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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. VOL. VT-35. NO. 4. NOVEMBER 1986 133 Signals in Mobile Communications: A Review RODNEY G. VAUGHAN, MEMBER, IEEE Abstract-The signals in mobile communications are reviewed both in derivatives withrespect to position (or time? for amoving terms of the physical scenario and as the hasis of the transfer function of vehicle) and frequency. These derivatives lead to the random the mobile channel. The transfer function is arranged to demonstrate the of FM and dispersion characteristics the channel, respectively. inherent limitations (the irreducible bit error rate effect) resulting from using single port antennas, in both narroH- and wide-band systems. A Measurements and simulations by the author and results from new model for the average source scenario at the urban-based (vehicular) the literature are used to demonstrate aspects of the channel mobile is determined and an analogous model for the base station is which cause the “irreducible”’ bit error rate (BER)effects for formulated. The models are useful for deriving diversity antennas. single port antennas. The discussion of the transfer function and its irreducible BER characteristics applies toall communi- I. INTRODUCTION cations links that feature Rayleigh-like fading. Section I1 reviews the channel mobile transfer function URPRISINGLY LITTLE is known about the scenario of S sources producing the incident fields at the mobile or base station. In this article. results from the literature are drawn on derived from signalsatthe mobile. Section I11 developsthe scenario model for the sources producing the incident fields at the mobile. Signals at the basestation are the subject of to formulate a model. Much postulation is also required and Section IV, in which a simple model for the source scenario is the resulting model for the sources incident on an urban-based formulated.Themeasurements andsimulations are briefly vehicle (referred asto the MCS-mobile communications discussed in Section V. scenario) is based to some extent on guesswork and wishful thinking.The model is different from those previously SIGNALS 11. AT THE MOBILE forwarded and believed to be more accurate while maintaining A . The Two-Source Model a convenient form. However, the object is not to find a model which gives a better fitto measurements than previous models. Itis instructive to model the incident multipath signals by Thepurpose is to gaina better appreciation of themobile considering discrete sources around the mobile. Sources in the channelandthe scenariomodelsarerequiredforderiving forward and backward directions offer simplest model, and the diversity antennas (Vaughan and Bach Andersen [32]). it is sufficient to provide much insight into the behavior of the At the mobile, the MCS contains sources which extend to more complicated real world scenario. The situation is finiteelevation in all azimuthaldirections.Thesourcesare depicted in Fig. 1, which is taken from Lee [ 18. p. 291, except distributedandspatially uncorrelated.The polarizations are that the phase plot has been added. The two sources (one is a uncorrelated and equally likely (although this actually depends reflection of the other. but it is assumed. for simplicity, that on thenature of the urbansurroundsandthe basestation they have the same amplitude) givea total signal at the mobile polarization, and some knowledge of this dependence is as available). At the base station. the sources are contained in a s ( t )= aoej(uf-kvf) a o e ; ( u f - k L ’ f - d 7 ) - (1) small beamwidth which can often be well approximated by a The are single direction. polarizations considered equally likely (though again. by reciprocity, this depends on the polarization of the mobile antennaand physical surrounds, and some information on this dependence is available) and where k is the wavenumber, Vis the speed of the vehicle, a is 0 uncorrelated for at least one choice of orthogonal polariza- the source signal amplitude and is the delay of the reflected tions. The choice of orthogonal polarizations depends on the signal relative to the direct one. For linear detection, the signal choice of antennas; in land mobile communications, there is envelope is of the form little justification for from departing the usual vertical/ horizontal set forcharacterizing the scenario. The spatial distribution of the time delays in the source scenarios is not considered here. which is shown in Fig. 1. This model gives signal zeros (fades Thetransfer function is portrayed in terms of phase of - CQ dB) when WT Manuscript received February 20, 1986: revised June 1. 1986. nr=kVr--, n = 0 , 1, (4) The author is with the Physics and Engineering Laboratory, Department of 2 Scientific and Industrial Research. Private Bag. Lower Hutt. New Zealand. Telephone 666-9 19. I The limiting bit error rate is normall) to “irreducible.” referred as IEEE Log Number 8610663. despite the possibility of reducing it by equalization techniques. 0018-954518611 100-0133$01.00 0 1986 IEEE 134 IEEE TRANSACTIONS OS VEHICULAR TECHSOLOGY. VOL. VT-35. NO. 4. NOVEMBER 1986 or position and frequency H ( r , w) by noting Vt = r . TheDopplerspectrum of the receivedsignal is clearly dependent on the sourcedistribution (and of course the antenna pattern) relative to the velocity vector. The maximum Doppler frequency contributions arise from the forward and backward directions (unless some of the sources are moving) and are k V/X for linear detection, as already noted from the two-source model. For any symmetric source distribution and symmetric antenna pattern, the Doppler spectrum will be symmetric. A static scenario (in the sense that the sources are not moving relative to the mobile) has been assumed. In reality, Fig. 1. Signal envelope and phase (to within a constant) at a mobile with two the scenario is not static. It is reasonable to expect that other incident plane waves. from one the front and one from behind. The moving vehicles will contribute scattered components. Traffic envelope and vehicle sketch are copied from Lee [18. p. 291. traveling in the opposite direction to V may give rise to Doppler shifts of much more than that predicted by the static kd sources scenario. Measurements describedbelow indicate that =kVr-- often most of the energy is incident from the end street 2 directions-exactly whereother traffic is, so the higher where d/2 is the distance from the scatterer to the mobile. It frequency Doppler contributions may well be significant. follows that the fades occur when Theshort-term statistics of thesum signalamplitude are usually considered well represented by the Rayleigh [25] distribution, The phase can take on only two complementary values since the two incident waves are of identical frequency. The jumps where between the phase values occur when the modulus is zero. so of course there are no discontinuities in the signal. Still, the R=E{r*}. (10) behavior of the phase offers a strong hint of what will happen when more reflected components are added to the scenario. Normally, there is an incident signal which is stronger than For square law detection, the sine-squared form of the the others. This dominant signal can be from a line-of-sight to envelopegives it an instantaneousrate of change which is the transmitter or an effective line of sight permitted by the different from that of linear detection, but the time between opacity of the obstructions (buildings,hills, etc.) between base zeros, or - m dB fades,isthesame in both cases.The and