Subject: [NEXTEL-1] Defining reliability & comparing model expectations

From: Marcel <[email-masked]>
Date: Wed, 04 Dec 2002 19:30:22 -0500

------- Original Message --------
From: "Terry S, Cory, P.E." <[email-masked]>
Subject:  Defining reliability & comparing model expectations

Defining Communications Reliability: Comparing Propagation Models

There appears to be some confusion regarding the application of statistics to
modeling telecommunications links...especially regarding the margin needed to
assure a threshold C/I or C/Nt is achieved. It most ofter shows up in papers
alluding only to lognormal shadowing and omitting a fading component. While
lateral multipath fading itself may not dominate link performance, a fading
component must be used to account for the performance of the digital
demodulator in the receiver. This is because the amplitude variations in the
composite signal envelope due to interference (not under target-sector power
control) emulate that of a flat fading environment in the demodulator
threshold characteristic. Once both lognormal(shadowing) and Rayleigh, or
triangular, or some other fading distribution are considered jointly, the
margin needed is fairly insensitive to the particular fading law chosen near
the 90% reliability level.

The following is an unpublished note I wrote earlier this year to refocus
thinking on the subject

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Communications reliability is the probability of communicating in a true
dynamic signal environment.and, also in a given physical environment,  based
on an estimator metric of these environmental effects.   This reliability
depends on achieving at least a minimum threshold ratio of C/I and, in the
case of CDMA, on the C/Nt available in this environment. The Nt is is "noise
equivalent interference,"  due to the unform spectral spreading of the
composite CDMA signal envelope, including external and system noise sources.
If we are actually immersed in the network environment(s) and are actually
communicating (or trying to communicate), the instanteous value of the
estimator is reduced to zero, as we are experiencing the available C/Nt in
real time. For all other situations, a margin must be provided whereby the
C/Nt is exceeded according to an appropriate probability law. For a given
value of this margin, then, we attest to the probability of instantaneously
achieving the required C/Nt.in which "instantaneous" means the minimum latency
interval of the presumably coded and interleaved digital signal data stream.

The estimator provides a measure of the observed value of C/Nt in the presence
of temporal, spatial, and observation process variations. According to the
probability law(s) being applied, an estimator of "0" (in which the threshold
C/Nt is just met) is said to achieve the mean value of the statistical
process; which is often very nearly the median or 50-percentile probability.
Greater assurance of achieving the threshold requires a margin of excess C/Nt.
This margin is a function of the standard deviation of the expected variations
to be encountered.

As the variations include those of the estimation process.typically prediction
or measurement error., for a given desired probability of achieving the
theshold C/Nt, the margin is higher for greater estimation uncertainty (or
error). This mistake is often made of excluding this process error in the
margin allowance of a wireless link budget. We often believe that measurements
have no error.or, else, emulate a true operating situation.  As there are a
multitude of "true operating situations".because of many types of vehicles and
phone locations within them. you would have to know how typical a given
situation is and the deviation from this situation over the population of
situations. Even with precise calibrated measurements using a rooftop antenna,
the azimuth radiation pattern of this rooftop antenna is not
omnidirectional.therefore, there is measurement error.

A well-known and often-applied probability law to mobile communications is
lognormal .used as a descriptor of diffraction shadowing. Another such law is
Rayleigh .used to describe fading of the composite signal envelope. The joint
lognormal-Rayleigh distribution is used in Athena.  For sigma = 0 dB (sigma =
1) the law is lognormal, with a 9 dB 90% margin; for sigma = large (> 12 dB)
the law is Rayleigh, with a 14 dB 90% margin.  In this case, the sigma is
partitioned into components of 1) prediction error, 2) spatial error, and 3)
noise. While the noise is "Nt" of the C/Nt ratio, it may also account for
envelope such as occur with the composite interfering signal; the level, of
which is not under power control. Mathematically, the reliability model has
been defined by Hufford, "A Guide to the Use of the ITS Irregular Terrain
Model in the Area Mode," NTIA 82-100, April 1982 as follows:

            s2 = (sp + sd)2 + sn2

                        where, sp = standard deviation of prediction (or
measurement) error, dB

                                    sd = spatial standard deviation per ITS in
Boulder, CO,  dB

                                    sn = standard deviation of noise envelope,
Nt,  dB

and,                             sd = 3*e(-DE*10^-5)

                                    where, DE = 130*103 + d - d1 - ds1

                                                            d     = path
length in meters

                                                            dl    =
3*103*((2*h1e)0.5 + (2*h2e)0.5) in meters

                                                            ds1 =
65*103*(100/f)0.3333 in meters

                                                            h1e, h2e are the
antenna heights in meters

                                                            f      = frequency
in Mhz

Even with perfect prediction or measurements and spectrally-flat noise having
a 2 dB sigma, the sigma for a typical PCS path is about 3.3 dB.resulting in a
10 dB required margin for 90% reliability. The corresponding unloaded
noninterfering variations and required margins are:

