EsN0

EsN0 refers to the energy per symbol to noise power spectral density ratio, commonly written as Es/N0. In digital communications, Es denotes the average energy carried by one transmitted symbol, while N0 is the one-sided power spectral density of additive white Gaussian noise. Es/N0 is used to characterize how strong the transmitted symbol is relative to the noise, on a per-symbol basis, and is a key parameter in evaluating modulation performance over AWGN channels.

The relationship to Eb/N0 (energy per information bit) depends on the modulation order M and the coding rate R. Each symbol carries log2(M) bits, and with a coding rate R (k information bits per n transmitted bits), the number of information bits per symbol is log2(M) × R. Therefore Es = Eb × log2(M) × R, and the corresponding relationships are Es/N0 = Eb/N0 × log2(M) × R and Eb/N0 = Es/N0 / [log2(M) × R]. For uncoded systems (R = 1), Es/N0 = Eb/N0 × log2(M).

Es/N0 is widely used to plot and analyze symbol error rate (SER) or bit error rate (BER) curves for modulation schemes such as BPSK, QPSK, and M-ary QAM/PSK. It provides a common, modulation-dependent measure of link quality and enables comparison across different schemes and coding rates. In theoretical limits, Es/N0 also relates to the Shannon limit for reliable communication over AWGN channels.