mobile, or simply a reflected effective line-of-sight signal. Doppler shift can be inferred from (6) as fd = 2 V/A. The two- The ensuing amplitude distribution of the sum signal is then source model indicates three important features of the signal Rayleigh with a constant (cf. dc component) term: known as that are encountered in the real situation: a fading envelope, a the Rician distribution (Rice [27]), phasewhich rapid displays changes and the presence of different time delays. B. The Many-Source Model where u2 is the variance of the component Gaussian variables The real worldscenario consists of a large number of of r , Io is the zero-order modified Bessel function and A is the reflected signals which could well be closer to a distributed positive offset value from the Rayleigh distribution. When A continuumin many urban situations. The receivedsignal is = 0, theRiciandistribution reducestoRayleigh, in which now the sum of many reflected contributions (plus possibly a E { r 2 }= u*. direct contribution) To include the effects of shadow fading, there is a host of distributions which have been proposed. Of these, the Suzuki. Weibull, and Nakagami-m distributions have been compared with measurements in London by Parsons and Ibrahim [22]. where ki and V are the propagation and vehicle velocity The Suzuki [31] distribution, which is the Rayleigh distribu- vectors, respectively, and theai are complex. Equation (7) can tion superimposed on a log normal distribution for R , gave the be considered as the transfer function for the mobile channel best fit to these measurements. Other measurements taken in a (e.g. Lee, [18, p. 321) as a function of time and frequency (the suburban area in Malmo, Sweden, by Aulin [3], gave a best fit to the Nakagami-mdistribution. Aulin [3] suggests that the Rayleigh, Rice, Suzuki and Nakagami-m were all rather poor fits to these measurements. The shadow fading can be averted only by macrodiversity- placingbasestations far apart so that the shadow areas are independently distributedforeachbasestation.Curing the short-term fading is a problem well suited to antenna diversity. The statistics model is usually Rayleigh. since it allows much theoretical progress from established results and corresponds to the worst case short-term fading. This model is chosen in spite of the knowledge that the signal is usually much "better" than Rayleigh distributed. C. Real World Signals As far as the author is aware, no measurements have been reported in which the signal envelope has been more than 40 dBbelowthelocal mean. This suggests that either thereal world signal departs from the Rayleigh distribution at signal levels approaching 40 dB belowthe local mean. or else. if the signal is Rayleigh. the equipment or techniques used in existing measurements have not beenup to recording fades deeper than the 40 dB level. Figs. 2(a) and 2(b) show the square law detected envelope measured in an urban area and its plot on a Rayleigh diagram. respectively. The frequency carrier MHz. was 463 The dynamic range is about 35 dB. In Fig. 2(b). theprobability curve dips well below the Rayleigh reference for deep fade levels. indicating something closer to the Rician distribution caused by the presence of a dominant source. Lee and Yeh's [20] measurements at 836 MHz from NJ, Broadway, are within 1 dB of the curve of Fig. 2(b) down to -25 dB.the limit of theirmeasurementrange.Urban measurements in Birminghamat 441MHz by Henze and Parsons [ 131 also depart from the Rayleigh reference at about the same position asthe curve given here. Note that if thescalein Fig. 2(b) extended only to - 20 dB, as it does in many Rayleigh diagrams. a verdict of Rayleigh fading could be confidently in passed. There seems reasonable justification referring to the short-term receivedsignal envelope distribution in an urban area as Rayleigh-like. In Figs.3(a).3(b),the effect of the presence of avery dominant source is illustrated. The measurement was taken in a suburban area. The base station was 120 m high and 2 km away. with only a single large concretebuilding between it and the mobile. The path of travel was at right angles to the base station direction. The dynamic range is now only about 17 dB, and the cumulative distribution is far from Rayleigh. In Figs. 2 and 3. the standard deviation in dB is defined by UdB = 10 log (:;) - where p and u are the conventional definitions for the mean and standard deviation of the envelope power. For M-branch maximal ratio combination (of uncorrelated Rayleigh signals of equal means), the normalized standard deviation is a / p = 136 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. VT-35, NO. 4, NOVEMBER 1986 l/&. To get a feel for the values, the dB standarddeviation TABLE I for the above definition is given in Table I for several values of THE dB STANDARD DEVIATIOS FOR M UNCORRELATED, RAYLEIGH SIGNALS WITH EQUAL MEANS COMBINED IN A MAXIMALRATIO SENSE M. D. The Phase Derivative of the Transfer Function Number of branches Standard deviation of maximal ratio combination M UdB = 10 log ((1 + 1/2,~%)/(1 - 1/2&7)) The carrier phase of the received signal is usually assumed 8 uniformly to be distributed values over all possible (as 4.11 required in Rayleigh statistics), 3.21 2.58 1 2.22 p(e)=-, 2K o G e~2n. (12) 1.98 1.80 1.39 As far as the author is aware, there are no absolute phase measurements reported in the literature. Some measurements of the relative phase between diversity antenna elements on a mobile are available (e.g. Parsons etal. [24]), however. Continuous wave (CW)simulations inwhichthemobile is surrounded by many discrete sources will of course, yield a phase distribution given by (12). Nevertheless, such simula- of tions offer good insightinto real world behavior the signals. The simulationmodel isanavenue of stationary sources through which the mobile moves. However, the position of the sources is not of great interest for now, as long as there is a sufficient number for the fading to be approximately Rayleigh distributed. Fig. 4 is from asimulation(seeSection V) and shows the fading envelope, its absolute phase and the random The frequency modulation. envelope is proper Rayleigh 50 fading; the range covers almost dB, which is about the limit due to the sampling rate and sample size. The absolute phase is a random walk including frequent jumps of random polarity, analogous to the discontinuities of the phase in the two-source model. The maximum excursion of the phase is nearly + 60 rad in this example,althoughotherexampleshaveshown excursions of over 200 rad over the same distance. The value of the absolute phase is not so important, but its first derivative with respect to distance, the (instantaneous) random FM a f,= - phase H ( r , w) (13) ar (C) is very important. Fig. 4. Simulations of the received signal by a mobile in a multipath The jumps in the phase give rise to spikes in the random scenario. (a) Rayleighfading envelope. (b) Absolute phase. Phase (c) derivativewithrespect to the distance canbeinterpretedastherandom FM. Since the phase jumps are randomly polarized, the spikes frequency modulation for a speed of 1 mis. The carrier frequency is 450 arealso randomly polarized.Fortheexampleshown, the MHz. The samples are every cm, giving 66.7 samples per wavelength. maximum excursionisto about + 300 radim.Fig. 4 thus summarizes two of the features of the narrow-bandmobile why just two-channel antenna diversity offers such impressive radio channel, the fast Rayleigh fading and the random FM. returns for improving the channel. The random FM is independent