IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 5, OCTOBER 2007 1901
Optimal Settings for Frequency-Selective
Measurements Used for the Exposure Assessment
Around UMTS Base Stations
Christof Olivier and Luc Martens, Member, IEEE
Abstract—To estimate the exposure around a base station,
the frequency-selective electromagnetic field measurement with a
spectrum analyzer and antenna is the most appropriate method.
In this paper, a theoretical model for the wideband code division
multiaccess signal, which is measured by a spectrum analyzer, is
extended to the measurement of the signal used in the universal
mobile telecommunications system (UMTS), where the transmit-
ted signal is subject to power control. The developed model is suc-
cessfully validated by measurements. It is shown that the presence
of power control has important implications on the achievable
accuracy of the measurements. Based on the developed model,
the optimal settings of the spectrum analyzer are proposed for the
exposure assessment around UMTS base stations.
Index Terms—Code division multiaccess (CDMA), electromag-
netic radiation, land mobile radio, spectral analysis.
I. INTRODUCTION
P
EOPLE have increasingly been worrying about the possi-
ble adverse health effects of the exposure to electromag-
netic radiation. These concerns have been intensified by the
massive deployment of base station antennas, which are nec-
essary to provide capacity and coverage for an ever-increasing
number of subscribers and a growing demand for bandwidth.
The introduction of third-generation mobile systems, which en-
able integrated mobile telephony and data services, implies the
deployment of even more base stations and will not alleviate the
problem. In answer to these questions, several authorities have
issued guidelines on the maximum permissible electromagnetic
field levels (e.g., [1]) to protect the general public from an
excessive exposure to electromagnetic radiation. In most cases,
the limits have been based on the recommendations given by
international expert organizations [2], [3]. These guidelines
have resulted in regulations on the installation and exploitation
of electromagnetic transmitters, which have been or are being
harmonized by several standardization bodies [4]–[8].
In order to check whether the present electromagnetic fields
comply with the exposure limits, electromagnetic field mea-
surements are being executed. Because the reference levels
to which the measured fields have to be compared depend
Manuscript received August 15, 2006; revised March 15, 2007. The work
of C. Olivier was supported by a Grant of the Fund for Scientific Research
Flanders (F. W. O.-Vlaanderen).
C. Olivier is with Mobistar, 1140 Brussels, Belgium (e-mail: Christof.
Olivier@telenet.be).
L. Martens is with the Department of Information Technology, Ghent Uni-
versity, 9000 Ghent, Belgium (e-mail: Luc.Martens@intec.UGent.be).
Digital Object Identifier 10.1109/TIM.2007.903617
on the frequency, and since the electromagnetic spectrum is
densely populated with a whole range of applications, the
measurements should be able to distinguish between the several
emitting sources and to determine the responsible party for each
exposure level. Since each application and/or operator have
been assigned a separate frequency band, the use of narrowband
measurements (e.g., with a spectrum analyzer) is obvious.
Although for the application to signals that use code division
multiaccess (CDMA), frequency-selective measurements do
not provide as much information as signal analyzers, where
the measured electromagnetic signal is resolved in the code
domain, the general applicability of spectrum analysis to every
modulated signal remains an important advantage. This is also
emphasized by the introduction of new measurement equip-
ment where portable spectrum analyzers are combined with
isotropic field probes. These devices enable the quick analysis
of an exposure situation, together with a characterization of the
different sources.
In [9], Olivier and Martens have discussed the measurement
issues that arise when mobile communication signals of the
second generation (i.e., global system for mobile communica-
tions or GSM) are measured. In [10], Olivier and Martens have
extended the discussion to the measurement of the wideband
CDMA (WCDMA) signal, which is used in the third-generation
systems [in particular for universal mobile telecommunications
system (UMTS)] and developed a theoretical model for the
behavior of the measured WCDMA signal for the different de-
tector modes of the spectrum analyzer. Although power control
is a very important feature of UMTS, it was not included in
the model. In this paper, the theoretical model developed in
[10] will be extended to a UMTS signal where power control is
present. The resulting model will be validated on measurements
of a generic UMTS signal (GUS). After the demonstration of
the importance of power control on the achievable accuracy of
the measurement, the optimal settings of the spectrum analyzer
for the exposure assessment of a UMTS signal will be derived
from the developed theoretical model.
II. I
NFLUENCE OF POWER CONTROL
In this paper, the theoretical model for the UMTS signal
developed in [10] is extended to also include the effect of power
control on the UMTS signal. Power control is applied to prevent
the near–far problem of CDMA, where a mobile located near
the base station can shout down a mobile that is far away
0018-9456/$25.00 © 2007 IEEE
1902 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 5, OCTOBER 2007
Fig. 1. Low-pass model for the UMTS signal with power control.
due to the higher path loss to which the latter is subject.
