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the launcher. The geometric theory of diffraction [6] was used to
determine the effects of the finite ground plane, and the magnitude
of the ripples were found to be in close agreement with those in
the measured pattern. The H-plane ripples are negligible due to
the pattern null at the ground plane elevation, resulting in a small
diffracted field. For the 12” diameter ground plane, the H-plane
pattern shows a gain of 4dB, which is near 4.76dB, the theoretical
gain of a short dipole on an infinite ground plane. The difference
in gain can be attributed to the large diffraction ripples in the Eplane and from spillover into the backlobes. The crosspolarisation
levels were, on average, 1SdB below the copolarisation levels,
which were similar to the crosspolarisation levels measured for the
unbiased antenna.
Biasing in the x-direction resulted in an interesting observation.
The copolarisation levels were similar to those of the unbiased
case, whereas the crosspolarisation levels increased significantly to
an average of lOdB below the copolarisation. This result is not
unexpected because the permeability of the ferrite is a tensor with
nonzero off-diagonal components [4]. Therefore, a linearly polarised magnetic field can generate a component of magnetisation in
an orthogonal direction (e.g. an x-directed field can produce magnetisation in they direction as well). This effect suggests the possibility of obtaining polarisation agile antennas. More research is
intended to study this effect further.
Conclusions: The effects of magnetic bias on the resonance frequency and radiation patterns of a ferrite resonant antenna have
been investigated. The antenna exhibits a shift in frequency of up
to 8% above or 8% below the unbiased resonance, depending on
the direction of magnetic bias. The radiation patterns of the biased
antenna were similar to those of the unbiased antenna. Increases
in the crosspolarisation levels for the y-directed bias suggests the
possibility of magnetic control of the polarisation. Future work
wil investigate the polarisation agility of these antennas.
Adaptive reception of MPSK on fading
channels
0 IEE 1994
18 April 1994
Electronics Letters Online No: 19940698
A. Petosa and J.S. Wight (Dept. of Electronics, Curleton University.
Ottawa. ON K l S 586, Canaah)
R.K. Mongia and M. Cuhaci (Communications Research Centre,
Ottawa, ON K2H 8S2. Canada)
References
LONG, s.A., MCALLISTER, M.w., and SHEN, L.c.:
‘The resonant
cylindrical dielectric cavity antenna’, IEEE Trans., 1983, AP-31,
pp. 406-412
KISHK, A.A., ZUNOBI, M.R., and KAJFEZ,D.: ‘A numerical study of a
dielectric disk antenna above a grounded dielectric substrate’,
IEEE Trans., 1993, AP-41, pp. 813-821
ITTIPIBOON, A., ANTAR, Y.M.M., BHARTIA, P., and
‘A half-split cylindrical dielectric resonator antenna
using slot-coupling’, IEEE Microw. & Guided Wave Lett., 1993, 3,
pp. 38-39
WALDRON, R.A.: ‘Ferrites: an introduction for microwave engineers’
(D. van Nostrand Co., London, 1961)
MONGIA, R.K.,
CUHACI, M.:
MONGIA, R.K., ANTAR, Y.M.M., BHARTIA, P., and
‘Aperture fed rectangular and triangular dielectric
resonators for use as magnetic dipole antennas’, Electron. Lett.,
1993, 29, pp. 2001-2002
IT TI PI BOON, A.,
CUHACI, M.:
BALANIS, c.A.: ‘Antenna theory: analysis and design’ (Harper and
Row, New York, 1982), Chap. 11
This Letter proposes an adaptive estimator of the fading process that requires no knowledge of the spectrum of the latter. The
estimates obtained are used in place of the MMSE estimates for
coherent detection of MPSK. The receiver is shown in Fig. 1,
assuming diversity reception over L independent, identical channels. The received signal over the ith channel is given by
P.Y. Kam and S.Y. Tay
Indexing terms: Adaptive signal processing, Fading, Phase shft
keying, Detectors, Mobile radio systems
An adaptive estimator of the complex gain of a fading channel is
proposed. Tracking of the fading process is achieved without
knowledge of the fading spectrum. This enables coherent
detection of MPSK to be performed. Simulations show good
error rate performance. The receiver finds applications in mobile
radio communications.