of signal-to-noise ratio (SNR) Therandomdirection of thephasejumpscanbe well so increasing the transmitter power to ensure that even the explained by viewing the signalbehavior in the complex plane. deep fades are well above the noise level will not improve the and The real imaginary components are both zero mean channel degradations causedby the random FM.A closer look Gaussian processes. The fades occur when the signal passes at the situation is worthwhile. and close to the origin, the directionof the phase jump depends Fig. 5 shows some detail from Fig. 4. It is clear that the on which side of the origin the signal passes. The complex phase jumps are associated with the deep fades in the signal locus around the two deep fades of Fig. 5 is shown in envelope. phase the The and random are FM otherwise Fig. 6 . The locus of each fade passes the origin in the same reasonably well behaved,which, of course, coincides with general direction but on different sides of the origin. explain- when the envelope is well behaved. This, along the with ing the random FM spikes havingopposite polarity. As the observation that the badly behaved portions are of rather short envelopedistributionbecomesRician,as in therealworld duration relative to their frequency of occurrence, is the key to case,thepower in the highfrequency components of the VAUGHAN: SIGNALS IK MOBILE COhlMUNICATIONS 137 4 -3: ' 0 10 l o 20 , IO -i- _. 40 SO 60 A Y E M U CNR ( d B ) Fig. 7 . The irreducible BER effect for a single port antenna caused by the random FM in a fading signalwith a fade rate offD. The marked points are simulations and the solid lines theoretical (Adachi [ l ] .) The static curve is for a nonfading channel. The carrier frequency is 920 MHz.(Copied from Miki and Hata [21].) Fig. 5 . A portion of Fig. 3. The jumps in phaseandassociatedspikes of frequencymodulationcan fades be identified with the deeper of the in CNR makes improvements drastic to the BER.The envelope. The random frequency modulation will clearly be reduced if the deep fades can be averted. introduction of a fading signal alters the type of the curve so that the returns for increased CNR are considerably less. As the fading rate increases, a limit to the improvement in BER \ t from increasing CNR is evident,the limitbecomingmore severe with the fading rate. The case f d = 40 Hz corresponds ,\ to a mobile speed of about 50 kmih and a carrier frequency of 900 MHz. E. The Frequency Derivative of the Transfer Function The simulation showing the irreducible error rate due to the !I i random FM is necessarily of finite bandwidth. Other measure- mentsandsimulations already discussed concern a carrier frequency only. Clearly, as the wavelength changes. the sum of the multipath signals will change. An alternative (in some Fig. 6. The signal behaLior around the two deep fades in Fig. 5. The axes are linear in power and the labels are the sample numbers. The figure shows ways) presentation of the signal against position for a constant that the polarity of the random FM spike depends on which way the signal frequency. is to plot the signal against frequency for a constant passes the origin. position. Fig. 8 shows thesituation at 450 MHz with the familiar Rayleigh-fading envelope. The absolute phase is not random FM will be reduced since the signal does not come so shown-this is a constant average slope ( - 10 rad per MHz) close to the origin. on average. The spectrum of the random with some deviations near the fade positions of the envelope. FM thus depends on the size of A in the Rician distribution. The first derivative of the phase with respect to frequency is The spectrum is well known when both antenna pattern and the instantaneous group delay of the mobile channel transfer source distribution are even and omnidirectional (e.g. Jakes function [ 14. p. 451). In this case, the cutoff frequency is the same as the maximum Doppler frequency. a r g = -- phase { H ( t , a)} (14) The effect of the random on FM the communications aa channel is to limit the BER improvement asthe carrier-to- noise ratio (CNR) is increased. The effect is depicted in Fig. which is plotted under the envelope in Fig. 8. The behavior of 7. from simulations by Miki and Hata [21]. The parameter fd the group delay is similar to the random FM. Spikes of random isthe(average)fadingrate of the signal envelope. i.e. the polarity occur at the same frequencies as the envelope fades. spikerate of therandomFM.The modulation is (twobit) The offset value of about 17 ps is the average group delay differentially encoded Gaussian minimumshift keying which is a result of the sources being about 5000 m from the (GMSK) giving 16 kbitis in a 16 kHz 3 dB band. The static receiving antenna. As far as the average group delay time is case shows the usual curve behavior in which a small increase concerned, the example is unrealistic; the scatterers around a 138 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. NO. VT-35, 4, NOVEMBER 1986 contributionsfromother(broadside)anglesare below the detection level of the measurements. It is reasonable to assume that, on average,thesignals in each delay bin arrive with similar angular distributions. A measure of thebandwidthover which thesum signal remainscorrelatedisthecoherencebandwidth.Thereare several definitions for coherence bandwidth which stem from the choice of correlation coefficient which defines the border- line between signals being correlated and uncorrelated. In the mobile communications literature, the value of 0.5 seemsto be preferred(e.g.Jakes [14, p. 511, Lee [18,p. 1981). If the incident sources and antenna pattern are omnidi- rectional confined and to the plane on which themobile moves, the envelope correlation is (Lee [18, p. 1981) 'SliDGl 453.5I '11.0' ,SI.; rsz.; as:.; 153.3' 453.5' '540' w.51 FRESII*CT !L ,*I Fig. 8. The received signal at a constant position with respect to the sources, as a function of frequency. The groupdelay is the negative derivative of the where Aw, to are the frequency and time correlation separa- phase with respecttoangular frequency.The simulationscenariois a cylinder of sources distributed from 0" to 30" in elevation from the center tions, and 7 is the delay spread. For a zero time separation, the with radius 5000 m. The antenna is omnidirectional and sits in the center of coherence bandwidth for an envelope correlationcoefficient of the scenario.The average group delay as follows about 17 ps. These 0.5, is just quantities are exaggerated for demonstration purposes. mobile will be much closer than 5000 m of course, but the exaggerated average group delay is more clear on the scale. The sources aredistributed evenly in elevation between 0" and Typical mean time delay spreads for the bulk of the signal 30" such that the sources sit on a cylinder. The finite energy are reported by Jakes [14, p. 511 (Lee [18, p. 421) as difference of range to each elevationpointgivesthefinite 0.25 (0.5) ps in suburban areas and 1.3 ps in urban areas. For delay spread. The delay difference in this case is 5000/c(2/ T = 0.25 p s , equation (16) gives B = 636 kHz, which 6 - 1) (c isthespeed of light), i.e., about 0.23 p s . For provides a ballpark figure for the 900 MHz carrier frequency larger delay spreads. the excursions become larger. Note that region. means This that about 25 X 25 channels, kHz a sphere or ring of sources with the receiver in the center (cf. corresponding typically to a quarter of the simplex band in Clarke's [7] model) will give no delay spread. It is noted that mobile communications, will have