There are many ways of characterizing W-CDMA transmitter performance. However, the Third Generation Partnership Project (3GPP) specifications require two measurements to verify the in-channel modulation quality of W-CDMA transmitters - error vector magnitude (EVM) and peak code domain power (peak CDE). This article explores the purpose behind these key transmitter modulation quality conformance measurements for W-CDMA user equipment, why they are important and the relationship between them.

In constant-amplitude modulation schemes such as Gaussian minimum shift keying (GMSK), phase and frequency error are the metrics for modulation quality. However, this metric is not very effective for non-constant amplitude modulation formats that can also have errors in amplitude. The accuracy of non-constant amplitude modulation schemes such as quadrature amplitude modulation (QAM) and quadrature phase-shift keying (QPSK) can be assessed effectively by looking at the constellation of the signal. Signal impairment can be objectively evaluated by taking the displacement of each measured symbol from the reference position as an error vector (or phasor). The error vector is the vector difference between the measured and reference vectors, and the reference position is determined from a reference signal that is synthesized by demodulating the data bits from the received signal and remodulating these bits "perfectly."

The EVM is defined as the square root of the ratio of the mean error vector power to the mean reference power, expressed as a percentage:

When evaluating the modulation accuracy of W-CDMA signals, it becomes evident that this definition of EVM, while sufficient for ordinary QPSK or QAM, needs further elaboration. Questions arise such as whether EVM should be measured at the chip or at the symbol level, whether it should be measured for a signal with a single dedicated physical data channel (DPDCH) or with another channel configuration, and how the reference should be calculated. As a result, there are three types of EVM measurements - QPSK EVM, composite EVM and symbol EVM.

The EVM measurement described in the 3GPP specifications corresponds to a composite EVM measurement. Although QPSK EVM and symbol EVM are not required, they can be useful when designing and troubleshooting a W-CDMA transmitter. The differences and benefits of each EVM measurement are explained below.


A W-CDMA uplink signal can consist of one dedicated physical control channel (DPCCH) and several DPDCHs. Each channel is binary phase-shift keying (BPSK) encoded, assigned to either the I or the Q paths, and spread with an orthogonal variable spreading factor (OVSF) code. The individual BPSK channels for each path are typically added at this point, and the complex-valued chip sequence is hybrid phase-shift keying (HPSK) scrambled. The resulting chip sequence is then root raised cosine (RRC) filtered, and the result is applied to the QPSK modulator. Since multiple amplitude levels are applied to the I and Q paths of the modulator, the final constellation does not usually look like QPSK or any other known constellation.

However, there are a few channel configurations that map onto a QPSK constellation. A single DPCCH (or DPDCH), for example, results in a QPSK constellation after the HPSK scrambling. A signal with a DPCCH and a DPDCH at the same power level maps onto a 45° rotated QPSK constellation. The rotation is caused by the complex scrambling. Since the receiver does not care about the absolute phase rotation, it effectively sees a QPSK constellation. The modulation quality of a single-channel signal (or other simple channel configurations) can be evaluated at the scrambled chip level with a QPSK EVM measurement.

The QPSK EVM actually compares the measured filtered samples with the filtered samples for an ideal QPSK reference. The filtered sample reference signal is calculated by obtaining the ideal scrambled chips. The QPSK EVM measurement does not descramble and despread the signal into symbols and back into chips to calculate the reference. Consequently, the ideal scrambled chips that are obtained are really uncoded chips.

The signal under test is downconverted (the baseband I and Q signals are recovered and sampled), and passed through an RRC receiver filter. In order to calculate what the ideal chips are, the measurement algorithm assumes that they are going to map onto a QPSK constellation, so the measured samples go through a decision process that can be considered a QPSK decoder. This process samples the chip timing and decides to which QPSK state they correspond. This is equivalent to obtaining the "ideal'' chips. Like any other QPSK decoder, the algorithm assumes that the error will be small enough for the sample to fall onto the correct quadrant. Once the ideal uncoded chips are obtained, they are QPSK encoded again (assigned to the reference QPSK states), and passed through a raised cosine (RC) filter that is equivalent to the filtering experienced by the measured signal.

The QPSK EVM measurement is the starting point for the RF engineer. Before all the baseband algorithms are ready, the RF designer can evaluate the performance of the RF section by analyzing the trajectory of the baseband samples. Errors such as phase modulation or in-channel spurious content can be detected by looking at displays such as the constellation, phase error versus time, or error vector spectrum. The QPSK EVM measurement can also identify I/Q errors and linear impairments in the baseband filtering.

