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Quality Measures for Complex Modulated
Signals Reaching for Standardization
Application Note
Introduction
The reputation of complex modulation is growing rapidly due to its successful use in optical
transmission. It is becoming increasingly adopted, especially in the core networks, due to its
superiority over traditional on-off-keying (OOK) in terms of bit transfer eficiency.
Along with these new concepts, a new set of parameters for determining the quality of complex
modulated signals and of standardized test conditions is also provided. But why should you get
used to new test parameters and install new test setups if you can avoid it? Before you invest in this
change, you will probably ask for the proof that any previously used method has severe limitations or
even that it does not work.
In some cases where a new quality parameter provides a clear advantage in both ease of use and the
cost of test, standardization will follow what is already broadly accepted and implemented.
In this application note, we analyze whether we need a new parameter to quantify complex modulated
signal quality and, if so, consider the necessary steps to make this broadly accepted and
standardized.
03 | Keysight | Quality Measures for Complex Modulated Signals Reaching for Standardization - Application Note
Do we need a new quality parameter for complex
modulated signals?
In conventional OOK we only use one dimension to code the Figure 1 shows typical parameters that are derived from an
information onto the carrier signal, represented by the eye-diagram of on-off keyed signals. In many cases, an estimate
amplitude of the light. In complex modulation we typically add of the bit error ratio (BER) is derived from the noise distribution
one more dimension on top of the amplitude -- the optical phase. during the ,1` and ,0` amplitude segments of the signal. Assuming
The quadrature phase shift keying (QPSK) modulation scheme a Gaussian noise distribution, the Q-factor can be derived, which
is a special case where information is coded only in the phase of is then directly related to the expected BER, based on statistical
the carrier signal, but the signal is still usefully represented in rules. In addition, a hit ratio of the mask is often determined as
two dimensions. (As dual polarization is more like an additional another parameter describing the quality of the signal or system.
transmission channel than a 3rd modulation parameter, we do not Performance standards specify a limiting number of allowed hits
need to consider this as a third dimension.) This two-dimensional of the mask. This mask is deined in a standard and the relevant
coding already implies an answer to the question: "Do we need a inluencing factors from measurement receiver behavior are
new quality parameter for complex modulated signals?" standardized, for example the use of a Bessel-Thompson ilter
with deined bandwidth at the input of the test instrument.
Before analyzing this in more detail, let us look at how on-off
keying signals are typically speciied and analyzed, and and how
they are at their limits, when transferring this concept to complex
modulated signals.
Figure 1. Eye diagram of a signal modulated with on-off-keying
04 | Keysight | Quality Measures for Complex Modulated Signals Reaching for Standardization - Application Note
Looking into the details of what an eye diagram represents when
applied to a complex modulated signal, we see immediately that
these are not really comparable test concepts. We will start with
a QPSK signal as used on current 100 Gbit/s transmission
systems. Figure 2 illustrates what an eye diagram of a QPSK
signal represents. The eye diagram is a projection of the signal to
the real axis or to the quadrature axis, resulting in a set of two eye
diagrams for complex modulated signals.
Q (quadrature or imaginary part)
01 11
I (in-phase or
real part)
00 10
Only I values versus time are visible
Figure 2. Eye diagram of a QPSK modulated signal
05 | Keysight | Quality Measures for Complex Modulated Signals Reaching for Standardization - Application Note
Q (quadrature or imaginary part) We can see for example that a transition from low to high in the
I-graph does not let us distinguish whether this is a symbol
transition from ,01` to ,11`, from ,01` to ,10`, from ,00' to ,11' or from
,00' to ,10', as shown in the constellation diagram. For the Q eye
01 11 we have of course the same ambiguity, leaving doubts about the
helpfulness of eye diagrams in characterizing complex modulated
signals.
I (in-phase or In on-off keying it is usual to determine the best decision level
real part) by changing the decision level in small steps and calculating
the Q factor or BER at each step. The lowest BER occurs at the
optimum decision level. Since a coherent receiver doesn't decide
00 10 based on an amplitude threshold, but on a two dimensional
search for the nearest symbol in the constellation diagram at
a distinct time, the role of the eye diagram in measuring signal
quality is also less direct.
The additional complication that we have to distinguish between
the eye diagrams of the I and Q projections requires a clear
documentation of the assignment in test.
Only Q values versus time are visible
06 | Keysight | Quality Measures for Complex Modulated Signals Reaching for Standardization - Application Note
Finally, consider the example of Figure 3, showing the result of a
special 16-QAM constellation (Reference 1). This QAM signal has
a nonrectangular distribution of the constellation points for
higher robustness against distortions along an optical link.
Looking at the projected axes of this signal makes it
immediately clear that any signal quality measure based on
eye diagram analysis would fail.
As a conclusion of the previous analysis, we cannot just keep the
test concepts we used in on-off keying without severe limitations
due to: