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Thanks are also due to S . Shimada, K. Ishihara, and M .Kawase for guidance and continuous encouragement,M. OHASHI 15th July 1991K. SHIRAKIN T T Transmission Systems LaboratoriesToka i, Ibaraki-ken 3 / 9 - 1 1 ,Japan

References1 SAITO, s., MAI, T., SUGIE, T., OHKAWA, N., ICH IHASHI, Y. , and ITO, T. :An over 2,200km coherent transmission experiment at 2.5Gbit/s

using erbium-doped fibre amplifiers. Tech. Dig. Opt. FiberCommun. Conf., Postdeadline pap. PD2-1, San Francisco, 1990I., and CRAI G-RYAN, s. P.: High-gain, broad spectral bandwidtherbium-doped fibre amplifier pumped near 1.5&, Electron. Lett.,1989,25, pp. 91@911MI L L E R,c. A., BRIERLEY, M. c., and FRANCE, P. w.: Optical amplifi-cation in an erbium-doped fluorozirconate ibre between 1480nmand 1600nm. ECOC 88,1988, part I, pp. 66694 SNITZER, E. , and TUMMINELLI, R.: SO,-clad fibres with selectivelyvolatilized soft glass cores, Opt. Lerr., 1989, 14, pp. 757-7595 YAMADA, M., SHIMIZU, M.,HORIGUCHI, M.,OKAYASU, M., and SUGITA,E. : Gain characteristicsof an Er-doped multicomponent glasssingle-mode optical fibre, IEEE Photonics Techno l. Lett. , 1990,2 ,pp. 656-6586 LINES, M. ., MACCHESNEY, I. B., LYONS, K. B., BRUCE, A. I., MILLER, A.E., and NASSAU, K.: Calcium aluminate glasses as potentialultralow-loss optical material at 1.5-1.9pm: J . Non-Cry st. Solids,1989,107, pp. 251-260CHINLON LIN, BILOOEAU, F., and HILL, K. 0.: Er-dopedGeO,-CaO-AI,O, silica core fibre amplifier pumped at 813nm.OFC 91, FA6,1991

2 ATKINS, C. G., MASSICOTT I. f.,ARMITAGE, J. R.,W Y A T T , R., AINSLIE, B.

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7 SAIFI, M. ., ANDRWCO, M. ., WAY, W I., VON LEHMAN, A., YI-YAN, A. ,

CORRELATION MODEL FOR SHADOWFADING IN MOBILE RADIO SYSTEMS

Indexing terms: Electromagnetic waves, Mobile radio systems,Wave propogationA simple autocorrelationmodel for shadow fading in mobileradio channelsIS proposed. The model is fitted to both largecells and microcells. Results show that the model fit is goodfor large lo moderate cell sizes. It is however shown that themodel does not provide adequate results for microcells.

Introduct ion: Fading in mobile radio systems may be dividedinto two different types, fast and slow fading. Fast fading iscaused by multipath propagation. The statistical properties ofmultipath fading have been studied extensively in the liter-ature. The other type of fading, slow fading or shadowfading, is caused by obstacles in the propagation path betweenthe mobile and the base station. Slow fading has been charac-terised in the literature by its one-dimensional distributionfunction, which can be well approximated by a log-normaldistribution. In the design of diversity and handover schemesa better understanding of the correlation properties of theslow fading process is required. We propose a simple modelfor these autocorrelation properties. Very good results areachieved when the model is fitted to measured d ata from asuburban environment,Signal model : Signal strength measurements are in mostmobile communication systems performed at regular intervalswhich is why we have chosen a time discrete model. Weassume the received analogue signal strength is sampled everyT seconds. Let us then denote the logarithm of the receivedsignal strength as A (n) . Assume that A ( n ) has a Gaussian dis-tribution with an average dependent of the distance betweenmobile and base a s

a =K , - , log(4 (1 )

