·......
EFFECTS OF PATH LOSS AND FRINGE USER DISTRIBUTION
ON CDMA CELLULAR FREQUENCY REUSE EFFICIENCY
Theodore S. Rappaport
Mobile & Portable Radio Research Group
Dept. of Electrical Engineering
Virginia Polytechnic Institute and
State University
Blacksburg, VA 24061'-0111
~·
.
...--.._..___.__.. -...-.;-.. _..-
6L.Of?WM '10
-r:e:. 3, 1990
Sa.~"~
Laurence B. Milstein
Dept. of Electrical and
Computer Engineering
Univ. of California at San Diego
La Jolla, CA 92093-0407
Dtejo ~ CA
ABSTRACT
IT. PROPAGATION
This paper determines expressions which quantitatively
describe the impact of path loss and user distribution on
CDMA cellular radio system performance. Path ·ross in
typical microcellular and cellular channels is shown to
increase exponentially with distance to between the second
and third power, as opposed to the commonly quoted fourth
power law. Then, two performance measures, frequency
reuse efficiency and bit error rate probability, are evaluated
for CDMA cellular systems. Values for frequency reuse
efficiency are derived for the uplink using different
propagation rules and spatial distributions of subscribers in
adjacent cells. Bit error rate probabilities as a function of the
number of users are found for a two cell downlink model that
assumes the subscriber is straddling the cell boundaries.
I. INTRODUCTION
In this paper, we quantify some limiting factors in mobile
CDMA communications. We begin by concentrating on the
propagation path loss exponent that is appropriate for mobile
channels which employ CDMA. As is well known, for free
space, e~ectromagnetic ·waves attenuate according to the
factor d , where d is the transmitter-receiver separation
distance. Stated differently, the propagation path loss
exponent for free space is two. Similarly, for channels used
by classical cellular and terrestrial microwave systems, the
most commonly accepted exponents vary from 3.6 to 4.
However,· these latter results correspond to situations where
the transmitter and receiver are separated by distances much
greater than 1 km. In modern cellular communications, and
especially in microcellular communications, the relevant
distances are much smaller than those which make the fourth
power law valid. We show here that a two-ray multipath
model suggests that the correct exponent is much closer to
two than it is to four. This is confirmed experimentally. We
then estimate the so called "reuse factor" on the CDMA
mobile-to-base link (uplink) by considering vanous
propagation exponent values.
For the base-to-mobile link (downlink), we investigate the
performance of mobiles which are straddling the edge of two
adjacent cells. That is, any time a mobile is in the _interior
of a given cell, because of the large scale propagatwn law
referred to above, it receives a signal from its own base
station which is nominally (i.e. without fading) stronger than
that from base stations in adjacent cells.
However,
irrespective of what the large scale path loss exponent is, a
mobile at the boundary of two cells, and equidistant from
both base stations, receives no such advantage. Hence, this
latter location corresponds to the worst-case location with
respect to base station interference effects, and we
concentrate on it below. To make the analysis tractable, we
only consider two base stations here, although the approach
can be extended to more than two cells.
Portions of this research were supported by the Mobile & Portable Radio Research
Group Industrial Affiliates Program at Virginia Tech, and by the NSF I/UCRC for
Ultra-High Speed Integrated Circuits and Systems at UCSD.
Accurate propagation modeling is vital for accurately
predicting the coverage and capacity of cellular radio
systems.
This is particularly true in evolving CDMA
systems, since capacity is limited by co-channel interference
rather than path loss between the desired base and mobile.
Unlike conventional cellular radio system design which
strives for excellent base station coverage in each cell, and
then relies on judicious frequency management within a
service area to mitigate co-channel interference, CDMA
requires no frequency planning. As is shown here, CDMA
reuse efficienc~, and thus system capacity, is reduced
2.0
dB when a d path loss law is used in place of a d law.
Thus, an average propagation path loss model which pre_dicts
too much attenuation over a particular distance. will
overestimate the capacity of CDMA since it underestimates
noise power from adjacent cells. In this paper, we use a
simple two ray model to show how received signal power
varies with distance between transmitter and receiver due to
the physical nature of the channel. The simple model
provides a propagation rule that agrees with measured data.
Its simplicity evolves from a quasi-static approach, whereby
the two rays are considered to have amplitudes which do not
vary with time, but which vectorially combine in different
ways as the mobile travels over space. Thus, the model'
considers large scale path loss, and not small scale fading
effects.