                                                      Modeling Reliability in
Unloaded Noninterfering Environment

                 Model(accuracy)                         C/Nt Variation
90% Reliability

            Perfect Model (0 dB sigma)               3.3  dB sigma
10.0 dB margin

            Athena   (3.8 dB rural sigma)             6.7
10.7

            Athena   (4.8 dB suburb sigma)         7.8
13.9

            Lee Model( 7 dB sigma)                     9.8
16.2

            Hata (8.6 dB sigma)                          11.3
17.8

            Drive-Test( 6 dB sigma, typ)               9.7
16.0

The estimated sigma of the Nt envelope (due to traffic in interfering
cells/sectors) is about 4.5 dB.providing that it can be predicted to a
relative accuracy of about 3 dB or less.component-to-component. For
drive-test, the 4.5 dB applies even though the drive test sigma itself is
greater than 3-4 dB (6 dB typical). For Athena in a suburban environment the
predicted interference estimate will rise from 4.5 dB to about 5.2 dB. Without
this accuracy, the sigma of the computed envelope is expected to rise above
it's true 4.5 dB estimate to about 7 dB in the case of Lee's model. With Hata,
the best-case interference sigma would be even higher..i.e.not less than the
8.5 dB prediction sigma. The best-case predicted performance, comparing
Athena, Lee's model, and Hata in an imbedded-cell interference-limited
traffic-loaded environment is

                                                        Modeling Reliability
in Traffic Loaded Interference

                 Model(accuracy)                          C/Nt Variation
90% Reliability

            Perfect Model (0 dB sigma)                5.2  dB sigma
11.2 dB margin

            Athena   (3.8 dB rural sigma)              7.8
13.7

            Athena   (4.8 dB suburb sigma)          9.1
15.1

            Lee Model( 7 dB sigma)                   11.9
18.5

            Hata (8.6 dB sigma)                          14.1
21.0

            Drive-Test( 6 dB sigma, typ)               9.7
16.0

Notice the difference in margins. Athena, with it's good absolute accuracy.but
even higher relative accuracy is only about 2.5-to-3.9 dB from perfect. With
the other models, the relative accuracy of the interference calculation
compared to a calculation of "C" alone diverges as one would suspect cue to
the n-fold convolution of interference component  sigmas involved. Lee's model
is only slightly less accurate in an interference environment than in
calculating C alone..7.3 dB more margin than perfect vs 7 dB prediction error.
Hata requires  9.8 dB more margin than perfect to assure 90% reliability.
These numbers are best case estimates.meaning that the expected performance
will be worse in the majority of cases.

The greatest errors from all models are expected in urban situations at street
level, with the high resolution clutter establishing a realistic median level
in this type environment. Whereas the spatial variations are predicted in
rural-to-suburban morphologies, the urban localized spatial variations will
add to prediction error..but may not affect the reliability results
significantly in some situations.  In situations where the target sector is
isolated.well-protected from interference, the propensity of scattering at
street-level and the use of a RAKE receiver will establish a lower bound such
that the normal reliability calculation still applies and will be a
conservative estimator of performance. The greatest errors in the reliability
calculation will come if there is significant urban interference..again at low
user heights.  For elevated users.within three or four stories of the average
building height, the reliability calculation will again be a good and usually
conservative measure of performance. In these instances, interference is
expected to be a controlling factor, enhanced from the rural-to-urban
street-level case. It is imperative that an accurate statistical calculation
be made for elevated users. Of course, street-level drive test calibration of
empirical models is impossible for elevated users; thus, the use of such
models in an urban environment will be useless in accurate planning.

                         Appendix

A note: the Nortel 3G drive resting in Calgary produced essentially 71% link
availability for the fundamental channel only (voice) for an admit margin of
4.7 dB. This result is directly predicted using the lognormal-Rayleigh law for
the "perfect" model having a 5.2 dB sigma..which applies network wide as
availability was the direct metric.

>From the classic MSI June 1995 San Diego Drive Test,  the standard error and
RMS error for line of sight paths were 8.6 and 8.8 dB respectively. The errors
over all drive points were 10.1 and 9.1 dB respectively. This is the accuracy
basis for the Hata model, using the most optimistic value for bast-case
analysis..

A note: the most suitable relative metric for interference with CDMA is the
forward-link Ec/Io. At a 3-sector boundary with only self-interference (no
traffic) the Ec/Io = -6 dB. For full traffic loading at this boundary, the
Ec/Io value is -14 dB.essentially coincident with the threshold value. At this
same boundary The 8-dB delta corresponds to C/Nt power ratios of 1/3 and 1/24
respectively, with a geometric mean of 1/8.5. The deviation from this mean is
a power ratio of 2.8, corresponding to 4.5 dB. Or, the standard deviation will
be roughly 70% of half the peak deviation (4:1 in power) which is
2.8.translating to 4.5 dB. The optimistic estimate assumes the 4.5 dB includes
the noise spectrum itself.otherwise, for a 2-dB noise sigma, the overall Nt
sigma becomes 4.9 dB.

Respectfully,

Wave Concepts Intl

Terry S. Cory, P.E.

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