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5524 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 11, NOVEMBER 2014
Multiobjective Design of Linear Antenna Arrays
Using Bayesian Inference Framework
Chung-Yong Chan, Member, IEEE, and Paul M. Goggans,Member,IEEE
Abstract—The Bayesian inference framework for design intro-
duced in Chan and Goggans [“Using Bayesian inference for linear
antenna array design,” IEEE Trans. Antennas Propag., vol. 59, no.
9, pp. 3211–3217, Sep. 2011] is applied to design linear antenna ar-
rays capable of realizing multiple radiation patterns while satis-
fying various design requirements. Many design issues are involved
when designing a linear antenna array. This paper focuses on four
practical design issues: the need for minimum spacing between two
adjacent array elements, limitations in the dynamic range and ac-
curacy of the current amplitudes and phases, the ability to produce
multiple desired radiation patterns using a single array, and the
ability to maintain a desired radiation pattern over a certain fre-
quency band. We present an implementation of these practical de-
sign requirements based on the Bayesian inference framework, to-
gether with representative examples. Our results demonstrate the
capability and robustness of the Bayesian method in incorporating
real-world design requirements into the design of linear antenna
arrays.
Index Terms—Automated multiobjective design, Bayesian data
fusion, inference-based design, linear antenna array.
I. INTRODUCTION
THE Bayesian inference framework for design has been ap-
plied to the design of linear antenna arrays [1]. A linear an-
tenna array design problem is presented as a generalized inverse
problem and is solved using Bayesian parameter estimation and
model selection. The inference framework has the ability to in-
corporate all design parameters, particularly the number of an-
tenna elements, in a design process and to design linear antenna
arrays with complexity appropriate to the desired radiation pat-
tern. In addition to the desired radiation pattern, practical de-
sign problems involve further design requirements. These real-
world design issues include the requirement to have a minimum
spacing between adjacent array elements, limitations in the dy-
namic range and accuracy of the current amplitudes and phases,
the ability to produce multiple desired radiation patterns using a
single array, and the ability to maintain a desired radiation pat-
tern over a specified frequency band. The present work extends
the methodology set out in [1] to incorporate these practical de-
sign requirements into the design problem.
Manuscript received April 15, 2012; revised June 10, 2014; accepted July 25,
2014. Date of publication August 20, 2014; date of current version October 28,
2014.
C.-Y. Chan is with the Department of Electrical Engineering and Computer
Science, University of Central Florida, Orlando, FL 32816 USA (e-mail:
ChungYong.Chan@ucf.edu).
P. M. Goggans is with the Department of Electrical Engineering, The Uni-
versity of Mississippi, University, MS 38677 USA (e-mail: goggans@olemiss.
edu).
Digital Object Identifier 10.1109/TAP.2014.2350521
The spacing between two adjacent array elements is critical.
Having two array elements too close to each other induces sig-
nificant mutual coupling and renders a linear antenna array de-
sign physically unrealizable, while having two adjacent antenna
elements too far apart results in grating lobes. To achieve a
good balance, many synthesis methods [2]–[4] for designing
uniformly spaced linear antenna arrays use an element spacing
of . The implementation and fabrication of an uniformly
spaced linear antenna array is easier than of a nonuniformly
spaced linear antenna array; however, uniformly spaced linear
antenna arrays are inferior to unequally spaced linear antenna
arrays in many other aspects. The primary advantage of using
unequal spacing is that lower sidelobe levels can be produced
with fewer array elements. For these reasons, the design of un-
equally spaced linear antenna arrays has been studied exten-
sively [5]–[17]. In the design of unequally spaced linear antenna
arrays, the positions of the array elements are not fixed and thus,
inappropriate element spacings may arise. The Bayesian infer-
ence framework has the ability to design unequally spaced linear
antenna arrays having the number of array elements and element
spacings appropriate to the design requirements. Appropriate el-
ement spacings can be achieved by imposing a minimum value
on the spacing between two adjacent array elements. No upper
bound is imposed as grating lobes are suppressed by the pre-
scribed design pattern specifications.
