User Ordering and Subchannel Selection for Power Minimization in MIMO Broadcast Channels using BD-GMD Winston Ho and Ying-Chang Liang, Institute for Infocomm Research (I2R), Singapore NUS
VTC 2008 Fall, Calgary
Overview Optimal Power Minimization Preliminaries: GMD and BD-GMD Subchannel Selection ZF-based Power Minimization Efficient Method Simulations Conclusion NUS
BD-GMD
Power Minimization Objective: To minimize the transmit power for the MIMO broadcast channel, given user rate requirements, using Dirty Paper Coding.
Cases: Interference-Balancing (IB). Zero-Forcing (ZF). NUS
BD-GMD
Optimal Power Minimization (1) Interference-Balancing (IB) Case IUI, noise Theoretical optimum – convex optimization Better performance than ZF in low SNR region Higher complexity than ZF case Many iterations Each iter. ↑ computations No. iter. random NUS
BD-GMD
Optimal Power Minimization (2) Zero-Forcing (ZF) Case Lower complexity
User ordering and subchannel selection Search over encoding orders and subchannel combinations Limited predictable complexity
Suboptimal method with much reduced complexity NUS
close to IB-optimal power BD-GMD
Overview Optimal Power Minimization Preliminaries: GMD and BD-GMD Subchannel Selection ZF-based Power Minimization Efficient Method Simulations Conclusion NUS
BD-GMD
Preliminaries (1) Transmission Strategies for Single-User MIMO Singular Value Decomposition (SVD) H = USVH Subchannel with different SNRs
Geometric Mean Decomposition (GMD)[1] H = PLQH L is lower triangular, equal diagonal Subchannels with identical SNRs NUS
[1] Y. Jiang, J. Li and W. W. Hager, “Joint Transceiver Design for MIMO Communications Using Geometric Mean Decomposition,” IEEE Trans. Signal Processing, vol. 53, no. 10, pp. 3791-3803, Oct. 2005. BD-GMD
Preliminaries (2) Block-Diagonal GMD for Multi-User MIMO H = P L QH Block Diagonal & Unitary
Each Pi is unitary. NUS
Unitary Lower Triangular
Each Li is equal diagonal.
Block-equal-diagonal
S. Lin, W. W. L. Ho, and Y.-C. Liang, “Block Diagonal Geometric Mean Decomposition (BD-GMD) for MIMO Broadcast Channels,” IEEE Trans. Wireless Commun., vol. 7, no. 7, pp. 2778-2789, Jul. 2008. BD-GMD
Overview Optimal Power Minimization Preliminaries: GMD and BD-GMD Subchannel Selection ZF-based Power Minimization Efficient Method Simulations Conclusion NUS
BD-GMD
Subchannel Selection Block diagonal geometric mean decomposition with subchannel selection (BD-GMD-SS) Successive GMD Select singular values Reduce transmit power NUS
BD-GMD
Overview Optimal Power Minimization Preliminaries: GMD and BD-GMD Subchannel Selection ZF-based Power Minimization Efficient Method Simulations Conclusion NUS
BD-GMD
ZF-based Power Minimization (1) Rate req’m for each user = Rk bps/Hz SNR req’m
NUS
# transmit antennas = NT # receive antennas = n1, n2, …, nK sum=NR ≤ NT Multiplexing: user k has ηk data subchannels BD-GMD
ZF-based Power Minimization (2) Optimization problem: minimize Tr (F H F )
subject to AHF = N 0 Γ1/2 B
B∈L , A∈B A(i, :) = 1
for 1 ≤ i ≤ N D
N0 NUS
A
H
1/2
Γ
F
SNR req’m: Γ k = γ k Iη BD-GMD
1s
B k
ZF-based Power Minimization (3) Solution: BD-GMD-SS: P HQ = L H
Minimum power = NUS
BD-GMD
Transceiver Design A1
n a
MOD
s
F
x
H
y
MOD
z1
MOD
zK
:
B-I Channel
F
H
NUS
BD-GMD
AK
A
User Ordering Rearranging the Channel Matrix NT
n1
DH =
NR
: nK
to achieve minimum transmit power.
NUS
PH
D
L
Q
H
Λ BD-GMD
Overview Optimal Power Minimization Preliminaries: GMD and BD-GMD Subchannel Selection ZF-based Power Minimization Efficient Method Simulations Conclusion NUS
BD-GMD
Efficient Method Best Choice Ordering Best of three methods Successive selection of users Top down manner
Optimum subchannel selection NUS
BD-GMD
Overview Optimal Power Minimization Preliminaries: GMD and BD-GMD Subchannel Selection ZF-based Power Minimization Efficient Method Simulations Conclusion NUS
BD-GMD
Simulation Results
NUS
BD-GMD
Equal Rate Requirements
Figure 1:
R = [ ρ , ρ , ρ , ρ ]. NUS
Uncorrelated channels.
BD-GMD
Equal Rate Requirements
Figure 1:
R = [ ρ , ρ , ρ , ρ ]. NUS
Uncorrelated channels.
BD-GMD
Unequal Rate Requirements
Figure 2:
R = [ ρ/2,2 ρ , ρ/2,2 ρ ]. NUS
Uncorrelated channels. BD-GMD
Unequal Rate Requirements
Figure 2:
R = [ ρ/2,2 ρ , ρ/2,2 ρ ]. NUS
Uncorrelated channels. BD-GMD
Correlated Channels
Figure 3:
R = [ ρ , ρ , ρ , ρ ]. NUS
BD-GMD
Correlated Channels
Figure 3:
R = [ ρ , ρ , ρ , ρ ]. NUS
BD-GMD
Uneq. Rate, Correlated
Figure 4:
R = [ ρ/2,2 ρ , ρ/2,2 ρ ]. NUS
BD-GMD
Uneq. Rate, Correlated
Figure 4:
R = [ ρ/2,2 ρ , ρ/2,2 ρ ]. NUS
BD-GMD
Conclusion ZF-based Power Minimization for MIMO Broadcast Channels Block-diagonal Geometric Mean Decomposition (BD-GMD) Optimal ordering and subchannel selection Non-iterative solution Power close to IB-optimal NUS
BD-GMD
