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Receive Diversity Revisited:

Correlation, Coupling and NoiseCarlo P. Domizioli Brian L. Hu hes

Kevin G. Gard, and Gianluca Lazzi

North Carolina State University

[email protected]

November 28, 2007

Foundation under grants CCF-0312686 and CCF-0515164



Motivation Performance of receive diversity systems dependent on fading

–

In spatial diversity, receiver space constraints limit the antenna

spacing, resulting in correlation between the multipath components

and mutual coupling between the antennas

Most research on mutual coupling focuses on fading (signal)

correlation while assuming spatially white noise

Performance metrics in communications depend on both the signal

and noise; therefore we should also consider how closely spaced

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antennas affect noise correlation



Recent Work Morris & Jensen ’05: Realistic model for front-end amplifiers,

Gans ’06: Evaluated MIMO capacity for sky-noise limited and

certain am lifier-noise limited scenarios

Goals of this study:

Develop a receiver noise model that articulates the dominant

sources of noise and includes effects of mutual coupling on

both the si nal and noise correlation

Evaluate performance of the optimal diversity receiver under

a variety of different noise sources

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O timal Combiner for Correlated Noise Consider an M -branch diversity receiver in which both the fading

nhr += x M x C ∈nh,symbol;Tx~

),(~

),(~

n

h

0n

0h

ΣΣ

CN

CN Fading path gain:

(Correlated) AWGN:

rw H y =

11 −− Σ H

Determine the optimal (w.r.t. SNR) linear combiner

nn ..,Σ

Traditional MRC (w∝h) is suboptimal for correlated noise!

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Need a receiver noise model to determine specific form of Σn



Receiver Noise Model Consider a typical post-detection diversity receiver:

. . .

. .

. .

. .

Assume coupling in

antennas only

Each component contributes noise to the total output noise n

Use noisy circuit theory to construct a noise model for each

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component, then calculate output noise correlation Σn



Antenna Arra Model with a Thevenin equivalent network:

uiZvA

+=

ZA

~ antenna impedance matrix

Off-diagonal elements of ZA represent

u ~ open-circuit (induced) voltage

Terminal (observed) voltages related to incident field by array

mutual coupling between antennas

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Antenna Thermal Noise Open-circuit voltage u contains a signal and noise component:

),(~, ohooo0hnhu Σ+=

CN x

o

interference from other electronic devices

For thermal noise in an isotropic environment (Twiss ’55)

]Re[4),,(~ 0 AnnoZ0n

oo

⋅= BkT CN

For antenna separations less than a few wavelengths ZA

is

0 ≈ ×

-

z a s an ar emp. ; ~ an w

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non- agona – no se s corre a e



Am lifier Noise Amplifiers typically represented by the Rothe-Dahlke (’56) model:

resistancenoiseequivalent~)4,0(~ r Br kT v CN

econductancnoiseequivalent~)4,0(~ 0 aaa g Bg kT i CN

This adequately models both thermal and shot noise

Important amplifier metric is the noise figure NF:

dB)(in NFSNR SNR inout −=

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NF function of noise parameters {r a ,g a ,z cor } and source impedance



Downstream Noise Downstream components consist of filters, mixers, amplifiers and

–

Alternative – assume each component performs a linear operation

on the com lex baseband si nals and enerates AWGN

Can reference total downstream noise to the amplifier output,

model with a Thevenin equivalent load:

,~ 0 d d r v CN

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Matchin Network

Noise figure of amplifiers minimized iff (multiport match)

Practical subo timum solution: Use M two- ort MNs self match

IZin opt z =

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Numerical Exam le Performance metric – Diversity gain at 1% outage probability vs.

Incident electric field – 32 vertically-polarized plane waves:

An les-of-arrival uniforml s aced in azimuth from 0 to 2π

i.i.d. phases uniformly distributed on [0,2π]

Antenna array – Two half-wavelength (λ/2) dipoles with radius10-3λ. Impedance matrix and radiation pattern evaluated by NEC

Amplifier – Maxim 2642 LNA, NFmin=1.04 dB

owns ream no se – ssume componen s ave a compos enoise figure of 10 dB at a source impedance of 50 Ω:

NF

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=−= sd



Matchin Network Performance13

12

B ]

10 i t y G a i n [

9 D i v e r s

7

8 i.i.d. Fading & NoiseMultiport Match

Self Match

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0 0.2 0.4 0.6 0.8 1

d/λ



Individual Noise Sources Self Match13

11

12

d B ]

10 i t y

G a i n

9 D i v e r

i.i.d. Fading & Noise

7

8 n enna o seAmplifier Noise

Downstream Noise

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. . . .

d/λ



Conclusions In a compact receive diversity array, both the signal and noise

components of the diversity branches may be correlated

Traditional MRC is suboptimal for correlated noise Different noise sources can impact performance in profoundly

different ways

Accurately representing the dominant noise sources is critical to

-

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QUESTIONS?



References1. M. L. Morris and M. A. Jensen, “Improved network analysis of

”coup e an enna vers y per ormance, rans. re ess

Commun., vol. 4, pp. 1928-1934, Jul. 2005.

2. M. J. Gans, “Channel ca acit between antenna arra s – Part I: Sk

noise dominates,” IEEE Trans. Commun., vol. 54, pp. 1586-1592,

Sep. 2006.3. M. J. Gans, “Channel capacity between antenna arrays – Part II:

Amplifier noise dominates,” IEEE Trans. Commun., vol. 54, pp.

1983-1992, Nov. 2006.

4. R. Q. Twiss, “Nyquist’s and Thevenin’s theorems generalized for

non-reciprocal linear networks, J. Applied Physics, vol. 26, pp. 599-

602, May 1955.



References cont.5. H. Rothe and W. Dahlke, “Theory of noisy fourpoles,” Proc. IRE ,

vo . , pp. - , un. .

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