Instrumentation & Measurement Magazine 24-4 - 80

Table 2 - Change the noise level σG gradually
ϕ
30
30
30
30
30
σG
0.1
0.3
0.5
0.7
1
Proposed
DOA
30.2
29.4
30.2
29.3
28.1
MUSIC
(peak 1)
44.1
44.5
44.2
44.1
42.3
MUSIC
(peak 2)
-135.9
-135.5
-135.8
-135.9
-137.7
Conclusions
Fig. 3. The result of applying the MUSIC algorithm. This figure shows the
log spectrum with respect to angle change (-180 degrees to 180 degrees). Two
peaks occur at 45 degrees and -135 degrees, respectively.
two peaks in bearing estimation, we present two angles associated
to two peaks, considering the MUSIC algorithm. In fact,
four peaks appear as we use the MUSIC algorithm (ϕ ∈ {75,
165, -105, -15} in Table 1). See that the proposed estimator outperforms
the MUSIC algorithm considerably in all cases.
Change the Noise Level Gradually
Recall that G in (14) is a Gaussian noise with mean zero and
standard deviation σG
for S4
= 0.1. Considering every sensor, except

In this subsection, we change the noise level σG
20log 10 20.
G
Am


gradually
and test the performance of the proposed DOA estimation.
Table 2 presents the simulation results. Since the MUSIC algorithm
provides two peaks in bearing estimation, we present
two angles associated with two peaks, considering the MUSIC
algorithm. The units for ϕ in the table is degrees. See that the
proposed estimator outperforms the MUSIC algorithm considerably
in all cases.
, we set the signal amplitude as Am = 1. Thus, the Signalto-Noise
Ratio (SNR) is
This paper handles the micro positioning platform which is
equipped with only four receivers. This paper considers estimating
the DOA of a signal using only four isotropic receivers.
As a signal is reflected or scattered, its amplitude attenuates
significantly. Thus, as we estimate the DOA, we use receivers
with high signal amplitude, since they have more probability
to receive a direct signal (not a reflected signal). Every receiver
uses both the phase difference and the signal amplitude in order
to estimate the DOA. The efficiency of the proposed DOA
estimation is verified by comparing it with the MUSIC algorithm
using MATLAB simulations. In the future, we will
verify the performance of the proposed DOA estimator using
experiments with real isotropic hydrophones in underwater
environments.
References
[1] A. AlShehhi, M. L. Hammadih, M. Zitouni, S. A. Kindi, N. Ali,
and L. Weruaga, " Linear and circular microphone array for
remote surveillance: simulated performance analysis, " ArXiv,
vol. abs/1703.02318, 2017.
[2] Y. Ozaki, J. Ozawa, E. Taillefer, J. Cheng, and Y. Watanabe, " A
simple doa estimator using adjacent pattern power ratio with
switched beam antenna, " Progress in Electromagnetics Research C,
vol. 22, pp. 55-71, 2011.
[3] C. Vaidyanathan and K. M. Buckley, " Performance analysis of the
mvdr spatial spectrum estimator, " IEEE Trans. Signal Process., vol.
43, no. 6, pp. 1427-1437, 1995.
Table 1 - Change the transmitter's
bearing angle ϕ gradually
ϕ
30
75
120
165
-150
-105
-60
-15
80
Proposed
DOA
30.1
75.9
120.2
164.7
-150.3
-104.7
-59.2
-15.1
MUSIC
(peak 1)
44.3
90
134.7
-135.4
-45.5
MUSIC
(peak 2)
-135.7
-90
-45.3
-180
44.6
180
134.5
180
[4] S. R. Tuladhar and J. R. Buck, " Unit circle mvdr beamformer, "
in Proc. 2015 IEEE Int. Conf. Acoustics, Speech and Signal Process.
(ICASSP), pp. 2484-2488, 2015.
[5] J. Lin, X. Ma, S. Yan, and C. Hao, " Time-frequency multiinvariance
esprit for doa estimation, " IEEE Antennas and Wireless
Propagation Letters, vol. 15, pp. 770-773, 2016.
[6] R. H. Roy and T. Kailath, " Esprit-estimation of signal parameters
via rotational invariance techniques, " IEEE Trans. Acoust. Speech
Signal Process., vol. 37, pp. 984-995, 1989.
[7] Z. I. Khan, M. M. Kamal, N. Hamzah, K. Othman, and N. I.
Khan, " Analysis of performance for multiple signal classification
(music) in estimating direction of arrival, " in Proc. 2008 IEEE Int.
RF and Microwave Conf., pp. 524-529, 2008.
[8] R. Li, K. Li, and C. Zhao, " Application of multiple signal
classification algorithm to frequency estimation in coherent
IEEE Instrumentation & Measurement Magazine
June 2021

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