To overcome this situation, the transmit power of the mobile
station is adapted with a rate of 1500 times/s (corresponding
to a power control period of T
PC
=0.67 ms), which is based
on the quality perceived at the base station receiver. In the
downlink, it is used to deliver some more power to mobiles
located at the cell edge, which experience a higher interference
from the neighboring cells. The power control of UMTS can
even compensate the Rayleigh fading effect for slowly mov-
ing mobiles. In UMTS, the transmit power is adapted every
0.67 ms with a step within the range of 0.5–3 dB. Even in
the case where there is no need to change the transmit power,
the power is continuously augmented and diminished with an
elementary power step.
In Fig. 1, the low-pass representation for the UMTS sig-
nal with power control is given, which has been based on
the representation developed in [10] for the WCDMA signal
without power control. The UMTS signal is constructed from
a number of independent spreading channels, and for each
spreading channel j, a random chip stream is generated for
both the in-phase (c
(j)
I,n
) and quadrature branch (c
(j)
Q,n
) of the
signal at a rate of 3.84 MHz. The value of the chips is modeled
to be equally probable between {−1, 1}; it is assumed that
subsequent chips or chips from different spreading channels
are mutually independent. The in-phase and quadrature chips
of each subchannel are then multiplied with their respective
channel gain g
j
and summed together. The combined symbol is
then sent through the pulse-shaping filter, which is a root-raised
cosine filter with a roll-off factor of 0.22. Next, the in-phase
and quadrature branches are combined into a complex low-pass
signal. Finally, the signal is multiplied with the power control
gain G
PC
, which changes at a rate of 1500 Hz. The resulting
signal r
PC
(t) is then the low-pass representation of the UMTS
signal with power control. A more extensive description of the
air interface of the UMTS system can be found in [11].
In the following, the expressions for the mean and standard
deviation of the measured signal will be elaborated for the
different detector modes (sample, root mean square (rms) and
positive peak) of the spectrum analyzer. The signal is assumed
to have a constant average power level over the long term but,
on the other hand, to be subject to continuous power control.
This means that the signal will subsequently switch over from
a “high” to a “low” state and vice versa, which is modeled
by assuming that, in the high state, the power control gain
G
PC
equals to 1, and that, in the low state, the power control
attenuates the signal with a factor G
PC
= α<1 (e.g., for a step
of 3 dB, this corresponds to α =1/
√
2).
A. Sample Detector
If several measured samples can be considered as indepen-
dent (this is the case if the sample period is not a multiple
of 2T
PC
, and a sufficient number of samples are taken), the
probability that the signal is in the “high” or “low” state will
be equal to 1/2. The probability distribution function (pdf)
f
|S|
PC
(s) of the signal with power control, which is measured
by the sample detector S
PC
, can then be written as
f
|S|
PC
(s)=Pr[s<|S|
PC
≤ s + ds]
=
1
2
f
|S|
(s)+
1
2
f
|S|
s
α
1
α
(1)
where f
|S|
(s) denotes the pdf of the signal measured with
the sample detector if no power control was present. In [10],
it appears that this distribution is approximately a Rayleigh
distribution. The mean and standard deviation can then easily
be calculated as
µ
smp,PC
=
1+α
2
µ
smp
(2)
and
σ
2
smp,PC
=
1+α
2
2
σ
2
smp
+
(1 − α)
2
2
µ
2
smp
(3)
where µ
smp
and σ
smp
are, respectively, the mean and the
standard deviation of the signal measured with the sample
detector if there would have been no power control. It is clear
that in the case with power control, the standard deviation on
the sample signal will be much larger, which is reflected by
the second term of the standard variation. If the sample time
would equal an even number of power control periods, only one
state of the signal would be measured, which leads to an under-
or overestimation of the actual power. If the sample period is
chosen as an odd number of power control periods, both states
will definitively be measured.