2Y
Figure 1 illustrates a classic two-ray propagation geometry
that is often used to model terrestrial microwave systems.
There is a 11' radian phase shift induced by the ground
reflection. Note that this geometry does not consider any
other multipath effects other than the ground reflected path,
and· the individual strengths of the LOS and ground reflected
components do not fade over time and are virtually identical
for fixed T-R separation distance (d). The amolitude of each
signal component obeys free space propagation, and if the
mobile moves, the phase change of each component varies
linearly with distance. If these two signal components arrive
as shown in Figure 1, the impulse response of the channel can
then be given by two impulse functions, separated by the
propagation time delay between the direct LOS signal and.
the ground reflected signal.
If a narrow band (CW) transmitter and receiver use the
chann~l of Figure 1, the received signal envelope appears as
the phasor sum of two CW signals which have propagation
delays on the order of a few nanoseconds. In this case, the
bandwidth of the transmission is much less than the flat
fading bandwidth of the channel, and the resultant received
envelope undergoes very -slow flat fadin-g as the mobile -rrroves
over space. The two signal components add constructively at
some distances and destructively at others. Since the two
components have virtually identical strengths, it is possible
for them to completely cancel at a few particular T-R
separations. If, instead of just two signals, many ·
'
404.6.1
0500
CH2827-4/90/0000-0500 $1.00 © 1990 IEEE
components with equal mean strengths arrive from random
directions, then the central limit theorem predicts a Rayleigh
fading envelope will occur as the mobile moves over small
distances (on the order of a few meters). In the Rayleigh
fading model, complete cancellation of the fading envelope is
virtually impossible. Unlike the Rayleigh fading model,
which describes fading as the mobile moves over a small
distance in a heavy multipath environment where the mean
signal strength is assumed to be constant, the physical model
of Figure 1 uses a deterministic ray tracing technique to
explain the large scale variation in path loss.
We need accurate propagation models to determine the
impact of propagation path loss on system design. The
geometry in Figure 1 is a well accepted physical model which
accounts for the large scale propagation phenomenon
observed in terrestrial and analog cellular systems. In such
systems, coverage distance is usually maximized, and
historically, no attention has been paid to the close-in
propagation effects of such systems. In fact, traditional use
of the model strives to predict the received signal le"Vel
several kilometers away, based on a received signal level at a
1 km reference point. We now consider Figure 1 for modern
cellular systems, and justify its use ·by the good fit to
measured data. Intuitively, the model can be justified by
considering that in cellular channels, there will always be one
distinct path (and its ground reflected component) between
the base andmobile. Whether this distinct path is via LOS,
or occurs via a building reflection when the mobile's LOS
signal is shadowed, we conjecture that over large scale
distances, the underlying propagation mechanism is
dominated by the physical situation like that in Figure 1.
That is, on average, as the mobile travels over the wide range
of distances in the cell, the propagation mechanism described
by Figure 1 holds. Although real world channels have many
additional signal components which' arrive due to reflection
and diffraction, these signals undergo independent shadow
fading, and arrive at random time delays. It can be shown
that the additional components would have little net effect
when averaged over large scale distances. As is shown here,
actual measurements agree with this simple geometric model
at close-in distances.
In Figure 1, the direct path between base and subscriber
follows a free space propagation law having an electric field
intensity inversely proportional to distance, and a power loss
inversely proportional to the distance squared. The ground
induced reflection provides nearly identical electric field at
the receiver, as low grazing angles at UHF provide almost
perfect reflection. The only difference in the two signals is
the propagation delay of the bounced signal with respect to
the line of sight signal, which results in a flat fading mobile
channel for CDMA system using chip durations greater than
a fraction of a microsecond.
From Figure 1, it can be shown that for a narrow band (CW)
transmitted signal having an electric field intensity
E(d;t)=(A/d)cos(27rft) V /m for d>O, the total received
electric field envelope at the mobile, as a function of
transmitter antenna height (ht), receiver antenna height (hr),
and T-R separation distanced, is given by
IE( d) I
t
= 2 sin(~)
A is the wavelength in meters and ht, hr are in meters. From
(~), the received power is proportional to
given by
2
P(d) oc
(3)
P(d) oc A 2 (41rhthr\2
d4
A· )
.