correlatedenvelopes. the cylindrical distribution is not necessarily a good instanta- When dealing with a single channel at a time, the system may neous model; it rather represents an average (of instantaneous well be considered as narrow band. For frequency hopping scenarios) taken over a period while the vehicle is moving. diversity,employingfrequenciescloser than thecoherence The (instantaneous) channel bandwidth is related tothe bandwidth will give a reduced diversity gain. inverse of the group delay. It is clear that a channel with a It is usually assumed that the time delay distribution is of nonzero bandwidth near one of the group delay spikes will be exponential form strongly dispersive.Fortheexampleshown, channel a at 451.18 MHz would be an unfortunate choice. However, the p(Tl)=-1 e-7'17 channel bandwidth is clearly a function of the position of the (17) 2 x7 antennas, so a given channel will be no better than any other for the case of a moving receiver. The noteworthy feature is which is often, but not always, a goodapproximation. An that the large dispersion characteristics are associated with the extreme departure from the exponential distribution may rise deeper fades of the signal envelope. Arnold and Bodtmann [2] from reflections from a distant mountain which results in twoa noted this effect by observing the eyepatterns for a wide-band humped distribution with significant energy arriving at delay signal passed through a hardware simulator. times of say 100 p s (cf. a mountain 15 km away). However, it For a larger bandwidth required for transmitting at higher is well known, Jakes [14, p.521 that the coherence bandwidth, bit rates, the delay spread becomes of interest because it will or rather the envelope correlation as a function of frequency cause intersymbol interference. In urban areas, the time delay difference andgiven time delay spreads,is not particularly spread is reported (e.g. Cox [9], Bajwa and Parsons [5]) to be sensitive to the shape of the delay distribution. rarely more than 10 p s (see Fig. 11). A curious observation The coherence bandwidth can also bedefined for the phase, made by Bajwa and Parsons [5] is that the energy arrivingwith rather than envelope correlation. It turns out to be half of that larger delay times arrives from the end directions the street. of for the envelope (Lee [18, p. 219]), i.e., about 316 kHz. There seems no reasonable physical explanation for such The effect of the time delay spread is felt more athigh behavior. It is felt that since the bulk of the energy arrives transmission rates,whereintersymbolinterferencebecomes from the building lined street end directions, the lower power the limiting factor for the BER. Fig. 9, from Sakoh et a/. [28] brieflyreviewed here. not for themerits of their diversity system, but for the interesting information about the mobile signals that can be inferred from their experimental data. 10- Their system was two identical horn antennas at the base station oriented so that one received only vertical polarization and the other only horizontal. No information is given regarding the horn spacing but it is stated as being immaterial. The mobile antenna was a vertical half-wavelength dipole with a 5 cm ( 2 in) loop around. The height above therooftop of thesecolocated antcnnas could be varied.Theexperiments used at a height of 1.5 wavelengths. Themean power levels of eachpolarizationremainedequal for heights as lowasone wavelength.belowwhichtheverticalpolarizationbecomes dominant. L The locations of the measurementsaregiven. but their 32 ksCs -- -- 0 . nature (urban. suburban, etc.) is not. Transmission was from 16 k b w IO-^ - the mobile at the frequency of 836MHz.The polarization 0 10 2(: 30 GO sa transmission and coupling coefficients are depicted in Fig. 10 AVE.UGE U R (d3) from Lee and Yeh. Fig. 9 . Theirrsducible BER effezt for a single port antennacaused b the! Lee and Yeh's conclusions were as follows. time dela) spread. The marked points are measurements from Tokbo and the cur\ss are from a tho-path model hith a dlfferential delay of 1 ps. The 1 ) The Rayleigh (i.e.. short-term) fading of rlI and r 2 is 2 carrier frequent! is 920 MHz. Copied from Sakoh et al. [?E] uncorrelated. (envelope correlation coefficients were less than 0.2). shows BER limiting similar to that caused by the random FM. 2 ) Theshadow(i.e..long-term) fading of r l land F12 is The curves are from a two path model with a delay difference almost the same(within3 dB of each other,for 90 (spread) of 1 p . The fading rate is 40 Hz and the parameter is percent of the time) andindependent of basestation the bit rate. Two-bit differential MSK was used in the Tokyo height implying that both polarizations follow the same metropolitan area for the measured points on the graph. Sakoh general path influenced by the same major obstructions. et al. suggest that 16 kbitis represents a good choice of bit rate 3) The mean level of r l Iwas about 6 dB higher than rzl. for the single mobile channel. This bit rate is also compatible Similarly. the mean value of rl?was about 6 dB higher with the 25 kHz channel spacings used in many countries. than rI2. It is worth emphasizing that this irreducible BER phenome- Conclusion 1) is presumptuous sincetheantennaelement non (for a single port antenna and no equalization processing) plus ground plane image array patterns form a decorrelation will occur for a static mobile as well. since the delay spread is mechanism through (elevation) angle pattern diversity. How- independent of vehicle speed. ever. the measurement data of 2 ) and 3) above is valuable. An 111. THE SOURCE SCESARIO MOBILE AT THE obvious extension of Lee and Yeh's data processing is to find the correlation coefficient between r l land rll,and r12 and The scenario in which the sources are evenly distributed in azimuth and confined to a plane can be written r2?. Vaughan and Bach Andersen [32].) (See More information is available from themeasurements of Rhee and Zysman [26]. Lee [18. p. 1671 concludes from these (18) measurements that the cross couplings and rzl are noticeable in urban areas but not in suburban areas. Also, the where So is the power densit). of the distributed sources and the larger the distance between the base station and the mobile, the mobile is at the origin.This model features only vertically larger rll becomes than rZ2. cross coupling is also The polarized sources since a ground plane is usually assumed. It is distance dependent. This is a result of an increasing number of often referred to as Clarke's [7] model. Aulin [3] discusses a signal reflections.More information on thedistance depen- model which extendsto three dimensions and contains an dence is discussed below. elevateddominant source. but is still restricted toa single polarization. Another model is derived below, not for finding B. The (Urban) Mobile Cotnr?runications Scenario a better fit to measurements. but to investigateantenna distributed Denote the incident electric field from the diversity. sources of the MCS as A . The Measurements of Lee and Yeh h(0, 4, f)=hO(B, 6 , t)e+h,(0, 4, (1% Lee and Yeh [20] proposed a polarization diversity system where the units of h , ho, and h, are Vimisteradian. The origin in which thehorizontal-to-horizontalandvertical-to-vertical is considered at the mobile antenna. so that the antenna polarizations constituted the two branches. The configuration patterns are independent of time. When the vehicle is moving, is effectively a frequencyreuse system. Their experiment is h is constantly changing. Even vehicle when the is not 