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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