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Computer simulation: We assume 4DPSK transmission (M = 4)
over AWGN channels and investigate BER performance improvements using computer simulations. The BER dependence on the
observation symbol length L is shown in Fig. 2 at EbINo= 6dB.
The VA decoding depth to output the detected sequence was set at
D = 20 symbols. Also shown are the simulated BERs for 16 state
( L = 3) and 64 state ( L = 4) Viterbi DPD (note that RSVDPD
equals Viterbi DPD when L = 2). For large values of L, the performance of RSVDPD approaches that of coherent phase detection with differential decoding (CPD). When L = 10, the simulated
BER of the proposed scheme is 5.90 x lC3and that of CPD is 4.5
x l e 3 . The simulated BERs of RSVDPD using L = 1-10 are
shown in Fig. 3 together with those of lDPD and CPD as a function of EdN,. Also in the Figure, the theoretical BER performance
curves of lDPD and CPD are shown as dotted lines. It can be
clearly seen in Fig. 3 that the proposed scheme outperforms
1DPD. Using L = 2 and 4 can yield performance improvements of
-1.2 and 1.5dB at BER = lC3,respectively. When L = 10, performance approaches that of CPD with an EdN0 difference of
only -0.2dB.
Conclusion: The reduced state Viterbi DPD, called RSVDPD, was
described for MDPSK signal reception. An M state Viterbi
decoder is used. Its BER performance improvements were evaluated by computer simulation for 4DPSK transmission in AWGN
to show that with L = 10 performance close to that of CPD is
achieved with an EbINodifference of only -0.2dB. The RSVDPD
decoder can simply be added to conventional lDPD receivers. It is
much less complex than the Viterbi DPD [3] with respect to the
number of branch metric computations per symbol, and is considered very practical.
0 IEE 1996
I5 January I996
Electronics Letters Online No: 19960365
F. Adachi (R&D Department, N T T Mobile Communications Network
Incorporated, 1-2356 Take, Yokosuka-shi, Kanagawa-ken, 238 Japan)
References
1
2
3
4
5
‘Multiple-symbol differential
detection of M P S K , IEEE Trans. Comrnun., 1990,38, pp. 300-308
MAKRAKIS, D., and FEHER, K.: ‘Optimal noncoherent detection Of
PSK signals’, Electron. Lett., 1990, 26, pp. 398400
ADACHI, F.: ‘MLSE differential phase detection for M-ary DPSK,
IEE Proc. Commun., 1994, 141, pp. 407412
DEUL-HALLEN, A., and HEEGARD, c.: ‘Delayed decision-feedback
sequence estimation’, IEEE Trans. Commun., 1989,37, pp. 428436
RAHELI, R.,
POLYDOROS, A.,
and TZOU, c.-K.: ‘Per-survivor
processing’, Digit. Signal Process., 1993, pp. 115-161
DIVSALAR, D.,
and
SIMON, M.K.:
omega medium, known as thie uniaxial omega medium, was introduced [2] by immersing two orthogonally-positioned ensembles of
omega-shaped particles in an isotropic host medium. It has been
found that the uniaxial omega medium has potential applications
in the design of anti-reflecting shields. Here, a triaxial omega
medium is proposed to generalise the already studied omega
medium and the uniaxial omega medium.
In practice, a triaxial omega medium with linear magnetoelectric interaction can be fabricated by arranging three types of
omega-shaped microstructures in a host dielectric: all axes of the
first type of particles are arranged along the x and y directions,
those of the second type along the y and z axes, and those of the
third type along the z and x axes. From a phenomenological point
of view, a homogeneous triaxial omega medium can be characterised by the set of constitutive relations (the harmonic exp(iot) time
dependence is adopted and suppressed hereafter)
D
=E.
E+E.i’l
B =P.H+
t .E
(1)
where E = E G , = p.6 are permittivity and permeability dyadics,
respectively, with G = a,e,e,-tq,e,e, +a,e,e, determined by the distributions and electrical d-hensions of the omega-shaped particles.