Multiple-beam antenna arrays are desired in various appli-
cations in communications and radar. The ability to produce
multiple desired radiation patterns using a reconfigurable linear
antenna array greatly simplifies the design and practical imple-
mentation of the resulting antenna. Gies and Rahmat–Samii [18]
set out the design of a reconfigurable linear antenna array that
has common current amplitudes and varying current phases to
produce two desired radiation patterns: a sector beam pattern
and a broadside pattern. Various authors [19]–[22] have ex-
tended their work to include practical limitations in the dynamic
range and accuracy of the current amplitudes and phases. Below,
the Bayesian inference framework is applied to design a linear
antenna array with reconfigurable digital attenuators to realize
the same dual radiation patterns, specifically the sector beam
and pencil beam patterns illustrated in [22]. Unlike the work in
[18]–[22], the present work aims to design multiple-beam linear
antenna arrays by allowing the signed real-valued current ampli-
tudes to be reconfigurable, without using the phase of the driving
currents as design parameters. The current amplitudes are con-
strained to discrete values that are represented by a fixed number
of bits. Two different representations are used to study the ef-
fects of using different numbers of bits on thedesign complexity
and geometry of the reconfigurable linear antenna arrays.
0018-926X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
CHAN AND GOGGANS: MULTIOBJECTIVE DESIGN OF LINEAR ANTENNA ARRAYS USING BAYESIAN INFERENCE FRAMEWORK 5525
Fig. 1. Linear array of antenna elements.
Real antennas are required to perform to a specified standard
over a desired operating frequency band. Hence, it is desired
to design antenna arrays that can maintain the desired radia-
tion pattern over a frequency band. The design of wideband an-
tenna arrays for use in radio communication, radar, and acous-
tics is discussed in [23]–[25]. Below, the Bayesian inference
framework is utilized to design narrowband linear antenna ar-
rays having a feed network composed of a single amplitude and
delay for each array element.
Below, Section II presents an overview of the Bayesian in-
ference framework. The implementation of the practical design
requirements along with representative design examples are dis-
cussed in Section III. Final thoughts are presented in Section IV.
II. REVIEW OF THE BAYE S I A N INFERENCE FRAMEWORK
The present authors [1] have set out the Bayesian inference
framework for solving linear antenna array design problems. In
the inference framework, the solution to a design problem is the
posterior distribution, given by Bayes’ theorem as
(1)
where is the number of array elements and repre-
sents the parameters of the elements. The desired radiation
pattern is specified by upper and lower bounds in decibels
at a finite set of designated angles, denoted, respectively,
by and
,where is
the far-field observation angle defined in Fig. 1. The vector
,comprisingpositive-valuedcon-
stants, indicates the required degree of compliance between the
desired and realized radiation patterns at the designated angles.
The value at each angle is assigned by the designer based on the
understanding that a smaller value produces a greater degree of
compliance.
The term in (1) represents the
prior for all design parameters, which include the number of
elements and the parameters of the elements .These
prior distributions are assigned by the designer according to
the background information, which may include the maximum
acceptable number of elements and the possible or accept-
able ranges of values for the element parameters. The term
is the likelihood, which takes the form
[1]:
(2)
where
for
for
otherwise.
(3)
The notation represents the parametric model
(4)
where is the array factor
(5)
for a linear antenna array having isotropic radiators on the
-axis. In (5), and is the free-space wavelength at
the operating frequency. The element parameters ,and ,
respectively, denote the current amplitude, phase, and position
of the th antenna element.
From the prior and likelihood, the posterior distribution is ap-
proximated computationally using a Markov chain Monte Carlo
(MCMC) method. In this approximation, an MCMC-based
computer sampling algorithm, known as BayeSys [26], is used
to draw a reasonable number of samples from the posterior.
In the context of linear antenna array design, each posterior
sample represents a potential design solution with specific
values for the design parameters. As a result, the solution to a
design problem consists of a number of design candidates rather
than a single final design. To obtain the final design, a designer
must choose a design candidate based on additional criteria.
Here, the final design is chosen using a multistep process. The
selection process begins by first choosing the design candidates
that have zero or the least weighted squared error. The next
step is to narrow down the remaining design candidates to
those designs that use the fewest antenna elements. Of all these
designs, the design with the smallest antenna aperture is then
selected as the final design.
III. IMPLEMENTATION OF PRACTICAL DESIGN
REQUIREMENTS IN DESIGN PROBLEMS
Real linear antenna array design problems involve a number
of requirements, which can typically be divided into two cate-
gories. The first category pertains to constraints on the design
parameters. These constraints can generally be implemented
by assigning prior distributions to the design parameters. The
second category pertains to design requirements associated with
the radiation pattern, which are implemented in the likelihood.
