Optimal noise benefits in Neyman-Pearson and inequality-constrained statistical signal detection
IEEE Transactions on Signal Processing
Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework
Digital Signal Processing
Noise-enhanced clustering and competitive learning algorithms
Neural Networks
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Electrical noise can help pulse-train signal detection at the nanolevel. Experiments on a single-walled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finite-variance and infinite-variance noise: small amounts of noise enhanced the nanotube detector's performance. The experiments used a carbon nanotube field-effect transistor to detect noisy subthreshold electrical signals. Two new SR hypothesis tests in the Appendix also confirmed the SR effect in the nanotube transistor. Three measures of detector performance showed the SR effect: Shannon's mutual information, the normalized correlation measure, and an inverted bit error rate compared the input and output discrete-time random sequences. The nanotube detector had a threshold-like input-output characteristic in its gate effect. It produced little current for subthreshold digital input voltages that fed the transistor's gate. Three types of synchronized white noise corrupted the subthreshold Bernoulli sequences that fed the detector. The Gaussian, the uniform, and the impulsive Cauchy noise combined with the random input voltage sequences to help the detector produce random output current sequences. The experiments observed the SR effect by measuring how well an output sequence matched its input sequence. Shannon's mutual information used histograms to estimate the probability densities and computed the entropies. The correlation measure was a scalar inner product of the input and output sequences. The inverted bit error rate computed how often the bits matched between the input and output sequences. The observed nanotube SR effect was robust: it persisted even when infinite-variance Cauchy noise corrupted the signal stream. Such noise-enhanced signal processing at the nanolevel promises applications to signal detection in wideband communication systems and biological and artificial neural networks