Bit Error Rate (BPSK)

BER = 0.5 × erfc(√(Eb/N0))

Quick answer

This calculator solves BER = 0.5 × erfc(√(Eb/N0)) for Bit Error Rate. With Eb/N0 0.02 dB, the result is 0.07817.

Calculator

Result
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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.

Symbols and units

Symbol Meaning Default unit Accepted units
BER Bit Error Rate — —
EbN0 Eb/N0 dB dB

Step by step

  1. 1. What you know: Eb/N0 0.02 dB
  2. 2. The relation: BER = 0.5 × erfc(√(Eb/N0))
  3. 3. Substitute: EbN0 = 0.02 dB
  4. 4. Result: Bit Error Rate = 0.07817

Worked examples

Minimum range

Given: Eb/N0 0.3 dB

Result: Bit Error Rate = 0.07161

Low range

Given: Eb/N0 3 dB

Result: Bit Error Rate = 0.02288

Typical

Given: Eb/N0 0.02 dB

Result: Bit Error Rate = 0.07817

High range

Given: Eb/N0 0.06 dB

Result: Bit Error Rate = 0.07722

Maximum range

Given: Eb/N0 0.6 dB

Result: Bit Error Rate = 0.06484

How Bit Error Rate changes with Eb/N0

Eb/N0 (input) Bit Error Rate (result)
0.002 dB 0.0786
0.005 dB 0.07853
0.01 dB 0.07841
0.015 dB 0.07829
0.02 dB 0.07817
0.03 dB 0.07793
0.04 dB 0.0777
0.08 dB 0.07675
0.14 dB 0.07533
0.2 dB 0.07393

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Frequently asked questions

How do you calculate Bit Error Rate (BPSK)?

Use BER = 0.5 × erfc(√(Eb/N0)). With Eb/N0 0.02 dB, Bit Error Rate works out to 0.07817.

How do you calculate bit error rate bpsk awgn eb/n0?

Rearrange for Bit Error Rate: with Eb/N0 3 dB, Bit Error Rate is 0.02288.

What is the formula for Bit Error Rate (BPSK)?

The formula is BER = 0.5 × erfc(√(Eb/N0)). 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.

Related Concepts

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