The QPSK EVM measurement can also be used by the system integrator to troubleshoot the design when other measurements are failing. This may occur, for example, if the spreading and scrambling algorithms or the synchronization algorithms are not working properly. A correct QPSK EVM measurement will confirm that the problem does not occur in the RF section, so it must lie somewhere in the spreading or scrambling algorithms.

Composite EVM

Although measuring EVM for a signal with a single DPCCH (or other simple channel configuration) may be useful, in general the overall modulation quality of the transmitter for any channel configuration is the point of interest. The constellation of this signal will vary depending on its channel configuration. The composite EVM measurement evaluates the modulation quality of the signal regardless of its channel configuration. To synthesize a reference signal for the uplink signal, the active channels must be identified and despread to the encoded bit level, and EVM is calculated only for the scrambled chip samples.

After the baseband I and Q signals are recovered and filtered, the signal is descrambled and the active channels are identified, despread and BPSK-decoded to bits. The BPSK decoding refers to the assignment of "0''s and "1''s for either the I or Q path depending on the symbol amplitude values obtained for that path after the despreading. It actually corresponds to a bit detection process. The composite EVM measurement algorithm does not perform the complete decoding (deinterleaving, etc.) of the encoded bits. Instead, the reference signal is built from those encoded bits assumed to be correct. So if errors occur during the signal coding and interleaving, they will not be reflected in the measurement result.

In order for the measurement to identify the active channels and despread the channels correctly, it must synchronize to the DPCCH pilot sequence. A correct DPCCH pilot bit pattern is essential to make accurate measurements. As required by the W-CDMA 3GPP specifications, "the square root of the ratio of the mean power of the error signal to the mean power of the reference signal" is computed and expressed as a percentage EVM. In other words, EVM is defined as the ratio of the RMS power of the error vector to the RMS power of the reference signal. The error vectors are calculated only for the samples at the chip times. The algorithm described in the specifications includes descrambling and despreading of the signal, so it is suitable for measuring composite signals, and the specifications require an EVM measurement interval of one time slot.

The 3GPP specifications also describe the channel configuration to perform the modulation quality conformance test (EVM). The channel configuration is the 12.2 kbps uplink reference measurement channel, which consists of a DPDCH and a DPCCH. The DPCCH is -5.46 dB lower than the DPDCH. The specifications require an EVM better than 17.5 percent. The modulation quality test of the 12.2 kbps uplink reference measurement channel, as required by the specifications, is shown in Figure 1 . In addition to conformance testing, there are several main applications for which the composite EVM measurement (and its related displays and metrics) would be used instead of a QPSK EVM measurement.

Evaluation of the Quality of the Transmitter for a Multi-channel Signal

This is particularly important for RF designers, who need to test the RF section (or components) of the transmitter using realistic signals with correct statistics. In general, the peak-to-average power ratio of the signal increases as the number of channels increases. By measuring modulation quality on a multi-channel signal, the performance of the RF design for W-CDMA uplink signals with different loading can be evaluated. An example of a composite EVM measurement on a signal with the DPCCH and three DPDCHs is shown in Figure 2 .

Analyzing Errors that Cause a High Interference Level in the Signal

If the interference level is too high, the QPSK EVM algorithm may not be able to determine the ideal reference. In this case, QPSK EVM is not accurate. The composite EVM measurement descrambles and despreads the signal, so it takes advantage of its spreading gain. The true reference is recovered even when the signal is well beyond the interference level that will cause multiple chip errors. This allows system integrators to verify the minimum allowable modulation quality of the transmitter in order for the BTS (signal analyzer) to demodulate the signal in realistic field environments.

Detecting Spreading or Scrambling Errors

Depending on the degree of the spreading or scrambling error, the test equipment may show an intermittent or permanent unlocked condition for the composite EVM measurement. When this problem occurs, the QPSK EVM measurement can be used to confirm that the rest of the transmitter is working as expected. If the scrambling or spreading error does not cause an unlocked composite EVM measurement condition, the error vector versus time display can be used to find the problematic chip. This is mainly useful to baseband engineers and system integrators.

Symbol EVM

Symbol EVM provides the constellation and EVM for a specific code channel at the symbol level, even in the presence of multiple codes. An impairment that affects symbol EVM will also affect the composite EVM. For example, an amplifier compression problem will appear both in the composite EVM and in the symbol EVM measurement. However, because of the spreading gain, symbol EVM will attenuate the impairment. Symbol EVM is used because it provides the bridge between RF and the demodulated bits. Since it includes the spreading gain, it provides a measure of modulation quality that determines the error rate for that code channel.

