Making noise power ratio measurements with real-world signals
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.
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.
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.)
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.
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.
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.
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.
Keysight Technologies · www.keysight.com
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.