Also known as: EbNo, Eb over N0, energy-per-bit to noise-density ratio
Eb/N0 (spoken “E-b over N-zero”) is the ratio of the energy carried by one information bit, Eb, to the noise power spectral density, N0.1 It is a normalized, bandwidth-independent form of signal-to-noise ratio and is the metric of choice for comparing digital modems, because it strips out the effects of bit rate, bandwidth, and modulation order — leaving a fair basis on which to plot bit error rate.
How it works
The link is Eb/N0 = SNR × (B / Rb), where B is the noise bandwidth and Rb the information bit rate. Equivalently, since Eb = S/Rb and total noise N = N0·B, the two SNR forms differ only by the ratio of bandwidth to bit rate — that is, by the system’s spectral efficiency. Because Eb/N0 divides signal power by the number of bits per second it carries, a slow, robust link and a fast, dense link that achieve the same BER report the same Eb/N0, even though their raw SNRs differ. That is exactly what makes it the fair comparison metric.
Every modulation-and-coding scheme has a characteristic BER-versus-Eb/N0 curve. The required Eb/N0 for a target BER is the headline number quoted in link budgets and standards. Coding gain is the reduction in required Eb/N0 that forward error correction buys at a given BER — modern turbo and LDPC codes operate within a fraction of a dB of the theoretical limit.
In practice
- The Shannon–Hartley theorem sets an absolute floor: as spectral efficiency approaches zero, the minimum Eb/N0 for error-free communication converges to ln 2 ≈ −1.6 dB. No system, however cleverly coded, can operate reliably below it.
- Uncoded BPSK needs about 9.6 dB of Eb/N0 for a 10⁻⁵ BER; a good LDPC code reaches the same BER a few dB lower, and dense QAM needs more.
- Deep-space and satellite links quote Eb/N0 directly because their power budgets are tight and every tenth of a dB of coding gain matters.
Relevance to SDR
Eb/N0 is the currency of link-budget engineering and the reason different digital voice systems have different range. P25 and DMR at 4800 symbols/s, TETRA at higher gross rates, and narrowband NXDN each demand a specific Eb/N0 for reliable decoding, and comparing them meaningfully requires normalizing out their differing rates and bandwidths — which is precisely what Eb/N0 does. For a decoder like GopherTrunk, the practical takeaway is that a signal’s raw SNR must be interpreted against the mode’s bit rate: a healthy SNR for a slow control channel may be marginal for a faster voice channel sharing the same site.