4500B Digital Sampling Power Analyzer for Wireless Communication Signals
Mazumder Alam
Product Marketing Manager, Boonton Electronics
Richard H. Blackwell
Former Director of Engineering, Boonton Electronics
Abstract
Digital modulation methods of cellular and other wireless communications
system present a challenge for making accurate peak power measurements.
Although there are many different implementations, the Orthogonal Frequency
Division Multiplexing (OFDM) and Spread Spectrum Modulation are the latest
technologies. Of many wireless communication systems, WCDMA (Wideband Code
Division Multiple Access) is the one which uses several modulation schemes.
Digital
modulation methods of cellular and other wireless communications system present
a challenge for making accurate peak power measurements. Although there are many
different implementations, the Orthogonal Frequency Division Multiplexing (OFDM)
and Spread Spectrum Modulation are the latest technologies. Of many wireless
communication systems, the technology associated with 3G like EVDO (Evolution
Data Optimized) or WCDMA (Wideband Code Division Multiple Access) is the one
which uses several modulation schemes. EVDO Rev A has a peak data rate of 3,000
kbps, but realistic speeds average around 600 Kbps to 1,400 Kbps for download
and 500 Kbps to 800 Kbps for upload. HSPA provides speeds of around 7001700kbps
for Download and 5001200 kbps upload. The EVDO channel has a bandwidth of 1.25
MHz with the forward link data rate up to 3.1 Mbps and the reverse link data up
to 1.8 Mbps. In EVDO Rev. A, the forward link of the system consists of a single
data channel that is divided into 1.67 ms timeslots. The transmitter has to ramp
up to the full power while remaining within a specified power/time profile. A
peak power video bandwidth of at least 1 MHz is required to assure compliance
with the profile.
Similarly, the latest technology LTE (Long Term Evolution) supports modulation
types up to 64 QAM (for both uplink and downlink) as per the specification ,
which has channel transmission bandwidth scalable from 1.25 MHz to 20 MHz and
maximum uplink and downlink speeds 50 Mbps and 100 Mbps. Many methods employed
in LTE are relatively new in cellular applications. These include OFDM, OFDMA
(Orthogonal Frequency Division Multiplexing Access), MIMO (Multiple Input
Multiple Output) and SCFDMA (Single Carrier Frequency Division Multiple Access)
modulation techniques. OFDM communication systems do not rely on increased
symbol rates in order to achieve higher data rates. OFDM systems break the
available bandwidth into many narrower subcarriers and transmit the data in
parallel streams. Each subcarrier is modulated using varying levels of
modulation, e.g. QPSK, QAM (Quadrature Amplitude Modulation) or possibly higher
orders depend on signal quality.
Average Power Measurement
The average power of an unmodulated RF carrier can be measured accurately by a
Average type power meter with a thermoelectric or diode detector. The
thermoelectric detector offers good accuracy over a dynamic range of about 50
dB. The diode detector can provide a much larger dynamic range, about 90 dB. The
average power of a modulated RF carrier which has constant envelope amplitude,
e.g. FM, can also be measured accurately using these techniques. For modulated
RF carriers with nonconstant envelope amplitude, e.g. pulse modulation, the
thermoelectric detector will still respond accurately to the average power of
the signal. The long time constant associated with thermal effects prevents this
type of detector from following the envelope at the modulation rate, and
therefore, is unable to provide any measure of instantaneous power. The
conventional Average type diode detector will also respond accurately, provided
that it is used at low power in its squarelaw response region. This usually
corresponds to a power at the diode of no more than 20 dBm or 10 µW. The higher
input power is accommodated by placing an attenuator between the input signal
and the diode. In a Average type detector the diode is loaded by a fairly large
capacitance which filters the noise and improves sensitivity. The resulting time
constant is long compared with modulation frequencies and prevents the detector
from following the instantaneous value of the envelope.
Pulse Power Measurement
Pulse power is determined traditionally by adjusting the average power reading
of a Average type power detector for the duty cycle of a modulating pulse. In
this way, a peak power measurement of moderate accuracy can be obtained from an
average power value, provided certain conditions are met. First, the modulation
must consist of constant amplitude rectangular pulses of known duty cycle
(on/off ratio). Second, the linear power range of the detector must not be
exceeded by the peak power applied. This requirement is often overlooked,
resulting in invalid readings or damage to the detector. The pulse power
measurement technique is not suitable for digital modulation systems in which
the duty cycle is not constant and pulse amplitude and shape varies.
Peak Power Measurement
What is needed for complex digital modulation is true instantaneous power
measurement with a bandwidth sufficient for the modulation format in use often
of 25 MHz or above. The Boonton
Model 4500B RF Peak Power Meter / Analyzer provides
the capability to measure peak power accurately with a dynamic range of as much
as 80 dB and a demodulated video bandwidth as large as 80 MHz (sensor
dependent). Knowledge of the modulation method or modulating signal is not
required for accurate average and peak power measurements. In simplified form
the Model 4500B peak power measuring system consists of the following:See
Figure 1.
Figure 1  Simplified view of peak power measurement system.

