Noise stability of signal reception algorithms with multipulse pulse-position modulation

An algorithm for estimating time positions and amplitudes of a periodic pulse sequence from a small number of samples was proposed. The number of these samples was determined only by the number of pulses. The performance of this algorithm was considered on the assumption that the spectrum of the original signal is limited with an ideal low-pass filter or the Nyquist filter, and conditions for the conversion from one filter to the other were determined. The efficiency of the proposed algorithm was investigated through analyzing in which way the dispersion of estimates of time positions and amplitudes depends on the signal-to-noise ratio and on the number of pulses in the sequence. It was shown that, from this point of view, the efficiency of the algorithm decreases with increasing number of sequence pulses. Besides, the efficiency of the proposed algorithm decreases with decreasing signal-to-noise ratio. It was found that, unlike the classical maximum likelihood algorithm, the proposed algorithm does not require a search for the maximum of a multivariable function, meanwhile characteristics of the estimates are practically the same for both these methods. Also, it was shown that the estimation accuracy of the proposed algorithm can be increased by an insignificant increase in the number of signal samples. The results obtained may be used in the practical design of laser communication systems, in which the multipulse pulse-position modulation is used for message transmission.