А.V. Rabin – Ph.D. (Eng.), Associate Professor, Director of the Centre of Scientific Research Coordination, Saint-Petersburg State University of Aerospace Instrumentation
Noise immunity is one of the most important characteristic parameters of modern communication systems. Research and development of approaches to its greater increase at the fixed transfer rate by use of special mathematical methods is a relevant scientific problem. This article is devoted to a solution of this problem.
In modern ways of noise immunity’s increase a channel is fixed as a rule. Thus, transitional probabilities of output signals (with the fixed probabilities of input signals) don’t change. As a result, the number of phases in modulation in such systems doesn’t change also. For the reason specified above there is no channel parameters dependence on the applied way of channel coding. The feature of signals’ processing in receivers in telecommunication systems are the basis of the offered orthogonal coding: the transmitted signals are chosen according to the decision of developers, and processing of the transmitted signals and noise is made with use of special approach. If in this case orthogonal codes are applied, increase of transmitted signals and decrease of noise are provided. This characteristic exists not only in the channels with additive noise, but also in the fading channels.
For formation of orthogonal codes, it is required to implement the synthesis of matrices with equal number of lines and columns. The product of these matrices is the unitary matrix multiplied by the monomial characterizing the correcting ability of a code.
This problem is solved with the condition that elements of the matrices are polynoms of the degree 1. As a result, the class of the matriсes allowing to solve practical problems of noise immunity’s increase was synthesized.
Technical realization of orthogonal coding is characterized by low complexity: on each step a decoding process is reduced to calculation of several dot products and comparison with fixed (zero, in this case) threshold. For this reason, the offered way of coding and design of receiving and transmitting devices can be implemented in various communication systems.
The gain in the signal-to-noise ratio is got as a result of a more effective use of an energy of transmitted signals. For a transmitting of one symbol energy of several symbols is accumulated. In the example reviewed in the article each information symbol is transmitted by eight symbols, that increases energy of the received signal.
Thus, the proposed way of orthogonal coding can be considered as a variety of reception of signals of M-ary DPSK with an optimum choice of a modulation code. Optimization is reached by averaging of error rate on all digits of the M-ary code.
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