140 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. VT-35, KO. 4. NOVEMBER 1986 azimuth, at least in thedirectionsmeasured.Parsons and Ratliff [23] measured in an urban environment with vertically polarized, spaced antennasand notedthat thecorrelations well match with those from expected an omnidirectional scenario. Corresponding measurements (loc. cit) in a subur- ban area had the zeros of correlation spread further apart and their conclusion was that the were sources not placed omnidirectionally. Reudink (in Jakes [14, p. 1081) measured Fig. 10. Transmission and cross coupling coefficients in Lee Yeh's and patterns by rotating a vertically polarized horn mounted on a polarization diversity system. (Copied from Lee and Yeh [20].) stationaryvehicle in an urbanstreet.The patterns werefar fromomnidirectional with dominant contributions fromthe moving,there is sometimedependence becausereflections end directions of the street. These measurements? however, can occur via other moving vehicles. These components are were at 11 GHz,well removed from the frequencies of interest evidently not atrivial contribution; for astationary vehicle, here.Nevertheless,measurements byStridham[30] at 836 Halme et al. [12] reported (orally) a decrease in BER of two MHz, inwhichmoving averagesweretaken, show similar orders of magnitude from daytime (heavy traffic) to nighttime behavior. (lighttraffic) measurements. It is not clear,however, how Another indication of the azimuthal behavior of So can be much of the BER decrease was due to a decrease in inferred from measurements of the Doppler shift distribution. nonvehicular effects(e.g.,man-madenoise).Themeasure- Fig. 11 from Cox [9] (also in Jakes [14]) shows results from ments were in Helsinki at 900 MHz where the mobile received wide-band measurementspresentedas signal power against (incoherently) Gaussian tamed frequency modulation (GTFM) Doppler frequency and propagation For time delay. the of 16 kbitis. narrow-bandcase,the totalsignal arrival distribution is of Apolarization coherencematrixfor the sources can be interest. The figure showsthat the Doppler frequency behaves defined (cf. Collin and Zucker [8, p. 1121) in abasically even fashion about the center (zero) Doppler frequency. Frequencies away from zero dominate the distribu- tion.Thisdoes not conclusively determine that thepower distribution is concentrated at the front and back directions. where each of the elements is of the form Clarke'somnidirectionalmodel,forexample, gives anin- verted cosine form for the Doppler frequency distribution (see Jakes [14,p.-321).Themeasurement of Fig. 11 is from building-lined streets of New York. Not a great deal is known about r ' for the mobile Similar measurements by Bajwa and Parsons [5] show environment; its characteristics have not been explicitly similar behavior for building lined streets. Measurements at described as far the as author is aware. However,some intersections from Bajwa and Parsons [5] and suburban areas informationcanbe inferred from measurements reported in possess components with zero Doppler shift, indicating more the literature. It should be emphasized that only the average evenly distributed sources. characteristics are meaningful for the time being. Thevariousmeasurements suggestthat onaverage,the There appear tobe no measurements of angular correlations urban area illuminates a mobile from all azimuthal directions. available. It is reasonable to expect finite coherence angles in Here, asin Clarke's model, the sources are assumed to be many directions while the mobile is stationary.However, alwaysevenlydistributedin azimuth and of equal strength. ensemble averages in the sense of integrating while the mobile The justification for such a simplification does not lie is moving can be quite reasonably assumed as uncorrelated in completely with analytical temptations. The characteristics of angle. The motion of the vehicle be can viewed as the thesignalreceived by the mobiledo not change much by decorrelation mechanism. Thediagonal elements of the source modeling So fromthemeasurements (inclusion of (an un- polarization coherence matrix can therefore be expressed as known) directional probability weighting) or by a constant as in Clarke's Nevertheless, scenario. thesmall differences r;o(el,41; e2, 42)= so(el,1 ) w l- e2)6(41 42) 4 - should be borne in mind: the fading rate (for an omnidirec- tional antenna) may be slightly different (lower, if e.g.. the sources in the end directions of the street are stronger than where &(e, 4) and &(e, 4) are the powerdensity (per steradic those at broadside) than in reality and the Doppler frequency square) distribution of theverticalandhorizontalpolariza- distribution may be slightly altered. tions, respectively. In the scenario model, then Some knowledge of S is available from measurements. Lee o [ 161 notes that in an urban area, vertically polarized w e , $1 = sow. (23) antennas with horizontal half-power beamwidths of 45 26", O , Some information is available regarding the extentin and 13.5" do not alter thesignalstrength compared to that elevation of Se. Lee andBrandt[19]measured theaverage received from an omnidirectional antenna. This shows that the powers received from two omnidirectional antennas with sources must have been distributed approximately evenly in different elevation dependences at 836 MHz. They concluded polarization ensure that even single for each sources will convey uncorrelated signals in each polarization. Hence which constitutes the final property of the MCS. Strictly speaking, the polarization base of the station, mobile surroundings anddistancebetweenmobileandbase should figure in the MCS. from the results of Lee and Yeh. andKozono etal. (see Section IV).For an urban based mobile. for example, there is about 6 dB difference between the LHS and RHS of (25).thelargercorrespondingto the polarization of the base station. The dependenceof the mobile- base distance is also mentioned in Section IV. These parame- ters are omitted from the model for simplicity and so r,k = r;, . Note, however. that if a vertically polarized base station Flg. 1 1 . Signalstrengthagainst Doppler spectrum andpropagation dela!, in is used (as is usual practice). then for an urban based mobile, S e n York Clt! . (Copied from Cox [ 9 ] . ) the ratio of r,k and is about 6 dB. for Similarly, a horizontally polarized base station, the ratio of rqoand Fie is that most of thesignal arrival is concentrated in elevation about - 6 dB. angles than less 16". The measurements were taken in In conclusion. the MCS is a necessarily crude model of the suburban and smalltown areas. Lee [ 18. p. 1581 concludes average source distribution around a mobile in an urban further that the elevation angles can be somewhat larger than environment. Sources are assumed to be evenly distributed in 16" but less than 39". Yeh (in Jakes [14. p. 1491) concludes the region 60" < 6 ,< 90", 0" < 4 < 360°, where the mobile from the same measurements that the elevations are somewhat is at the origin. Both polarizationsare equally likely.The larger than 11 but less than 39". No othermeasurements source polarization matrix is seem to be available from which similar information for urban areas can be inferred. If sources reside along roof edges of buildings, as would probably be the case with incident signals from an elevated base station, it is reasonable to expect So to extend higher in the urban environment than in the suburban where S is a constant representing the power density of either environment. In the absence of any further