Bandwidth Analysis of Low-Complexity Decoupling Networks for Multiple Coupled Antennas

Bandwidth Analysis of Low-Complexity DecouplingNetworks for Multiple Coupled Antennas

Ding Nie and Bertrand Hochwald

University of Notre Dame

[email protected]@nd.edu

November 4, 2014

Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 1 / 14

Overview

1 Introduction to Decoupling Networks

2 Bandwidth of Decoupling Networks

3 Summary


Antenna Mutual Coupling

Where it can happen

Closely spaced antennas, compactdevices, wearables, massive MIMO

At all frequencies, WiFi, LTE, 5Gtechnologies ⋯

Generally harmful in wireless communications

Correlated channels in MIMO communications

Reduces the total radiation power

Negative impacts on capacity

Can be compensated: do not over-engineer the antennas


Impedance Matching Networks

Compensate the mutual coupling

Impedance matching networks can compensate

Envelope correlation can be made zero

Maximizes the radiation power

Compensate the negative impact on capacity

Matching Network

⋯ ⋯

Matching Network: A lossless reciprocal multi-port network


Decoupling Networks for Multiple Antennas

Two-port matching network matches a single source to a singleantenna

2N-port matching network

N coupled antennas

.

.

.

.

.

.

.

.

.

0Z

0Z

Two-port matching network

LZ 0Z0Z

0Z

0Z

.

.

.

Decoupling network matches decoupled sources to coupled antennas

Transforms the impedance of coupled antennas into the decoupledcharacteristic impedances


Complexity of Decoupling Networks

The decoupling networks arecomplicated in general 2N2 + N

But the realization is not unique. . .

. . .

1

2

3

1N −

N

1N +

2N +

3N +

2 1N −

2N

Minimum-complexity decoupling networks

Systematic and unified decouplingnetworks design methods for arbitrarycoupled antennas

Decoupling networks design methodwith minimum complexity N2 + N

Alternative design methods withclose-to-optimum complexity N2 + 2N

. . .

. . .

1

2

3

1N −

N

1N +

2N +

3N +

2 1N −

2N

. . .

. . .

1

2

3

1N −

N

1N +

2N +

3N +

2 1N −

2N


Examples of Low-Complexity Decoupling Networks

Three Dipoles (at design frequency fd = 2.4 GHz)

ZL =

77.64 + 43.08j 72.09 + 3.36j 54.17 − 24.97j72.09 + 3.36j 79.18 + 42.18j 72.09 + 3.36j

54.17 − 24.97j 72.09 + 3.36j 77.64 + 43.08j

Ω

10λ

10λ

2λ

1

2

3

4

5

6

12.2 nH 6.50 μH0.53 pF

0.02 pF

0.17 pF

0.98 pF

708 nH

0.05 pF

23.0 nH

13.7 nH

1.22 pF

0.2 fF179 nH

0.07 pF

0.79 pF

0.79 pF

14.1 nH

24.6 μH

109 nH

11.2 nH

9.0 nH

1

2

3

4

5

6

13.51 pF

0.30 nH

0.30 nH

1.38 nH

1.38 nH

1.14 nH0.22 nH

4.71 pF

13.51 pF

7.71 nH

7.71 nH

5.08 pF

1

2

3

4

5

6

8.22 nH

7.93 nH

5.31 nH

5.17 nH

11.01 nH

210 nH

8.22 nH

0.79 pF

0.79 pF

0.38 pF

0.06 pF

0.66 pF

0.11 pF

0.17 pF

0.53 pF

(a) (b) (c)


Examples of Low-Complexity Decoupling Networks

Three Dipoles (at design frequency fd = 2.4 GHz)

ZL =

77.64 + 43.08j 72.09 + 3.36j 54.17 − 24.97j72.09 + 3.36j 79.18 + 42.18j 72.09 + 3.36j

54.17 − 24.97j 72.09 + 3.36j 77.64 + 43.08j

Ω

10λ

10λ

2λ

−10 −5 0 5 10 15 20 25 300

5

10

15

20

25

30

35

Signal−to−noise ratio (dB)

Cap

acity

(bi

ts/tr

ansm

issi

on)

7 dB


Bandwidth of Decoupling Networks

Power reflection ratio

The ratio between the expected reflectedpower and the expected incident power atfrequency f

r(f ) =E tr~bH(f )~b(f )E tr~aH(f )~a(f )

=1

N‖SLM(f )‖2F

0Z

0Z

2N-port matching network

.

.

.

( )LS f( )LMS f

( )a f

( )b f O

utput ports N

+1~2N

Input ports 1~N

.

.

.

