Adaptive Antenna Grouping For Capacity

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



Simulation Results

Contents

1

Motivation

2


3

Adaptive group selection - Proposed MIMO order selection followed by antenna group selection

4

Simulation Results

5

Questions?

Questions?

Motivation



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



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 systems-An Overview

Simulation Results

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Motivation



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

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Motivation



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

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Motivation



Simulation Results

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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



Simulation Results

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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



Simulation Results

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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



Simulation Results

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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



Simulation Results

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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



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



Simulation Results

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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



Simulation Results

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Performance analysis of AGS Capacity curve of AGS dominates in correlated channel. 12


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



Simulation Results

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Performance analysis of AGS Capacity curves crossing point shifts up at high correlation 12


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



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



Simulation Results

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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



Simulation Results

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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



Simulation Results

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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



Simulation Results

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