Presented on 11/4/2014, at 2014 Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA

1. Bandwidth Analysis of Low-Complexity Decoupling
Networks for Multiple Coupled Antennas
Ding Nie and Bertrand Hochwald
University of Notre Dame
nding1@nd.edu
bhochwald@nd.edu
November 4, 2014
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 1 / 14

2. Overview
1 Introduction to Decoupling Networks
2 Bandwidth of Decoupling Networks
3 Summary
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 2 / 14

3. Antenna Mutual Coupling
Where it can happen
Closely spaced antennas, compact
devices, wearables, massive MIMO
At all frequencies, WiFi, LTE, 5G
technologies
…
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
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 3 / 14

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

5. Decoupling Networks for Multiple Antennas
Two-port matching network matches a single source to a single
antenna
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 decoupled
characteristic impedances
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 5 / 14

6. Complexity of Decoupling Networks
The decoupling networks are
complicated 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 decoupling
networks design methods for arbitrary
coupled antennas
Decoupling networks design method
with minimum complexity N2 + N
Alternative design methods with
close-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
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 6 / 14

7. 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 − 24.97j
72.09 + 3.36j 79.18 + 42.18j 72.09 + 3.36j
54.17 − 24.97j 72.09 + 3.36j 77.64 + 43.08j

 Ω
10
λ
10
λ
2
λ
1
2
3
4
5
6
12.2 nH 6.50 μH
0.53 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 fF
179 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)
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 7 / 14

8. 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 − 24.97j
72.09 + 3.36j 79.18 + 42.18j 72.09 + 3.36j
54.17 − 24.97j 72.09 + 3.36j 77.64 + 43.08j

 Ω
10
λ
10
λ
2
λ
−10 −5 0 5 10 15 20 25 30
0
5
10
15
20
25
30
35
Signal−to−noise ratio (dB)
Capacity(bits/transmission)
7 dB
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 8 / 14

9. Bandwidth of Decoupling Networks
Power reflection ratio
The ratio between the expected reflected
power and the expected incident power at
frequency f
r(f ) =
E tr{bH(f )b(f )}
E tr{aH(f )a(f )}
=
1
N
SLM(f ) 2
F
0Z
0Z
2N-port
matching
network
.
.
.
( )LS f( )LMS f
( )a f

( )b f

Outputports
N+1~2N
Inputports
1~N
.
.
.
Bandwidth of N matched antennas
The frequency range for which the power reflection ratio r(f ) is no greater
than a threshold τ in the vicinity of design frequency fd
fBW(τ, fd ) = max
f1≤fd ≤f2
r(f )≤τ,∀f1≤f ≤f2
f2 − f1.
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 9 / 14

10. Bandwidth of Low-Complexity Decoupling Networks
1
2
3
4
5
6
12.2 nH 6.50 μH
0.53 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 fF
179 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
)
Powerrefelctionratior(f)
(a) actual
(b) actual
(c) actual
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 10 / 14

11. Bandwidth Analysis for Decoupling Networks
Assume constant loads
across frequency
Introduce a small
frequency offset ∆f
First-order analysis on
decoupling networks
r(f ) ≈ c∆f 2
c depends on the
decoupling 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
)
Powerrefelctionratior(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 ∆f
introduced
Small capacitors and large inductors
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 11 / 14

12. Bandwidth of Decoupling Networks Design Methods
1
2
3
4
5
6
12.2 nH 6.50 μH
0.53 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 fF
179 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 bandwidth
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 12 / 14

13. Summary
Mutual coupling can be compensated by decoupling networks
Decoupling networks can be obtained from design methods that
achieves minimum- or low-complexity
The bandwidth is not necessarily sacrificed with low-complexity
decoupling networks
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 13 / 14

14. References
D. Nie, B. M. Hochwald and E. Stauffer, “Systematic design of
large-scale multiport decoupling networks,” IEEE Transactions on
Circuits 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 circulant
symmetric antenna arrays,” IEEE Antennas and Wireless Propagation
Letters, vol. 8, pp. 291–294, 2009.
A. Krewski and W. L. Schroeder, “N-port DL-MIMO antenna system
realization using systematically designed mode matching and mode
decomposition network,” in Proceedings of the 42nd European
Microwave Conference (EuMC), pp. 156C159, Oct. 2012.
B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact
of matching network on bandwidth of compact antenna arrays,” IEEE
Transactions on Antennas and Propagation, vol. 54, pp. 3225-3238,
Nov. 2006.
Ding Nie and Bertrand Hochwald (University of Notre Dame)Bandwidth Analysis of Decoupling Networks November 4, 2014 14 / 14