Solution for detecting nonlinear distortion using vector signal analyzer

A key performance parameter of power amplifiers used in mobile communication networks is nonlinear distortion. However, excessive nonlinear distortion will increase the bit error rate (BER), resulting in a degradation of the quality of voice and data signals transmitted in mobile communication networks. Fortunately, the vector signal analyzer can be used not only to accurately detect vector and scalar modulation errors, such as error vector magnitude (EVM) characteristics, but also to evaluate amplifier and system distortion characteristics. Because the analyzer does not require any special test environment or test signals for effective measurement, the analyzer can analyze impulse signals from base stations while the mobile communication network is operating normally. The

compression point of the device under test (DUT) is usually determined using a two-tone or multi-tone method1 with an adjustable range voltmeter or spectrum analyzer. Network analyzers use power sweeps for similar analysis. The signals used in both methods are test signals or signals that are optimized only for spectral bandwidth or statistical distribution, not signals in actual working environments. Vector

signal analyzers can be used to measure scalar, vector modulation parameters, and modulation errors of digitally modulated mobile wireless signals. According to modern concepts, these devices should also be able to measure and evaluate linearity errors, since all necessary data are collected during the regular measurement process. In fact, only a set of standard test equipment is required, and no additional measurement equipment or special test signals are required.
Figure 1 shows a typical test configuration for measurements using a vector signal analyzer. A signal generator with in-phase and quadrature modulation capabilities generates an RF mobile radio signal and sends it to the input of the device under test (DUT, such as a mobile communication output amplifier). The output of the amplifier is connected to the input of a vector signal analyzer (such as Rohde & Schwarz's FSQ-K70) through an attenuator (to avoid high voltages outside the instrument's operating range). Even the RF output signal of a base station can be directly measured with this set of equipment.

Figure 2 shows the block diagram of a vector signal analyzer. The digitally modulated RF input signal passes through the RF and IF stages (modules 1, 2) to the input of the analog-to-digital converter (module 1). The digital signal processor DSP demodulates the baseband signal to the bit level (module 7 in Figure 2) and generates a reference signal corresponding to the undistorted transmitted signal. The signal analyzer only needs to understand the modulation structure and filter appropriately (module 8). After calibration of the center frequency offset, phase and symbol timing (synchronization module 9 in Figure 2), the amplitude and phase of the measured signal are adapted to the reference signal to obtain the root mean square value (RMS) of the EVM. In the last stage, the measured signal is compared with the reference signal (module 11 in Figure 2). Typical modulation errors (such as amplitude error corresponding to time, phase error corresponding to time) are calculated at this time. These signals are used to represent vector and constellation diagrams or for later calculation of distortion characteristics.
Figure 3(a) shows the ideal constellation diagram of the undistorted 16-state quadrature amplitude modulation signal after rising cosine filtering. Figure 3(b) shows the output signal of the pure amplitude distortion amplifier. The vector diagram of the complex baseband signal is marked in both figures. The actual constellation point (Figure 3(b)) is near its ideal position. The curvature of the grid represents the nonlinear amplitude distortion based on amplitude modulation to a certain extent. Figure 3(c) shows the amplitude-time characteristic. The ideal signal is the blue curve and the actual signal is the red curve. For easy identification, the symbol time is marked with a square or circle. The three amplitude levels of the ideal signal are represented by the horizontal lines from R1 to R3, while the measured signal is represented by the horizontal lines from D1 to D3.

Although the ideal signal and the actual signal are basically consistent in the low-level segment, the deviation increases as the level increases. If the distorted signal samples at each level are represented by x/y coordinates and the corresponding ideal signal samples, the result is the modulation-amplitude characteristic. For better judgment, the level segment can also be represented as a straight line. The deviation of the characteristic curve from the logarithmic line (linear gain) is a measure of the amplifier's nonlinear distortion [see Figs. 3(a) and 3(b)].

