Repeatable Characterization of Distortion Caused by Nonlinearities in Wideband Communication Systems
By Steve Pettis and Pete Thysell, Agilent Technologies

Advances in digital modulation and signal processing are enabling commercial and military systems to transmit data at ever-higher rates. However, with more data being transmitted at wider bandwidths, signal quality is more likely than ever to be affected by distortion, especially distortion caused by system nonlinearity.

When characterizing nonlinearities in wide-bandwidth systems, a measurement called noise power ratio (NPR) is a valuable tool that provides insight into how the system may affect data quality. NPR measurements can be implemented using analog or digital methods, but the digital method has two key advantages. Foremost, it provides accurate, repeatable characterization of nonlinearities. It also reduces test time and therefore lowers the cost of test.

One key to successful, repeatable NPR measurements is the use of a deterministic stimulus that resembles the noise-like nature of actual wideband signals. This type of signal will stress the communication channel in ways that resemble real-world conditions, revealing nonlinear behavior and helping the designer ensure proper operation in actual use. Creating stimulus signals that ensure repeatable test results requires an arbitrary waveform generator (AWG) that provides precise control over a few key attributes of the stimulus.

Examining Types of Distortion
In today’s communication systems, two types of nonlinearities are major causes of distortion. One is nonlinearity of the amplitude response versus the level of the input signal. The other is non-uniformity of the phase response versus the frequency of the input signal.

In a wideband system, those effects can induce four common types of distortion: harmonic distortion, cross-modulation distortion, phase distortion and intermodulation distortion (IMD). Although each has a different source, all will distort the input signal. This results in harmonic and non-harmonic spurious outputs from a wideband circuit, device or system.

When a wideband signal (or a large number of narrowband signals) is present—as in wideband or multi-channel systems—these mechanisms contribute to IMD. Because the IMD of a noise-like signal reduces signal-to-noise ratio and degrades overall system bit error ratio (BER) performance, it is a primary concern in wideband systems. The noise-like nature of wideband data signals compounds the problem because the resulting noise-like artifacts will degrade system performance over a broad range of frequencies.

These effects underline the importance of measuring IMD in wideband systems. There are several ways to measure IMD but, unfortunately, the various approaches can produce vastly different results.

Measuring IMD
A simple, repeatable approach is the two-tone third-order intermodulation technique called IP3. This method measures the third-order distortion products caused by nonlinear elements.

Using a narrowband (e.g., two-tone) stimulus has two important shortcomings: it is inconvenient and incomplete. It is inconvenient because a wideband measurement must be constructed from a long series of two-tone tests—a very time-consuming process. It is incomplete because the narrowband stimulus does not resemble a real-world signal. As a result, this method does not induce a real-world response from the circuit, device or system under test. Further, it does not provide enough data to determine BER performance.

In contrast, the NPR measurement uses a wideband stimulus and creates large signal peaks that stress or “light up” the communication channel in ways that resemble real-world conditions. This is the most accurate way to reproduce multi-carrier intermodulation effects and estimate system BER performance under “real traffic” conditions. In use since the 1950s, NPR is currently used as a figure of merit for evaluating the performance of power amplifiers, transmitter circuits and receiver circuits that use solid-state and traveling-wave-tube (TWT) technologies.

Characterization of NPR requires a signal source that can produce either additive Gaussian white noise (AGWN) or narrowband Gaussian noise (NBGN). Such signals can be produced with analog or digital technologies. In either case, the characteristics of the stimulus affect the quality of the measurement results.

To perform the NPR measurement, the required AGWN or NBGN signal must have a notch from which a portion of the frequency spectrum has been removed (Figure 1). This stimulus is applied to the unit under test (UUT) and the response is measured with a spectrum or signal analyzer. Any nonlinearity in the UUT will cause spectral components to appear in its output signal within the notch (Figure 2). The calculated NPR value is the ratio of the average power across the notch spectrum versus the average power in an equal bandwidth of the stimulus passband.

Comparing Approaches and Results
Although the various analog and digital approaches produce equivalent results, analysis has shown that the digital method is superior in terms of repeatability and test time. These benefits are important in both product development and manufacturing.

The analog technique uses an analog white-noise source as the stimulus. A white-noise signal is continuous and its spectral shape depends on the filters being used to control its bandwidth. Consequently, it is difficult to obtain reproducible results between UUTs or across test systems. This can be remedied with longer averaging periods in the measuring receiver, but this will extend overall test time.

In contrast, the digital technique uses an AWG to produce a stimulus that is more deterministic than white noise (Figure 3). The required stimulus signal contains a series of equally spaced discrete tones that have random phase relationships.

The most suitable AWG makes it possible to create an accurate representation of system data traffic while also ensuring measurement repeatability. To achieve these goals, the AWG must provide control over key attributes of the stimulus signal: the number of spectral lines and their spacing; overall spectral shape; notch depth and width (1 to 10 percent of overall noise-signal bandwidth is recommended); and statistical characteristics such as the cumulative complementary density function (CCDF).

The digital technique provides three important advantages. One is accuracy: because NPR is a relative measurement, many uncertainties are removed from the test. The basic accuracy of the measurement depends on the dynamic accuracy of the spectrum or signal analyzer used to measure the UUT’s output spectrum.

Repeatability and reduced test time are the other two advantages. Table 1 shows three groups of measurements made with different settings. In all cases, the NPR results were stable, exhibiting very low standard deviation. Measurement times varied, but the main determining factor was the number averages. This suggests that the key tradeoff in an NPR measurement will be the desired stability of the readings versus the expected throughput rate of the test system.

Looking to the Future
As digital modulation and signal processing technologies continue to advance, commercial and military broadband systems will transmit at increasingly greater data rates. Future systems based on LTE and WiMAX™ will continue to push the need for increased bandwidth and improved performance, making NPR testing increasingly important and useful.

References
Improved Methods for Measuring Distortion in Wideband Devices, Agilent application note, publication number 5989-9880EN.
Characterizing Digitally Modulated Signals with CCDF Curves, Agilent application note, publication number 5968-6875EN
Agilent Signal Studio for Noise Power Ratio, Agilent technical overview, publication number 5988-9161EN.
Noise Power Ratio: Theory And Applications, Stan Soonachan, Senior Staff Systems Engineer; Lockheed Martin Missiles & Space, Sunnyvale, CA; 20th AIAA International Communication Satellite Systems Conference and Exhibit, 12-15 May 2002, Montreal, Quebec, Canada.

Author Biographies
Steve Pettis is a market development engineer for Agilent Technologies. He has worked in and around the aerospace/defense industry for more than thirty years. Steve’s experience includes manufacturing and testing of missiles and airborne radar systems as well as RF/microwave measurements across all aero/defense applications for Hewlett-Packard and Agilent. Today, he supports the development of measurement solutions for aero/defense applications. He has a BSEE from University of Massachusetts, Lowell.

Pete Thysell is an R&D engineer for Agilent Technologies. He joined the company in 1984 as a marketing engineer and, after launching the 8770A arbitrary waveform synthesizer, moved to R&D. Pete has developed software or software applications for instruments such as the 8791A frequency agile signal synthesizer, the E2507/08 multi-format communications signal simulators, the E8267D vector microwave synthesizer, and several other RF and microwave signal generators. He has a BSEE from California State University, Sacramento.

WiMAX is a trademark of the WiMAX Forum.

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