Parameter K, is determined by the transmitter power, and K ,is a propagation constant in the range between 20 (line-of-sight propagation) and 60. This is the well known Okumuramodel of the large scale average of received signal strength inmobile radio systems.To model the correlation properties we have used a simpledecreasing correlation function. We assume that the mobilevelocity IS U. In the proposed model the correlat ion is given byR,(k) =u2aIk1 (2 )a =pJ (3)

The variance U* is usually in the range between 3 and lOdB.,The correlation coefficienta in eqn. 2 may be expressed as ineqn. 3. Here parameter E~ is the correlation between twopoints separated by distance D.The model is easy to analyse3 and is well suited for gener-ating shadow fading envelopes in simulators. It is easy to seethat a white Gaussian noise process, filtered through a firstdegree filter with a pole at a, will produce a log-envelopesignal with the required properties.Model veri f icat ion: The model defined in eqn. 2 is verified byfitting it to measured data. Measurement data are from twodifferent environments, a suburban area in a large Europeancity (macrocells) and an urban environment (microcells) inanother European city. The model is fitted by estimating theconstants in eqns. 1 and the parameter E~ in eqn. 3.The measurement data in the suburban case are from a900MHz measurement. To remove the effectof the multipathFading we have average the measured signal overa distance ofapproximately 27 m. During the measurement the mobilemoved in an area of approximately 15x 15km2. The basestation was located in the centre of this area.A typical result of the model fit is shown in Fig. 1.Thepropagation constant K, was found by mean square estima-tion to be 33. In Fig. 1 we see that the simple correlation

0 500 1000 1500 2000 2500j748111 distance, mFig. 1 Normalised autocorrelation (measured and Jifted ) in suburbanenvironment

Standard deviation of signal strength was estimated to be 7.5dB,and correlation at distanceof l00m was estimated to be 0.82~ fittedmeasured

- - _

model proposed here works satisfactorily for distances up toapproximately 500111 We can also see that the correl ation isquite high.The measurement data for the urban environment is from a1 7 0 0 M H z measurements. Here we have chosen to show theresults of mobile movements on a non-line-of-sight street. Thedistance from mobile to base was 1W 60 0m . In this case thepropagation constant K , was estimated to be approximately50. To remove some of the effects of fast fading, we averagedthe measured signal over a distance of 1.5m. In Fig. 2 we seethe result of the fitting of the autocorrelation function.The microcell measurement data have been averaged over avery short distance. Therefore, the filtered signal will certainlycontain both slow and fast fading components. When we aver-aged the signal over a longer distance it was shown that thesimple correlation model gavepoor results.

ELECTRONICS LETTERS 7th November 1991 Vol . 27 No. 23 21 45

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R esul t s : If we use the results in Fig. 1and assume that amobile IS moving wtth a velocity of 50km/h and that th esampling interval is 0.5s (as in GSM) our estimate of the

signal will have almost the same value as the present sample.If we carry out the same calculahon for a mobile in a micro-cell we see that the correlation parametera 1s much less than1. In the design of mobtle communicatton systems this largedifference in the correlatton properties of the slow fadingshould be observed.Summa ry A correlation model for the received signal inshadow fading in a mobile radio system was proposed. Eventhough the model is simple results show good agreement wtthmeasurement data from suburban environments. In micro-cellular environments the signal envelope is contaminatedwith multipath fading and the model predictions were lessaccurate.

. - _ . . - . -* . _ _ . .

$ 001 M.GUDMUNDSON 5th September 1991Radio Communication SystemsRoyal Institute of TechnologyElectrum-207S-164 40 Kista, Sweden

-0 1 . . . . : . -.: , I0 5 10 15 20 25 30 35 40 45distance. m

Fig. 2 Normalised autocorrelation (measured and fi tted ) in urbanenvironmentStandard deviation of signal strength was estimated to be 4.3 dB,and correlation at distanceof 10mwas estimated to he 0.3_ _ _ _ measured~ fitted

