Bit Error Rate (BPSK)

BER = 0.5 × erfc(√(Eb/N0))

Calculator

Result
—

Formula

BER = 0.5 × erfc(√(Eb/N0))

Description

The bit error rate for binary phase-shift keying (BPSK) modulation is calculated using the complementary error function of the square root of the energy-per-bit to noise-density ratio. This formula gives the theoretical best-case BER for uncoded BPSK over an additive white Gaussian noise (AWGN) channel. It serves as the benchmark against which all other modulation schemes and coding techniques are compared. Higher-order modulations like QAM achieve higher data rates but require higher Eb/N0 for the same BER.

Variables

  • BER — Bit error rate (dimensionless probability)
  • Eb/N0 — Energy per bit to noise spectral density ratio (dB)

Practical Notes

An Eb/N0 of about 9.6 dB gives a BER of 10⁻⁵, which is the typical requirement for voice communications. Data links often require BER of 10⁻⁹ or lower, achieved through forward error correction (FEC) codes like Reed-Solomon, turbo codes, or LDPC codes.

Related Formulas

UART Baud Rate Error RS-485 Termination Resistor RS-485 Bias Resistor Shannon Channel Capacity Wireless Link Range Manchester Encoding Bandwidth

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App