The relationship between symbol EVM and EVM at the chip level depends on the spreading factor. At low spreading factors (high data rates), chip modulation errors have a significant effect on symbol EVM, but at high spreading factors, chip modulation errors have very little effect on symbol EVM. In that sense, symbol EVM is particularly useful for baseband engineers for evaluating symbol quality and analyzing how specific impairments affect the quality of dedicated physical channels at different data rates.

Another advantage of symbol EVM versus composite EVM is that the former typically provides analysis over longer periods of time. For the same amount of measurement points, the symbol EVM measurement covers longer periods of time than the single slot composite EVM conformance measurement. In the case of symbol EVM, the measurement interval can usually be selected from 1 time slot to 30 or 60, depending on the number of frames captured. The time slot offset can also be selected.

For example, Figure 3 shows the code domain power and symbol EVM for a W-CDMA uplink signal with a DPDCH and a DPCCH and with a periodic phase instability problem. The symbol EVM measurement is performed on the DPDCH for one time slot. Figure 4 shows the symbol EVM measurement for the following time slot. In this case, the symbol EVM result varies a lot from time slot to time slot (0.92 versus 8.67 percent), an indication that the signal should be analyzed over a longer period of time. Figure 5 shows the phase error versus time display for the DPDCH over 15 time slots. The period of the interfering signal that is causing the phase problem can be calculated from this display. In this case, the interfering signal is a square wave and its frequency is 400 Hz.

Peak CDE

In W-CDMA systems, the composite EVM measurement has been supplemented by peak CDE, which specifies a limit for the error power in any one code. In the case of phone conformance testing, this test is only required when multi-code transmission is provided. The phone must be configured with the UL 768 kbps reference measurement channel (which is the only UL reference measurement channel with two DPDCHs).

CDE is a projection of the error vector in the code domain. The projection of the error is interesting because it shows how the error power is distributed in the code domain. In general, Gaussian noise is distributed evenly throughout the code domain (both in active and inactive channels). Instead, transmitter impairments cause an uneven CDE distribution, where the larger errors concentrate on active channels, or in the case of a few specific impairments, in certain inactive channels. The error power should be evenly distributed throughout the code domain (as Gaussian noise), rather than concentrated in a few codes to avoid code-dependent channel quality variations.

One cause of unequal distribution of error power is LO instability. In essence, energy is lost from the active channels and appears in those channels with codes that are closely related to the active channel codes. In the case of OVSF codes, LO instability results in higher code domain noise for channels with the same codes as the active code channels but with different I/Q path. The error energy may also fall in channels consecutive to the active code channels, whether at the same or different I/Q paths, as shown in Figure 6 for a UL 768 kbps reference measurement channel (one DPCCH and two DPDCHs) signal with an LO phase instability problem.

The algorithm to calculate the CDE first goes through the composite EVM measurement. As part of this measurement, the error vector at the scrambled chip level is generated. This error vector is a composite error, so in order to obtain the error energy for each code channel, the composite error must be projected onto the code domain. As requested by the W-CDMA user equipment (UE) conformance test specifications for the peak CDE test, the projection is only performed for a spreading factor SF = 4. The error will thus be projected onto the four code channels at SF = 4, regardless of whether they are active or not. The peak CDE is then calculated from the code at SF = 4 that returns the largest error power relative to the composite reference signal. The peak CDE measurement is expressed (in decibels) relative to the power of the composite reference. The error must not exceed -15 dB.

Figure 7 shows the peak CDE measurement (in combination with the composite EVM) for the same signal (UL 768 kbps reference measurement channel) with the phase instability problem described earlier. In this case, the peak CDE falls in an active DPDCH (Cch, 4,1 in I or C2(1): I), so this is the code channel that accumulates the highest error. CDE and peak CDE are mainly of interest to system engineers and baseband engineers to identify the code channel where the error occurs.

While this article has mainly described the two measurements required by the 3GPP specifications, there are other measurements that also can provide useful information. Information about these measurements, as well as additional information about the measurements discussed here, can be found in Agilent Application Note AN-1356, available at

All the figures in this article were obtained from the Agilent E4440A PSA spectrum analyzer. The Agilent E4438C ESG vector signal generator was used to generate the W-CDMA uplink signals.

Marta Iglesias holds her BSEE degree from the Universitat Politecnica de Catalunya, Spain. She has performed technical support for RF and microwave spectrum analyzers, and is currently a wireless industry marketing engineer for Agilent Technologies, where she is responsible for understanding the test needs of the wireless communications industry.