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has been defmed and, in this framework, low complexity imple-mentation based on an energy approach has been described.Numerical results demonstrating the effectivenessof the proposedapproach have been presented.

Close to the transmitter, the variation of P / p , with d has theform of an oscillatory function with an underlying d2 behaviouras the direct and ground reflected waves add constructively ordestructively as phasors, namely:

0 EE 1999Electronics Letters Online No : 19990832DOZ: 10.1049/el:19990832A. Vanelli-Coralli, G.E. Corazza and A . Orsini (University of Bologna,Department of Electronics, Computer Science and Systems, VialeRisorgimento, 2-40136 Bologna, Ita ly)E-mail: avanelli@deis.unibo.it

3 June 1999

References1 JAYANT, N., JOHNSTON, J. , and SAFRANEK, R.: Signal compressionbased on models of human perception,ZEEE Proc., 1993,81,2 M O O RE, BCJ . : An introduction to the psychology of hearing(Academic Press, 1997), 4th edn.3 NOLL, P.: MPEG digital audio coding, ZEEE Sig. Process. Mag.,1997,31,4 BOSI, M., BRANDEN BURG, K., QUACKENB USH, S. , FIELDER, S. ,

AKAGIRI, K. , FUCHS, H. , DIETZ, M., HERRE, J., DAVIDSON, G., andOIKAWA, Y. : ISO/IEC MPEG-2 advanced audio coding, J. AudioEng. Soc., 1997,45 ,

Prediction of breakpoint d istance inmicrocel lular environmentsS.C.M. Perera, A.G.Williamson and G.B. Rowe

Experimental studies of path loss distance dependency in line-of-sight microcellular propagation almost always show a dual-slope- I behaviour. However, there is disagreement in the literature overthe best way to predict the breakpoint distance that delineates thechange in path loss distance dependency. A new breakpointequation is presented, the predictions of which are in excellentagreement with breakpoint distances observed in variouspropagation studies.

Introduction: There is general agreement in the literature thatmodelling microcellular radiowave propagation in line-of-sightstreets is best done using a dual-slope model where the propaga-tion loss L(d) in dB is described by an equation of the form [l ,21

10721log(d)ilOn2 log(d) for d 5 dbrkL ( d )=L b + 10(?Ll- 22 ) 10g(dbTk) (1)for d 2 dbTkwhere d is the propagation distance, darks the breakpoint distance,Lb is the basic .transmission loss parameter in dB (dependent onfrequency and antenna heights), n, is the slope of the best-fit linebefore the breakpoint ( d

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Ardmore sites.) The oscillatory behaviour of the received signalagainst distance for small distances and other similarities o Fig. 1validates the use of the two-ray theory of the previous Section tomodel the breakpoint behaviour in the practical multipath situa-

FrequencyMH Z900

tion.60

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0

1

h, hb Breakpoint distancedRx dc d~ dbrk dp

m m m m m m m1.92 1.5 34.6 54.3 8.6 72.6 72.4

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900900

t

1.87 2.0 44.9 70.5 11.2 94.3 93.31.6 8.7 167 262 42 351 300171

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1.92 1.5 69.1 108.6 17.3 145.3 145.41.7 3.7 159 250 40 335 884 [I , 211.7 8.5 366 575 91 769 884[1 , 21

Fig.2 Relative signal strength against distance measured in Parnellf measured datanl =2.0n2 =4.2- - - _.

A double regression analysis was camed out on the data in Fig.2, as it was evident that the data consisted of two distinct sectionscharacterised by different inverse power laws. The analysis soughtto determine where a breakpoint occurredin the data and theappropriate inverse power laws of the propagation characteristicson either side of the breakpoint. A breakpoint distance of 93.3mwas observed, together with path loss exponents of 2.0 and 4.2before and after the breakpoint, respectively, as shown in Fig. 2.The other measurement cases were similarly analysed, and thebreakpoint distance results are reported in the next Section.

Conclusions:A new formula for the breakpoint distance in line-of-sight microcellular situations has been presented, the accuracy ofwhich has been demonstrated by comparison with experimentalresults. This new formulat ion has been found to be more accuratethan previously reported formulations.