measurement polarization. The equal elements on the principal diagonal in information, and for simplicity of the model. So is assumed to (28)indicate that there are equal powers in thebasestation be evenly distributed between 0" and 30" in elevation. Thus, polarizations. (23) is taken a step further: C. Spatial Correlations The spatial correlation function for the signals turns out to haveonlya rather weak dependence on theextent of the where S is nonzero only for 60" < 9 < 90". sources in elevation. It is a straightforward process to find There is less information available about So than So. Lee and numerically the correlation function for the MCS. However, Yeh'smeasurements indicate similarpower levels at the this seems unnecessary because there are well-known analyti- mobile from each polarization. but it must be remembered that cal functions for Clarke's planar scenario as well as spherical the antenna patterns are different in elevation. Hence (assum- scenarios. Clarke's scenario gives a real signal spatial autocor- ing equal powers in the vertical and horizontal polarizations at relation Jo(kx), where x is thedistance on the plane.For the base station). spherical isotropic noise. often used as a model for sky noise, the function is sin k x / k x in form (Cron and Sherman [lo]). ii . ii s ( ,0 ) sin e de d d = s,(e, 4) sin e de dd These two extreme cases are shown in Fig. 12. The first zero ,e I L C of the Bessel function is 0.38 X, and for the sinc function, is 0.5 (25) X. For the MCS, the correlation will be between these curves where integration the is over the sources. again, Once and the first zero is at about 0.4 X. This is the value that can be mathematical convenience influences a model choice of used todescribe space diversitywith zerocorrelationfor omnidirectional antennas at themobile.The insensitivity of the zero crossing positions to the scenario limits highlights the danger of drawingconclusionsfrom measured correlations The off-diagonal elements of r ' can be fortunately deduced regarding scenariolimits. In Fig. 12, the argument kx is with sounder reasoning. It follows from (21) and (22) that the interchangeable with U T , where 7 is the correlation time orthogonal polarizations are spatially uncorrelated. In fact, the interval for a given vehicle speed V = X / T and w is the angular multiplereflections with associateddifferentphase changes frequency of the carrier. 142 IEEE TRAKSACTIONS ON VEHICULAR TECHNOLOGY. VOL. VT-35. NO. 4. KOVEMBER 1986 B . Polarization Matrix The source polarization matrix is defined in (20).The measurements of Lee and Yeh [20]. Kozono et al. [15], and Vaughanand Bach Andersen [32] reveal some information regarding r ' at the base station. Leeand Yeh's dataindicate that themeanratio of and rLo at the base station is 6 dB, the dominant quantity corresponding to the polarization of the mobile antenna. Measurements by the author with the mobile in an urban area with aprincipallyverticallypolarizedmobile antenna agree withthis In figure.suburban areas, the difference was measured to be as high as 12 dB. The base station was sited i Clarke's model some 20 km from the urban area and much of the area between 1 J i kx) , the base and station urban area was open land. In these measurements, the vertical and horizontal polarizations were -1 I uncorrelated (normalized envelope correlations less than 0.02). Fig. 12. Spatial correlation of signals in Clarke's model (cylindrical) and a spherical scenario. The correlation in the MCS falls between these curves. Recent measurements by Kozono et al. [ 151 in urban Tokyo with its first zero at about X = 0.4 h. at 920 MHzwereundertaken with a similarsetup.Their results are in good agreement with the author's, with an envelope (power) correlation coefficient median value of 0.02, IV. SIGNALS THE BASESTATION AT with extreme values of - 0.2 and 0.3. Their results include a A . Introduction phase difference distribution which is essentially uniform over all angles.Kozono et al. also measured the cross polar Most of the discussion from Section I1 applies at the base discrimination (XPD), a quantity equal to the ratio of Tio and station as well:thesignal characteristics, with thepossible FLo, i.e. the ratio of incidentsignal power in the vertical exception of SNR, will be the same owing to reciprocity. The polarization to theincidentsignal power in thehorizontal scenario of sources producing the incident fields at the base polarization. They offer an empirical for formula urban station is quite different from that at the mobile. The scatterers environments as a weak function of base-mobile distance: around a mobile are usually confined to the closer buildings andlampposts,etc.Lee [ 18, p. 2021 concludesfrom an l'ti# idealized model that the effective radius of scatterers is about X P D = - 0 . 3 6 0 + 7 dB=- (29) 20 m. distancethe The to base station be can several r of3 kilometers, so the incident signals at the base station fill a very where D is the distance to the base station in kilometers. The narrowangle.Thebase stationantennapatternnecessarily rms error for the XPD formula is 4.5 dB indicating the very covers a large angle,so the proportion of the pattern used for a large rangeof measured values. Thedistance D is all via urban single mobile channel is normally very small. This is an area, and the formula is derived for distances up to 6 k m . For important difference from the situation at the mobile, where a the urban areas,then. r ; o l r ~ oon is average 5-7 dB, in large proportion of a mobile antenna pattern contributes to the agreement with Lee and Yeh's and the author's results of 6 dB. channel. The spatial correlation function for the base station The spread of measurements from Kozono et a/. is - 5 dB to depends on both the incident angle of the sources relative to 18 dB. theplanecontaining theantennaelements and theangular No information appears to be available regarding the power width of incident signals. The result is that for space diversity, density distribution of the sources from a mobile incident at the antenna spacings of many wavelengths are required. Lee [18, base station. The distribution is probably not important since p. 2011 provides plots of some experimental results for the the solid angle(s) of dominant incident sources is a rather small envelope correlation coefficient for several scenario parame- portion of thebase stationfield of view.From the above ters. measurement information, the source polarization matrix for Base stations are not necessarily sited in the urban environ- the station be base can written,here using solid angle Q ment.Often,thereisconsiderableopenterrainor lightly notation, in the form and housed suburban areas between the base mobile. An effect could be suppression of the horizontal polarization component propagating between the base station and the scatterers around the mobile. The suppression would depend onthe length of the path, basestation height, and groundtype.The mechanism can be viewed by noting that the horizontal E-field is strongly from which reflected away the from conducting partially openland surface. The vertical polarization will propagate much more freely at ground level. + P ( Q )= P#(Q)6 P,(Q)& (3 1) VAUGHAN: SIGNALS IN MOBILE COMMUKICATIONS 143 is the incident power density distribution. It has been assumed signal on the and tape is later digitized processed in the that theincident sourcepolarizationsare uncorrelated over laboratory to present theenvelope plotsandtheRayleigh spatial angles (including zero), although there is