(4)_
Eqn. (4) is called a large scale path loss model . sin~e it,
accounts f?r the aver<;ge ~ign<;Ilevels incurred ov~r a large
range of distances, which Imphes over a large range -of ,time
for a mobile. Eqns. (1) - (4) assume unity gain antennas and
yield the power detected by a receiver that is unable to
uniquely distinguish the two individual components upon
reception (i.e. flat fading). If the two signals could be
resolved, the received powers of each would be proportional
to inverse distance squared, and not inverse distance to the
fourth power as indicated by the denominator of (4). From
(4), flat fading signal path loss has historically been described
as following a distance to the fourth power. relationship and
this is often quoted in the literature. · This is als~ the ·
propagation law implicitly assumed in [2]. However, it must
be realized that (4) is an asymptotic result which holds when
d is large, typically much larger than 1 km for terrestrial
systems. Eqn. (4) does not relate the actual power of distant
users to close-in users, although such a relationship is needed
for meaningful performance prediction, of CDMA systems.
Rather, (4) relates the power of very distant users to other··
distant users. Thus, in what follows, we propose an alternate
path loss. modeling technique that better represents .the
actual large scale path loss effects in real world cellular
systems.
II.A. PATH LOSS
We use the geometry in Figure 1 to determine the
power law exponent as a function of T-R separation for
CDMA channels.
We use· two realistic system
implementations at 900 MHz and 1800 .. MHz for examples.
The first case assumes ht=50 m and hr=2 m (cell site case)
to provide a radial coverage of up to 10 km. The second case
assumes ht=10 m and hr=2 m for a 2.0 km coverage range
(microcell site case). We now define the path loss exponent n
to be a function of the both the closest and farthest distance
likely to be covered in a cellular system. That is, unlike the
asymptotic result in (4), we suggest that a more p.ppropriate
path loss model is given by
P(d)dB - P(a) dB
=-
10 log 10 (~)n
(5a)
Eqn. (5a) implies that if P( d), the power received at distance
d, is desired, then the proper value .of n depends on: 1) the
chosen distance between the transmitter and the nearest
user, denoted by a; and 2) the distance d over which one is
concerned with predicting path loss. From (5a)
·
n(a,d) =
- where
for
1E(d)l 2 =~'\ (~-~cos11)
Note that when T-R separation is much greater ·than hth
(3) simplifies to
r•
(1)
(2)
IE(dW, and is
P(d)dB - P(a) dB
-10 log10 (d/a)
(5b)
For modern systems, a is on the order of tens of meters,
particularly in emerging microcell systems within heavily
populated areas, and P(a) is the received power, relative to
the. transmitter power, received at a distance a ·over free
space.
404.6.2
0501
'\·
Using (3), Figures 2 and 3 show path loss behavior of typical
cellular and· microcellular systems. Eqn. (5b) was used to
compute n as function of a and distance. Note that at typical
cell fringe distances of between d=l.O km and d=10 km, path
loss exponents range between 2.0 and 2.8 when a= 100 m,
and even lower n values fit (5!>) for smaller d. The dyn~ic
range on received power is seen to he. about 6q ~B, dependn~g
on the exact distance from the cell stte. AdditiOnal dynamtc
range is required for small scale fading effects. The free space
power loss between unity gain transmitter and receiver
antennas can be shown to be 78 dB over a 100 m path at 900
MHz so the total large scale dynamic range is on the order
of 140 - 150 dB. Greater dynamic range is required to
accommodate users closer than a or users in adjacent cells
beyond the designed fringe. Occasional deep fades caused by
phase cancellation of the LOS and ground reflected path can
occur and are predicted by the two ray model. It should be
clear that the d to the fourth power assumption on path loss
is a poor model a~ locati?ns less than_ several km fro~ a
terrestrial base statiOn. Thts can be readily seen by observmg ·
Figure 2 and noticing the received power at 10 km is 34 dB.·
down from the power at 1 km. In a fourth power model, this
difference would be 40 dB. Between 0.1 km and 1 km, the
error in the fourth power assumption is even more striking.
Experiments have shown tha~ the power ~aw exponent is
indeed a function of the close-m reference dtstance used (see
[4]- [6]). In [4],. a ~00 ns probe was used to obtain an
experimental data base of about 6000 power delay profile
measurements in 6 cell sites. The power was best fit by a
d3.U path loss law when the free space reference distance was
1.0 km, but when... a· 0.1 km reference distance was ~sed, the
best fit was d 2 • f. The measurements in [4] venfy that
average path:loss for the direft sign~ component obeys mean
path loss power la'!s of d2 · ~o d ·8 when _ref~renced to a
close-in free space stgnal, and IS normally dtstnbuted about
the average with standard deviation ranging between 7 and
12 dB. Table 1 gives channel parameters from ~easurements
in six cellular and microcellular systems. Maxtmum excess
delay spread, which refers to the m_aximu~ d~lay induced by
a multipath signal which has amplitude wtthm 10 dB of the
maximum received signal, usually does not exceed 15
microseconds. Figure 4 is a scatter plot o~ path loss me.asured
in real urban channels and shows that m most locatiOns, a
fourth power . law ~redicts excessive attenuation o~er
distance. Each point in Figure 4 was found ~y averag~ng
path loss over distances of about 10 to 50 m m a movmg
receiver.
