Signals in Mobile Communications A Review

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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
                                                                              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
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
  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
                        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]

   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
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
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
to be         distributed                         values
                                  over all possible        (as                                                          4.11
required in Rayleigh statistics),                                                                                       3.21
                        1                                                                                               2.22
                                   o   G e~2n.                (12)                                                      1.98
   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-
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
frequency modulation. envelope              is proper Rayleigh
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
                     f,= - phase H ( r ,   w)                  (13)
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
                                                                         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

       -3:   '

                                                                                                  0      10
                                                                                                              o  20

                                                                                                                                    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
                                                                                                   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,
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.
                                                                                       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
               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
  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
                                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].)
                                                                                       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
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
                                                                          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
                                                                          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
[ 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]).
       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
         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
 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
                                                                               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
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)
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
                                                                      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
                                                                      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
    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.
    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
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                                                                        D. Berthoumieux. “Hardware wideband multipath channel simulator,”
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adjacentchannel frequenciesfor eachdiversity branch and                 R. H. Clarke. “A statisticaltheory of mobileradioreception,” Bell
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                                                                        R. E. Collin and F. Zucker, AntennaTheory, Part 1. New York:
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convenient tool for investigating some channel properties and           various noise models,’’ JASA, vol. 34. pp. 1732-1736, 1962.
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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
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                                                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
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nas. The derivative of the transfer function phase with respect                -,     MobileCommunicationsEngineering.             New York:  Wiley,
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                                                                               W . C. Y . Lee and Y. S. Yeh. “Polarization diversity system for mobile
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VAUGHAN:SIGNALS IN MOBILE COMMUNICATIONS                                                                                                                 145

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    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
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                                                                                         mobile satellite               antenna              arrays.and signal
    J . R. Stridham, “Experimental study of UHF mobile radio transmis-            processing.
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    VC-15,pp.16-24,1966.                                                          Vehicular Technology Societies.

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