

[n]m ≥ 0, ∀m, n

P[n]m ≤ Pm,max/N, ∀m, n

(11)5: Update k according to (7)6: Set i = i + 17: until convergence or i = Imax


Numerical Results: our toy model...

We consider a cellular OFDMA system with N = 16 tones, eachwith bandwidth B = 1kHz.

A cluster of M = 7 coordinated cells is considered.

The distance between adjacent base stations is 2 km, and users areuniformly distributed around the serving access point within acircular annulus of internal and external radii of Ri = 500m andRe = 1000m, respectively.

We assume that all the BSs have the same maximum transmitpower, i.e., Pm,max = Pmax ∀m and that all the BSs serve the samenumber of users |Bm| = 3 ∀m.

The noise power at each mobile is N [n]s = 10−9W and the total

signal processing overhead is∑

m

∑n θ

[n]m = 40dBm.


Average EE


Weighted sum-rate


Conclusions

User scheduling and power allocation for the downlink of a multi-cellOFDMA system has been considered.

Fractional programming results (Dinkelbach’s algorithm) have beenused

Results show that moderate reduction in the achieved rate enableslarge savings in the required energy

Current research is focused on: consideration of MIMO; use ofalternative energy-efficiency metrics (geometric mean); advantagesgranted from a cloud-RAN architecture.


We gratefully acknowledge the support of the EUCommission and German Research Foundation!

The work of L. Venturino, S. Buzzi and C. Risi has received funding fromthe European Union Seventh Framework Programme (FP7/2007-2013)under grant agreement n. 257740 (Network of Excellence TREND).

The work of A. Zappone has received funding from the German ResearchFoundation (DFG) project CEMRIN, under grant ZA 747/1-1.


THANK YOU!!

Stefano Buzzi, Ph.D.Universita di Cassino e del Lazio Meridionale

[email protected]