B. RMS Detector
First, the influence of power control on the mean-square
(MS) signal will be examined. Assume that, during the mea-
surement, the signal occurred during a period T
L
in the low
OLIVIER AND MARTENS: MEASUREMENTS USED FOR THE EXPOSURE ASSESSMENT AROUND UMTS BASE STATIONS 1903
state, and for the rest of the measuring period, T
H
= T
S
− T
L
in the high state. The measured MS signal will then be given by
S
MS,PC
(T
S
)=
T
L
T
S
S
MS,L
(T
L
)+
T
H
T
S
S
MS,H
(T
H
) (4)
where S
MS,L
(T
L
) and S
MS,H
(T
H
) are the random variables
describing the MS value of the signal when it is in the low and
high states, respectively. If it is assumed that both random vari-
ables are independent (which is acceptable if the inverse of the
resolution bandwidth (RBW) of the spectrum analyzer is small
compared to the power control period T
PC
), the characteristic
function of the measured MS level, given the period that the
signal is in the low state, is
Ψ
MS,PC|T
L
(u|T
L
)
= E [exp (uS
MS,PC
) |T
L
] (5)
=Ψ
MS,H
T
S
− T
L
T
S
u|T
L
· Ψ
MS,L
T
L
T
S
u|T
L
(6)
=exp
T
S
− T
L
T
S
µ
H
u
× exp
−σ
2
MS,H
(T
S
− T
L
)
(T
S
− T
L
)
2
T
2
S
u
2
× exp
T
L
T
S
α
2
µ
H
u
exp
−α
4
σ
2
MS,H
(T
L
)
T
2
L
T
2
S
u
2
(7)
where µ
H
L
and σ
H
L
denote the mean and standard deviation of
the MS level of the signal when it is in either the high or the
low state. To obtain (7), the second-order approximation of the
distribution of the measured MS level of a WCDMA signal
by a Gaussian distribution has been used [10], together with
the relationships µ
L
= α
2
µ
H
and σ
L
= α
2
σ
H
. Thus, (7) is the
characteristic function of a normal distribution with mean and
standard deviation given by
µ
MS,PC|T
L
(t
L
)=µ
MS
1+(α
2
− 1)
t
L
T
S
(8)
and
σ
2
MS,PC|T
L
(t
L
)=σ
2
MS
1+(α
4
− 1)
t
L
T
S
. (9)
The mean and standard deviation of the measured MS level can
be calculated if the distribution of T
L
, which is the period that
the signal is in a low state, is known. Given a measuring period
T
S
, the signal will approximately be in the low state during a
period NT
PC
, where 2N is the even number of power control
periods closest to the measuring period
N =
T
S
2T
PC
. (10)
The operator [ · ] denotes the rounding to the closest integer.
The exact length of the low period T
L
will depend on the start
time of the measuring period, which is assumed to be uniformly
Fig. 2. Different scenarios for the beginning of the measuring periods. (1)
R
S
is completely located in the high state [T
H
=(1/2)(T
S
+ R
S
), T
L
=
(1/2)(T
S
− R
S
)]. (2) and (4) The remaining interval R
S
comprises both
a high period and a low period (T
H
= T
S
− t
L
,T
L
= t
L
). (3) The signal
is during the remainder period R
S
continuously in the low state [T
H
=
(1/2)(T
S
− R
S
),T
H
=(1/2)(T
S
+ R
S
)].
distributed along the high and low states of the signal (i.e., an
interval with length 2T
PC
).
If the measuring period is written as T
S
=2NT
PC
+ R
S
, and
the closest even number of power control periods is smaller
than T
S
, the remainder part R
S
will be positive and smaller
than T
PC
. As it is indicated in Fig. 2, four situations can be
distinguished.
1) The remaining part of the measurement period R
S
is
completely located in the high state of the signal. This
situation has a probability of (T
PC
− R
S
)/(2T
PC
), which
is the ratio of the shaded part of the interval to the
double power control period. In this case, T
L
will be equal
to NT
PC
.
2) The remaining period R
S
starts during the high state of
the signal and ends in the low state. The part of the
measuring period where the signal is in the low state
varies between NT
PC
and NT
PC
+ R
S
.
3) The state of the signal during the entire remaining period
is low; therefore, T
L
will be equal to NT
PC
+ R
S
with a
probability (T
PC
− R
S
)/(2T
PC
).
4) The period R
S
starts during the low state and ends in
the high state of the signal. This situation is completely
analogous to the second case.
To summarize, the pdf of T
L
is given by
Pr
T
L
=
T
S
− R
S
2
=
T
PC
− R
S
2T
PC
Case (1) (11a)
Pr [t
L
<T
L
≤ t
L
+ dt
L
]
=
1
T
PC
dt
L
,T
L
∈
T
S
− R
S
2
,
T
S
+ R
S
2
Case (2) and (4) (11b)
Pr
T
L
=
T
S
+ R
S
2
=
T
PC
− R
S
2T
PC
Case (3). (11c)
If the closest even number of power control periods is
larger than the measuring period T
S
, this period can be written
as T
S
=2NT
PC
− R
S
, where 0 ≤ R
S
<T
PC
. Following an
1904 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 5, OCTOBER 2007
analogous argumentation as above, it can be shown that the
distribution of T
L
is, in this case, also given by (11). Therefore,
by defining R
S
as
R
S
= |T
S
− 2T
PC
N| (12)
and with N defined by (10), (11) provides a general distribution
of the part of the measuring period that the signal was in a
low state.
