Design of a device for optimal reception of signals against the background of a two-component Markov interference - Ananieva, Olha; Babaiev, Mykhailo; Blyndiuk, Vasyl; Davidenko, Mykhailo (Eastern-European Journal of Enterprise Technologies, 2017)
We synthesized optimal receiver of signals observed against the background of a two-component additive Gaussian Markov interference. The inclusion of such a receiver into an automated locomotive signal system would significantly increase its noise immunity. We obtained mathematical expressions for the transformations that need to be performed over the counts of voltage of the observed mixture of signal and interference. It is shown that in a general case these transformations are nonlinear and require summing the specified counts with weight coefficients whose exact numerical values are rather difficult to calculate without specifying statistical properties and relationships of the interference components. We refined expressions that make it possible to calculate specified coefficients for the case of a Markov Gaussian interference. They proved to be variable magnitudes, expressed through the variance of interferences, their correlation coefficients and magnitudes of voltages of time-adjacent counts of the observed mixture of signal and interference. As a result, the operations, required for optimal reception, of calculating a weighted correlation sum and a weighted energy sum are nonlinear. They are based on the fulfillment of four arithmetic operations and squaring, which is easy in terms of technical implementation. Under condition of statistical independence of counts, the solvers accumulate sums of increments of the input and reference signals, respectively. The quality of signal recognition ensured by the designed optimal receiver was estimated using computer simulation. It is shown that for actual situations the probability of error recognition of informational signals does not exceed 10-2 per one coded parcel. The practical application of results obtained in our study would make it possible to improve safety and rhythmicity in the motion of trains