Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Adaptive Antenna Grouping For Capacity Maximization In Correlated MIMO Channels Waqas Ahmad Center of Advance Studies in Engineering, (CASE), Islamabad Pakistan Mobile Communication Limited, Mobilink
[email protected]
October 26, 2014
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Contents
1
Motivation
2
MIMO–State-of-the-Art
3
Adaptive group selection - Proposed MIMO order selection followed by antenna group selection
4
Simulation Results
5
Questions?
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Motivation Deployment of higher order MIMO configurations to fulfill the dramatic increased demand for high data rate. MIMO link adaptation, adaptive control of number of active RF chains with antenna grouping precoding. Find simple solutions for correlated MIMO channels Contribution: Two steps approach:MIMO order selection followed by Adaptive antenna grouping
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
MIMO systems-An Overview
MIMO 1
Multiple antennas at the Tx and Rx.
2
Popular antenna arrays ULA and UCA.
ON
OFF
Figure : UCA with random correlation and ULA with uniform correlation
Spatial correlation reduces MIMO channel capacity. Non-uniform correlation between UCA antenna pairs.
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
MIMO systems-An Overview
Simulation Results
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Spatial Multiplexing (SM) All antennas transmit different data stream.
Si
S
Spatial multiplexing
Sj Sl Sm tk
Figure : Spatial Multiplexing with power NPT allocated equally to NT antennas. For all Si 6= Sj 6= Sl 6= Sm at time instance tk
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Dominent Eigen mode transmission (DEM) All antennas transmit same data stream.
Si Si S
W
Si Si tk
Figure : DEM with power
P NT
allocated to NT antennas
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Hybrid System Antennas of same group transmit same data stream by DEM transmission =⇒ BF. Each group transmits different data streams =⇒ SM. [5]. G1
w1 S
G2
w2
Si
si
Si
si s
Sj Sj tk
W sj sj
Figure : Hybrid System with equal power ’P’ divided equally among all Gr groups. For each symbol Si 6= Sj and wi is weight vector
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Proposed system model Groups adaptively turned ON or OFF based on MIMO channel correlation and SNR setup. G1
w1 S
Si Si tk
G2
w2 Figure : Proposed system with equal power ’P’ divided among selected groups. wi is weight matrix
max
Gr X
! (ρi )
i=1
Where, ρi is the mean transmit correlation per group.
(1)
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Proposed system model (Continued) Assumptions: 1
1
1
Kronecker channel model (H = R 2 GT 2 ), frequency flat
2
Tx side : Randomly distributed dedicated High Correlation (HC) pairs in correlation range 0.96-0.98.
3
Rx side : Uncorrelated, because of simplification
4
kHp k2F = 1 : Fixed channel gain irrespective of number of Tx used. Hp is the selected channel. Hp is the channel matrix with dimensions NR × LT . LT ⇒ Total no.of transmit
Received signal Y
antennas to be used per transmission.
Y =
Gr X i=1
Hi is the channel matrix with dimensions NR × L. L ⇒ No.of transmit antennas
Hi wi si + n
Hi ∈ Hp
per group.
wi is Weight vector with dimensions L × 1 s is Transmit signal vector NR × 1 n is AWGN noise
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Spectral efficiency analysis per group
Capacity of Gr groups
C =
Pζ
i =1
log2
1+
Ex L T No
λ2 1,G
i
Capacity (Bits/Sec/Hz)
20 Lt=2 15
Lt=4
10 5 0 1 40 30
0.5
20 10
ρM
Figure :
0
0
SNR
4x2 MIMO system with 1 highly correlated antenna pair.
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Spectral efficiency analysis per group
1 0.9 LT=2
40
LT=4
30
LT=6
0.8 0.7
ρm
Capacity (bits/sec/Hz)
50
LT=8
20
0.6 0.5
10 0.4
0 1
60 0.8
40 0.6
20
0.4
ρm
0.2
0
(a) Front view
SNR(dB)
0.3 0.2 0
10
20
30
40
50
SNR(dB)
(b) Top view
Figure : Capacity curves using 1, 2, 3, 4 groups and 2 selected antennas L per group with 7 highly correlated antenna pair.