III. PROPAGATION EFFECTS ON FREQUENCY REUSE
We now find the cochannel interference at a cellular CDMA
base station receiver by finding upper and lower bounds on
the amount of out~of-cell and in-cell noise provided by mobile
users. The uplink is considered here, but the same approac_h
may be applied to . the downlink, as well. This analysts
address a specific question: "What is th~ ratio o.f in-~ell noi~e
to total noise received at a base statiOn recetver? . Thts
ratio, denoted by f, is given by
~
~
~
( Ni + MNa)
where N. denotes the noise power due to subscriber
transmissions in the desired cell and Na denotes the noise
power received from all subscribers in one of_ the M cells
adjacent to the desired cell. The parameter f 1s a figure of
merit called the frequency reuse efficiency of a spr:ead
spect~um system, since it represents ~he ·ratio of interference
due to in-cell noise (caused by other m-cell users sharmg the
same frequency band but using unique PN codes) as
compared to interference due .to all mobile users in the
cellular network.
III.A ASSUMPTIONS
The argument is made that if each cell can support a
particular number of users withit;t the same. s~t~ at a
particular level of performance (wttJ:lout constdeilllg adJacent
cell interference), then the same cell can support, on avera~e,
f times that particular number of users when the entue
cellular network reuses the spectrum. Our results are based
on simple but reasonable assumptions which are as follows:
(1) we assume uniform distribution of mobile users ov_er
space within each cell, although our method allows spatial
distribution of users to be adjusted easily; (2) cells have
equal area A, and th~re ar~ K users pe; unit are~; (3)
distance of closest mobile to 1ts own base IS a; (4) a IS the
same for all cells; (5J distance of the farthest user from its
own base is d; (6) 'desired" cell has radius d; (7) power
received from mobiles > 3d from desired cell fringe · is
ignored; (8) ideal power control is assumed within .each cell;
(9) . omnidirectional antennas at base and .mobiles; (10)
received powers from all users add at base recetver.
Figure 5 shows the geom~try used. for analysi_s. ·The ce~ter
cell is the desired cell which contams the desued subscnber
transmitting to the base in the center of the figure .. Each
mobile also interferes with adjacent bases, and adJacent
mobiles interfere with the desired base. We use wedges from
an anriullus made by concentric circles to repres_~nt adjacent
cells. For the equal loading case, the adjacent cells must
each contain an area (i.e. number of users) equal to that of
the center cell, and this defines Om over which the adjacent
cell wedges span.
This· geometry is. different from th~ tr~tional hex g~me~ry
in two ways. Ftrst, the concentnc c1rcle geometry Implies
that more users are located at the outer part of the adjacent
cells (farther away from desired base), and thus will yield
optimistic results for f; The area in. the outer part o~ the
adjacent cell is approXImately 1.66 t1mes that .of the mner
part and the total area (i.e. number of users) must be equal
to the center cell for equal.lo~ng: We use the geometry as
is for an upper bound (which Implies 62.5% of the KA lfsers
are in the outer part), and perform a scaling t?at effectively
redistributes the adjacent cell users so that, as m a hexagonal
cell layout, there are an equal number of users between r=d
to 2d-a as there are between r=2d+a to 3d, and the total
number of users in inner and outer parts sum to KA. A lower
bound on f is obtained by redistributing the K~ u.sers in
adjacent cells so that they are all clustered umformly
between d and 2d-a. Thus, we can find the impact that user
distribution has on f.
We assume mobiles in adjacent cells cannot be within the
annullus made by the radii 2d-a and 2d+a in order to m~e
the analysis tractable. This assumption can be made With
virtually no impact on results. w~en a<d.
