Maximum throughput loss of noisy ISI channels due to narrow-band interference

Narrow-band interference (NBI) could occur in transmission media such as twisted pair or coaxial cable. In this letter, we analyze the effect of such interference on the data throughput for finite-blocklength transmission over noisy intersymbol interference channels. It is shown that the worst NBI spreads its power over the sweet spots of the signal. More precisely, the auto-correlation matrix of worst-case narrow-band (rank-deficient) interference is shown to have the same eigendirections as the signal. We derive the exact spectral shape of the worst NBI and its associated minimum channel block throughput in closed form.