Bandwidth of N matched antennas

The frequency range for which the power reflection ratio r(f ) is no greaterthan a threshold τ in the vicinity of design frequency fd

fBW(τ, fd) = maxf1≤fd≤f2

r(f )≤τ,∀f1≤f≤f2

f2 − f1.


Bandwidth of Low-Complexity Decoupling Networks

1

2

3

4

5

6

12.2 nH 6.50 μH0.53 pF

0.02 pF

0.17 pF

0.98 pF

708 nH

0.05 pF

23.0 nH

13.7 nH

1.22 pF

0.2 fF179 nH

0.07 pF

0.79 pF

0.79 pF

14.1 nH

24.6 μH

109 nH

11.2 nH

9.0 nH

1

2

3

4

5

6

13.51 pF

0.30 nH

0.30 nH

1.38 nH

1.38 nH

1.14 nH0.22 nH

4.71 pF

13.51 pF

7.71 nH

7.71 nH

5.08 pF

1

2

3

4

5

6

8.22 nH

7.93 nH

5.31 nH

5.17 nH

11.01 nH

210 nH

8.22 nH

0.79 pF

0.79 pF

0.38 pF

0.06 pF

0.66 pF

0.11 pF

0.17 pF

0.53 pF

(a) (b) (c)

−5 −4 −3 −2 −1 0 1 2 3 4 5

x 10−3

0

0.05

0.1

0.15

0.2

0.25

Frequency offset/Design Frequency (∆ f/fd)

Pow

er r

efel

ctio

n ra

tio r

(f)

(a) actual(b) actual(c) actual


Bandwidth Analysis for Decoupling Networks

Assume constant loadsacross frequency

Introduce a smallfrequency offset ∆f

First-order analysis ondecoupling networks

r(f ) ≈ c∆f 2

c depends on thedecoupling network −5 −4 −3 −2 −1 0 1 2 3 4 5

x 10−3

0

0.05

0.1

0.15

0.2

0.25

Frequency offset/Design Frequency (∆ f/fd)

Pow

er r

efel

ctio

n ra

tio r

(f)

(a) actual(a) first−order(b) actual(b) first−order(c) actual(c) first−order

Criteria for High-Bandwidth Decoupling Networks

Small change in admittance of the decoupling network when ∆fintroduced

Small capacitors and large inductors


Bandwidth of Decoupling Networks Design Methods

1

2

3

4

5

6

12.2 nH 6.50 μH0.53 pF

0.02 pF

0.17 pF

0.98 pF

708 nH

0.05 pF

23.0 nH

13.7 nH

1.22 pF

0.2 fF179 nH

0.07 pF

0.79 pF

0.79 pF

14.1 nH

24.6 μH

109 nH

11.2 nH

9.0 nH

1

2

3

4

5

6

13.51 pF

0.30 nH

0.30 nH

1.38 nH

1.38 nH

1.14 nH0.22 nH

4.71 pF

13.51 pF

7.71 nH

7.71 nH

5.08 pF

1

2

3

4

5

6

8.22 nH

7.93 nH

5.31 nH

5.17 nH

11.01 nH

210 nH

8.22 nH

0.79 pF

0.79 pF

0.38 pF

0.06 pF

0.66 pF

0.11 pF

0.17 pF

0.53 pF

(a) (b) (c)

. . .

. . .

1

2

3

1N −

N

1N +

2N +

3N +

2 1N −

2N

. . .

. . .

1

2

3

1N −

N

1N +

2N +

3N +

2 1N −

2N(a) (b)

(a) has the minimum complexity (b) has a higher bandwidthDing Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 12 / 14

Summary

Mutual coupling can be compensated by decoupling networks

Decoupling networks can be obtained from design methods thatachieves minimum- or low-complexity

The bandwidth is not necessarily sacrificed with low-complexitydecoupling networks


References

D. Nie, B. M. Hochwald and E. Stauffer, “Systematic design oflarge-scale multiport decoupling networks,” IEEE Transactions onCircuits and Systems I: Regular Papers, vol. 61, no. 7, pp. 2172–2181,July 2014.

J. C. Coetzee and Y. Yu, “Design of decoupling networks for circulantsymmetric antenna arrays,” IEEE Antennas and Wireless PropagationLetters, vol. 8, pp. 291–294, 2009.

A. Krewski and W. L. Schroeder, “N-port DL-MIMO antenna systemrealization using systematically designed mode matching and modedecomposition network,” in Proceedings of the 42nd EuropeanMicrowave Conference (EuMC), pp. 156C159, Oct. 2012.

B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impactof matching network on bandwidth of compact antenna arrays,” IEEETransactions on Antennas and Propagation, vol. 54, pp. 3225-3238,Nov. 2006.


Bandwidth Analysis of Low-Complexity Decoupling Networks for Multiple Coupled Antennas

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