;\ll users
propae:.ate with a path loss law that mcreases as dtstance to
the nth power relative to the reference free space distance
P(a) as given in (5). All mobiles are assumed to be ~der
power control within their own cells such that all desired
mobile signals arrive with the same power P n as the clo~t
user within the cell. Thus, we reference all mobile
transmitted powers to the power transmitted by the closest
mobile within the cell, which is denoted as P a·
404.6.3
0502
. ANALYSIS
By power control, the received power of the desired mobile at
the base receiver is P "' and the interfering power due to inusers will be Pn(K-1)A 1'::1-KPnA. Each mobile in the
desired cell has a transmitted power equal to P 0lr/a)" where
r is the distance from mobile to base, and n is the
:propagation path loss exponent in (5). Since users are
assumed uniformly distributed over the plane, the total
received noise from the in-cell mobiles (neglecting multipath)
is given by
Ni=
KP nA = K ~~,.J: (P a(r/at] r dr d9
(7)
and the area in the center cell is given by
.A= j"_,. Jda rdrd9
(8)
The adjacent cell mobiles are under power control with their
own cell and are distance r' from their base station. · As
shown in Figure 6, the relationship between r' and r is given
by (9). The true transmitter power for each mobile in the
adjacent cell can be related by P a and r', and r' is related to
r nearly exactly by the relationship
1/2
r'=( r 2sin29 + (2d -a-rcos9) 2
)
r'=( r2 sin29 + (rcos9 -2d-a )2
)
1/2
for d ~ r ~ 2d-a
for 2d+a ~ r ~3d
(9)
Then the power P a received from a subscriber in an adjacent
cell, referenced to P a• is given by
(10)
Writing r' in terms of r, the power contributed by an
adjacent cell is
'
Na=KAPa =
different values of path loss exponent n. Note that f values
for n=4 are comparable to those given in [2]. For uniform
user distribution over space, f is 64% for n=4, 55% for n=3
and 42% for n=2. These values decrease by an additional s%
2to 12% when a second layer of adjacent cells is considered.
The largest decrease occurs for lowest n values. When
adjacent users are clustered withi~ the inner regions, f drops
to 30% for free space propagatiOn and just one layer of
adjacent users.
IV. BER PERFORMANCE ON FRINGE OF CELL
Co~sider now th~ base-to-mobile link (do~nlink). It is
desired to determme the performance of mob1le users in a
cellular CDMA. system when th.ey. straddle the boundary
between two adJacent cells. The sigmficance of mobiles being
at the edge of a cell is very simple; in general, due to
propagation path loss, a mobile in the interior of a given cell
experiences a power advantage in the reception of the signal
transmitted from his own base station relative to signals
received from neighboring cells (which are further away from
the mobile). However, when the mobile is at the boundary
between two cells, this advantage disappears.
To analyze this problem, consider the following model. Two
neighboring cells are considered, and a mobile with an omnidirectional antenna is assumed to be located on the
boundaries of the cells and equally distant from each base
station. The signal from ei'ther base is composed of K' DS
waveforms, all of which are asynchronous with each other.
However, the composite signal from either base station is
assumed to undergo flat shadow fading with either a
Rayleigh or log-normal distribution about the nominal large
scale power received at the fringe. That is, because we are
considering the downlink, and because all signals from the
base arrive at a given mobile via the same propagation path,
we can assume they all shadow fade in unison.
With the above model, the received waveform at the mobile
is given by
Inner
K'
r(t) = ~Ba 1 di(t-1JPNi(t-Ti)cos(w0 H9.)
=1
·\.
(11)
+
2K'
2:: Ba2di(t-Ti)PNi(t-Ti)cos(w0 H9i) + nw(t),
(12)
i=K'+1
and the limits of integration for 9 are found by equating the
areas of one adjacent cell wedge and the center cell. 9m is
slightly larger than 45 degrees, which implies there are
approximately M=8 adjacent cells. Eqns. (7) and (11) can be
solved numerically for specific values of a, d, and 9.
Frequency reuse efficiency, f, can then be computed from (6).
Weighting factors w. and w t may be applied to the innP-r
and outer integrals in (11) ;3 that the distribution of users
within the inner annullus (d,2d-a) and outer annullus (2d+a)
can be altered without changing the total area of the
adjacent cell. For w. = w t=1, there are approximately
twice as many adjacentn user~uwithin (2d+a) than there are
between (d,2d-a). For w. =1.38 and W0 u =0.78, an equal
number of users in each a:'djacent cell are \ocated on either
side of the r=2d boundary. This provides a user-distance
distribution comparable to the hexagonal representation of
cell sites. A rough lower bound for f can be achievedwith.
w. =3.0 and w t=O.O, as this corresponds to the case of all
adjacent users ~lustered uniformly in the inner part, and no
users in the outer part of the adjacent cells.