The likelihood in (2) implements the requirement to generate a
radiation pattern that satisfies the desired pattern specifications.
A design problem may have multiple requirements associated
with the radiation pattern, such as the ability to produce more
than one desired radiation pattern and the need to maintain a
desired radiation pattern over a frequency band using a single
linear antenna array. These requirements can be implemented
in the likelihood by suitably modifying (2). By expressing the
requirement to produce a desired radiation pattern as
(6)
5526 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 11, NOVEMBER 2014
the likelihood in (2) can be modified to implement a number of
requirements as follows:
(7)
Equation (7) is based on the notion of Bayesian data fusion [27],
which facilitates the integration and extraction of information
from data obtained from two or more sources. By drawing
parallels between data sources and requirements, multiple
practical design requirements in a linear antenna array design
problem can be formulated and implemented using (7). Notice
that in (7) represents the overall likeli-
hood, which incorporates all design requirements. Since the
assignment of a likelihood distribution for any one requirement
is not influenced by the knowledge of any other requirement,
the overall likelihood is the product of the likelihood for each
requirement, whence (7). In probabilistic terms, the proposition
of meeting one design objective is logically independent of the
proposition of meeting another design objective.
A. Multiple Radiation Patterns
The design of a reconfigurable linear antenna array capable
of generating multiple radiation patterns can be implemented
using (7), where denote the requirements
to generate the desired radiation patterns. The modification
of the likelihood in (2) follows as
(8)
where and , respectively, denote the error and the re-
quired degree of compliance between the achieved and desired
radiation patterns at the th designated angle of the th desired
pattern.
Equation (8) facilitates the generation of multiple radiation
patterns using a single antenna array, with feasibility dependent
on the number of radiation patterns , the shapes of all radi-
ation patterns, and the design parameters that are allowed to
be reconfigured. The design example below is a well-studied
problem [18]–[22] with only two desired radiation patterns that
can be produced using a single antenna array by reconfiguring
one of the design parameters. In problems where the specifica-
tions of all desired radiation patterns cannot be satisfied entirely,
a designer may choose to compromise certain pattern specifica-
tions by assigning appropriate values that reflect the compro-
mise to . This type of multiple-beam design problem, with
or without pattern compromise, is of genuine practical interest
and will be studied in future research.
B. Maintaining Radiation Pattern Over a Frequency Band
In practice, an antenna has an operating frequency bandwidth
that is defined as the range of frequencies within which the per-
formance of an antenna conforms to a specified standard [28].
In the design of a linear antenna array, the task is to ensure that
all the radiation patterns produced by a single linear antenna
array operating at different frequencies satisfy the design pat-
tern specifications. This task is challenging but can be solved
using the Bayesian inference framework for design. To incor-
porate the ability to maintain a desired radiation pattern over a
frequency band, (7) is used, as follows.
Denoting the upper, lower, and center frequencies of a fre-
quency band by ,, and , respectively, the relative fre-
quency bandwidth of a linear antenna array is defined as
(9)
Equation (9) can be rewritten as
(10)
where and denote the wavelengths at and ,re-
spectively. For the phase of each driving current, a different
time delay must be implemented for each different operating
frequency in the design. This requirement results in extremely
high implementation costs and renders a linear antenna array
design impractical. The solution to this issue is to incorporate
the variation of the current phases with respect to the operating
frequency into the design problem. Upon denoting the current
phases of the th array element at and by and ,
the use of a constant time delay can be achieved by satisfying
the following conditions:
(11)
Numerically, a frequency band can be represented using a rea-
sonable number of frequency points; these points generally in-
clude the upper, lower, and center frequencies. Equation (11),
which is applicable to the lower frequency only, can be gener-
alized to all frequency points of interest, for ,as
follows:
(12)
where is a real number in the range ;thevalues
correspond to the lower, upper, and center fre-
quencies. From (12), the array factor in (5) can be rewritten for
frequency as
(13)
To ensure that the antenna power gain does not vary greatly
with frequency, the radiation patterns obtained at all frequencies
are normalized with respect to thepeakvalueofallradiation
patterns combined. The parametric model for frequency is
written as
(14)
CHAN AND GOGGANS: MULTIOBJECTIVE DESIGN OF LINEAR ANTENNA ARRAYS USING BAYESIAN INFERENCE FRAMEWORK 5527
for . With the parametric models for all frequencies
determined, the likelihood in (7) becomes
(15)
where is defined as in (3), with replaced by .