Knowing this distribution, the mean and standard deviation
of the measured MS signal for the signal with power control
can easily be derived from (8), (9), and (11) as
µ
MS,PC
=
1+α
2
2
µ
MS
(13)
σ
MS,PC
=
1+α
4
2
σ
2
MS
+
(1 − α
2
)
2
4
×
1 −
2
3
R
S
T
PC
R
S
T
S
2
µ
2
MS
. (14)
The standard deviation shows an important dependence on the
length of the measuring interval. It is also clear that the MS
signal will show minimal variation whenever the measuring
period is an even number of power control intervals, since, in
that case, the signal is during an exactly equal portion of the
measuring time in the high and low states, respectively.
The pdf of the measured rms signal of a WCDMA signal
with power control can be derived directly by integrating the
dependence of the pdf on the low period t
L
as
f
RMS,PC
(r)=
1
2
(T
S
+R
S
)
1
2
(T
S
−R
S
)
f
T
L
(t
L
)
2
π
r
σ
MS,PC|T
L
(t
L
)
×exp
−
r
2
− µ
MS,PC|T
L
(t
L
)
2
2σ
MS,PC|T
L
(t
L
)
dt
L
(15)
where µ
MS,PC|T
L
(t
L
) and σ
MS,PC|T
L
(t
L
) are the mean and
standard deviation, respectively, of the measured MS signal,
given the low period t
L
, which are defined by (8) and (9);
f
T
L
(t
L
) denotes the pdf of the part of the measuring period
where the signal is low and is defined by (11). This distribution
can numerically be calculated, from which the mean and stan-
dard deviation of the rms signal can also be derived. To obtain
(15), the fact that the MS distribution can be approximated by a
Gaussian function (7) and that the rms distribution is related
to the pdf of the MS signal by f
RMS
(r)=2rf
MS
(r
2
) has
been used.
To verify the model developed in [10], the predicted results
have been compared to measurements of a GUS, as described in
[12]. The GUS has been developed for biological experiments,
and it mimics the worst-case power behavior of the UMTS
signal. The GUS signal generator has been chosen to validate
the theoretical model because it produces a repetitive signal
while representing the characteristics of a realistic UMTS sig-
nal (spread spectrum through CDMA, power control, config-
ured according to the specifications). To model the effects of
TABLE I
C
OMPARISON BETWEEN THE MEASURED AND PREDICTED MEAN RMS
V
ALUES AS A FUNCTION OF THE RBW FOR A MEASUREMENT
PERIOD T
S
OF 1.3 ms
power control on the signal, the GUS signal generator produces
during one period (approximately 45 s) a signal with a constant
average level, while during the next period, the power of the
generated signal is continuously adapted to mimic strong fading
conditions. For the measurements considered here, the GUS
signal was only measured in the period where the (average)
transmitted power was kept constant. For the GUS signal, this
means that the power is continuously adapted with steps ±3dB
(to represent a worst case scenario). It should also be mentioned
that the power of the GUS signal showed a small slowly
changing variation of 0.15 dB.
As it appears from (13), the expected MS value will show
no dependence on the length of the measuring period. The
expected rms value will neither show a significant dependence
on the chosen measurement time. In Table I, the comparison
is made up of the mean rms levels that are measured on
the GUS signal and the mean rms levels that are predicted
by the theoretical model when the measurement period T
S
is
chosen as 1.3 ms. There is a good agreement between the pre-
dicted and measured mean rms values, except for the RBW of
5 MHz, where the theoretical model is no longer valid. Indeed,
in [10], it was assumed that the resolution filter was located
entirely within the flat frequency part of the WCDMA pulse-
shaping filter, and this assumption is no longer valid for a RBW
of 5 MHz, as illustrated in Fig. 3. Because, in the theoretical
model, it is assumed that the UMTS signal has a constant
power density over the entire width of the resolution filter, the
predicted levels for the 5-MHz filter will be higher than the
actual measured levels.
