Error vector magnitude (EVM)

What is error vector magnitude (EVM)?

The difference between the measured and reference points may be caused by:

• Magnitude error: the received vector is too long or too short
• Phase error: the angle of the received vector is incorrect

We can quantify these two error sources by drawing a vector that connects the reference and measured points. This vector is the error vector.

Like all vectors, the error vector has both a magnitude and a direction. But in digital signal modulation, we’re mostly concerned with how far we are from the ideal point, not the direction to the ideal point. Therefore, the important measurement is the error vector magnitude (EVM). EVM is measured at each symbol time, and larger values of EVM indicate greater distance between the measured and reference points. Greater distances mean a higher probability that the receiver will mistake one symbol for another, so a higher EVM value means a greater probability of bit errors. As such, minimizing EVM is one of the most important goals in the design and operation of wireless data systems.

Contributors to EVM

The sources or causes of increased EVM fall into four main categories:

• Amplitude effects
• Phase effects
• I/Q imperfections
• Configuration issues

Compressions or non-linearity is a frequent contributor to EVM, especially at higher power levels. For lower power signals, a low signal-to-noise ratio (SNR) can increase EVM. Any frequency response or frequency-specific attenuation can also degrade EVM. Other amplitude-related factors are intersymbol interference (ISI), spurious interferers and propagation- or channel-related phenomena like multipath or fading.

The primary phase effect is phase noise in the transmitter and/or receiver. The contribution of phase noise to EVM is particularly important in systems using orthogonal frequency-division multiplexing (OFDM). Other types of phase response, where phase changes a function of frequency, can also lead to higher levels of EVM.

Imperfections in an I/Q modulator or demodulator, such as gain imbalance, quadrature offset or carrier feed through can be significant contributors to EVM.

Finally, there are some types of configuration issues that can affect EVM, e.g., having mismatched filters or different symbol rates at the transmitter or receiver.

EVM and modulation order

Even relatively minor contributors to overall EVM can become important with increasing modulation order. Higher order modulation, i.e., a greater number of symbols, means better throughput since there are more bits per symbol. For example, 16QAM is only 4 bits per symbol, and 64QAM Is 6 bits per symbol, and higher modulation orders have even more bits per symbol. However, as the number of symbols increases, the symbols become closer together, and this increases the change of mistaking one symbol for another. Therefore, higher modulation orders generally require lower EVM values. In fact, the maximum allowable EVM is often including in various wireless specifications, e.g., cellular or 802.11 Wi-Fi standards and in these specifications, maximum EVM is given as a function of modulation order and coding, with stricter EVM requirements as modulation order increases.

How to calculate EVM

Recall that EVM is the magnitude (or length) of a vector that connects the reference endpoint with the measured endpoint. In EVM measurements, the magnitude of this error vector can be reported relative to the maximum power in the constellation or relative to the root mean square (RMS) of the constellation.

When comparing EVM values, it’s very important to ensure that the same normalization reference is used for each set of values.

EVM can be expressed either as a percentage value or in decibels.

EVM is calculated on a per-symbol basis: at each symbol time, you calculate the magnitude of the error vector connecting the reference and measured symbol locations. However, EVM is reported over many symbols, often in terms of the maximum value, minimum value, average value, etc. Since EVM is essentially the distance between where the symbols are supposed to be and where they actually are, lower EVM indicates better modulation accuracy. When EVM is reported in decibels (dB), the values will always be negative, so the more negative the values, the better the EVM.

Different ways of looking at EVM

Since EVM is computed on a per-symbol basis, you can plot EVM values as functions of time. This can provide useful information on the sources of error or inaccuracy in the received signal. For example, slight differences between the transmit and receive symbol rate will appear as a V- or “bathtub”- shaped curve. EVM may also be higher at the beginning or end of a burst or pulsed signal due to various amplifier effects or timing. In addition, if the amplitude changes over time, this may increase the EVM of symbols with relatively high or low amplitudes.

You can also look at EVM as a function of frequency. This is also sometimes called the EVM spectrum, which is created by taking the fast Fourier transform of an EVM vs. time graph. One of the more useful and interesting applications of EVM vs. frequency is finding in-band spurious signals or interferers. In some cases, a spurious signal may be difficult to detect when looking at a standard “power vs. frequency” trace. For example, in the image below, the magnitude vs. frequency trace does not appear to contain any spurious signals, but the corresponding EVM vs. frequency trace clearly shows the presence of a narrowband spurious signal. EVM vs. frequency can be used to find spurious signals because the combination of the desired and undesired signal will cause increased EVM only at or near the frequency of the spurious signal.

Another useful way to look at EVM is to plot EVM as a function of input power. This is common when measuring devices such as amplifiers, mixers, etc. Below, you can see a typical curve of EVM vs. power. At very low input power levels, the SNR tends to be high, and a low SNR can often lead to poor EVM. Conversely, very high input power levels may push the DUT into compression, and this will also degrade EVM. There is typically an optimal power region, which is where the best EVM performance is achieved. Plotting EVM vs. power is a convenient way to determine the limits of this region.

Finally, it can be useful to plot EVM as a function of both power and frequency. Using these types of three-dimensional graphs makes it easier to identify trends or problem regions for the DUT. In the image below, you can see that EVM increases by frequency more rapidly at lower power levels, and you can also see the combination of frequency and power that leads to an unusually high level of EVM.

Instruments for measuring EVM

Now that we understand how EVM is and what it is used for, let’s see how it is measured. Most often, a signal or spectrum analyzer is connected to the DUT output. User-supplied parameters describing the signal properties are used to demodulate the signal and calculate EVM. In some cases, a vector signal generator is used to supply a modulated signal to the DUT input. In either case, it is important that the instruments used in the measurement setup have better EVM performance that the DUT. A common rule of thumb is a margin of 5 to 10 dB, but the larger, the better.

Measurement best practices

There are numerous recommended practices for measuring EVM:

• The reference level should be set correctly to have a good SNR. A reference level that is set too low can cause the signal to be clipped, leading to distortion. A reference level that is too high will increase the influence of noise and raise EVM. In many cases, analyzers have an “auto EVM” routine that automatically determines the optimum reference level for an EVM measurement.
• The number of averages should be high enough to guarantee stable, repeatable results, but keep in mind that too many could lead to an excessively long test time. Recall that EVM is computed on a per-symbol basis, so you would typically average EVM results over multiple measurements.
• Enabling equalization and/or frequency response correction is recommended.

When a vector signal generator is used in conjunction with the analyzer to provide a modulated input to the DUT, it’s usually a good idea to have both the generator and analyzer share a common frequency reference