Symbolfehler

Symbolfehler is a term used in digital communications to describe an error that occurs when a transmitted symbol is received or decoded incorrectly. A symbol, in this context, represents a constellation point that encodes multiple bits, so a single symbol error can correspond to several bit errors depending on the modulation scheme. Symbolfehler are distinguished from bitfehler (bit errors) because they originate at the symbol level rather than at the level of individual bits.

Causes of symbolfehler include additive noise, channel fading, interference, nonlinearity in amplifiers, timing and carrier recovery errors, and imperfect demodulation. In practice, the likelihood of a symbolfehler depends on the modulation format (for example M-PSK or M-QAM), the signal-to-noise ratio (SNR), and the characteristics of the transmission channel. In fading channels, symbolfehler rates are influenced by diversity, coding, and equalization techniques.

In AWGN (additive white Gaussian noise) channels, the probability of a symbolfehler, P_s, can be described by approximate expressions that depend on the modulation order M and the SNR per symbol. For common schemes, high-SNR approximations show that P_s decreases as SNR rises and as the constellation becomes more efficient. For M-PSK, a typical approximation is P_s ≈ 2 Q(√(2 γ) sin(π/M)), and for square M-QAM, P_s ≈ 4(1−1/√M) Q(√(3 γ/(M−1))), where γ is the Es/N0 per symbol. In fading channels, the symbolfehler rate is averaged over the fading distribution, and performance can be improved by diversity, coding, and equalization.

Symbolfehler are commonly measured as symbol error rate (SER) in experiments and simulations, and they relate to bit error rate (BER) through the chosen mapping from symbols to bits. See also: Bit error rate, Modulation, QAM, PSK, Channel coding.