Making noise power ratio measurements with real-world signals

Story

January 14, 2020

A newly developed method to test satellite signals based on
spectral correlation can produce better test results, as the traditional noise
power ratio (NPR) test can overstate distortion during actual operation.

Noise power ratio (NPR) is one of the most common distortion
measurements for active components like amplifiers. It has its origins back in
the 1930s in testing frequency division multiplexed (FDM) analog telephone
trunks. The measurement is still in use today because it isolates the
intermodulation distortion products generated by a nonlinear component. The
distortion measured by the NPR test is in-band distortion, so it cannot be
filtered away. Because it is nonlinear, it resists correction via predistortion.

The traditional NPR measurement uses as a stimulus a noise
pedestal, which has a roughly Gaussian power profile. However, most signals
sent over satellite links have a much more conservative power profile, with
lower crest factors and narrower complementary cumulative distribution function
(CCDF) curves. As a result, the traditional NPR test (Figure 1) can overstate
the distortion that would be present during operation. To avoid this
discrepancy, a test method based on spectral correlation measures NPR using
real-world signals.

Figure 1 | NPR test signal.

In a satellite link, designers are always looking for ways to
get more power from the amplifiers. More power means a better signal-to-noise
ratio (SNR) at the ground station, making it possible to increase the data rate
of the link. Because these amplifiers already operate at or near their
nonlinear regions, however, more power also means more distortion. The NPR value
at a given power level is used as a relative measure of quality for power
amplifiers.

Traditional NPR

As shown in Figure 1, the traditional NPR test signal
consists of a wideband noise signal with a notch in the middle with little to
no power in it. This signal is generated either by a wideband noise generator
with filters to shape the pedestal and the notch or by an arbitrary waveform
generator using multitones. The idea for the test is simple: Under nonlinear
operation, the different frequency components of the wideband pedestal will mix
and create intermodulation distortion. This process will send energy to
different frequencies and create spectral regrowth both inside and outside of
the pedestal bandwidth. Some of this energy will land inside the notch; because
there was little or no energy in the notch to begin with, the distortion
contribution of the amplifier can be isolated and measured.

Figure 2 shows an example of such a test. The yellow trace is
the signal at the input to the DUT [device under test], while the green trace
is the output. The pedestal is clearly defined and the test stimulus (the
yellow trace) shows very little energy in the notch. After passing through the
amplifier (blue trace), energy is clearly evident within the notch. The ratio
of this energy to the pedestal energy is the NPR. (Figure 2.)

Figure 2 | Input and output traces from an NPR test.

The amount of distortion is highly dependent on the power of
the signal, leading to an important characteristic of the test signal: the
power profile. The test signal is a wideband signal and therefore the power of
the signal varies over time. There are many ways to relate this variance to the
average signal power, such as crest factor or peak-to-average power ratio
(PAPR). The most useful for this discussion is the CCDF curve (Figure 3), which
shows the percentage of time that a given signal exceeds a given power level.
For the green trace in Figure 3, for example, the signal clearly has a power
level that is at least 6 dB higher than the average signal power for 2% of the
time.

Remember that distortion is largely determined by the power
of the input signal. As a result, understanding the power profile of the test
signal is important to understanding the result. The traditional NPR signal is
generated by additive white Gaussian noise (AWGN) and its power profile has a
Gaussian shape. The green trace in Figure 3 shows how this looks on the CCDF
plot.

Figure 3 | CCDF curves for a traditional NPR signal (green)and a 64 QAM [quadrature amplitude modulation] signal (red).

But is this the right signal to use as a test stimulus? The
signal that is sent through the satellite may or may not have a similar power
curve. The traditional NPR test signal was originally designed to model the FDM
analog channels found in 20th-century telephone networks. These
channels, as a group, have a Gaussian power profile. Many orthogonal frequency
division multiplexing (OFDM) signals have a similar profile because – like the
old networks – the signals comprise many individual carriers. However, Single-carrier
channels have very different power profiles, however.

In many cases, these signals are chosen specifically because
their more conservative CCDF curves require less power to transmit and create
less distortion. This certainly applies to single-carrier signals like QPSK,
QAM, and APSK. It also applies to multicarrier signals. Recently, new
modulation schemes have been proposed (e.g., DFT-spread OFDM) that modify OFDM
to reduce the peak power needed. These methods hope to combine the high data
rates and spectral efficiencies of OFDM with the lower peak power and
distortion of single-carrier channels.

How different are these power profiles? Remember, it is the
power profile that impacts the distortion measurements of the system. The red
curve in Figure 3 shows the CCDF curve for a typical 64 QAM single-carrier
signal. This signal appears to have a much narrower range of power levels,
never going higher than 6 dB above the average power level. The NPR measurement
would very likely be much different if tested with this signal instead of the
noise-based signal.

The spectral correlation method

Can an NPR test be performed using a test stimulus that looks
like a real-world signal? This was one of the goals in the development of the
spectral correlation method. The key to this method lies in measuring the input
and output signals to and from the DUT at the same time and comparing the power
at each frequency across the wideband signal. For a linear system, this
comparison would give us the frequency response of the DUT. For a nonlinear
system, there are two additional factors: compression and intermodulation. The
compression is the change in the frequency response at a given frequency due to
energy being lost to harmonics. This would be present even if the signal were
made of a single tone. The other factor is the intermodulation distortion,
which is the energy present due to the intermodulation products. This term is
the source of the noise power ratio.

How can the two be separated? There is a critical distinction
between the compression and distortion terms: the compression term is
correlated to the input signal, and the distortion is not. By applying a correlation
test between the input and output signals, the compression and distortion can
be separated. This approach is called the spectral correlation method.

The measurement

This method has been implemented as the modulation distortion
application for the Keysight PNA-X Vector Network Analyzer. This application is
used to measure the distortion trace for a traditional NPR test stimulus and
for a single-carrier 64 QAM test signal as the test stimulus. Figure 4 shows
the two tests, with traditional NPR on the left and the 64 QAM signal on the
right. In both cases, an arbitrary waveform generator was used as the test
stimulus.

Figure 4a and 4b | NPR tests using the spectral correlation method.

There are two important observations to be made here: On the
left side of Figure 4, three traces are displayed. The yellow trace is the
input to the DUT, and the blue trace is the output (as in Figure 2). The third (purple)
trace is the distortion trace, as calculated by the spectral correlation
method. As shown in the figure, this floor lines up with the notch floor in the
output signal. The two measurements are interchangeable. Even in parts of the
signal where there is no notch, this method shows where the notch floor would
be. A notch in the test signal is no longer needed to measure NPR. A much wider
variety of wideband signals can therefore be used as test signals -- specifically,
test signals that more closely match the operational signals in the system
under test.

The right side of Figure 4 shows the same test on the same
amplifier, but using the 64 QAM signal as the stimulus. Because the 64 QAM
signal has a more conservative CCDF curve, the distortion is lower. In fact,
the NPR measurement using this signal is 4 dB lower than for the traditional
NPR test. In actual use, this amplifier would be much “cleaner” than the
traditional NPR test would show. With the spectral correlation method, the difference
is obvious.

Using the spectral correlation method, developers now have
the flexibility to use real-world signals for distortion testing. This new
method gives more information about the nature of the distortion and the
performance of the DUT in real-world conditions. Traditional NPR is still
useful as an apples-to-apples comparison between components, but real-world
signals are better for modeling the link as it will be used.

Donald Vanderweit joined Keysight Technologies in 2006 as an
application engineer. He supports Keysight RF and microwave test solutions
across the space industry, with a focus on link and component testing. He
received his MSEE from the University of Colorado at Boulder in 1988.

Keysight Technologies · www.keysight.com

References

Keysight Application Note: Characterizing Digitally
Modulated Signals with CCDF Curves: 5968-6875EN

J. Verspecht, A. Stav, J. Teyssier, and S. Kusano,
"Characterizing Amplifier Modulation Distortion Using a Vector Network
Analyzer," 2019 93rd ARFTG Microwave Measurement Conference (ARFTG),
Boston, MA, 2019, pp. 1-4.