Table 2 gives values of f using a = 0.1 km, for d = 2 km and
10 km. The tables show how reuse efficiency is affected by
where B represents the unfaded amplitude of any of the
received PN signals, a1 and a 2 are independent random
variables representin~ the shadow fading about some large
scale signal level, di( t) is the binary data of the ith signal,
and T· and (J. represent the time delay and ·RF phase,
respedively, of the ith signal. The delays and phases are
assumed independent· of each other and independent of the
data. Finally, the noise nw(t) is additive white Gaussian
noise (AWGN) having two-sided power spectral density
TJ 0 f2.
Assume that each user employs a long spreading sequence
(i.~., one that sp.ans many bits), such that the processing gain
L 1S
(13)
where Tis the bit duration and Tc is the chip duration. Also
a.Ssume K'>>l.
From the Gaussian approximation
developed in [7], we can approximate the conditional
probability of error of the system, conditioned upon a 1 and
J
a 2, a.q
404.6.4
P(eial,a2) =
<P
l
-al [
~E + :~( a12 +
] -1/2}
a22)
'
(14)
0503
!
~
where
2
z
<P(x)
~ fz'; J e
-v
2
1
dy.
J
-oo
E is the energy per bit. If we further assume that
(15)
f>> 1, we
~::::rM[ ~(!+~) ]_, , J.
V. CONCLUSION
(16)
Define u=ada2 and v=u2• If a 1 and a2 are independent
and identical Rayleigh random variables, then it can be
shown that
f (>t)u
-
v~O
1
(l+v)2
(17)
= 0
v<O
Hence the average probability of error is given by
On the other hand, if ai, i=1,2, has the density
tJf
where f3 ~
and· where d and u2 are the standard log0
normal parameters, then it can be shown that
(20)
=
and hence that
P,=
0
u
I{-~{!~0f,(u) du.
<0
~
ft·
t
i=e+l
i ( ~) P ei(1-P e)n-i.
(21)
t
Equations (17) and (20) were evaluated numerically to obtain
values for Pe1 and those results were used in (21) to obtain
the decoded BER. Typical performance results are shown in
Figure 7, wherein BER is plotted against K', the number of
active users in each of the two cells. There are three curves
shown in Figure 7, one corresponding to Rayleigh shadow
fading and the other two corresponding to log-normal·
shadowing with the assumption that path loss from both base
stations to the mobile are equal. In all cases, the processing
gain was L = 511, and the forward error correction was
provided by the (23,12) Golay code, for which e = 3.
If we assume that, fgr satisfactory voice communications, a
decoded BER of 10· or better is required, we see that for
Rayleigh fading, K can be about 100; for log-normal fading
with u=3.16, K can be about 170, while if u = 2.0, K can
0504
This paper used a simple two ray model for path loss
prediction, and showed how the historic use of this model
fails to accurately describe propagation for emerging cellular
and microcellular communication systems. Using the model
in a new way, path loss propagation laws were found which
vary as distance to between the second and third power.
Measurements have confirmed this path loss model. Simple
expressions for computing the reuse efficiency of CDMA
cellular radio were developed and evaluated for a. variety of
propagation path loss laws and coverage distances. We foun<;l
that the frequency reuse efficiency varies in typical cells from
a high of 0.64 wfen a d4 path loss law is assumed, to a low of
0.42 when a d path loss law is used. Different spatial
distributions of the users were shown to change the
efficiency. The BER for a subscriber on the fringe of two cells
was evaluated, and the maximum number of users which can
be supported for a. reasonable performance level was
computed for different shadowing distributions.
The effects of frequency selective multipa.th and additional
cell sites were not considered in this study, and at this time
it is not known exactly how these aditional interference
sources will impact CDMA performance. However, in order
to predict real world system performance, such effects must
be quantified. They presently are a. topic of research.
ACKNOWLEDGEMENT
The authors wish to thank Morton Stern of Motorola, Inc. for
discussions about this work.,
REFERENCES
Finally, if we assume an (n,k) block code capable of
correcting all combinations of e and fewer errors is used at
the output of the demodulator, then the final decoded bit
error rate (BER) can be approximated by
P6
increase to about 200. Note that the results only consider two
base stations in order to keep the analysis tractable, so they
are probably optimistic.
