THEORETICAL FOUNDATIONS OF EQUIVALENT TRANSFORMATION OF UNEQUAL-ENERGY COMPLEX SIGNAL ENSEMBLES FOR CODE DIVISION MULTIPLE ACCESS SYSTEMS

Abstract

A promising direction in the development of ultra-wideband access systems is the transition to code division multiple access based on ensembles of unequal-energy complex pulse signals. In contrast to equal-energy signal ensembles, for which the relations for efficiency evaluation mostly have a simple form suitable for application, the efficiency evaluation of unequal-energy complex signal ensembles usually requires the use of the corresponding relations in general forms. The article develops the theoretical foundations of the equivalent transformation of unequal-energy complex signal ensembles for code division multiple access systems, which provide the reduction of the relations for efficiency evaluation to a form similar to that of the equal-energy case. An approximate transformation of an unequal-energy complex signal ensemble into an equivalent equal-energy complex signal ensemble, equivalent in terms of the total signal energy, is determined. This transformation represents the effect of nonuniform signal energy distribution on multiple access interference through a change in the volume of the equivalent equal-energy complex signal ensemble at a constant value of the maximum ensemble cross-correlation. This is achieved by the approximate reduction of the set of signal energies to a scalar value of the volume of the equivalent equal-energy complex signal ensemble, which results in reducing the relations for efficiency evaluation of unequal-energy complex signal ensembles to a form similar to that of equal-energy complex signal ensembles. To implement the equivalent transformation, two interrelated variants of approximate scalar reduction of the set of signal energies of the ensemble to a scalar value are proposed. These variants are based on a concentration measure and its inverse concentration normalized to the equal-energy value. They have opposite effects on the change in the volume of the equivalent equal-energy complex signal ensemble and thereby define two different interpretations of the effect of multiple access interference on users with the lowest and highest signal energies, which directly corresponds to different degrees of manifestation of the signal dominance effect.