Formulation of Envelope Correlation Coefficient for Multiple Sensors

Based on Scattering Parameter

Abstract: - The Envelope Correlation Coefficient (ECC) is crucial for assessing multiple sensor systems in

wireless communication, sensing, and microwave imaging. ECC measures signal similarity between sensors,

with higher values (close to 1.00) indicating strong correlation. Efficient power transmission, reception, and

multiband path transmission enhance sensor network performance by improving data rates and reliability through

multiple frequency bands. This study uses scattering parameters to calculate ECC for four different sensors in a

single arrangement. Most of the sensors exhibit higher correlation at f2 and f3, while f1 shows a low ECC.

between signals received from different sensors is

measured by the Envelope Correlation Coefficient

(ECC), which significantly impacts system

performance parameters, including diversity gain and

capacity. Strong correlation is indicated by a high

ECC (near 1.00), whereas signal independence is

demonstrated by a low ECC (near 0.00) [1]. The use

of ECC in microwave imaging for security screening,

non-destructive testing, and medical diagnostics is

understudied despite its extensive research in MIMO.

power is maintained using methods such as radiative

power transmission, resonant inductive coupling, and

inductive coupling. Moreover, the implementation of

multiband path transmission further enhances sensor

network performance. By utilizing multiple

frequency bands, multiband transmission improves

data rate and reliability, reduces interference, and

maximizes bandwidth utilization. This capability is

particularly beneficial in dynamic environments

This method makes it necessary to do appropriate

numerical or experimental analysis, which makes it a

time-consuming procedure. The second method uses

Clarke's formula and has gained popularity recently

scattering parameters from the sensor’s elements,

making it suitable for experimental measurements

[10-12]. In this study, the ECC of four pairs of

sensors, using scattering parameters, was analyzed.

The sensors have different resonant frequencies,

The fundamental Equation (1) [3] that calculate the

ECC requires 3-dimensional radiation pattern

consideration.

 󰇻

The parameter 

of the sensors. This parameter can only be used when

port  is excited, and all other ports are terminated to

a 50 Ω load. The symbol of • denotes the Hermitian

product, which is used in linear algebra and quantum

mechanics.

The radiation pattern in Equation (1) is much more

complicates the calculations compared to the

envelope correlation in Equation (2). The second

equation is straightforward to use and produces

accurate results in all situations, even inside with

high multipath propagation performance.

pairs of sensors. These sensor pairs are referred to as

Sensor 1, Sensor 2, Sensor 3, and Sensor 4. The

characteristics of these sensors are summarized in

Table 1. Each transmitter and receiver pair has a

similar resonant frequency. Fig. 2 shows the return

loss of Sensors 1 through 4.

Sensor 1 has a triband operating frequency at 1.67,

2.15, and 2.64 GHz with return losses of 22.07,

24.34, and 20.50 dB, respectively. Sensors 2 through

GHz with return losses of 21.26 and 11.24 dB,

respectively. The vector network analyzer used is a

portable vector network analyzer (NanoVNA V2).

The introduced sensor system has been studied and

investigated in terms of ECC measurement using a

circular arrangement. Pairs of Sensors 1 through 4 are

connected using individual portable vector network

analyzers, and scattering parameters are recorded, as

shown in Fig. 3. The arrangement was set with

Sensor 3. The transmitter of Sensor 1 is adjacent to

the transmitters of Sensors 4 and 3. The measurement

of ECC has been repeated 50 times for all

configurations to ensure the data is consistent and

reliable.

Acknowledgment

This work was supported by the Universiti Teknikal

Malaysia Melaka under the FRGS research grant

(FRGS/1/2021/FKEKK/F00471), and by the

Ministry of Higher Education of Malaysia.

References:

and B. K. Kanaujia, “MIMO Antennas:

Design Approaches, Techniques and

Isolation for Microwave Imaging

Applications,” Micromachines (Basel), vol.

14, no. 9, Sep. 2023, doi:

10.3390/mi14091732.

[3] C. Votis, G. Tatsis, and P. Kostarakis,

“Envelope Correlation Parameter

Measurements in a MIMO Antenna Array

Configuration,” International Journal of

Communications, Network and System

Sciences, vol. 03, no. 04, pp. 350–354, 2010,

of envelope correlation coefficient for faster

analysis in MIMO antenna systems,”

Ingeniería Investigación y Tecnología, vol.

23, no. 4, pp. 1–14, Jul. 2022, doi:

10.22201/fi.25940732e.2022.23.4.028.

[6] D. Sarkar, S. Mikki, K. V. Srivastava, and Y.

Antar, “Far-field Envelope Correlation

Coefficient and Near-field Reactive Energy of

MIMO Antennas: An FDTD-IDM-CGF

Approach.”

Applications to Frequency Correlation

Analysis,” 1994.

[9] Institute of Electrical and Electronics

Engineers and EurAAP., 2017 11th European

Conference on Antennas and Propagation

[10] Y. A. S. Dama et al., “An envelope

correlation formula for (N, N) MIMO antenna

arrays using input scattering parameters, and

including power losses,” Int J Antennas

Propag, vol. 2011, 2011, doi:

10.1155/2011/421691.

[11] S. Wang, “Envelope Correlation Coefficient

correlation in (N, N) mimo antenna array

from scattering parameters,” Microw Opt

Technol Lett, vol. 48, no. 5, pp. 832–834, May

2006, doi: 10.1002/mop.21490.