C. Minimum Spacing between Two Adjacent Array Elements
To ensure that no two antenna elements are too close to each
other, a minimum value is imposed on the spacing be-
tween adjacent antenna elements. Since the computer algorithm
used in the present work, BayeSys, requires the prior probability
distribution function (pdf)forall to have the same functional
form, the constraint on the element spacing cannot be incorpo-
rated into the prior pdf for . Instead, minimum spacing is en-
forced by modifying the likelihood in (7) as follows:
(16)
where
for
otherwise
(17)
(18)
Equations (16) and (17) ensure that, when the minimum value of
all separations between two adjacent array elements is smaller
than the desired minimum spacing ,adesignispenalized
with additional error denoted by . This penalization scheme
enforces a zero-error design to produce radiation patterns that
comply fully with the design pattern specifications and also pos-
sess a minimum element spacing of at least .Similarto
, the quantity in (16) has to be assigned a value. The as-
signment of depends on the relative importance of two design
objectives, which are realizing the desired radiation patterns
and achieving the minimum required element spacing. Gener-
ally, these two design objectives can be satisfied concurrently
in a linear antenna array design problem, and thus, can be
given any reasonable value. If these two design goals cannot be
achieved concurrently, a compromise is necessary, and the rela-
tive importance of these two design objectives can be reflected
through the relative values assigned to and .Sincehaving
a minimum element spacing is considered as a basic design re-
quirement in practice, it is included in all the design examples
presented in the following section.
IV. DESIGN EXAMPLES
A. Dual-Pattern with Digital Attenuators
This section sets out the design of a symmetric linear antenna
array with real-valued currents which can produce two different
radiation patterns. The two desired radiation patterns are the
sector beam and Chebyshev patterns presented in [1]. Here, the
design pattern specifications of both radiation patterns are mod-
ified slightly in accordance with the pattern specifications of the
design problem presented in [18]. The modifications made to the
sector beam pattern are a reduction in the beam width at 25 dB
from 41.4 to 40.0 , and an increase in the width of the ripple
region from 23.4 to 24.0 . For the Chebyshev pattern, there is
an increase in the beam width at 30 dB from 16 to 20 and at
3dBfrom6.3 to 6.4 . In this design problem, the real-valued
current amplitudes are reconfigurable so that a dual-pattern can
be realized. Since the design objectives are to produce the two
desired radiation patterns with appropriate element spacings, the
likelihood in (16) becomes
(19)
where denotes the error between the achieved and desired
sector beam patterns, and denotes the error between the
realized and desired Chebyshev patterns.
In practice, the current amplitudes are limited in dynamic
range and accuracy. This requirement is incorporated in the cur-
rent design problem with the current amplitudes constrained to
discrete values that are represented by a fixed number of bits.
Since the design problem considers only the shape of both sector
beam and Chebyshev patterns, the normalized antenna array
pattern is used as the parametric model for both radiation pat-
terns. The parametric models and are written as
and
The number of bits used to represent the current amplitudes in-
fluences the design of a linear antenna array. Here, two cases
are presented, in which the number of bits used are 6 and 5, ex-
cluding the sign bit. In both cases, 101 uniformly spaced angles
over the range 0 90 are used for each of the two
desired radiation patterns. The value assigned to is ,
and the following assignments are made:
for 6-bit scheme
for 5-bit scheme
1/5 dB for 0 78.0
1/40 dB for 78.0 90.0
and
1/5 dB for 0 86.8
1/40 dB for 86.8 90.0
The results are summarized in Tables I and II and Figs. 2–5.
Using the parameter values of the array elements for the two
final designs, the resulting radiation patterns at the 101 prede-
fined angles are plotted in Figs. 2–5. The two final designs have
zero error, which indicates that in addition to having all spacings
between two adjacent antenna elements to be at least ,the
design pattern specifications for both desired radiation patterns
5528 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 11, NOVEMBER 2014
Fig. 2. Sector beam pattern achieved using a reconfigurable linear antenna
array with 6-bit representation of the current amplitudes. and are de-
noted by dashed lines.