However, the results do not
account for speaker activity factors. If, for example, the
active users are only transmitting, in some average sense,
50% of the time, the above values of I\ wi)l.~ouble.
[1] G.R. Cooper, R.W. Nettleton, "Cellular Mobile
Technology: The Great Multipli:er," IEEE Spectrum, June
1983, pp. 30 -37.
[2] A. Salmasi, "An Overview of Advanced Wireless
Telecommunication Systems Employing Code Division
Multiple Access, IEEE International Symposium. on Spread
Spectrum Techniques and Applications, King's College University of London, 24 September 1990.
[3] T. S Rappaport, S.Y. Seidel, R. Singh, "900 MHz
Multipa.th Propagation Measurements for U.S. Digital
Cellular Radiotelephone, IEEE Trans. VT, vo. 39, no. 2,
May 1990, pp. 132 - 139.
[4] S.· Seidel, S.' Jain, M. Lord, R. Singh, T. Rappaport,
"Path Loss and Multipath Delay Statistics in Four European
Cities for Digital European Cellular and Microcellular
Radiotelephone, IEEE Trans. VT, in review.
f5J A.J. Rustako, N. Arnitay, G. J. Owens, R.S_Roman,
'Radio Propagation Measurements at
Microwave
Frequencies for Microcellular Mobile and Personal
Communications,n 1989 IEEE International Communications
Conference, Boston, pp. 15.5.1 - 15.5.5.
404.6.5
,~
Table 1. Experimental results of wide band propagatio:
measurements in six cellular and microcellular channeh
Exponent values computed assuming 100 m free spac
reference distance.
'6] P. Harley, "Short Distance Attenuation Measurements at
·iOO MHz and 1.8 GHz using Low Antenna Heights for
•Microcells," IEEE Journal on Sel. Areas. Commun., vol. 7,
no. 1, January 1989, pp. 5-11.
.l7J
Height (m)
Maximum
M&Xim'um T-R Maximum Rmo
Antenna
M.B. Pursley, "Performance Evaluation for Phase-Coded
:;pread Spectrum Multiple-Access Communications, Part I:
System Analysis,"IEEE Trans. Comm,Aug.1977, pp. 795-799.
Excess
Delay Spread
O'(dB) Separation
n
pelay
(pa)
(km)
Spread(pa)
Hamburg
40
2.5
8.3
8.5
2.7
7.0
Stuttgart
23
2.8
9.6
6.5
5.4
5.8
Dusseldorf
88
2.1
10.8
8.5
4.0
15.9
Frankfurt (PA Bldg.)
20
3.8
7.1
1.3
2.9
12.0
6.5
8.3
18.4
Frankfurt (Bank Bldg.) 93
2.4
13.1
KronbOrg
2.4
8.5
10.0
19.6
51.3
All (100m)
2.7
ll.S
10.0
19.6
51.3
All (1 km)
3.0
8.9
10.0
19.6
51.3
50
Table 2.
Frequency Reuse Efficiency
of COMA Cellular Uplink as a !unction
of n !or two system implementations.
a.•0,1km
Fig. 1. Geometry for the two ray path loss model.
frequency reuse efficiency
d(km)
Received Power and Path Loss Expo11ent vs. T-R Separation
Relative to 1 00 m free space path
-2
n~
o
c
"c:
0
2.0
2
0.326
0.434
2.0
3
0.423
0.571
0.625
2.0
4
0.499
0.666
. '0.721
0.310
0.422
0.457
1-20
0.399
0.553
0.606
Received Power (two-roy model)
,--10
n: Path Loss Exponent
10.0
4
0.466
0.638
0.698
..
0
...:~7\r-.
0
~*~~.~~f.~~.\------------------~-10
:.:
··.\~·
8.
"'
....~
E
"'"'
3 r-:-..;...;--.-;:!:-:~.t.-.--1+.-------~.,..."'-----1-30
~
.s::
4 1--:--+.--...
..,..---+--+--------_::,...
~-~ -40
c..
c
0.471
w,-1.0
~,-1.
3
8
0
upper bound
2
2 J--;--;t:::-4,--4/-;-7\. . -f.:
t.:.: .c:_•'-~~_:_"
·..:..:..,;·.·:..:....·..,..,..,....,.-.--1-20
.3
hex case
w1•1.38
W•0.78.
10.0
8.
~
lower bound
w1-3.o
w,-o. o
10.0
~---1
-1
n
""'
.. ..