5 = :(L&,)’/~A
x I , and 5 = -i(&,pJ1/ZA
x I denote the magnetoelectric pseudo-dyadics, whei-e A = crcr,+~e,+yexis determined by
the physical properties of the omega-shaped inclusions. For p = y
= 0, the medium reduces to the already studied uniaxial omega
material [2]. Here, I = e,e,+e,e, +e,e, denotes the unit idem factor,
and e, represents the unit vector in t h e j direction. 6 and p,, represent the permittivity and permeability of free space, respectively.
Green dyadic: Substituting the constitutive relations eqn. 1 into the
source-incorporated Maxwell1 equations, a set of field equations
can be obtained
(V + koA) x E 1-iwbCi. H
+ koA) >< H = J + iweSE. E
(V
(2b)
where ko = u)(q,~)L/2.
To simplify the analysis, we introduce a set of auxiliary fields
E = e-koA,rg
H = e-koA.r~l
(3)
where r = xe,+ye,+ze,. Then,, the E’-field vector wave equation is
obtained
Vx
Ci-’
. V x E’ - k 2 & .E’
= -iwpekoA“J(r)
(4)
with kz = Ozw.
To solve eqn. 4, we introduce the coordinate transformation h
= ti r. Then, V = C i VI, and eqn. 4 can be represented in the h
coordinate system
V x x v xxE‘-k2E’ = - , j W b e k o A . f i - l . x - - l a
.J(SE-l.X) (5)
Noting the linearity property of eqn. 5, E’ can be constructed
using the concept of the Green dyadic [3]
Green dyadic and dipole radiation in triaxial
omega medium
E’ = -iwp
lI:
e k o A . a - l . q q A - A’). &-I
. J ( 6 - 1 . X’)dA’
(6)
The vector wave equation that the Green dyadic G(h)must satisfy
can be obtained by substituting eqn. 6 in eqn. 5
D. Cheng
Indexing terms: Electromagnetic$eld theory, Polymers
vx x vx x G ( A ) - k 2 G ( A ) = [email protected])
(7)
Using the Levine-Schwinger operational method [3], we fmd
A triaxial omega medium, which can be artificially realised by
embedding three types of omega-shaped particles in an isotropic
host medium, is proposed. The Green dyadic and the
electromagnetic field of a dipole radiator are presented, by
introducing a set of auxiliary fields and coordinate
transformation.
where [email protected]) is the solution of
V2,g(A)
+ k2g(A) = -6(A)
(9)
with
Introduction: With recent advances in polymer synthesis techniques, increasing attention is being given to the analysis of interaction between electromagnetic waves and novel microwave
materials to determine how to use these materials to provide better
solutions to current engineering problems. Among these novel
microwave materials, the omega medium should be mentioned. It
was first proposed in [l] for its potential application in constructing a reciprocal phase shifter. Recently, a modification of the
ELECTRONICS LE7TERS
74th March ‘1996 Vol. 32
For a,, q,a, > 0 the solution of eqn. 9 is
e--zkX
g(X) =
with h = I h j = I G . r 1 = [(a,~)~+(a~y)’+(sz)~]’~~.
No. 6
Introduction: It is well known that multilayer dielectric structures
Noting the identity
and
the Green dyadic can subsequently be represented in the r coordinate system.
Electromagnetic Jields of dipole source: For a dipole source located
at the origin, J(r) = (I,e,+I,e,+I,e,)S(r). It can be rewritten in the h
coordinate: J( E l . A) = (Ixex+IJ,ey+Izezj
a,q,a,S(A).
are excellent surface waveguides, having a fundamental surface
wave mode with no cutoff. In planar transmission line applications the surface wave power leakage can cause undesirable crosstalk aud unexpected package effects. In printed circuit antenna
applications the antenna performance can be severely degraded
owing to improper excitation of surface waves, e.g. the reduction
of antenna efficiency.
So far some research work has been carried out to find the excitation characteristics of surface waves in multilayer dielectric
structures. All the investigations dealt with the dielectric structures
of few layers with only embedded horizontal sources, and no general expressions for surface wave power were given.
