Funems 2013 talk

Green Joint User Scheduling and Power Control in
Downlink Multi-Cell OFDMA Networks
L. Venturino1
C. Risi1
A. Zappone2
S. Buzzi1
1
CNIT/ University of Cassino and Lazio Meridionale, Italy
{l.venturino, chiara.risi, buzzi}@unicas.it
2
Dresden University of Technology, Germany
Communications Laboratory
Alessio.Zappone@tu-dresden.de
July 3, 2013
Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA

The considered system: a downlink multi-cell OFDMA
system
OBJECTIVE: Find user scheduling and power allocation policies to
maximize energy eﬃciency, assuming coordinated decisions by the BS

System Model
M coordinated access points employing N subcarriers and universal
frequency 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 tone
n is given by
r
[n]
k(m,n) = H
[n]
m,k(m,n)x[n]
m
useful data
+
M
=1, =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 m
on tone n is written as
SINR[n]
m =
p
[n]
m G
[n]
m,k(m,n)
1 +
M
=1, =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 by
the 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 of
co-channel users on each tone and 2) the power allocation across
subcarriers 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,k
EE(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
k
EE(p, k)
s.t. k(m, n) ∈ Bm, ∀ m, n
is achieved at
ˆk(m, n) = arg max
s∈Bm







ws log2







1 +
p
[n]
m G
[n]
m,s
1 +
M
=1, =m
p
[n]
G
[n]
,s














, (7)
e.g., each BS assigns each subcarrier to the user with the best
channel

Next, since
log2(1 + z) ≥ α log2 z + β, with
α = ¯z
1+¯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 = ln p, 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 thus
recast as a concave/convex fractional problem, which can be
optimally 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 = 0
2: 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, . . . , N
4: repeat
5: Update p by solving the following non-linear fractional problem using
the Dinkelbach’s procedure (p = exp{q}):
arg max
q
EELB(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, . . . , N
8: Set i = i + 1
9: until convergence or i = Imax

Dinkelbach’s algorithm
Algorithm 2
1: Set > 0, π = 0, and FLAG = 0
2: repeat
3: Update q by solving the following concave maximization problem:
arg max
q
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}) < then
5: FLAG = 1
6: else
7: Set π = f (exp{q}, k)/g(exp{q})
8: end if
9: until FLAG = 0

The noise-limited scenario
In the noise-limited operating regime (wherein the intercell
interference is neglected) the objective function EE(p, k) is strictly
pseudo-concave, which implies that any local maximum is a global
maximum. In this case, the optimal solution to (6) can be found by
directly 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 = 0
2: Initialize p and compute k according to (7)
3: repeat
4: Update p by solving the following concave/linear fractional problem
using the Dinkelbach’s procedure:



arg max
p
B
M
m=1
N
n=1 wk(m,n) log2 1 + P
[n]
m G
[n]
m,k(m,n)
M
m=1
N
n=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 + 1
7: until convergence or i = Imax

Numerical Results: our toy model...
We consider a cellular OFDMA system with N = 16 tones, each
with bandwidth B = 1kHz.
A cluster of M = 7 coordinated cells is considered.
The distance between adjacent base stations is 2 km, and users are
uniformly distributed around the serving access point within a
circular annulus of internal and external radii of Ri = 500m and
Re = 1000m, respectively.
We assume that all the BSs have the same maximum transmit
power, i.e., Pm,max = Pmax ∀m and that all the BSs serve the same
number of users |Bm| = 3 ∀m.
The noise power at each mobile is N
[n]
s = 10−9
W 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-cell
OFDMA system has been considered.
Fractional programming results (Dinkelbach’s algorithm) have been
used
Results show that moderate reduction in the achieved rate enables
large savings in the required energy
Current research is focused on: consideration of MIMO; use of
alternative energy-eﬃciency metrics (geometric mean); advantages
granted from a cloud-RAN architecture.

We gratefully acknowledge the support of the EU
Commission and German Research Foundation!
The work of L. Venturino, S. Buzzi and C. Risi has received funding from
the 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 Research
Foundation (DFG) project CEMRIN, under grant ZA 747/1-1.

THANK YOU!!
Stefano Buzzi, Ph.D.
Universit´a di Cassino e del Lazio Meridionale
buzzi@unicas.it

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