sdr.PSK.symbol_error_rate(esn0: ArrayLike | None = None) → ndarray

Computes the symbol error rate (SER) at the provided \(E_s/N_0\) values.

Parameters:
esn0: ArrayLike | None = None

Symbol energy \(E_s\) to noise PSD \(N_0\) ratio in dB.

Returns:

The symbol error rate \(P_e\).

See also

sdr.ebn0_to_esn0, sdr.snr_to_esn0

References

  • John Proakis, Digital Communications, Chapter 4: Optimum Receivers for AWGN Channels.

Examples

See the Phase-shift keying example.

Plot theoretical SER curves for BPSK, QPSK, and 8-PSK in an AWGN channel.

In [1]: bpsk = sdr.PSK(2); \
   ...: qpsk = sdr.PSK(4); \
   ...: psk8 = sdr.PSK(8); \
   ...: esn0 = np.linspace(0, 10, 1000)
   ...: 

In [2]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.ser(esn0, bpsk.symbol_error_rate(esn0), label="BPSK"); \
   ...: sdr.plot.ser(esn0, qpsk.symbol_error_rate(esn0), label="QPSK"); \
   ...: sdr.plot.ser(esn0, psk8.symbol_error_rate(esn0), label="8-PSK"); \
   ...: plt.title("SER curves for BPSK, QPSK, and 8-PSK in an AWGN channel"); \
   ...: plt.tight_layout();
   ...:
../../_images/sdr_psk_symbol_error_rate_1.png