References1 IAKFS, w. c.: Microwave mobile communication (John Wiley&Sons, 1974)2 LEE, w. c. Y.: Mobile communications engineering (McGraw-Hill,1982)3 GUDMUNDSON, M.: Analysis of handover algorithm. 41st IEEETrans.Veh. Conf., 1991, pp. 537-542correlation parameter a will be very close to 1. This implies avery high probabil ity that the next sample of the measured

FOUR-QUADRANT MULTIPLIER COMBININGSIGMA-DELTA A ND MULTIRATEPROCESSING TECHNIQUES

Indexing term; Multipliers, Modulation, Integrated circuitsA mixed analogucdigital solution combining sigmadeltaand multirate processing techniquesis proposed for realisingfour-quadrant multipliers. This overcomes the major l i -tations of purely analogue circuits and still achieves theattractive benefitsof l o w power consumption and small chipsize which cannot be afforded using digital signal processingtechniques together with auxiliary analogucdigital anddigital-analogue convertors.

greatly reduce the complexity of the multiplication algorithmand hardware requirements. By using the well known linear-ised models for the analysis of the ZA modulator: it can beserial inputs1bit at MF,

MFsparalleloutputs

Introduct ion: Several approaches have been considered toimplement in integrated circuit (IC) form the multiplicat ion oftwo analogue signals,-3 namely those eithe r based on purelyanalogue or employing a combination of both ana-logue and digital circuits. Whereasth e former can suffer fromtechnology constraints yielding poor accuracy and reducedsion as desired but this requires fine quantisation to minimisethe noise power and thus complex auxiliary analog uedigit al wheren is the order of the system and X ( z ) and E(z) , respec-and digital-analogue convertors are needed. Furthermore, this tively, are thez transforms of the input signal and quantisa-obviously increases the power consumption and the silicon tion noise.As can be seen from the previous expression, thearea for IC fabrication. system is basically transparent to the signal whereas the quan-We describe a mixed-signal analogue-digita l architecture in tisat ion noise is highpass shaped and pushed to higher fre-which the high speed output hit stream of a sigma-delta(ZA) quencies.Thus, o achieve a good performance in terms of themodulator is used to control the operation of a switched- signal-to-noise ratio, it is necessary to adequately lowpasscapacitor (SC) decimator for filtering and sampl ing rate filte r those high frequency components. This is provided byreduction. The multiplication itself is accomplished in the the SC decimator which, in addition, also reduces the sam-charge domain and, depending on the values of capac itance pling rate of the signal from MF, o F, . Depending on th eratios, can be defined with an accuracy as high as 0.1%. The require d specifications, we can always adop t for th e SC deci-range of the analogue input signals, with both positive and mator an efficient architecture for reducing the overall capac-negative values, is limited only by the operat ion of the ampli- itance spread and relax the speed of theamplifier^.^.^fiers in the circu its and the voltage reference needed in theZA The hit stream at the output of the ZA modulator enters amodulator. digital shift register whose outputs control the operation ofthe input branches of the SC decimator as shown schemati-Archi tecture and operation principle: The proposed architec- cally in Fig. 2. When the controlling bit is 1 the correspond-ture, shown in Fig. 1, consis ts of a ZA modulator, a digital ing SC branch is configured in a positive charge transfer modeshift register and an SC decimator. The ZA modulator and when the control ling bit is 0 it is configured in a negativeencodes one continuous-time input signal into a bit stream at charge transfer mode5s6 (we should note that the binary01high rate MF, nd whose average is a good representation of representat ion adopted here actual ly corresponds, respec-the input signal. Such coarsely quantised signals (binary 01 tively, to minus and plus the voltage reference of th e X4representation) possess a high signal-to-noise ratio and can modulator). Such an operation produces the multiplication2146 ELECTRONICS LETTERS 7th November 1991 Vol. 27 No. 23

riS.s c k t i c bloc. diOerMt ofdigital multipliershown that the signal plus noise output components mayexpressedas

four-qundront onolosue-

dynamic range, the latter can potentiallyoffer as much preci- Y ( z )CY X( 2 )+ 1 - - Y E ( z ) ( 1 )

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