Estimation of the energy of interfering signals in a code division multiple access system based on unequal-energy complex signals for users susceptible to dominance by other users' signals

In a code-division multiple access system, when a user’s signal is received, the signals from the other users are treated as interfering signals and produce multiple-access interference. For unequal-energy complex signal ensembles, a nonuniform signal-energy distribution causes the total energy of interfering signals to differ among users and gives rise to the signal-dominance effect. This study aims to obtain an estimate of the energy of interfering signals for users susceptible to signal dominance from other users, to be used as a pessimistic estimate for the ensemble as a whole. To reduce the set of individual values to a single estimate, the unequal-energy complex signal ensemble is equivalently transformed into a hypothetical equal-energy complex signal ensemble while preserving the total signal energy. It is shown that the normalized total energy of interfering signals for users susceptible to signal dominance from other users is approximately equal to the structural equivalent size, which therefore provides a pessimistic estimate for the unequal-energy complex signal ensemble as a whole. For equal-energy complex signal ensembles, the structural equivalent size is equal to the actual ensemble size, corresponding to a uniform signal-energy distribution. As the degree of nonuniformity in the signal-energy distribution increases, the structural equivalent size increases monotonically toward an upper bound corresponding to concentration of the total ensemble energy in a single signal—the highest possible nonuniformity for a fixed total signal energy. Thus, the structural equivalent size of an unequal-energy complex signal ensemble represents the calculated number of equal-energy complex signals in an ensemble with the same total signal energy as the original ensemble. It increases with the degree of signal-energy nonuniformity, provides a pessimistic estimate of the normalized total energy of interfering signals for users susceptible to signal dominance from other users, and allows performance metrics developed for equal-energy complex signal ensembles to be extended to unequal-energy complex signal ensembles by substituting the structural equivalent size into the corresponding expressions for equal-energy complex signal ensembles.