Fig. 3. Chebyshev pattern achieved using a reconfigurable linear antenna array
with 6-bit representation of the current amplitudes. and are denoted by
dashed lines.
Fig. 4. Sector beam pattern achieved using a reconfigurable linear antenna
array with 5-bit representation of the current amplitudes. and are de-
noted by dashed lines.
are fully satisfied, as shown in all four plots. Tables I and II pro-
vide insight into the effect of using different number of bits to
represent the current amplitudes. The design complexity of the
final design with 5-bit representation for the current amplitudes
is greater than with 6 bits. The former design uses one more pair
of array elements and has an antenna aperture that is
wider. The results presented here cannot be compared directly
to the results in [22] because of the different nature of the two
design problems. The reconfigurable linear antenna array doc-
umented in the literature [18]–[22] has a variable phase shifter
attached to each array element and uses the same power dividing
Fig. 5. Chebyshev pattern achieved using a reconfigurable linear antenna array
with 5-bit representation of the current amplitudes. and are denoted by
dashed lines.
TAB L E I
ESTIMATED POSTERIOR PROBABILITY FOR THE NUMBER OF ELEMENT PAIRS
FOR THE DUAL-PATT E R N DESIGN.FOR 6-BIT REPRESENTATION,
AND FOR 5-BIT REPRESENTATION
network to produce the desired dual beams. Although the recon-
figurable linear antenna array designed here uses variable digital
attenuators (accompanied by a 180 phase shifter), which may
make the antenna system harder to construct, the present success
in solving the design problem provides an attractive alternative
solution to those presented in the literature.
B. Sector Beam Pattern with a Frequency Bandwidth
The design example in this section uses the sector beam pat-
tern in [1]. The sector beam pattern is characterized by two dis-
tinctive regions, as indicated by the dashed lines in Fig. 6. The
first region, in the range 78.3 101.7 ,containsripples
that are required to be smaller than 0.5 dB. The second region,
in the range 0 69.3 and 110.7 180 ,hasde-
sired sidelobe levels that are less than 25 dB. For this design
problem, the desired radiation pattern is not required to be sym-
metric; hence, an asymmetric linear antenna array with complex
currents is used as it requires fewer array elements to achieve the
desired radiation pattern. Since the radiation pattern produced
is asymmetric, 101 uniformly spaced angles are used over the
range 0 180 . The frequency bandwidth considered
in the current design example is narrow, with .Itis
therefore sufficient to use only three frequency points, namely
the upper, lower, and center frequencies, to represent the entire
operating frequency band. The likelihood in (16) becomes
(20)
where ,,and are defined as in (3), with
being the parametric model for the lower, upper, or center
frequency.
CHAN AND GOGGANS: MULTIOBJECTIVE DESIGN OF LINEAR ANTENNA ARRAYS USING BAYESIAN INFERENCE FRAMEWORK 5529
TAB L E I I
CURRENT AMPLITUDES AND POSITIONS OF THE ANTENNA ELEMENTS FOR THE FINAL DESIGNS OF THE DUAL PATT E R N
Fig. 6. Achieved sector beam pattern at , , and using an asymmetric
linear antenna array with constant time delays. and are denoted by
dashed lines.
For this problem, is specified to be ,andthefol-
lowing assignments are made:
and
1/100 dB for
1/8 dB otherwise.
For a complex-valued current, the pdf assigned to the current
value is in the shape of a cylinder. The magnitude of the com-
plex current is distributed uniformly over the specified range
of ,andthephaseisdistributeduniformlyover .The
program BayeSys [26, Sec. 5.1.2] facilitates a subroutine that
draws samples from the cylindrical distribution. The samples
drawn are represented by their real and imaginary values, which
are, respectively, and .
Tables III and IV and Fig. 6 summarize the results. Table IV
sets out the parameter values of the antenna elements for the
final design. Using these parameter values, the radiation patterns
at 1001 angles for ,,and are plotted in Fig. 6. The
number of angles used for plotting is chosen to be more than
the number of predefined angles so that radiation pattern plots
with higher resolution can be achieved.
