Method of synthesis and reduction of ML-algorithm for division demodulation of unequal power synchronous QPSK signals

In the theory of multi-user detection of digital signals (DS), the best in terms of noise immunity are Maximum Likelihood (ML) algorithms, which involve the formation of posterior probabilities of the states of information group and individual discrete parameters (DP) of each user. The known results of the synthesis and analysis of the noise immunity of ML algorithms for separation-demodulation of mutually non-orthogonal BPSK signals indicate their high, potentially achievable noise immunity and at the same time the exponential dependence of their complexity on the number and position of the signals to be separated. At present, the results of the reduction (simplification) of such algorithms to a form acceptable for practical applications have already been obtained. Of undoubted interest are the answers to further questions about the possibilities of such simplifications in cases where mutually non-orthogonal signals are more complex than binary ones. The synthesis results are presented and the possibility of technologically acceptable simplifications of the algorithm for the separation-demodulation of two mutually non-orthogonal QPSK signals, optimal according to the criterion of minimum error probability in the estimation of information DPs of each individual user, is considered. The possibility of approximations of analytically complex hyperbolic transfer functions of compensation paths by simple linear-polygonal ones is investigated. A structural diagram of a reduced algorithm for the separation-demodulation of two mutually non-orthogonal QPSK signals is proposed. It is demonstrated that, while ensuring a cancellation in instantaneous powers between the signals of about 9 dB, it is possible to abandon the compensation of the influence of a less powerful signal on a more powerful one, which significantly simplifies the separation-demodulation algorithm. Additional simplification is achieved by abandoning the elimination of the mediated reverse influence of a less powerful signal through a more powerful one. The proposed simplifications lead to losses in noise immunity in the range of 1-2.5 dB, depending on the degree of mutual non-orthogonality.