EVM (Error Vector Magnitude)

Error Vector Magnitude (EVM) is a measure of the difference between a transmitted signal and the corresponding received signal in a communication system. It is used to evaluate the quality of the transmitted signal and to identify any impairments or distortions in the system. In this article, we will discuss the concept of EVM, its importance, calculation, and applications.

Why is EVM important?

In any communication system, the transmitter sends a signal to the receiver, which processes and demodulates the signal to recover the original information. During this process, the signal may experience several impairments, such as noise, interference, distortion, and attenuation. These impairments can affect the quality and reliability of the received signal and degrade the performance of the system.

To evaluate the performance of a communication system, it is necessary to measure the quality of the transmitted signal and compare it with the expected signal. The expected signal is the ideal signal that would be received in a perfect communication channel without any impairments. However, in practical systems, the received signal is always different from the expected signal due to various impairments.

EVM provides a quantitative measure of the difference between the received signal and the expected signal. It is a critical parameter in evaluating the performance of modern digital communication systems, such as Wi-Fi, 4G, 5G, and satellite communication systems. EVM is used to measure the accuracy of the transmitted signal, identify the source of any impairments, and optimize the system performance.

What is EVM?

EVM is a measure of the difference between the transmitted and received signal, expressed as a percentage of the ideal signal magnitude. It is a complex parameter that considers both the amplitude and phase errors in the signal.

The EVM value is calculated by comparing the received signal with the ideal signal and determining the magnitude and phase difference between the two signals. The magnitude difference is calculated as the root mean square (RMS) error between the received and ideal signal magnitudes, normalized to the ideal signal magnitude. The phase difference is calculated as the angular error between the received and ideal signal phases, normalized to the ideal signal phase.

EVM can be expressed in dB or percentage. The dB value of EVM is calculated as:

EVM(dB) = 20*log10(EVM%)

where EVM% is the percentage value of EVM.

The lower the EVM value, the better the quality of the transmitted signal. An EVM value of 0% indicates that the received signal is identical to the ideal signal. An EVM value of 100% indicates that the received signal is completely different from the ideal signal and contains significant impairments.

How is EVM calculated?

To calculate EVM, we need to measure the received signal and the ideal signal and then compare them to determine the magnitude and phase difference between the two signals.

The ideal signal can be generated by the transmitter or calculated theoretically based on the transmitted signal parameters. The ideal signal is assumed to be free from any impairments and is used as a reference signal to calculate the EVM value.

The received signal can be measured using a receiver that is synchronized with the transmitter. The receiver demodulates the received signal and extracts the signal parameters, such as amplitude, phase, and frequency.

Once we have the received and ideal signals, we can calculate the EVM value using the following formula:

EVM% = (RMS error / ideal signal magnitude) * 100

where RMS error is the root mean square error between the received and ideal signal magnitudes, and the ideal signal magnitude is the average magnitude of the ideal signal.

The RMS error is calculated as:

RMS error = sqrt(1/N * sum(|r(t)|^2 - |i(t)|^2)^2)

where N is the number of samples, r(t) is the received signal at time t, and i(t) is the ideal signal at time t.

Similarly, the phase error is calculated as:

Phase error = atan2(sum(imag(r(t)*conj(i(t)))) , sum(real(r(t)*conj(i(t)))))

where imag() and real() are the imaginary and real parts of the complex numbers, respectively, and conj() is the complex conjugate.

The EVM value can be expressed in dB by taking the logarithm of the percentage value:

EVM(dB) = 20*log10(EVM%)

Applications of EVM

EVM is a critical parameter in evaluating the performance of modern communication systems. It is used in several applications, such as:

1. System design and optimization: EVM is used to optimize the system design by identifying the sources of impairments and improving the signal quality. It helps in selecting the appropriate modulation and coding schemes, filter designs, and power amplifiers to achieve the desired system performance.
2. Quality control: EVM is used to ensure the quality of the transmitted signal and to verify that the system meets the specifications. It is used as a pass/fail criterion in production testing and quality control.
3. Troubleshooting: EVM is used to diagnose and troubleshoot system performance issues. It helps in identifying the source of impairments, such as noise, interference, distortion, and phase errors.
4. Interference analysis: EVM is used to analyze the impact of interference on the system performance. It helps in identifying the sources of interference and optimizing the system to mitigate the interference.
5. Spectrum analysis: EVM is used to analyze the spectrum of the transmitted signal and to identify any spectral regrowth or spurious emissions that may cause interference to other systems.
6. Link budget analysis: EVM is used to analyze the link budget and to determine the minimum signal-to-noise ratio (SNR) required to achieve the desired system performance.

Conclusion

EVM is a critical parameter in evaluating the performance of modern communication systems. It provides a quantitative measure of the difference between the transmitted and received signals and helps in identifying the sources of impairments and optimizing the system performance. EVM is used in several applications, such as system design and optimization, quality control, troubleshooting, interference analysis, spectrum analysis, and link budget analysis. Understanding the concept and calculation of EVM is essential for designing, testing, and maintaining communication systems.