Received Power and Path Loss Exponent vs. T-R Separatiol"t
Relative to 100 m free space path
~
~
~~ -50 f~
5 r.·~~-"--~--+--f~=~9~0~0~M~H~z~----..
..
Base Ant. Ht. = 50 m
It
6 l--:---:--=--_;_--l--=..::::.:::..:::...:..::..:..:::..:....:..:.:.:_...::::.::::.:..!!._J_60
'0
1.,
Mobile Ant. Ht. = 2 m
0
7r---~------~~~~~~~~-=~~-70
..
0:
0.1
1
T-R Separation (km)
-1
~
10
Cll
Cll
.3
.s::
0
a.
c
)
Figs. 2 ~an-d 3. Path .loss and path- ~oss exponent valu~s for
typical cellular and mtcrocellular rad10 systems as functwn of
T-R separation (d) and close-in reference distance (a). Path
loss is computed from Eqn. (3) in paper.
:
.,c:
·.~
:. \f... ··""'•·,~.
11
10
U:
0
~
-10
-r
20 j
r.-;----~--------------~~~------"-"~··~"
~
~
-303
4
5
~
f = 1800 MHz
Base Ant. Ht.
= 10 m
-40
"'-., -50
6~~~~~~~~~~--~~----~
Mobile Ant. Ht.
=2m
7~--~~~~~~~~--~~----~
-60
-70
a~--~~--~~~~L---~--~~~~
-80
10
0.1
T-R Separation (km)
404.6.6
1
E
\·
""~;; ·.........
2
3
I-
~ ~
.\1:
....c
-20
Received Power (two-ray model).
n: Path Loss Exponent
.
0
8.
a '---J...--L--L--<-...i....L.~L---'---'--'--'-...L...L-'-'-Lao
'?
-2~-~
0505
\..
~
~
',>
t!l
1-
.........
-..- .._ ....
~
__
~--·
All Measurement Locations
140
n = 5 ,.·
3
130
120
co
~
.e-y
~
X
IX
X
110
E
In
In
0
....J
.r.
+J
100
"'
c..
90
.,..~
80
If
n
Fig. 6. By breaking the adjacent
cells into two parts (inner and outer
part), the impact of the distribution
of users close to, and far from, the
70
desired cell can be found easily.
1.0
0.1
10 . 0 This figure shows the geometry used
to relate the distance of adjacent cell
users to the distances of users in the
T-R Separation, [kilometers]
desired
cell.
Fig. 4.
Scatter plot of absolute path loss measured in six cellular and
microcellular ·systems. The different asymptotic values for n have been
comp~~. from a 100. m referenc~ distance using e<;ln· (5) in paper. Note;:.:·:·. ·~,.-l...: . . :______. __d,:;=..:.::::~·.:.:.........:--"'· . ·-·
~hat d ··IS the best hnear regre.sswn fit to the log distance law of Eqn. (5h-~:~~~~~~~-=~--=~::::-;-:::::·-~·- ..·- ;;/<C~::..;;,.
m· paper. Also note that at distances less than 1 km, there are several . . -~:-·:;:-:·:--,.. ~~ -:7.':·--:-=::.:·:· /'~· :~ ..... ..·.. --locations which undergo deep fades, just as in Figure 2.
·· :·:-:. -::-::=::=-~~~~:_];;·-sTf7
.
~/"''L~ :1 o!:_"fq/
·-/~ . ~2)
sigma • 11.8 dB
.....
~~--~.:£.;=. . :····~
.
.
.
.
..
.'···
.......------·----::
.
~:,_:o.··:-r~ .:::=...J........ - - - · ··-:-:-:::, • , .... " .. :· . . .
---- ·. ~::~- ~:~:-:1·~=-:~··::~-;:~·:·;:;~~~~!;
.
··- ...:;.:.;,::..
-.
...... ·-·
~
~d.!!:::'::
!._.. ·.: __ __;, •. -.
____
·-·~.:_..:..~!:;.......!..!.:...i:t:.~·~·
__::~:::~- .· ·. ::. : .. ~::..L~-:-i.:~-~... ~-~~~ :.·.-...:.:.
~----~
Fig. 5. Simple cell geometry used to analyze frequency reuse
efficiency for CDMA.
0506
404.6.7
:
. ·:----.. -····::
·--.
·-~:;"
Fig. 7. Downlink BER for a subscriber
on the fringe of two adjoining cells, as a
function of number of simultaneous
users in each cell.
-~-·"-::-:--:-