In [IA],it has been shown that coherent detection of Mary phase
shift keying (MPSK) on a fading channel is achieved using minimum mean square error (MMSE) estimates of the in-phase and
quadrature components of the complex channel fading process.
This result enables us to build coherent receivers digitally without
using carrier tracking loops which perform badly in the presence
of signal fading [SI. Its only shortcoming is that MMSE estimation
of the channel fading process requires knowledge of the power
density spectrum of the latter as well as the intensity of the
receiver front-end noise. This limits its practical application to,
say, mobile radio communications.
Here, Fz(k)= Ec(t = tk), N k ) = +(f = f k ) , and $k) is the sample at
time f = fk of the I F output due to input AWGN At{f). For simplicity, the IF filter is assumed wideband so that it does not distort
the phase modulation +(f) and the channel fading process E l f ) . IF
filtering is used mainly to bandliiit the input AWGN.
In [ l 4 ] , it has been shown that for optimum data detection, the
receiver computes the decision statistic
eqn 4
Fig. 1 Adaptive receiver
1022
Here, E, is the symbol energy, T is the symbol duration, wo is the
carrier radian frequency, and Nf)is the phase modulation process.
The fading process E,(t), for each i = 1, .._,L, is only known to be
a complex Gaussian random process with aE,(t)] = 0. Its spectrum is unknown except for the fact that it is symmetric around wo
so that the in-phase component Re[E,(f)] and the quadrature component Im[EXt)] are independent and identically distributed processes. The processes {E,(t)},f., have identical spectra. The complex
envelope of additive white Gaussian noise (AWGN) on the ith
channel is A,(f), which is a complex Gaussian process with aAZ(f)]
= 0 and 4Az(f)A,’(f-~)]= N&) (superscript * denotes the complex
conjugate). The processes {Ez(t)riz(t)},f.i are all independent of one
another. Each signal r,(t) is fed into a wideband IF filter centred at
ww The I F filters are assumed identical. Each IF output is sampled once in each symbol interval [kT, ( k + l ) T )at time fk = k T + T,
where T E [0, T) is the optimum sampling instant, giving the signal
sample zE(k),where
m
ELECTRONICS LETTERS 23rd June 1994
Vol. 30 No. 73
for each possible value $, I = 1, ..., M that the current phase N k )
can take on, and decides that $(k) = $m if q,(k) = “7t qkk). In eqn.
3, vi&) is the MMSE estimate of Pik) formed from all the past
received signals {z,(O},=$-l = 0 with assistance from the past decisions (l)],=,k-l= 0 on the transmitted phases {$(O],=$-’= 0. The
generation of this MMSE estimate requires knowledge of the spectrum of the process PE(+
We now consider a receiver in which data decisions are made
using the same decision statistic in eqn. 3, except that the coherent
reference v,(k) is replaced by the estimate t,(k) which is generated
by the following adaptive, decision-aided estimator:
10’
(iii)
{4
t,(k + 1)= a & ( k ) + (1 - a)Zt(k) i = 1,.. . , L (4)
Here, i , ( k ) = (EJT)-”z egMk) z,(k), and a (real) is a factor to be
chosen adaptively, where la1 < 1. We choose a at each time k to
minimise the risk function R(k), where
In eqn. 5, p is a weighting factor with IpI < 1, and is chosen based
on the receiver’s knowledge of the fading rate. Using eqn. 4 in
eqn. 5 and setting dR(k)/da to 0, we find that a is given by A(k)l
B(k) where
(-
+Re z;(l)[&(l-l)
- i t ( l - l ) ] - &(l-l)Z%*(l-l))])
(6)
and
(c3’k-‘e
*
10
16
18
SNR .dB
Fig. 3 BER of QPSK with dual diversity
12
14
20
22
24
bllill
6 = 0.99
(i) coherent, theoretical
(ii) differental detection, simulated
(iii) adaptive receiver, simulated
transmission started after the preamble period, and the bit error
rate (BER) was measured. Fig. 3 shows the BER obtained for
QPSK with dual diversity, plotted against the total mean received
SNR per hit, y = 2azE&/2N,,BT, measured at the I F output. Here,
E, = EJ2 is the energy per bit, and B is the I F bandwidth so that
2N&i = E[j ijr(k)12].Because of error bursts during periods of deep
fades, ‘runaway’ of the decision-aided estimator can occur. We
prevented this by retraining the estimator with 10 known symbols
periodically. The results in Fig. 3 are obtained by retraining after
every 100 data symbols. Simulations show that the BER does not
improve significantly by retraining after every 50 data symbols. In
both cases, the improvement over differential detection is 2 3dB, which is significant. In fact, the performance is close to that
of coherent detection which is computed using the results from [3].