noexperi- diagrams. A voice channel on the tape recorder was used to mental evidence to establish or refute this. It is further note details of the measurement environment. assumed that orthogonal the polarizations of the power During all measurements, the car was driven at a constant distributions are coincident and equal, speed(in principle) of 30kmih.This speedrepresenteda compromise between a conveniently long tape record timl (the tape record speed dictates the bandwidth). an acceptabl) ow bandwidth signal a speed and vehicle which would not inconvenience other urban traffic. Of course. practical prob- and also constant, so that lems arose in maintaining this speed. Themain result is that no guarantee can be offered regarding the speed of the vehicle. In principle, all envelope plots feature one sample per cm, but this is only approximate and clearly badly in error in Fig. 2. =0, elsewhere. (34) The digitization was eightbits for each channel, which The extent of P I ,i.e., Q, - Q L , depends on the distance to corresponded very approximately to a worst case quantization the mobile from the base station. The actual direction of P1 of 3 dB (not all of the dynamic rangecan always be used). The depends on the position of the mobile with respect to the base bandwidth of the tape recording was 0-1250 Hz and the station. The above assumptions seem reasonable; the incident sampling rate was 833 Hz which is every cm at 30 kmih. This signals polarization matrix for the base station can be written rate guaranteed complete detection of fades of down to 1.2ms in duration, to dB corresponding 21 below the mean for average fades in a Rayleigh signal.Simulations,however, indicate that sampling every cm at 450 MHz ( - 67 samples wavelength), per is quiteadequate characterizing for a Strictly speaking, PI(a) should also have D as an argument Rayleigh signal downto 40 dB below the mean. The since (a, - Q,) depends on D.Q, and Q, in (34) are left to equipment was capable of measuring levels down to - 115 define explicitly the location and extent of Pl(Q). dBm, well below the deepest fades in Figs. 2 and 3. which are From Lee and Yeh's measurements, the XPD factor is also about - 110 dBm (from Fig. 2). dependent on the polarization of the mobile antenna. For a The sampling frequency needed to be kept low because of vertically polarized mobile antenna, the XPD is, on average, 4 data file size limitations. The sample length for each measure- (i.e., 6 dB) to 16 (i.e., 12 dB) in urban and suburban areas ment is limited to 4500 samples, or, in principle, 45 m. This respectively. No such range of values is available for a sample size for each channel was again limited by data storage horizontally polarized mobile antenna.However,from Lee limitations. This sample size gave correlation coefficients in and Yeh's measurements, the average XPD this case is 0.25 between the same diversity channels for measurements in the ( - 6 dB) in an urban environment. The polarization of the same urban environment that were stable to a few percent. mobile antenna is not includedasa factor inthe XPD; a vertically mobile polarized is antenna assumed. It is not B. Channel Simulation unreasonableto postulatethatamobile antenna with equal The problems and expense associated with mobile measure- powers in both polarizations will produce a 0 dB XPD at the mentsoffer strong motivation for simulation in the labora- base station. A zero, or low correlation between base station tory. Several hardware simulations havebeen proposed, tested polarizations in this case offers an attractive configuration for and reported in the literature. The synthesis of a narrow-band polarization diversity (see Vaughan and Bach Andersen [32]). channel with Rayleigh envelope, random phase and appropri- V. MEASUREMENT SETUP AND SIMULATIOKS not ate (ideal) random FM is a problem. The superposition of a (for example) log normal distribution is also straightforward. A . Measurement Setup The synthesized channel is extremely useful for BER measure- The experimental setup used by the author for the various ments of various modulation and coding schemes. However, measurements is briefly described in this section. As noted in the uncertainty remains of how well the synthesized channel Section 11, the agreement of the second-order statistics with resembles the real. world channel. Actual tests from a moving other reported measurements is excellent, so it can be at least vehicle provide the only really reliable results. Some compro- stated that the measurements are no worse than others in the mise is possible through the stored channel method, in which literature. For the mobile receive measurements, the antenna characteristics of the real channel are stored on tape and later is connected to a receiver from which the 450 kHz second IF used in the laboratory for channel simulation. Wide-band signal is extracted before the automaticgain control (AGC) channel simulators present new problems, with the delay stage.This signal is fed to a squarelawdetector andlog spreadbecomingthe majorparameter of interest.The cost amplifier whose dc output level is approximately proportional dependsverymuch on thedelay lines. which are normally to the log of the power of the input IF signals. proposed to be surface acoustic wave (SAW) devices requiring These dc signals, along with reference calibration levels, many taps-a figure of 30 has been suggested (Berthoumieux are stored using a suitable multichannel FM tape recorder. The [6]) for thoroughly covering the possible delay spreads of the 144 IEEE TRAKSACTIONS ON VEHICULAR TECHKOLOGY. VOL. VT-35, S O . 4 , NOVEMBER 1986 real world.The maximum delayspread in urban areas is station (due to a single mobile) have been formulated. These usually regarded tobe in the order of 10 ps and the current cost models can be used for deriving diversity antennas (Vaughan of asuitabledelayline - is formidable ( U.S. S 100,000), and Bach Andersen [ 3 2 ] ) . Some basic knowledge of the mainly because such a chip has yet to be made. After the first scenarios is still missing, however. Measurement of the is made, prices will plummet in the normal manner. Alterna- polarization coupling and correlation coefficients for various tive delay lines such as a few kilometers of optic fiber may baseand mobile polarizations is suggested for future work. offer cheaper solutions forthe present time.Thetransfer Thesemeasurements would fairly be straightforward, yet functionapplied to eachdelayedsignal can then be synthe- would contribute fundamental knowledge inthisimportant sized, or preferably undergo storedchannel processing. A area. different stored channel for each delay tap may be necessary to account for any apparentchangingangle-of-arrival distribu- ACKKOWLEDGMEKT tion with delay time.Here,the storedchannelprocessing Theauthor is indebted to J. Bach Andersen, of Aalborg would be very useful. For urban environments, a simple two- University, Denmark, for his assistance and encouragement. path model with a 1 ks delay spread seems to be capable of Thanks are also due to Aalborg University, the Danish Post giving reasonable agreement with measured BER results (see Office and Storno AIS for their cooperation while talung the Fig. 9). mobile measurements. method A for implementing the narrow-band channel characteristics for each delay bin is as follows. A CW signal is REFERENCES transmitted through the mobile channel and demodulated down F. Adachi. “Postdetection selection diversity effects on digital FM land to a low IF. The IF frequency is chosen to be sufficiently