EbN0

EbN0, short for energy per information bit to noise power spectral density ratio, is a dimensionless quantity used to express the quality of a digital communication link. It compares the energy allocated to each information bit with the power of the background noise, typically in AWGN channels, and is commonly reported in decibels. EbN0 provides a common figure of merit that allows fair comparison across different modulation schemes, coding rates, and bandwidths.

Basic relationships

In an M-ary modulation without coding, each transmitted symbol conveys log2 M bits. The energy per information bit Eb is related to the symbol energy Es by Eb = Es / log2 M, so Eb/N0 = Es/N0 divided by log2 M. Equivalently, Es/N0 = Eb/N0 × log2 M. When coding is used with code rate Rc (information bits per transmitted coded bits), the number of information bits per symbol is log2 M × Rc, and Eb/N0 = Es/N0 / (log2 M × Rc). Thus Eb/N0 accounts for both the modulation order and the coding rate in determining the information-bit robustness to noise.

Shannon limit and usage

The fundamental Shannon limit states that reliable communication is possible only if Eb/N0 is above a minimum value of about -1.59 dB in the limit of vanishing spectral efficiency (infinite bandwidth). In practical systems with finite M and Rc, higher Eb/N0 is required to achieve a target bit error rate. Practitioners plot BER or FER versus Eb/N0 to assess the power efficiency of modulation and coding schemes, and Eb/N0 is a standard metric in link-budget calculations and performance evaluations.