Extensive simulations also show that the value of 0.99 is about the
best value for the weighting factor p for the chosen fade rate of p
= 0.99995. No attempt has been made to choose p adaptively
using an algorithm.
In summary, we have developed an adaptive, digital coherent
receiver for MPSK which does not require knowledge of the channel fading spectrum or the intensity of the front-end additive
Gaussian noise. The receiver is suitable for application on fading
channels such as the mobile radio channel.
-
::m
B(k)=E
1=1
1=1
[ I ~ ~ ( l - l ) - Z ~ ~ l - ~ ) l ’(7)
])
The expectations of the quantities in eqn. 6 and eqn. 7 cannot be
computed in practice. Thus, we replace them by their actual realisations, resulting in a stochastic adaptation algorithm. Both A(k)
and B(k) can be computed recursively in time k.
21 April I994
0 IEE 1994
Electronics Letters Online No: 19940699
P.Y. Kam and S.Y. Tay (Department of Electrical Engineering,
National University of Singapore, I O Kent Ridge Crescent, Singapore
0511, Republic of Singapore)
do0 ..24
0
-0-2
(ii)
References
-0-4
10
0
30
20
40
1
50
[ee1121
k
Fig. 2 a against k
Dual diversity APSK,
(i) SNR y = lOdB
(ii) SNR y = 15dB
(iii) SNR y = 25dB
2
p = 0.99
3
4
The proposed receiver is simulated using a fading process with a
first-order Butterworth spectrum. The fading process {E,(k)} is
generated recursively as
Z,(k
+ 1) = pE,(k) + &(k)
i = 1,.. . ,L
5
KAM,P.Y., and T E H . C H . : ‘Reception of PSK signals over fading
channels via quadrature amplitude estimation’, IEEE Trans., 1983,
COM-31, pp. 102k1027
KAM, P.Y.: ‘Adaptive diversity reception over a slow nonselective
fading channel’, IEEE Trans., 1987, COM-35, pp. 572-574
KAM, P.Y.:‘Optimal detection of digital data over the nonselective
Rayleigh fading channel with diversity reception’, IEEE Trans.,
1991, COM-39, pp. 21&219
HAEB, R., and MEYR, H : ‘A systematic approach to carrier recovery
and detection of digitally phase modulated signals on fading
channels’, IEEE Trans., 1989, COM-37, pp. 748-754
STEIN, s.: ‘Fading channel issues in system engineering’, IEEE J.
Sel. Areas Commun., 1987, SAC-5, pp. 68-89
(8)
Here, p = exp[wda, where wd is the 3dB bandwidth of the Butterworth fading spectrum, and {Ckk)} for each i is a sequence of
independent, complex Gaussian variables with 4C,(k)] = 0 and
4C5(k)C*(l)]= uz(1-p2)1
&,, where 2 d = 41P,(t)12].The processes
{C,(k)})iI are independent of one another. Starting with an initial
a of 0 and t(0) = 1 for all i, the estimators are trained with an initial preamble of 50 known symbols (from k = 0 to k = 49). We
chose d = 0.25 and p = 0.99995 for all the simulations. Fig. 2
shows how a converges on some sample runs for dual diversity ( L
= 2) QPSK ( M = 4). In general, for the SNR range of interest, the
estimators were able to acquire tracking of the channel fading
processes within the duration of the preamble chosen. Actual data
ELECTRONICS LETERS
23rd June 7994
Vol. 30
No. 13
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