Error rates in digital transmission
In any real communication system, noise and distortion can cause the receiver to misinterpret data. A digital transmission is measured with an error rate, the ratio of incorrectly received units to all units. In a probabilistic model, it is the probability of an error.
Types of error rates
- Bit error rate (BER): This is the most common metric. It is the ratio of the number of erroneously received bits to the total number of bits transmitted. For example, a BER of means that, on average, one bit in every million is incorrect.
- Symbol error rate (SER): In systems where one symbol represents multiple bits (e.g., QAM), this measures the ratio of incorrectly received symbols to the total number of transmitted symbols.
- Word/byte error rate (WER/ByteER): Measures the ratio of incorrect words or bytes. A word is considered incorrect if even a single bit within it is wrong.
Bit energy and noise spectral density
The error rate depends on the signal energy relative to the noise characteristics, as well as on the modulation and detector. A system's energy efficiency describes the Eb/N0 level required to meet a target BER. A lower required level means less energy per bit for that target. A normalized metric is used to compare systems:
(energy per bit to noise power spectral density ratio): This ratio divides the energy of one information bit () by the noise power spectral density () in W/Hz. represents noise per unit bandwidth; total channel noise power also depends on the occupied bandwidth. For a fixed transmission model, a higher generally produces a lower BER.
Interpreting the graph
The graph shows BER as a function of for several modulations and indicates the tradeoff between required energy and the number of bits carried by a symbol:
- For a fixed BER target (e.g., ), under the same channel and detector model, systems using a modulation with more levels, such as 32-level modulation, require a higher than systems using a two-level modulation such as BPSK. The smaller constellation-point distances require a larger decision margin.
- For a fixed level (e.g., 14 dB), lower-order modulations achieve a lower BER under the same channel and detector assumptions. Their constellation points are better separated at the given noise level.
Spectral and energy efficiency
Choosing a modulation and coding scheme relates spectral efficiency to energy efficiency, as summarized in the table below. The values depend on the BER target, detector, coding, filter, and frequency spacing, so the table gives one reference point rather than universal parameters. For the columns, assume an uncoded AWGN channel, coherent detection, and BER of about ; the example values include about a 1 dB margin. The 2FSK spectral value also depends on frequency spacing and filtering.
| Modulation | Spectral efficiency η (ideal model) | Spectral efficiency η (example) | Eb/N0 (model) [dB] | Eb/N0 (example) [dB] |
|---|---|---|---|---|
| 4QAM | 2 | 1.7 | 8.4 | 9.4 |
| 2FSK | 1 | 0.8 | 11.4 | 12.4 |
| BPSK | 1 | 0.8 | 8.4 | 9.4 |
| QPSK | 2 | 1.9 | 8.4 | 9.4 |
| 8PSK | 3 | 2.6 | 11.7 | 12.7 |
| 16PSK | 4 | 2.9 | 16.1 | 17.1 |
Spectral efficiency describes how efficiently the available is used. Complex modulations such as 16-PSK and 32-QAM can carry more bits per symbol, increasing the bit rate over the same frequency range. They are bandwidth-efficient.
Energy efficiency describes the energy level needed to transmit the signal reliably. Simple modulations such as BPSK and QPSK have larger constellation-point distances and can achieve a lower BER at the same . They are power-efficient.
An engineer therefore matches the method to the link constraints: a channel with limited bandwidth and a strong signal can use a spectrally efficient modulation such as 16-QAM. A power-limited channel, such as a deep-space probe, with available bandwidth can use an energy-efficient modulation such as BPSK.