0 EE 1999Electronics Letters Online No: 9990834DOI: 10.1049/eI:I9990834S.C.M. Perera (Capability Management Division, Telecom N Z L td.,P O Box 293, Wellington, New Zealand)E-mail: chris.perera@telecom.co.nzA.G. Williamson and G.B. Rowe (Department o Electrical andElectronic Engineering, The University o Auckland, Private Bag 92019,Auckland, New Zealand)

3 June 1999

ReferencesBLACKARD,K.L., EUERSTEIN, M.J.,RAPPAPORT, T.s., SEIDEL, s .Y . , andXIA, H.H.: Path loss and delay spread models as functions ofantenna height for microcellular system design. IEEE 42nd Veh.Technol. Conf., Denver, May 1992, pp. 333-337FEUERSTEIN, M.J.,BLACKARD, K.L.,RAPPAPORT, T.s. , SEIDEL, s.Y., andXIA, H.H.: Path loss, delay spread and outage models as functionsof antenna height for microcellular system design, ZEEE Trans.Veh. Technol., 1994,43, pp. 487498ROWE, R., and GRINDSTAFF, L.: Radio propagation measurementsand modelling for line-of-sight microcellular systems. IEEE 42ndVeh. Technol. Conf., Denver, May 1992, pp. 349-354KUKUSHKIN, A.: Propagation modelling in mobilecommunications, J . Australian Telecommunication Research, 1994,CHIA, s.T.s., and SNOW, P.: Characterising radio wave propagationbehaviour at 1700MHz for urban and highway microcells. IEEColloquium on Microcellular Propagation Modelling, London,November 1992, pp. 1111-1 1/4NEVE, M.J.,ROWE, G.B.,SOWERBY, K.w., and WILLIAMSON, A.G.: Onthe investigation of radiowave propagation mechanisms for futurewireless communications services planning. IEEE 46th Veh.Technol. Conf., Atlanta, April 1996, pp. 615-619XIA, H.H., KIM, s., and BERTONI, H.L.: Microcellular propagationmeasurements in Dallas city. IEEE 43rd Veh. Technol. Conf.,New Jersey, May 1993, pp. 593-597GREEN, E.: Path loss and signal variability analysis for microcells.IEE 5th Int. Conf. Personal and Mobile Communications, 1989,pp. 3 842 (IEE Conference Publ. No. 315)CHI&S.T.S., and SNOW, P.: Radiowave propagation and handovercriteria for microcells, British Telecom Technol. J., 1990,8, pp. 50-61

XIA, H.H., BERTONI, H.L., MACIEL, L.R., LINDSAY-STEWART, A.,

28, (l), pp. 1-14

- .

10 TURKMANI, A.M.D., nd AROWOJOLU, A.A.: Estimation of signalstrength characteristics in typical microcell environments for PCNnetworks. IEEE 2nd Int. Conf. Universal PersonalCommunications, Ottawa, October 1993, pp. 69-73

RLS adaptive bl ind beamfo rming algor i thmfor cyclo stationary signalsY.X. Chen, Z.Y. He, T.S.Ng and P.C.K. Kwok

A new cost function, which is a modification of the cost functionof Castedo and Figuguas-Vidal for the adaptive blindbeamforming of cyclostationary signals, is proposed. Theproposed cost function enables the well-known recursive least-squares technique to be applied. Simulations demonstrate that theresulting algorithm has a faster convergence speed than thestochastic gradient-based algorithm of Castedo and Figugiras-Vidal.Introduction: In communication systems, most transmitted signalsuse a specific modulation scheme and they are cyclostationary.These signals generate spectral lines when they pass through cer-tain nonlinear transformations and these spectral line characteris-tics are known to the receivers. Based on this property, theauthors in [l] proposed a blind adaptive beamforming algorithmusing the cost function defined by

where y ( n ) is the complex-valued array output and denotesthe time average operation. The values of p and a are selectedaccording to the order and the frequency of the spectral line gen-erated by the signal to be extracted. A stochastic gradient-basedalgorithm (SGA)was proposed to compute the optimum weight ofthe array.

1136 ELECTRONICS LETTERS 8th Ju l y 1999 Vol. 35 No. 14