Transcript Multiuser OFDM with Adaptive Subcarrier, Bit, and Power

Multiuser OFDM with Adaptive
Subcarrier, Bit, and Power
Allocation
Wong, et al, JSAC, Oct. 1999
outline
•
•
•
•
•
Introduction
Problem Formulation
Optimal Solution
Pretty Pictures
Conclusion
introduction
• High speed data invites frequency
selective fading.
• OFDM approaches maximum capacity in
a single user channel.
• Simple time or frequency division misses
capacity gain from multiuser channel
diversity (Lectures 3&4).
multiuser system and notation
• K users, N subbands
• Rk bits per OFDM symbol for kth user
• ck,n bits assigned by kth user to nth
subband
ck,n  D = {0, 1, 2, …, M}
if ck’n  0, ckn = 0 for all k  k’
• fk(c) SNR required for c bits/symbol
• Pk ,n 
f k (ck ,n )

2
k ,n
so what’s the problem?
• Simple mathematical formulation:
N
K
P  min 
*
T
ck ,n D
n 1 k 1
1

2
k ,n
f k (ck ,n )
N
C1: For all k  {1, …, K}, Rk   ck ,n
n 1
C2: For all n  {1, …, N},
if there exists k’ with ck’,n  0,
then ck,n = 0 for all k  k’.
review: single user case
• Optimal single user subcarrier, bit, and power
allocation given a rate constraint has same
problems as multiuser case.
• No analytic solution, optimality arrived at
through successive (greedy) bit allocation:
Initialization:
For all n, let cn = 0, and DPn = [f(1)-f(0)]/n2;
Bit Assignment Iterations:
Repeat the following R times:
ñ = argminn DPn;
cñ = cñ + 1;
DPñ = [f(cñ + 1)-f(cñ)]/ñ2;
End;
modified problem
• Reformulate problem in a convex sense
(rk,n represents user k’s (continuous) rate in
subcarrier n, rk,n represents her “timesharing factor):
r k ,n
rk ,n
P  min  2 f k (
)
r [ 0 , Mr ]
r
n 1 k 1  k , n
k ,n
r [ 0 ,1]
N
*
T
k ,n
K
k ,n
k ,n
N
subject to:
Rk   rk ,n
n 1
N
and
1   r k ,n
n 1
lagrangian (ewww… math)
r k ,n  rk ,n  K  1

   k   rk ,n  Rk 
L   2 f k 


r
n 1 k 1

k ,n
 k ,n  k 1  n 1
N
K
 K

   n   r k ,n  1
n 1
 k 1

N
solution (math)
r r
*
k ,n
*
' 1
k ,n k
q ,k
f


q ,k
2
k ,n

 f k' 0 

 k2,n

 k
 f ' M 
 k
2

k ,n

H k ,n   
1
 k2,n
r
*
k ,n
0  n  H k ,n k ,n 

1  n  H k ,n k ,n 


f k'1 k k2,n  0



f k'1 k k2,n  M
 f  f   
k

0  f k'1 k k2,n  M
' 1
k
2
k ,n
2
' 1
k ,n k
f
 
2
k ,n
solution (intuition)
• Similar to Lecture 3 (Broadcast ISI),
optimal allocation depends strongly on
channel quality, required rate, and QOS
requirement (though here, the QOS
connection is masked).
• For any situation in which the total data
rate is < MN, there is a guaranteed
solution. (maximizing rate vs. minimizing
power)
adaptive solution
• Increase Lagrangian multipliers iteratively
until all users’ rate constraints are satisfied.
• But this is a modified problem. Generate
final solution using single user bit
allocation technique among assigned
subcarriers.
• PT  PT*  PT, and the difference between
final (suboptimal) and modified solutions
gives upper bound on performance.
simulation results (1)
simulation results (2)
simulation results (3)
simulation results (4)
“Increase in Capacity of
Multiuser OFDM System
Using Dynamic
Subchannel Allocation”,
W. Rhee and J. Cioffi,
Proc. VTC 2000.
conclusions and further work
• Clearly, multiple access channel has
larger freq.-selective fading capacity,
and the method proposed more fully
exploits this capacity than any of the
optimizations alone or pair-wise.
• Perfect channel estimation is a large
assumption, as is time-varying fading.
• Adaptive solution is guaranteed to
converge, but no iteration limit is given.
comments…
• In comparison with spread spectrum,
OFDM seems preferable in slowly
changing multiple-user freq.-selective
fading environments.
• The results of this paper could be
extended to FDMA (e.g. MAC rather than
broadcast) solutions, but the sensitivity to
implementation becomes a dominant
factor.