60
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Adaptive Group Selection Algorithm
Known channel H
Calculate Tx correlation (NICCM) and SNR at Rx
MIMO group order selection
Antenna group selection
Figure : Group Selection procedure of proposed scheme in a correlated MIMO channel with assumption of NT > NR
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
MIMO Group Order Selection
C
T {λi }Li=1
=
LT X
log2 1 + αλ2i , α =
i=1
P LT σn2
(2)
T C {λi }Li=i → MIMO channel capacity at SNR α by using first LT singular values. Poincar’s separation theorem: λLT (H) ≥ µLT (Hp )
(3)
λ1 ≥ µ1 ≥ λ2 ≥ µ2 · · · ≥ λLT ≥ µLT where λi is i th singular value H and µi is i th singular value Hp Corollary T T C {λi }Li=1 ≥ C {µi }Li=1 (4) Capacity of H using first LT singular values is upper bound of Hp .
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Performance analysis of AGS Capacity curve of AGS dominates in correlated channel. 12
Capacity (bits/sec/Hz)
10
Hybrid AGS (Proposed) DEM SM WF
8
6
4
2
0 0
5
10
15
20
25
SNR (dB)
Figure : 8 × 4 MIMO system with 14 highly correlated antenna pairs and ρm = 0.5.
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Performance analysis of AGS Capacity curves crossing point shifts up at high correlation 12
Capacity (bits/sec/Hz)
10
Hybrid AGS (Proposed) DEM SM WF
8
6
4
2
0 0
5
10
15
20
25
SNR (dB)
Figure : 8 × 4 MIMO system with 14 highly correlated antenna pairs and ρm = 0.9.
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Complexity analysis Table : Complexity order comparison of proposed AGS with different algorithms
Procedure DEM SM-OL SM-WF Optimal AS Hybrid AGS
Computational cost 2 O nR nT 2 O nR nT 2 O nR nT nT 2 LT O nR LT ζH O nR L2 ζA O nR L2 , ζA ≤ ζH
ζH ⇒ Total number of groups in Hybrid system. ζA ⇒ Total number of groups in proposed Hybrid antenna grouping systems.
Questions?
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Complexity analysis (Continued) Computational cost of the proposed system is significantly low. 350
Average # of flops
AGS (Proposed), ρm=0.5 300
AGS (Proposed), ρm=0.9
250
Hybrid SM DEM
200
150
100
50 0
5
10
15
20
25
SNR (dB)
Figure : 8 × 4 MIMO system with 14 highly correlated antenna pairs.
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
Conclusion and Future work We have proposed Adaptive antenna grouping scheme (AGS). AGS is an efficient transmission technique, because it can adaptively select number of groups based on channel correlation and SNR setups. Proposed scheme is particularly suitable for down-link transmission and D2D communication links where more Tx antennas than Rx. In future, we would like to evaluate the performance of AGS on realistic wireless channel obtained from channel sounding campaign in urban macro cells. Extensions of AGS to Multiuser MIMO applications would also be introduced.
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?
References
[1] J. Heath, S. Sandhu, and A. Paulraj, ”Antenna selection for spatial multiplexing systems with linear receivers,” IEEE Communications Letters, vol. 5, no. 4, pp. 142-144, april 2001. [2] S. Schwarz, C. Mehlfhrer and M. Rupp, ”Calculation of the spatial preprocessing and link adaption feedback for 3GPP UMTS/LTE,” in 6th Conference on Wireless advanced (WiAD), june 2010, pp. 1-6. [3] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge University Press, 2003. [4] L. Trefethen and D. Bau, Numerical Linear Algebra. SIAM, 1997. [5] K. Kim, J. Lee, and H. Liu, ”Spatial-correlation-based antenna grouping for mimo systems”, IEEE Transactions on Vehicular Technology, vol. 59, no. 3, pp. 2898(2905, 2010).
Motivation
MIMO–State-of-the-Art
Adaptive group selection - Proposed
Simulation Results
Questions?