Green Joint User Scheduling and Power Control in
Downlink Multi-Cell OFDMA Networks
L. Venturino1
C. Risi1
A. Zappone2
S. ...
The considered system: a downlink multi-cell OFDMA
system
OBJECTIVE: Find user scheduling and power allocation policies to...
System Model
M coordinated access points employing N subcarriers and universal
frequency reuse
k(m, n) ∈ Bm is the user se...
System Model
M coordinated access points employing N subcarriers and universal
frequency reuse
k(m, n) ∈ Bm is the user se...
System Model (cont’d)
The signal-to-interference-plus-noise ratio (SINR) for base station m
on tone n is written as
SINR[n...
Coordinated resource allocation
The coordinated base stations jointly determine 1) the set of
co-channel users on each ton...
Coordinated resource allocation
The coordinated base stations jointly determine 1) the set of
co-channel users on each ton...
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(...
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(...
Coordinated resource allocation (cont’d)
The problem is still non-convex. However....
for any given feasible power allocat...
Coordinated resource allocation (cont’d)
The problem is still non-convex. However....
for any given feasible power allocat...
Coordinated resource allocation (cont’d)
Next, since
log2(1 + z) ≥ α log2 z + β, with
α = ¯z
1+¯z , β = log2(1 + ¯z) − ¯z
...
Coordinated resource allocation (cont’d)
Using the transformation q = ln p, f (exp{q}) and g(exp{q})
become a concave and ...
Coordinated resource allocation (cont’d)
Algorithm 1
1: Initialize Imax and set i = 0
2: Initialize p and compute k accord...
Dinkelbach’s algorithm
Algorithm 2
1: Set > 0, π = 0, and FLAG = 0
2: repeat
3: Update q by solving the following concave ...
The noise-limited scenario
In the noise-limited operating regime (wherein the intercell
interference is neglected) the obj...
The noise-limited scenario (cont’d)
Algorithm 3
1: Initialize Imax and set i = 0
2: Initialize p and compute k according t...
Numerical Results: our toy model...
We consider a cellular OFDMA system with N = 16 tones, each
with bandwidth B = 1kHz.
A...
Average EE
Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
Weighted sum-rate
Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
Conclusions
User scheduling and power allocation for the downlink of a multi-cell
OFDMA system has been considered.
Fracti...
We gratefully acknowledge the support of the EU
Commission and German Research Foundation!
The work of L. Venturino, S. Bu...
THANK YOU!!
Stefano Buzzi, Ph.D.
Universit´a di Cassino e del Lazio Meridionale
buzzi@unicas.it
Venturino, Risi, Zappone, ...
Upcoming SlideShare
Loading in …5
×

Funems 2013 talk

232 views
135 views

Published on

L. Venturino, C. Risi, A. Zappone and S. Buzzi, "Green Joint User Scheduling and Power Control in Downlink Multi-Cell OFDMA Network" 2013 Future Networks and mobile Summit, Lisbon, July 2013.

Published in: Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
232
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
1
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Funems 2013 talk

  1. 1. 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
  2. 2. 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  3. 3. 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) Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  4. 4. 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) Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  5. 5. 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. Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  6. 6. 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  7. 7. 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  8. 8. 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) Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  9. 9. 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) Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  10. 10. Coordinated resource allocation (cont’d) 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  11. 11. Coordinated resource allocation (cont’d) 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  12. 12. Coordinated resource allocation (cont’d) 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) Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  13. 13. Coordinated resource allocation (cont’d) 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. Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  14. 14. Coordinated resource allocation (cont’d) 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  15. 15. 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  16. 16. 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. Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  17. 17. 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 Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  18. 18. 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. Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  19. 19. Average EE Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  20. 20. Weighted sum-rate Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  21. 21. 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. Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  22. 22. 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. Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA
  23. 23. THANK YOU!! Stefano Buzzi, Ph.D. Universit´a di Cassino e del Lazio Meridionale buzzi@unicas.it Venturino, Risi, Zappone, Buzzi Green Resource Allocation in Downlink Multi-Cell OFDMA

×