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5965-2898E


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                                                           Agilent PN 89400-14
                                                           Using Error Vector Magnitude
                                                           Measurements to Analyze and
                                                           Troubleshoot Vector-Modulated
                                                           Signals
                                                           Product Note




Error vector magnitude (EVM) measurements                  Vector signal analyzers such as the Agilent 89400
can provide a great deal of insight into the per-          perform the time, frequency, and modulation domain
                                                           analyses that provide these insights. Because they
formance of digitally modulated signals. With
                                                           process signals in full vector (magnitude and phase)
proper use, EVM and related measurements                   form, they easily accommodate the complex modu-
can pinpoint exactly the type of degradations              lation formats used for digital RF communications.
present in a signal and can even help identify             Perhaps most importantly, these analyzers contribute
their sources. This note reviews the basics of             a relatively new type of measurement called "error
EVM measurements on the Agilent Technologies               vector magnitude," or EVM.
89400 vector signal analyzers, and outlines a
                                                           Primarily a measure of signal quality, EVM pro-
general procedure that may be used to methodi-             vides both a simple, quantitative figure-of-merit
cally track down even the most obscure signal              for a digitally modulated signal, and a far-reaching
problems.                                                  methodology for uncovering and attacking the
                                                           underlying causes of signal impairments and dis-
The diverse technologies that comprise today's dig-        tortion. EVM measurements are growing rapidly
ital RF communications systems share in common             in acceptance, having already been written into
one main goal: placing digital bit-streams onto RF         such important system standards as GSM1, NADC 2,
carriers and then recovering them with accuracy,           and PHS 3, and they are poised to appear in several
reliability, and efficiency. Achieving this goal demands   upcoming standards, including those for digital
engineering time and expertise, coupled with keen          video transmission. This note defines error vector
insights into RF system performance.                       magnitude and related measurements, discusses
                                                           how they are implemented, and explains how they
                                                           are practically applied in digital RF communica-
                                                           tions design.



1. Global System for Mobile Communications
2. North American Digital Cellular
3. Personal Handyphone System
Understanding error vector magnitude                      Figure 1 defines EVM and several related terms.
EVM defined                                               As shown, EVM is the scalar distance between
Recall first the basics of vector modulation: digital     the two phasor end points (the magnitude of the
bits are transferred onto an RF carrier by varying        difference vector). Expressed another way, it is
the carrier's magnitude and phase such that, at           the residual noise and distortion remaining after
each data clock transition, the carrier occupies any      an ideal version of the signal has been stripped
one of several specific locations on the I versus Q       away. By convention, EVM is reported as a percent-
plane. Each location encodes a specific data sym-         age of the peak signal level, usually defined by
bol, which consists of one or more data bits. A con-      the constellation's corner states. While the error
stellation diagram shows the valid locations (for         vector has a phase value associated with it, this
example, the magnitude and phase relative to the          angle generally turns out to be random, because it
carrier) for all permitted symbols, of which there        is a function of both the error itself (which may or
must be 2n, given n data bits transmitted per sym-        may not be random) and the position of the data
bol. Thus, to demodulate the incoming data, one           symbol on the constellation (which, for all practi-
must accurately determine the exact magnitude and         cal purposes, is random). A more useful angle is
phase of the received signal for each clock transition.   measured between the actual and ideal phasors
                                                          (I-Q phase error), which will be shown later to
The layout of the constellation diagram and its           contain information useful in troubleshooting
ideal symbol locations is determined generically          signal problems. Likewise, I-Q magnitude error
by the modulation format chosen (BPSK, 16QAM,             shows the magnitude difference between the
/4DQPSK, etc.). The trajectory taken by the signal        actual and ideal signals.
from one symbol location to another is a function
of the specific system implementation, but is readily          Magnitude Error (IQ error mag)
                                                          Q
calculated nonetheless.
                                                                                                            Error Vector
At any moment in time, the signal's magnitude
and phase can be measured. These values define                Measured
the actual or "measured" phasor. At the same time,            Signal
a corresponding ideal or "reference" phasor can
be calculated, given knowledge of the transmitted
data stream, the symbol clock timing, baseband
filtering parameters, and so forth. The differences
between these two phasors form the basis for the
EVM measurements discussed in this note.                                                        Ideal (Reference) Signal


                                                                                   Phase Error (IQ error phase)
                                                                                                                           I
                                                          Figure 1. Error vector magnitude (EVM) and related
                                                          quantities




