Study of properties of complex time-division signal ensembles with a periodic structure for ultra-wideband code-division multiple access systems

This paper investigates unequal-energy ensembles of periodic complex time-division signals for ultra-wideband code-division multiple access (UWB CDMA) systems operating under interference-limited conditions. The study focuses on establishing analytical relationships between signal energy distribution, maximum mutual correlation, multiple-access interference (MAI), and achievable signal-to-interference-plus-noise ratio (SINR) characteristics for periodic impulse signal ensembles with minimum similarity properties. An analytical model of unequal-energy periodic signal ensembles is developed under the single-overlap condition, where no more than one pulse overlap can occur between arbitrary signal pairs for any temporal shift. Based on this model, analytical expressions for the maximum normalized mutual correlation, total MAI energy, normalized interference level, and interference-limited SINR are obtained. It is shown that, unlike conventional equal-energy ensembles, the interference characteristics of unequal-energy ensembles are determined jointly by correlation properties and by the internal energy distribution of the signals. The obtained results demonstrate that users employing lower-energy signals experience the most unfavorable interference conditions, whereas higher-energy users achieve significantly improved interference immunity and SINR performance. Additionally, the concept of structural equivalent ensemble size is applied to characterize ensemble-level interference behavior and to analyze the influence of ensemble size and signal energy distribution on system performance.