low mobile radio,” I€€€ Trans.Veh.Technol., vol.VT-31,pp. 166- 172,Nov.1982. for the received signal to be recorded directly onto a tape. The H. W . Arnold and W . F. Bodtmann. “Switched-diversity FSK in spectrum of the received signal should be kept sufficiently low frequency-selectiveRayleighfading,“ I€€€Trans.Veh.Technol., (by driving sufficiently slowly) for recording. The IF signal is vol. VT-33.no.3.pp.156-163,Aug.1984. T. Aulin. “A modified model for the fading signal at a mobile radio later played back in the laboratory and used to modulate a data channel,“ IEEE Trans. Veh. Technol., vol.VT-28.no. 3, pp. 182- signal for BER tests. For singlechannelmeasurements:the 203.Aug.1979. recording equipment can be at the base station. For multichan- -. “Characteristics of digital mobile radio channel.” IEEE Trans. Veh. Technol., vol. VT-30, no. 2, pp. 45-53, May 1981. nel measurements required for investigation of diversity A . S. Bajwa and J . D. Parsons, “Small-area characterisation of UHF antennas at the mobile, the recording equipment needs to be at urban and suburban mobileradio propagation.” Proc.Inst. Elec. the mobile. If the recording equipment is not compatible with Eng., pt. F. vol. 129, no. 2.pp.102-109,1982. D. Berthoumieux. “Hardware wideband multipath channel simulator,” the mobile, as is often thecase, it may be possible to use COST-207 Document. COST-207 Meeting, Helsinki. Feb. 1985. adjacentchannel frequenciesfor eachdiversity branch and R. H. Clarke. “A statisticaltheory of mobileradioreception,” Bell employ just a transmitter for each branch at the mobile. The Syst. Tech. J., vol. 47.pp.957-1000.1969. R. E. Collin and F. Zucker, AntennaTheory, Part 1. New York: signal combination is implemented in the laboratory. A three McGraw-Hill.1969. branchstoredchannel simulator is currently under develop- C. “Mobile propagation D. Cox, radio MHz; at 910 Multipath ment at Aalborg University, Denmark (Eggers, [l 13). characteristics in New York City.” IEEE Trans. Veh. Technol., vol. VT-22.pp,104-110.1973. Software simulation has its place, also. It provides a B. F. CronandC.H.Sherman,“Spatialcorrelationfunctionsfor convenient tool for investigating some channel properties and various noise models,’’ JASA, vol. 34. pp. 1732-1736, 1962. checking antenna performance. source The distribution is P. Eggers,“Storedchannelsimulatorformobilecommunications,” Aalborg Univ.. Denmark. to be published. normally defined by a number of discrete sources. Thenumber S. J . Halme. R. T. Jaakkola. and K. J. Rikkinene, “Bursterror of sources required to generate a Rayleigh signal is not large; characterisations of a digital transmission system for 900 MHz mobile it is well known that just 6 equal amplitude and random phase communications,” Proc.NordicSeminar in Digital and Mobile Radiocommun., Espoo,Finland,Feb.1985,pp.153-164. sources will sum to give a distribution which is a very good M. Henzeand J. D.Parsons,“Experimental dual diversitysingle- approximation to Rayleigh (e.g. Slack [29]). The simulations receiverpredictioncombinerfor UHF mobile.” Electron.Circuits of Figs. 4-6 and 8 used 200 sources. number This is Syst., vol. 1. no. 1. pp.2-10.Sept.1976. W. C. Jakes. Ed.. Microwave Communications. Mobile New unnecessarily large for the information displayed, but was also York:Wiley,1974. used to simulate the MCS for assessing diversityantenna S. Kozono. H. Tsuruhara. and M. Sakamoto, “Base station polariza- performance. tion diversityreceptionmobile for radio,” IEEE Veh. Trans. Technol., VT-33. no. 4. pp. 301-306, Nov. 1984. VI. CONCLUSIOK W . C . Y. Lee. “Preliminary investigation of mobile radio signal fading using directionantennas on the mobile unit.” I€€E Trans. Veh. Thetransfer function of the mobile channel been has Technol., vol. VT-15. no. 2 . pp. 8-15, Oct. 1966. -. “Finding the approximate angular probability density functionof reviewed with particular attention paid to themechanisms wave arrival by using a directional antenna,” IEEE Trans. Antennas causing the “irreducible“ BER effects for single port anten- Propagat., AP-21. no. 3.pp.328-334.1973. nas. The derivative of the transfer function phase with respect -, MobileCommunicationsEngineering. New York: Wiley, 1982. to the mobile position (random FM) explains the capacity limit W. C. Y. Leeand R. H. Brandt.”Elevationangle of mobileradio of the narrow-band channel. Similarly, the capacity limit of signal arrival,” IEEE Trans. Commun., vol. COM-31, no. 11,pp. the wide-band channel is explained using the derivative of the 1194-1197,1973. W . C. Y . Lee and Y. S. Yeh. “Polarization diversity system for mobile phase transfer function with respect to frequency (group radio.“ IE€€ Trans. Commun., vol. COM-20. no. 5, 1972. delay). Scenario models for the urban based mobile and base T. Miki and M. Hata. “Performance of 16 kbits GMSK transmission VAUGHAN:SIGNALS IN MOBILE COMMUNICATIONS 145 withpostdetectionselectiondiversityinlandmobile radio,” IEEE [31] H. Suzuki, “A statisticalmodel for urbanradio propagation,” IEEE Trans. Veh.Technol., vol. VT-33, no.3,pp.128-133,Aug.1984. Trans. Antennas Propagat., AP-20, vol. 25, pp. 673-680, 1977. J. D. Parsons and M. F. Ibrahim. “Signal strength prediction in built- [32]R. G . Vaughanand J. BachAndersen,“Antenna diversity in mobile up areas, part 2 : Signal variability,” Proc. Inst. Elec. Eng., pt. F, vol. communications,” Proc. Nordic Seminar on Digital Land Mobile 139, no. 5 , pp. 385-391, 1983. Radio Commun., Espoo, Finland, Feb. 1985, pp. 87-96. J . D. Parsons and P. A. Ratliff. “Diversity reception for VHF mobile radio,” Radio Electron. Eng., vol. 43, pp. 317-324, 1973. J . D. Parsons, P. A . Ratliff. M. Heme and M. J. Withers, “Single- receiver diversity systems,” IEEE Trans. Commun., vol. COM-21, no. 11,pp.1276-1280,Nov.1973. Lord John Rayleigh, “On the resultant of a large number of vibrations Rodney G . Vaughan (”82) received the B.E. and of the same pitch and of arbitrary phase.” Philosophy Mug., vol. 10, M.E.degrees in electrical from engineering the p.73,1880. University of Canterbury, New Zealand, in 1976 S. B. Rhee and G . E. Zysman, “Results of suburban base station spatial and 1977, respectively, and the Ph.D. degree from diversity measurements in the UHF band,” IEEE Trans. Commun., Aalborg University, Denmark, in 1985. VOI. COM-22, p. 1630, 1974. From 1977 to 1978 he was with the New Zealand S. 0. Rice, “Statistical properties of a sine wave plus random noise,’’ PostOfficeworking with toll trafficanalysisand Bell Syst. Tech. J., vol. 24, pp. 109-157,1948. been the forecasting. Since 1979, he has with K. Sakoh, K. Tsyjimaru. K. Kinoshita,and F.Adachi,“Advanced PhysicsandEngineering Laboratory,Department radio paging service supported by ISDN,” in Proc. Nordic Seminar of Industrial and Scientific Research, New Zealand, on Digital LandMobile Radiocommun., Espoo, Finland, Feb. 1985, developing a variety of computer based industrial pp. 239-248. and scientificequipment.Hestudied in Aalborgfrom1982to1985.asa M. Slack, “Probability densities of sinusoidal oscillations combined in recipient of a New Zealand government study award. His current interests random phase,” Proc. IEEE, vol. 93, pt. 3, pp. 76-86, 1946. include and communications, mobile satellite antenna arrays.and signal J . R. Stridham, “Experimental study of UHF mobile radio transmis- processing. sion using a directive antenna,” IEEE Trans. Veh. Commun., vol. Dr.Vaughan is amember of the IEEEAntennasandPropagationand VC-15,pp.16-24,1966. Vehicular Technology Societies.

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