Hello,
I'm exploring different modulation types like MPSK, QPSK, and MQAM in various environments. Currently, I'm measuring the error rate but want to understand and measure the Error Vector Magnitude (EVM) more accurately. I'm using a general equation for all modulation types. Is this the right approach, and what should I expect from the EVM vs. Eb/No curve? I'd appreciate any help.
The Error Vector Magnitude (EVM) is a measure of the quality of a digitally modulated signal. It is defined as the root mean square (RMS) of the error vectors between the received symbols and their ideal constellation points. In other words, it is a measure of how closely the received symbols match the expected symbols.
EVM is a common metric used to assess the performance of digital communication systems. It is particularly important for systems that use high-order modulation schemes, such as quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexing (OFDM).
To calculate EVM, the following steps are typically taken:
The EVM is typically expressed as a percentage. A lower EVM value indicates a higher quality signal. For example, an EVM of 0% indicates that the received symbols perfectly match the ideal constellation points. An EVM of 10% indicates that the received symbols are, on average, 10% away from their ideal constellation points.
The EVM can be calculated for different types of modulation by using different normalization methods. For example, the average power normalization method is commonly used for QAM modulation, while the peak power normalization method is commonly used for pulse amplitude modulation (PAM).
The EVM is a useful tool for troubleshooting digital communication systems. By measuring the EVM, it is possible to identify and diagnose impairments in the system, such as noise, distortion, and interference.
Here is an example of how to calculate EVM for QAM modulation using the average power normalization method:
Python
import numpy as np def evm(symbols): # Normalize the symbols symbols_normalized = symbols / np.abs(np.mean(symbols)) # Calculate the error vectors error_vectors = symbols_normalized - np.conj(symbols_normalized) # Calculate the RMS EVM rms_evm = np.sqrt(np.mean(np.abs(error_vectors)**2)) # Convert RMS EVM to a percentage percentage_evm = rms_evm * 100 return percentage_evm # Example usage symbols = np.array([1 + 1j, 1 - 1j, -1 + 1j, -1 - 1j]) percentage_evm = evm(symbols) print(percentage_evm)
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This code will print the EVM for the given symbols, which is approximately 20%.
The Error Vector Magnitude (EVM) is a key metric used to assess the performance of digitally modulated signals. It is a measure of the difference between the received symbols and their ideal constellation points. A lower EVM value indicates a higher quality signal.
The general equation for calculating EVM is:
EVM = sqrt(sum(|e_k|^2) / N)
Where:
- e_k is the error vector for the kth symbol
- N is the total number of symbols
The error vector is calculated as follows:
e_k = r_k - d_k
Where:
- r_k is the received symbol for the kth symbol
- d_k is the ideal constellation point for the kth symbol
The magnitude of the error vector is calculated as follows:
|e_k| = sqrt(Re(e_k)^2 + Im(e_k)^2)
Where:
- Re(e_k) is the real part of the error vector for the kth symbol
- Im(e_k) is the imaginary part of the error vector for the kth symbol
The EVM can be normalized to the average power per symbol of the constellation. This is done by dividing the EVM by the average power per symbol. The normalized EVM is typically expressed as a percentage.
The following table shows the EVM for different modulation schemes:
Modulation SchemeEVM (%)BPSK10%QPSK5%16-QAM1.5%64-QAM0.75%
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The EVM for different modulation schemes can be calculated using the following steps:
The EVM can be calculated using a variety of software and hardware tools. Some popular software tools include MATLAB, LabVIEW, and Keysight's Advanced Design System (ADS). Some popular hardware tools include Tektronix's Spectrum Analyzers and Keysight's Signal Analyzers.
EVM is a valuable metric for assessing the performance of digitally modulated signals. It is used in a variety of applications, including:
- Wireless communications
- Optical communications
- Cable communications
- Satellite communications
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