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Stochastic Resonance of Binary Signals

Stochastic Resonance (SR) is a phenomenon where added noise can be used to increase the Signal to Noise Ratio (SNR) of a noisy signal. This is accomplished by applying the nonlinear filter y‘ = ayby3 + x + ξ where x is the noisy signal, ξ is the extra noise, is the output signal, and a and b are parameters to be chosen. The nonlinear filter creates two stable states at y = ±(a/b)½, which the output signal jumps between due to the energy of the added noise.

Generally, SR is thought of as being applicable to a signal at the time of capture to remove noise which was inadvertently captured at the same time. Thus SR could be used to clean a speech signal before processing. SR can also be used to clean a binary signal that has been transmitted through a noisy channel. This signal is simpler to work with due to the fact that its ideal values are restricted to 0 and 1. If the Signal to Noise Ratio (SNR) of the received signal is small, for example around 0dB, then it becomes difficult to determine whether a section of signal is supposed to be 0 or 1. By applying SR, we can enhance the signal so that these  determinations can be made.

This form of SR enhancement has several important applications. It can be implemented on a wireless router or access point to increase its effective receiving range. Without SR, there would be data that were corrupted beyond repair because too much noise was introduced during transmission from a distant transmitter. With SR, this data can be reconstructed. This can also be used for the lawful interception of wireless transmissions. A receiver can be placed far enough away from the transceiver that is transmitting the data to be intercepted so that it is considered out of range, but by the use of SR it can retrieve the data.

VOCAL Technologies, Ltd.
520 Lee Entrance, Suite 202
Amherst New York 14228
Phone: +1-716-688-4675
Fax: +1-716-639-0713