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I understand that EVM is a root mean square of error vectors. If I have transmitted symbols and received symbols (once equalized), taking a root mean square would give me EVM. I believe this is actual EVM (we are using actual tx symbols and mapping them to equalized received symbols and then computing EVM).

How does a signal analyzer (which doesn't know tx symbols) computes EVM?

Does it calculate the EVM of each equalized received symbol with a closest ideal symbol on the constellation and then average it out to give final EVM value?

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The answer generally is yes- if the SNR is large enough then we can accurately estimate EVM just based on the raw decisions in the known constellation after all typical offsets have been properly corrected for (DC offset, IQ offset, phase offset, frequency offset, timing offset). In fact often the EVM is a measure of how good our corrections are for each of these items, as well as equalization and ultimately background noise.

If the SNR is not large enough, then we will have errors that are larger than the symbol decision boundaries, and such a "raw EVM" approach of using only the decisions without knowledge of what was actually transmitted will under-estimate the EVM since it will limit the maximum error to be half the distance between symbols.

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Does it calculate the EVM of each equalized received symbol with a closest ideal symbol on the constellation and then average it out to give final EVM value?

You very rarely test EVM on a low-SNR signal that's not according to any standard, especially because if that signal doesn't adhere to any standard, there would be very little for your signal analyzer to do equalization with.

If you buy a signal analyzer, you can often buy extensions that allow you to estimate properties of some specific communication / broadcasting standards (LTE, DVB-T, VDSL,…). Such standards have channel coding, with which you can (most of the time) recover incorrectly received symbols, and then actually calculate the error between reception and actually received symbol.

In other words, to know what your signal analyzer does in your current situation, you'll have to read its documentation.

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