2
Making EVM measurements                                   Step 3. Complex comparison
The sequence of steps that comprise an EVM                Taking the calculated reference waveform and
measurement are illustrated in Figure 2. While the        the actual incoming waveform (both now existing
Agilent 89400 Vector Signal Analyzers perform             as blocks of digital samples), the two need only
these steps automatically, it is still useful to under-   be subtracted to obtain the error vector values.
stand the basic process, which will aid in setting        This is only slightly complicated by the fact that
up and optimizing the measurements. Practical             both waveforms are complex, consisting of I and Q
steps and hints for making these measurements             waveforms. Fortunately, the 89400's DSP engine
are provided in the Appendix, "Ten Steps to a             has sufficient power to handle this vector subtrac-
Perfect Digital Demodulation Measurement."                tion and provide the desired measurement data.

Step 1. Precision demodulation                            A final note
Following analog-to-digital conversion of the             The analyzer's ADC samples the incoming signal
incoming signal, a DSP1 based demodulator recov-          asynchronously, so it will generally not provide
ers the transmitted bitstream. This task includes         actual measured data points at the exact symbol
everything from carrier and data symbol clock             times. However, a special resampling algorithm,
locking to baseband filtering. The 89400's flexible       applied to the incoming ADC samples, creates an
demodulator can demodulate signal formats rang-           entirely new, accurate set of "virtual samples,"
ing from BPSK to 256QAM, at symbol rates from             whose rate and timing are precisely in sync with
hundreds to several megahertz, yet can be config-         the received symbols. (This is easily seen on the
ured for the most common signal types with a              89400 by observing the time-sample spacings of
single menu selection.                                    an input waveform, first in standard vector mode,
                                                          and then in digital demodulation mode.)
Step 2. Regenerating the reference waveform
The recovered data bits are next used to create
the ideal reference version of the input signal. This
is again accomplished digitally with powerful DSP
calculating a waveform that is both completely
noise-free and highly accurate.




Figure 2. Block diagram of the EVM measurement process



                                                          1. Digital Signal Processing
                                                                                                                3
                        EVM Troubleshooting Tree

                                         Measurement 1
                                       Phase vs. Mag Error



                       phase error >> mag error           phase error  mag error


                         Measurement 2                        Measurement 3
                     IQ Error Phase vs.Time                    Constellation
                      waveshapes                                     asymmetric
    Residual PM                                                                           I-Q Imbalance
                                           symmetrical

                         noise                                          tilted             Quadrature
    Phase Noise
                                                                                             Error
                                                             Measurement 4
                                                              EVM vs. Time
                                                                     error peaks          Amplitude
                                                                                         Non-Linearity
                                         uniform noise

                                                                 (setup problem clues)
                                                                                         Setup Problems

                                                             Measurement 5
                                                             Error Spectrum
                                                                   discrete signals
                                                                                           Spurious
                                             flat noise

                                                                     sloping noise         Adj. Chan.
                                                                                          Interference
                                                              Measurement 6
                                                              Freq Response
                                                                   distorted shape
                                                                                         Filter Distortion


                                                                         flat
                                                                                         SNR Problems

Figure 3. Flow chart for analyzing vector modulated signals with EVM measurements




4
Troubleshooting with error vector measurements               Setup: from digital demodulation mode, select
Measurements of error vector magnitude and related
quantities can, when properly applied, provide               MEAS DATA           Error Vector: Time
insight into the quality of a digitally modulated sig-       DATA FORMAT         Data Table
nal. They can also pinpoint the causes of any prob-
lems uncovered during the testing process. This              Observe: When the average phase error (in degrees) is
section proposes a general sequence for examining            larger than the average magnitude error (in percent)
a signal with EVM techniques, and for interpreting           by a factor of about five or more, this indicates that
the results obtained.                                        some sort of unwanted phase modulation is the
                                                             dominant error mode. Proceed to measurement 2
Note: The following sections are not intended as             to look for noise, spurs, or cross-coupling problems
step-by-step procedures, but rather as general guide-        in the frequency reference, phase-locked loops, or
lines for those who are already familiar with basic          other frequency-generating stages. Residual AM is
operation of the 89400. For additional information,          evidenced by magnitude errors that are significantly
consult the instrument's on-screen Help facility,            larger than the phase angle errors.
the appendix to this note, or the references in the
bibliography.                                                In many cases, the magnitude and phase errors
                                                             will be roughly equal. This indicates a broad cate-
                                                             gory of other potential problems, which will be
Measurement 1
                                                             further isolated in measurements 3 through 6.
Magnitude vs. phase error
Description: Different error mechanisms will affect
                                                             Measurement tip
a signal in different ways, perhaps in magnitude
                                                             1. The error values given in the data table summary
only, phase only, or both simultaneously. Knowing
                                                                are the RMS averages of the error at each displayed
the relative amounts of each type of error can quickly
                                                                symbol point (except GSM or MSK type I, which
confirm or rule out certain types of problems. Thus,
                                                                also include the intersymbol errors).
the first diagnostic step is to resolve EVM into its
magnitude and phase error components (see Figure 1)
and compare their relative sizes.

