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15. Signal Quality Metrics: FFT, SNR, EVM and BER

Goal

Learn how to evaluate SDR experiments quantitatively, not only visually.

Main metrics:

  • FFT / spectrum: frequency-domain representation;
  • SNR: signal-to-noise ratio;
  • EVM: error vector magnitude;
  • BER: bit error rate.

1. Why metrics matter

In SDR it is not enough to say “the signal is visible”. An engineering answer is needed:

  • how strong the signal is compared to noise;
  • whether the receiver is overloaded;
  • how close the constellation is to the ideal;
  • how many bits are received with errors.

2. Analysis diagram

flowchart TB
    classDef data fill:#EDE9FE,color:#0F172A,stroke:#7C3AED,stroke-width:1px;
    classDef metric fill:#F1F5F9,color:#0F172A,stroke:#64748B,stroke-width:1px;
    classDef dsp fill:#DCFCE7,color:#0F172A,stroke:#16A34A,stroke-width:1px;

    IQ["IQ recording"]:::data
    PRE["Preprocessing<br/>DC removal / normalization"]:::dsp
    FFT["FFT spectrum"]:::metric
    SNR["SNR estimate"]:::metric
    EVM["EVM estimate"]:::metric
    BER["BER estimate"]:::metric
    REPORT["Engineering report"]:::data

    IQ --> PRE --> FFT --> SNR --> REPORT
    PRE --> EVM --> REPORT
    PRE --> BER --> REPORT

3. FFT

FFT is used for:

  • finding the tone peak;
  • estimating the occupied bandwidth;
  • finding spurious components;
  • diagnosing overload.

4. SNR

SNR shows how far the useful signal is above the noise:

SNR[dB] = 10·log10(P_signal / P_noise)

Both powers must be measured over the same bandwidth; an SNR without its bandwidth is not a number you can compare.

Engineering meaning:

  • low SNR → the signal is hard to see;
  • high SNR → there is margin;
  • a very high level with a dirty spectrum → possible overload.

5. EVM

EVM shows how far the received constellation points are from the ideal ones:

EVM_rms = sqrt( Σ |r[k] − s[k]|² / Σ |s[k]|² )

where r[k] are the received symbols after synchronization and s[k] the ideal ones.

Especially useful for:

  • BPSK;
  • QPSK;
  • QAM;
  • comparing the model with the hardware.

6. BER

BER is the final metric of digital reception:

BER = bit errors / compared bits

Always give the number of compared bits: BER = 0 over 280 bits says much less than over a million. With zero errors in N bits, the 95 % upper bound is about 3/N.

If BER is high, the cause may be:

  • noise;
  • CFO;
  • poor timing;
  • wrong demodulation;
  • overload of the chain.

7. Where the course goes further

8. Conclusion

Metrics turn a laboratory work from visual observation into an engineering measurement.