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In practice, the distortion characteristic can be described by the signal ratio of the ideal signal to the actual signal or by the logarithm of the difference signal between the ideal signal and the actual signal. If each signal difference sample is plotted with the ideal signal using x/y coordinates, the result is the AM/AM distortion characteristic (amplitude distortion based on amplitude). All test points are marked in the characteristic curve. In this way, the deviation between the characteristic curve and the horizontal 0-dB line is the amount of nonlinear distortion, see [Figure 3(e) and Figure 3(f)]. The phase error is obtained by considering the phase error as a function of the ideal amplitude of the AM/PM characteristic curve (amplitude-based phase distortion).

During the operation of the analyzer, the ideal signal is reconstructed using the demodulated bits. In this way, it is not necessary to know the previous transmitted data sequence or the ideal I/Q sampling. According to the above method, the actual characteristics can be determined by comparing the ideal signal with the measured signal. This allows the amplifier to be measured in the precise operating mode later.

To calculate the modulation error, the analyzer adapts the measured signal by minimizing the effective value (RMS) of the EVM of the symbol time. This type of adaptation is described in detail in common mobile radio standards such as EDGE.

Figure 4 shows the error signal after adaptation with symbol times marked. Expressing its relationship to the reference signal in logarithmic form, it can be seen that the adaptation leads to a slight vertical shift of the measurement points and the interpolated compression curves [Figures 3(f) and 4(b)].

After interpolation, the compression points are marked with two markers with a fixed horizontal spacing of 10 dB. The points where the vertical spacing between the two markers is 1 dB are determined by moving the markers on the characteristic curve. In this case, the position marked with marker C represents the 1 dB compression point, see Figure 4(b).

Figures 4(c) and 4(d) show actual measurement results for a 16 QAM modulation scheme with raised cosine transmit filtering. This transmit filtering does not require a receive filter and can automatically generate constellation points with no interference between symbols (i.e., centered). The adaptation produces the following figure: the positions of the constellation points are slightly shifted to higher levels. The constellation diagrams at the middle positions appear to match, while the outer points with high levels are slightly shifted inwards.

The AM/AM distortion curve of the amplifier is obtained by interpolating all the measurement points [see the upper part of Figure 4(d)]. The bottom of Figure 4(d) shows the AM/PM curve, i.e. the phase difference of the signal represented by the x/y axis versus the ideal signal level. Both characteristics are shifted in the vertical direction after adaptation, but the differential calculation of the compression point usually still provides the correct value.

The new distortion measurement method can also be used with all linear modulation schemes and any type of transmit filter. However, the new method requires a measurement signal without receive filtering. Any receive filtering with bandwidth limitation will cause nonlinear effects because the impulse response of the filter is distributed over a certain number of symbol periods. As a result, the signal characteristics will be degraded.

To explain the new distortion measurement method, an impulse signal based on the EDGE mobile radio standard is used as an example. The digital standard EDGE uses a 3?/8-8PSK modulation scheme. For the transmitter, there is a special filter that has no inter-symbol interference. As part of the demonstration test, the EDGE impulse signal is demodulated and the test results are aligned to the position of the synchronization sequence and limited to the effective range (useful part) of the impulse signal. Thus, the edges of the impulse signal and the area beyond it are not used for measurement analysis.

For measurements on a wideband, bipolar small signal amplifier (not shown), the vector signal analyzer calculates the applied sample input power, determines the compression point and phase error, and displays them on an absolute scale. For this amplifier, the calculated 1dB compression point is +10.36dBm (the output level of the device under test) and the phase distortion is 8.71deg. In addition to these level and phase characteristics, a comparison of the average power level and the crest factor (ratio of peak to average power) provides more information about the DUT distortion. These measurements show an average power compression of 0.68dB and a decrease in the crest factor of 0.82dB.

This state-of-the-art vector signal analyzer makes it easy to measure nonlinear distortion characteristics and modulation-related compression parameters. This test equipment can also be used for traditional vector analysis and distortion measurements, and can also directly verify the effectiveness of the power amplifier pre-distortion, which can only be achieved by inference as other test equipment, such as EVM, can achieve.