In this Letter, efforts are made to explore the excitation characteristics of surface wave power in grounded or ungrounded multilayer dielectric structures, as shown in Fig. la. The sources can be
any type of Hertzian dipole: horizontal electrical dipole (HED),
vertical electrical dipole WED), horizontal magnetic dipole
(HMD) or vertical magnetic dipole (VMD). General expressions
are derived for the power carried in surface wave modes.
The electric fields E(r) radiated from such a dipole source can
be straightforwardly obtained from eqns. 3, 6 and 11. The electric
field in the far region is
e-koA
r-zkX
(7- e x e x )
4nX
(Iza:,cy,ez
I y ~ z c y , e y+ I z ~ z c u y e z ) (15)
which unifies the counterpart of the isotropic medium (a, = a,
a,, and a = p = y = 0 in the constituent parameters).
It can be seen from eqn. 15 that for a triaxial omega medium
with a, @,y > 0, the electromagnetic waves are attenuated at the
rateof&r/I&.r(.
E(T) = -zap
t
+
Concluding remarks: In the present study, a triaxial omega material is proposed. Green dyadic and electromagnetic fields radiated
from a dipole source are formulated. The resulting expression indicates that the electromagnetic waves propagating in the triaxial
omega medium are attenuated at the rate of exp (-k,A.r/ I G r 1,
where A is the magnetoelectric pseudo-vector. This exponentiallike attenuation property of the electromagnetic waves propagating in a triaxial omega medium imply its potential applications in.
antenna array to reduce the mutual coupling between antenna elements in a wideband frequency range.
3 January 1996
0 IEE 1996
Electronics Letters Online No: 19960393
D. Cheng (Wave Scattering and Remote Sensing Centre, Department of
Electronic Engineering, Fudan University, Shanghai 200433, People’s
Republic of China)
References
SAADOUN, M.M.I., and ENGHETA, N.: ‘A reciprocal phase shifter using
2 medium’, Microw. Opt. Technol. Lett.,
novel pseudochiral or C
1992, 5 , pp. 18k-188
2 TRETYAKOV, S A , and SOCHAVA, A.A.: ‘A proposed composite
material for nonreflecting shields and antenna radomes’, Electron.
Lett., 1993, 29, pp. 1048-1049
3 TAI, c.T.:‘Dyadic Green’s functions in electromagnetic theory’,
1
(Intertext, New York, 1971)
‘22F22 D22
‘21 lJ-21 D21 dipole
E11
hl
D11
r’
FII
a
Fig. 1 Geometry of structure and equivalent transmission line models
a Geometry
b Transmission line models
Theoretical derivation: For the case of a dipole embedded in a
multilayer dielectric structure, the power generated by the source J
or M is [l]
J’J’J’ E . Jdw
(for an electric dipole)
(I)
/ / J ’H . Mdv
(for a magnetic dipole)
(2)
P=P=-
where E and H are the electric field and magnetic field associated
with J and M, respectively. For the structure considered here, the
expressions for E and H can be easily derived in the spectral
domain [2]. The surface wave and space wave are easily separated
from the Sommerfeld type integration of the total field: the fonner
comes from the residues and the latter from the remaining part of
the contour integral By applying the spectral domain dyadic
Green’s functions [2], the expressions for the power carried in surface wave modes for different type of Hertzian dipoles are derived
as follows:
(ij HED
Surface wave in multilayer dielectric
structures excited by various types of
ertzian dipoles
Q.X. Men and S.Z. Zhu
Indexing terms: Surface electromagnetic waves, Dielectric devices
The surface wave excitations of deferent types of Hertzian dipoles
in multilayer dielectric structures are investigated. General
expressions are derived for analysis of the surface wave power
produced by the dipoles in the structure. Numerical results are
given for some special cases, which are in good agreement with
earlier work reported by other researchers.
530
ELECTRONIC§ LETTERS
14th March 1996
Vol. 32
No. 6
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