The standard deviation on the measured rms level, in contrast
with its mean value, will depend on the length of the measuring
period, as it is shown in Fig. 4 for the measured rms level of the
GUS signal. The comparison is also made between the standard
deviation on the measured rms levels of the GUS signal and the
standard deviation predicted through (15). As could be expected
from (14), the standard deviation is smallest if the measuring
period contains an even number of power control periods. If the
measuring period is an odd number of power control periods,
the standard deviation shows a local maximum. Except for the
large RBW of 5 MHz, the agreement between simulations and
measurements is excellent. For 5 MHz, the deviation is due to
the false assumption that the resolution filter of the spectrum
OLIVIER AND MARTENS: MEASUREMENTS USED FOR THE EXPOSURE ASSESSMENT AROUND UMTS BASE STATIONS 1905
Fig. 3. Approximation of the 5-MHz wide UMTS signal by a flat spectrum
signal. The 5-MHz wide resolution filter is given as a reference.
analyzer is located completely within the flat frequency part
of the WCDMA pulse-shaping filter. It is also shown that,
for measuring periods T
S
< 2T
PC
, the standard deviation on
the rms value is mainly caused by the power variation of the
measured signal. For the small RBW of 10 kHz, the effect of
the power control on the standard deviation is less obvious since
the relative standard deviation inherent to the use of a small
resolution filter is much larger. In Fig. 4, it also appears that the
standard deviation of the rms measurement decreases with the
increasing measuring period, and if the effect of power control
can be neglected, the standard deviation decreases following
the law 1/
√
T
S
. In the model, the small slowly changing power
variation of the GUS signal has also be included and was sup-
posed uniformly distributed. The variation of the power causes
the decreasing trend of the standard deviation to deflect at a
certain level of standard deviation, since there remains a mini-
mum standard deviation due to this slow power variation of the
GUS signal.
C. Positive-Peak Detector
Given the part of the measuring period T
S
where the signal
is low T
L
, the cumulative distribution derived in [10] can be
extended for power control to
F
M,PC|T
L
(m|t
L
)
=Pr
max
0≤t<t
L
α|s(t)| <m
· Pr
max
0≤t<T
S
−t
L
|s(t)| <m
(16)
=
1 −
¯ν(m/α)
¯ν(0)
¯ν(0)t
L
·
1 −
¯ν(m)
¯ν(0)
¯ν(0)(T
S
−t
L
)
(17)
where ¯ν(m) denotes the average number of maxima within
a period of σ
t
, lying above the level m, where levels are
normalized to the square root of the expected MS level [10].
The pdf of the part of the measuring period that the signal is
Fig. 4. Comparison between the standard deviation on the measured rms
signal (indicated with markers) of the GUS signal and the standard deviation
calculated from the pdf (15) (indicated with lines) and its dependence on the
duration of the measurement period T
S
. The standard deviation is indicated for
different RBWs (10 kHz, 100 kHz, 500 kHz, 1 MHz, and 5 MHz).
low T
L
is given by (11). Given this distribution, the general
cumulative distribution of the measured positive-peak signal
with power control can be calculated as
F
M,PC
(m)
=
1
2
(T
S
+R
S
)
1
2
(T
S
−R
S
)
f
T
L
(t
L
)F
M,PC|T
L
(m|t
L
)dt
L
(18)
=
T
PC
−R
S
2T
PC
×
1−
¯ν(m/α)
¯ν(0)
¯ν(0)
T
S
+R
S
2
1−
¯ν(m)
¯ν(0)
¯ν(0)
T
S
−R
S
2
+
1−
¯ν(m/α)
¯ν(0)
¯ν(0)
T
S
−R
S
2
1−
¯ν(m)
¯ν(0)
¯ν(0)
T
S
+R
S
2
+
1
¯ν(0)T
PC
ln
¯ν(0)−¯ν(m/α)
¯ν(0)−¯ν(m)
×
1−
¯ν(m/α)
¯ν(0)
¯ν(0)
T
S
+R
S
2
1−
¯ν(m)
¯ν(0)
¯ν(0)
T
S
−R
S
2
−
1−
¯ν(m/α)
¯ν(0)
¯ν(0)
T
S
−R
S
2
1−
¯ν(m)
¯ν(0)
¯ν(0)
T
S
+R
S
2
.
(19)
Once the cumulative distribution function (cdf) of the signal
with power control is known, the pdf can be easily numerically
derived from (19).
![Fig. 2. Different scenarios for the beginning of the measuring periods. (1) RS is completely located in the high state [TH = (1/2)(TS +RS), TL = (1/2)(TS −RS)]. (2) and (4) The remaining interval RS comprises both a high period and a low period (TH = TS − tL, TL = tL). (3) The signal is during the remainder period RS continuously in the low state [TH = (1/2)(TS −RS), TH = (1/2)(TS +RS)].](/figures/fig-2-different-scenarios-for-the-beginning-of-the-measuring-uxvvprcm.webp)