           16QAM Meas Time 1
     1.5


I - Eye


    -1.5
           -1 Sym                                           1 Sym
EVM        = 248.7475 m%rms      732.2379    m% pk at symbol 73
Mag Error = 166.8398 m%rms       -729.4476   m% pk at symbol 73
Phase Error = 251.9865 mdeg      1.043872    deg pk at symbol 168
Freq Error = -384.55 Hz
IQ Offset = -67.543 dB                 SNR = 40.58 dB

      0    1110011010    0110011100   0110011010    0100101001
     40    0010100110    1000010101   0010010001    0110011110
     80    1001101101    0110011001   1010101011    0110111010
    120    1000101111    1101011001   1001011010    1000011001

Figure 4. Data table (lower display) showing roughly similar amounts
of magnitude and phase error. Phase errors much larger than magnitude
errors would indicate possible phase noise or incidental PM problems

                                                                                                                   5
Measurement 2                                           Examples:
IQ phase error vs. time
Description: Phase error is the instantaneous angle
difference between the measured signal and the
ideal reference signal. When viewed as a function
of time (or symbol), it shows the modulating wave-
form of any residual or interfering PM signal.

Setup: from digital demodulation mode, select

MEAS DATA           IQ Error: Phase
DATA FORMAT         Phase

Observe: Sinewaves or other regular waveforms
indicate an interfering signal. Uniform noise is a
sign of some form of phase noise (random jitter,
residual PM/FM, and so forth).
                                                        Figure 5. Incidental (inband) PM sinewave is clearly
Measurement tips                                        visible--even at only 3 degrees pk-pk.
1. Be careful not to confuse IQ Phase Error with
   Error Vector Phase, which is on the same menu.
2. The X-axis is scaled in symbols. To calculate
   absolute time, divide by the symbol rate.
3. For more detail, expand the waveform by reduc-
   ing result length or by using the X-scale markers.
4. The practical limit for waveform displays is from
   dc to approximately (symbol rate)/2.
5. To precisely determine the frequency of a phase
   jitter spur, create and display a user-defined
   math function FFT(PHASEERROR). For best
   frequency resolution in the resulting spectrum,
   reduce points/symbol or increase result length.




                                                        Figure 6. Phase noise appears random in the time domain.




6
Measurement 3                                              Examples:
Constellation diagram
Description: This is a common graphical analysis
technique utilizing a polar plot to display a vector-
modulated signal's magnitude and phase relative
to the carrier, as a function of time or symbol. The
phasor values at the symbol clock times are partic-
ularly important, and are highlighted with a dot.
In order to accomplish this, a constellation analyzer
must know the precise carrier and symbol clock
frequencies and phases, either through an external
input (traditional constellation displays) or through
automatic locking (Agilent 89400).

Setup: from digital demodulation mode, select
                                                           Figure 7. Vector display shows signal path (including
MEAS DATA            IQ Measured Time                      peaks) between symbols.
DATA FORMAT          Polar: Constellation
                     (dots only)
or
                     Polar: Vector
                     (dots plus intersymbol
                     paths)

Observe: A perfect signal will have a uniform con-
stellation that is perfectly symmetric about the ori-
gin. I-Q imbalance is indicated when the constella-
tion is not "square," that is when the Q-axis height
does not equal the I-axis width. Quadrature error
is seen in any "tilt" to the constellation.

Measurement tips                                           Figure 8. Constellation display shows symbol points only,
1. Result length (number of symbols) determines            revealing problems such as compression (shown here).
   how many dots will appear on the constellation.
   Increase it to populate the constellation states        3. To view the spreading of symbol dots more
   more completely.                                           closely, move the marker to any desired state,
2. Points/symbol determines how much detail is                press mkr 



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