📉 BER vs Eb/N₀ Curves

Bit error rate for BPSK · QPSK · M-PSK · M-QAM · FSK · DBPSK over AWGN

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Controls

Show modulations:

Required Eb/N₀ @ target BER

Modulationbits/symEb/N₀ (dB)

BER Curves

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📖 How to use

  1. Tick the modulation schemes you want to compare (the coloured swatches match the curves).勾选想对比的调制方式(彩色色块对应曲线颜色)。
  2. Set a target BER (e.g. 1e-6) — a reference line is drawn across the plot.设置目标 BER(如 1e-6)——图上会画一条参考线。
  3. Read the required Eb/N₀ for each scheme from the table on the right.在右侧表格读取每种调制所需的 Eb/N₀。
  4. Adjust Max Eb/N₀ to zoom the x-axis in or out.调整 Max Eb/N₀ 来缩放横轴范围。
  5. Use that required Eb/N₀ as the "required Eb/N₀" input in the link budget.把这个所需 Eb/N₀ 填进链路预算的 "required Eb/N₀" 输入。
  6. Curves marked * (16/32-APSK) are union-bound approximations.标 * 的曲线(16/32-APSK)为联合界近似。

Reading a BER curve

A BER vs Eb/N₀ curve shows the theoretical bit error rate of a modulation over an additive white Gaussian noise (AWGN) channel as a function of the energy-per-bit to noise-density ratio. Lower and further left is better. To hit a target BER (say 10⁻⁶), read across from the BER axis to a curve, then down to the required Eb/N₀ — that is the number you feed into a link budget as "required Eb/N₀".

Formulas (AWGN, uncoded)

BPSK / QPSK: P_b = Q(√(2·Eb/N0))

M-PSK: P_b ≈ (2/k)·Q(√(2k·Eb/N0)·sin(π/M)), k = log₂M

M-QAM: P_b ≈ (4/k)(1−1/√M)·Q(√(3k/(M−1)·Eb/N0))

Coherent FSK: P_b = Q(√(Eb/N0))   DBPSK: P_b = ½·e^(−Eb/N0)

16/32-APSK * (DVB-S2): no simple closed form — estimated by a nearest-neighbour union bound over the ring constellation (4+12 and 4+12+16), normalised to unit average energy. In linear AWGN, APSK sits just behind the equivalent QAM; its real advantage is robustness to amplifier nonlinearity. Curves marked * are approximate.

where Q(·) is the Gaussian Q-function. Higher-order schemes carry more bits per symbol (better spectral efficiency) but need a higher Eb/N₀ for the same BER. Forward error correction (e.g. LDPC in DVB-S2) shifts these curves sharply to the left. All computation runs locally in your browser.

如何看 BER 曲线

BER vs Eb/N₀ 曲线给出某调制在加性高斯白噪声(AWGN)信道下的理论误码率,作为每比特能量与噪声密度之比的函数。越低越靠左越好。要达到目标 BER(比如 10⁻⁶),从 BER 轴横向读到曲线,再向下读出所需 Eb/N₀——这个数就是你填进链路预算的 "所需 Eb/N₀"。

公式(AWGN,未编码)

BPSK / QPSK: P_b = Q(√(2·Eb/N0))

M-PSK: P_b ≈ (2/k)·Q(√(2k·Eb/N0)·sin(π/M)),k = log₂M

M-QAM: P_b ≈ (4/k)(1−1/√M)·Q(√(3k/(M−1)·Eb/N0))

相干 FSK: P_b = Q(√(Eb/N0))   DBPSK: P_b = ½·e^(−Eb/N0)

16/32-APSK *(DVB-S2):没有简单闭式——用环状星座(4+12 与 4+12+16)的最近邻联合界近似,并归一化到单位平均能量。在线性 AWGN 下,APSK 略逊于同阶 QAM,其真正优势是抗功放非线性。标 * 的曲线为近似。

其中 Q(·) 为高斯 Q 函数。高阶方案每符号携带更多比特(频谱效率更高),但要达到相同 BER 需要更高的 Eb/N₀。前向纠错(如 DVB-S2 的 LDPC)会把这些曲线大幅左移。全部计算在你的浏览器本地完成。