A Peak Power Sensor containing a dual diode detector with wide RF bandwidth
(up to 40 GHz) and a narrower video bandwidth (greater than 50 MHz), and a
precision log amplifier compatible with the video bandwidth (sensor
dependent).

A fast sample and hold amplifier, asynchronous with respect to the input
signal.

An analog to digital converter which operates at the sampling rate.

A Digital Signal Processor (DSP) for processing the samples at high speed.

A builtin, digitally controlled, precision Average power calibrator.

A host processor to control I/O interfaces all subprocesses and display
processed data.
Precision Digitally Controlled Calibrator
In order to eliminate the error associated with diode nonlinearity, a
calibration table is created for each sensor which stores the response to a
series of precision power levels covering the effective dynamic range along with
additional data. This is accomplished automatically by a precision, digitally
controlled, RF power source and control program. The resulting calibration table
is extended by interpolation to create a power entry for all possible A/D
converter values. This allows the DSP to calculate the instantaneous power of
each individual sample of the RF envelope. Average power is calculated by
summing the instantaneous power values. The nonlinear relationship between
instantaneous RF power level and diode output is resolved before any averaging
is done, thus, the averaged result is correct for any arbitrary waveform. It is
the characteristic which separates this method of power measurement from the
conventional average power method in which the output of the detector is
averaged before A/D conversion. Random power samples in time can be processed by
the DSP to provide results in any form needed by an application. This includes
peak power versus time, peak power relative to a trigger event, average power
over various time intervals, peak to average ratio, maximum peak power in a time
interval, etc.
For a stationary signal, the sum of the random samples over arbitrary, equal
length time intervals is the same, provided there is no periodic relationship
between the sampling rate and the modulating signal. In addition, there must be
a sufficient quantity of samples taken to ensure adequate coverage. The
advantage of a high sampling rate is the ease of accumulating a large number of
sample points for each reading. If the detected signal is stationary or
quasistationary in time, the waveform of the RF envelope can be reconstructed
from the random samples. In conventional pulse or linear amplitude modulation,
the RF carrier envelope and thus the detected signal correspond closely to the
modulating signal waveform. In wireless communication systems, the exact shape
of the pulsed RF envelope is critical for optimum performance. The Boonton Model
4500B is particularly suited to applications in which peak power versus time is
the primary concern.
Statistical Methods Using the Model 4500B
Digital modulation methods in which amplitude and phase modulation are combined
in a multilevel arrangement to represent a group of bit values from one or more
data streams, and multiple carrier spread spectrum systems, such as LTE, do not
have simple envelope waveforms which can be directly related to modulation
parameters. Traditional parameters such as modulation depth and modulation index
are not meaningful because the peak to average power ratio of the modulated
carrier is a complex function of the data stream content, rather than the
amplitude of the modulating signal. The resulting noiselike character of these
signals suggests a statistical approach to analysis. The Boonton
Model 4500B RF Peak Power Meter / Analyzer is
designed to extract the statistical properties of these signals in addition to
the time related properties discussed above.
Since the power of the individual random samples is known, they can be sorted
and counted by power level. For a 14bit A/D converter system there are 16384
possible power levels. If a memory array of this size is established, each
address corresponds to one of the possible power levels. With the array
initially cleared to zeroes, the value of each sample taken is interpreted as an
offset address into the array, and the count stored at that location is
incremented by one. As this process is repeated millions of times, the array
contents approaches N times the probability function for the signal, where N is
the total count of the entire array. The count at any address divided by N is
equal to the probability of occurrence of the power level represented by that
address. See
Figure 2.
Figure 2  Sample Count Array in memory.
The measurement process must keep track of the total number of samples taken in
order to scale the results properly and to estimate the statistical uncertainty,
which is inversely proportional to the square root of the number of samples. A
high degree of confidence is assured by a very large number of samples and a
long running time. A word size of 32 bits will account for at least 4.2 billion
