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Comments on “Detection of Distributed Sources
Using Sensor Arrays”
Sridhar Ramakrishnan, Student Member, IEEE, and
Satish Udpa, Fellow, IEEE
Abstract—In the above correspondence (Y. Jin and B. Friedlander,
“Detection of distributed sources using sensor arrays,” IEEE Trans. Signal
Process., vol. 52, no. 6, pp. 1537–1548, June 2004), Jin and Friedlander
develop a GLR-based detector for detecting a random spatially distributed
signal source using an array of sensors. We show that the expression for
required SNR (RSNR) has been incorrectly derived, which has led the au-
thors to draw incorrect conclusions in their work. In this correspondence,
we correct this particular error and a few other typographical errors, and
provide appropriate conclusions to the original work.
Index Terms—Distributed source, sensor array, signal detection.
In the above correspondence, [1, eq. (50)] expresses the required
SNR (RSNR) incorrectly as
(1)
The expression for RSNR when derived correctly should read as
(2)
Manuscript received March 10, 2006; revised July 15, 2006. The associate
editor coordinating the review of this manuscript and approving it for publica-
tion was Dr. Fulvio Gini.
The authors are with the Electrical and Computer Engineering Department,
Michigan State University, East Lansing, MI 48824 USA (e-mail: rsridhar@egr.
msu.edu; udpa@egr.msu.edu).
Digital Object Identifier 10.1109/TSP.2007.893740
Fig. 1. Normalized RSNR versus degrees of freedom ( , )
for different target and .
A simplified form of the above expression is obtained when we
consider the case where all the principal eigenvalues of are
approximately equal, i.e., , . Defining
as the degrees of freedom, we, thus, obtain
RSNR (3)
instead of
RSNR (4)
as expressed in [1]. Consequently, the expression for output SNR de-
fined as RSNR SNRG becomes
RSNR SNRG (5)
as opposed to
RSNR SNRG (6)
mentioned as [1, eq. (51)] in the original work by Jin and Friedlander.
As a result of the incorrect expression in (4), Fig. 8 in the
original correspondence, i.e., the plot of RSNR versus degrees of
freedom for different , fails to capture the variation in the
RSNR performance for changing (number of time snapshots)
and changing (effective rank of , which is a measure of the
angular spread of the signal), independently. The figure would be
correct only under a special case of snapshot, and not in
general for all . The number of degrees of freedom contains
information of both and , but the effect of increasing on
RSNR ( , being held constant at different values) is markedly
different from the effect of increasing ( , being held constant
at different values) on RSNR. Figs. 1–4 in this correspondence
depict this variation in the RSNR performance for four different
cases.
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