We study channel capacity when a one-bit quantizer is employed at the output
of the discrete-time average-power-limited Rayleigh-fading channel. We focus on
the low signal-to-noise ratio regime, where communication at very low spectral
efficiencies takes place, as in Spread Spectrum and Ultra-Wideband
communications. We demonstrate that, in this regime, the best one-bit quantizer
does not reduce the asymptotic capacity of the coherent channel, but it does
reduce that of the noncoherent channel.Comment: 4 pages. To be presented at the 2012 International Zurich Seminar on
Communications (IZS
