Methodology of Equivalent Transformations of Unequal-Energy Complex Signal Ensembles in Code-Division Multiple Access Systems

The paper develops a methodology of equivalent transformations for ensembles of complex signals with unequal energies in code-division multiple access (CDMA) systems. The relevance of this study arises from the limited applicability of classical equal-energy ensemble models to the analysis of CDMA systems under conditions of user energy heterogeneity. The proposed approach is based on preserving the total ensemble energy and its correlation structure, while transferring the effect of non-uniform signal energy distribution into scalar equivalence parameters. Within this framework, structural and energy equivalent transformations are introduced, forming a dual pair of equivalent volumes that ensure a consistent reproduction of the level of multiple-access interference for unequal-energy ensembles. It is shown that the proposed equivalent volumes retain the physical meaning of well-known correlation-based performance criteria and enable the use of analytical relations derived for equal-energy models without modification. The results of experimental modelling confirm the validity of the equivalent transformations and the adequacy of interference reproduction for various scenarios of energy heterogeneity. The obtained results can be employed for the analysis, comparison, and optimisation of signal ensembles in CDMA systems under conditions of non-uniform user energy distribution