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TECHNIQUE FOR MEASURING
PHASE ACCURACY AND AMPLITUDE PROFILE
OF CONTINUOUS-PHASE-MODULATED SIGNALS
Application to GMSK.3
Dr. Raymond A. Birgenheier, 8M IEEE
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ABSTRACT
A method and apparatus for determining the phase and amplitude accuracy of continuous-
phase-modulated signals is described. The modulated RF signal generated by the transmitter
unit under test is down-converted to a relatively low intermediate frequency which is filtered
and sampled by a high sampling rate analog-to-digital converter. A digital signal processor
processes the digital signals to produce measured amplitude and phase functions of the
modulated transmitter signal. From the measured values of amplitude and phase, ideal ampli-
tude and phase functions of the transmitter signal are synthesized mathematically. The
synthesized functions are compared to the measured functions to determine instantaneous
amplitude and phase errors as a function of time.
I. Introduction
A number of manufacturers manufacture and market radios for use in communications, such
as digital cellular radios and the like. Typically each manufacturer provides its own specifica-
tions for its products. Traditionally the accuracy of these specifications has been measured
using many separate, possibly indirect methods. Phase accuracy of the transmitted signal, for
example, typically is indirectly determined by measuring spurious signals, phase-noise, modula-
tion index, frequency settling time, carrier frequency and data clock frequency. Furthermore,
amplitude measurements present special problems because the amplitude versus time profile
must be synchronized to the data typically utilizing external equipment.
It has been proposed that a standardized mobile digital radio system be implemented
throughout Europe. Such a radio system would require that all components such as transmitter
and receiver, for example, be manufactured to standard specifications measured by a common
method. The Groupe Special Mobile (GSM) has proposed a measurement technique to measure
the accuracy of the modulation of the transmitted signal. In the measurement technique
described in this paper, a sampled measurement of the phase trajectory of the transmitted
signal is obtained. This measurement is compared with the mathematically computed ideal
phase trajectory to determine the phase difference between the transmitted signal and the
ideal signal. The phase difference is fitted to a linear regression line. The slope of the regression
line provides an estimate of the frequency error of the transmitter, and the regression line
subtracted from the phase difference provides an estimate of the instantaneous phase error.
The utilization of the standard method such as this would simplify the testing and manufacture
of radios. An individual manufacturer would then only need to ensure that the standardized
overall phase error specification be met rather than several interrelated specifications.
In section II of this paper, a general mathematical description of the phase and amplitude
measurement method is presented. Included are considerations of quantization effects, estima-
tion of transmitter clock phase and frequency, and detection of data. Then in section III an
implementation of the method utilizing an HP 70700A digitizer and an HP 9000-350 computer
is described. In this section, measurements of the phase and amplitude errors of a prototype
continuous-phase-modulated transmitter obtained by utilization of the method described in
this paper are presented. Finally in section IV, the summary and conclusions of the paper are
presented.
II. Mathematical Description of the Method
The Method
Referring to Figure 1, a flow chart illustrating a method for measuring the phase and frequency
errors and amplitude profile of a continuous-phase-modulated RF signal is shown. A modulated
RF signal generated by a transmitter is received and converted to digital form by a digitizer.
The digitized signal is then converted or transformed into its component in-phase and
quadrature-phase signals by a transformation circuit, and the transmitted signal amplitude
and phase functions are computed from the component signals. Utilizing a known synchroniza-
3
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tion signal which may comprise a known sequence of data bits in a preamble or midamble,
the bit sequence representing the transmitted data is synchronized to provide the transmitter
data clock and a test interval. A data detector detects the data bit sequence and provides the
transmitter data clock, test data interval and the data bit sequence to a synthesizer to synthesize
or mathematically calculate an ideal phase function corresponding to the transmitted signal.
The data detector may be implemented as a maximum likelihood sequence estimator utilizing
the Viterbi algorithm. The ideal phase function thus synthesized is subtracted from the
Figure 1
Measuring Phase, Frequency, and
Amplitude Profile of a CPM Signal
RF Signal
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measured phase function (i.e., the transmitted signal phase) to provide a phase difference. A
linear regression of the phase difference then provides the frequency error and the instaneous
phase error (as shown in Figure 16).
Figure 2
Apparatus for Measuring Phase,
Frequency, and Amplitude Profile
of CPM Signals
RF
Signal
Receiver Section
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Phase and Amplitude Measurement
Referring now to Figure 2, a conceptual block diagram of an apparatus for measuring the
phase and frequency errors and the amplitude profile of a continuous-phase-modulated RF
signal is shown. The modulated RF signal is coupled to a down conversion mixer to provide
an intermediate frequency (IF) signal. The IF signal is filtered in an analog anti-aliasing filter
and coupled to a digitizer to convert the analog IF signal to a discrete-time data sequence.
An HP 70700A digitizer manufactured by Hewlett-Packard Company may be used for this
purpose, or the digitizer may be implemented by an ADC sampling at a high rate. After
conversion to an IF the signal may be represented as:
y(t) = A(t)cos[(wo+Llw)t +