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tutorial on error vector magnitude (evm)

*introduction to evm*

error vector magnitude (evm) is a key performance metric used in communication systems to quantify the quality of a modulated signal. it measures the difference between the ideal signal and the actual transmitted signal. evm is expressed in decibels (db) and is particularly important in systems such as digital communications, where it helps to assess the performance of the receiver and the modulation scheme being used.

evm can be defined mathematically as:

\[
evm = 20 \log_{10} \left(\frac{||e||}{||s||}\right)
\]

where:
\(e\) is the error vector (the difference between the ideal and actual signal).
\(s\) is the ideal signal vector.
\(||\cdot||\) denotes the euclidean norm.

steps to calculate evm

1. **generate the ideal signal**: define the ideal signal (the reference).
2. **simulate the transmitted signal**: simulate the actual transmitted signal with some imperfections (noise, distortion, etc.).
3. **calculate the error vector**: compute the error vector by subtracting the ideal signal from the transmitted signal.
4. **compute the evm**: use the formula above to find the evm.

example code

here is a python code example that demonstrates how to calculate evm using numpy. this example simulates a simple qpsk (quadrature phase shift keying) signal.



explanation of the code

1. **`generate_ideal_signal(num_symbols)`**: this function generates random qpsk symbols. the symbols are represented in the complex plane.

2. **`add_noise(signal, noise_power)`**: this function simulates the actual transmitted signal by adding gaussian noise to the ideal signal.

3. **`calculate_evm(ideal_signal, transmitted_signal)`**: this function calculates the error vector and computes the evm using the formula provided.

4. **parameters**: you can adjust the number of symbols and the noise power to see how they affect the evm.

5. **execution**: when you run the code, it will print the evm value, which i ...

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Feature error vector magnitude EVM error analysis vector magnitude performance evaluation signal processing metrics measurement accuracy