All plots presented in this design problem show that the final
design is capable of producing radiation patterns in full compli-
TAB L E I II
ESTIMATED POSTERIOR PROBABILITY FOR THE NUMBER OF ARRAY ELEMENTS
IN THE SECTOR BEAM PATT E R N DESIGN PROBLEM WITH CONSTANT TIME
DELAYS SO AS TO MAINTAIN THE ANTENNA ARRAY PERFORMANCE OVER
AN OPERATING FREQUENCY BANDWIDTH.IN THIS CASE,
TAB L E I V
COMPLEX CURRENTS AND POSITIONS OF THE ANTENNA ELEMENTS FOR
THE FINAL DESIGN OF THE SECTOR BEAM PATT E R N DESIGN PROBLEM
WITH CONSTANT TIME DELAYS SO AS TO MAINTAIN THE ANTENNA ARRAY
PERFORMANCE OVER AN OPERATING FREQUENCY BANDWIDTH
ance with the design pattern specifications at the center, lower,
and upper frequencies.
This final design has been tested at 101 uniformly spaced fre-
quencies within the range . The results show that
all 101 radiation patterns completely satisfy the design pattern
specifications. Table IV indicates that all spacings between two
adjacent elements meet the minimum requirement. These results
affirm the ability of the Bayesian inference framework to incor-
porate diverse challenging and practical design requirements in
a single design problem. This success is noteworthy because a
10% antenna bandwidth, which is desired in many applications,
can be acquired using a network composed of a single ampli-
tude and delay for each array element. The design of a linear
antenna array that has wider antenna bandwidth is likely to re-
quire more amplitudes and delays, and this design problem can
also be tackled using the Bayesian inference framework.
V. C ONCLUSION
Two linear antenna array design problems with multiple re-
quirements have been solved using the inference-based design
framework. Every specified practical design requirement has
been met, including a minimum spacing between two adjacent
array elements, limitations in the dynamic range and accuracy
5530 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 11, NOVEMBER 2014
of the current amplitudes and phases, the ability to produce mul-
tiple desired radiation patterns, and the ability to maintain a
desired radiation pattern over a specified frequency band. The
linear antenna arrays designed to meet these requirements have
design complexity appropriate to, and not higher than necessi-
tated by the design requirements. The ability to balance design
complexity against performance is a valuable tool for antenna
designers, especially in design problems with complicated re-
quirements. The present design framework is readily extended
to incorporate other practical design requirements and conse-
quently has a great potential for automated antenna array design.
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Chung-Yong Chan (M’10) was born in Kuala
Lumpur, Malaysia, in 1979. He received the B.S. de-
gree in electrical engineering and the M.S. and Ph.D.
degrees in engineering science with an emphasis
in electrical engineering, all from the University of
Mississippi, Oxford, MS, USA, in 2000, 2003, and
2010 respectively.
He has been serving as a Lecturer in the Depart-
ment of Electrical Engineering and Computer Sci-
ence at the University of Central Florida, Orlando,
FL, USA, since 2011. His research interests include
the use of Bayesian inference in engineering design applications such as an-
tenna array and digital filter design, and Bayesian analysis in various inference
problems such as land-mine detection and sound energy decay analysis in room
acoustics.
Dr. Chan was an Organizing Committee Member of the Twenty-Ninth Inter-
national Workshop on Bayesian Inference and Maximum Entropy Methods in
Science and Engineering (MaxEnt 2009) and Co-Editor of the MaxEnt 2009
Proceedings. He is a member of the Phi Kappa Phi Honor Society.
Paul M. Goggans (S’78–M’89) was born in Opel ika,
AL, USA, in 1954. He received the B.S. and M.S.
degrees in electrical engineering and the Ph.D. degree
from Auburn University, Auburn, AL, USA, in 1976,
1978, 1990, respectively
From 1979 to 1985, he was employed by Sandia
National Laboratories, Albuquerque, NM, USA, in
the Radar Signal Analysis Division. From 1985 to
1990, he was with Auburn University as an Instructor
while working toward the Ph.D. degree. In 1990, he
was appointed Assistant Professor in the Department
of Electrical Engineering at the University of Mississippi, Oxford, MS, USA,
where he is currently a Professor. His research interests include the application
of Bayesian inference to engineering model-comparison, parameter-estimation,
and design problems, Markov chain Monte Carlo methods, and computational
electromagnetics.
Dr. Goggans was General Chair of the Twenty-Ninth International Workshop
on Bayesian Inference and Maximum Entropy Methods in Science and Engi-
neering and Co-Editor of the workshop’s Pr oce ed ing s. H e is a me mb er of t he
Audio Engineering Society and the IEEE Antennas and Propagation Society.
