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We report Monte Carlo simulations of the current response and noise spectrum in heavily doped nanometric GaAs Schottky-barrier diodes (SBDs) operating under periodic large-signal conditions in the forward bias region. Due to the rather thin depletion region and heavy doping of these diodes, we find that the returning carrier resonance is shifted well above the terahertz region, so that the low-frequency noise plateau extends over the terahertz region. Here, frequency multiplication and mixing can take place at noise levels equal or below than that of full shot noise. We show that the signal-to-noise ratio of these SBDs is definitely superior to that of bulk semiconductors exploiting velocity-field nonlinearity.