Abstract

This paper considers the capacity of sub-sampled analog channels when the sampler is designed to operate independent of instantaneous channel realizations. A compound multiband Gaussian channel with unknown subband occupancy is considered, with perfect channel state information available at both the receiver and the transmitter. We restrict our attention to a general class of periodic sub-Nyquist samplers, which subsumes as special cases sampling with periodic modulation and filter banks. We evaluate the loss due to channel-independent (universal) sub-Nyquist design through a sampled capacity loss metric, that is, the gap between the undersampled channel capacity and the Nyquist-rate capacity. We investigate sampling methods that minimize the worst-case (minimax) capacity loss over all channel states. A fundamental lower bound on the minimax capacity loss is first developed, which depends only on the band sparsity ratio and the undersampling factor, modulo a residual term that vanishes at high signal-to-noise ratio. We then quantify the capacity loss under Landau-rate sampling with periodic modulation and low-pass filters, when the Fourier coefficients of the modulation waveforms are randomly generated and independent (resp. i.i.d. Gaussian-distributed), termed independent random sampling (resp. Gaussian sampling). Our results indicate that with exponentially high probability, independent random sampling and Gaussian sampling achieve minimax sampled capacity loss in the Landau-rate and super-Landau-