(4.2 x 109) samples without overflowing any counter. Even at 25 M samples per
second, the maximum running time will be nearly three minutes before any
possible overflow can occur. The measurement could be allowed to run
indefinitely with a suitable decimation process, but not without loss of some
information. Unfortunately, ordinary right shifting of the data results in the
loss of the small counts which are typically the most important ones. Therefore,
this option is only acceptable when a large sample population has been acquired.
Welldefined modulation processes may show convergent results after only a few
million samples are collected and running times of only a few seconds may be
completely adequate for these applications. It is convenient for analytical
reasons to organize statistical data into one of several standard forms. The
Boonton Model 4500B displays the data both numerically and graphically on a
color LCD screen. The following symbols are used throughout the formulas: Y is a
discrete random variable with a range equal to all possible sampled values of
carrier power. y is a specific power value contained in Y.
PDF
The probability distribution function of Y. The PDF is the percentage of time
that the power is equal to a specific value, y. The percentage ranges from 0 to
100%, and the power extends over the entire dynamic range of the system. PDF
expressed as a percentage is: PDF = P(y) = 100*P[ Y=y ] where y ranges over all
values in Y, 0
ΣP(y) = 100% where y ranges over all values in Y The PDF is useful for analyzing
the nature of modulating signals. Sustained power levels such as the flat tops
of pulses or steps show up as lines. Random noise produces a Gaussian shaped
curve.
CDF
The cumulative distributions function of Y. The CDF is the probability that the
power is less than or equal to a specific value, y. The CDF is nondecreasing in
y, that is, the graph of CDF versus y cannot have negative slope. The maximum
power sample taken will lie at 100%. CDF expressed as a percentage is: CDF =
Q(y) = 100*P[Y
CCDF
It is often more convenient to use the complementary CDF, or CCDF, or 1CDF,
sometimes called the “upper tail area”. The CCDF is the probability that the
power is greater than a specific power value. CCDF is nonincreasing in y and
the maximum power sample lies at 0%. CCDF expressed as a percentage is: CCDF =
1Q(y) = 100*P[Y>y] where y ranges over all values in Y, 0
Figure 3. A CCDF with expanded time axis.
Note that the CCDF plot in Figure 3 has probability in percent on the Xaxis and
instantaneous envelope power in dBm on the Yaxis. The usual practice in texts
on statistics is to show probability on the Yaxis. This change is made so that
power always appears on the Yaxis in all instrument display modes. Keep in mind
that power is the independent variable. The probability scale in Figure 3 has
been expanded to better show the region around zero. On the Y axis at
probability 0% is the maximum peak power which occurred during the entire run.
Or, there is zero probability that a power level higher than Wmax occurred
during the run. At probability = 1% is the power level Wclp which was exceeded
only 1% of the time during the entire run. Note that this analysis does not
depend upon any particular test signal, nor upon synchronization with the
modulating signal and there is no time base involved. In fact, the analysis can
be done using actual communication system signals. Normal operation is not
disturbed by the need to inject special test signals. This type of analysis is
particularly suited to the situation in which the bit error rate (BER) or some
other error rate measure is correlated with the percentage of time that the
signal is corrupted. If known short intervals of clipping are tolerable, the
CCDF can be used to determine optimum transmitter power output. The CCDF is also
used to evaluate various modulation schemes to determine the demands that will
be made on linear amplifiers and transmitters and the sensitivity to nonlinear
behavior.
The Boonton Model 4500B provides the CCDF as well as the CDF and PDF graphs
along with power and pulse parameters for a comprehensive analysis of pulse or
spread spectrum digital modulation. On themodel
4500B, Option 10 is the RF Peak Power Analyzer in the statistical power
mode. In statistical power measurements, the instrument does not require a
trigger event from the signal to make power measurements. The signal is
continuously sampled at 25 million samples per second. The instrument can also
perform gated statistical measurements on burst or frame –oriented modulation
formats using a triggered statistical gate and 50 MHz sampling.
References
Abramowitz and Stegun, Editors,
Handbook
of Mathematical Functions, NBS Applied Mathematics Series 55, US Dept., of
Commerce, 1968.
Bic, J.C., Duponteil, D. and Imbeaux, J.C., Elements
of Digital Communication, John Wiley & Sons, 1991.
ISBN 0 471 91571 8 Lee, Y.W., Statistical
Theory of Communication, John Wiley & Sons, 1967.
GSM Base Station System Equipment Specification, GSM 11.20, European
Telecommunications Standards Institute.