The impact of non-ideal delay line (DL) along with group delay ripple (GDR) on the performance of ultra wide bandwidth (UWB) system has not yet been studied in previous literatures. In this paper, according to the currently designed DLs, we propose a statistical GDR model to achieve a practical UWB DL, and investigate the degradation in average bit error rate (BER) caused by the GDR for the transmitted-reference (TR) UWB communication systems. According to the analysis results, an improved autocorrelation receiver (AcR) is proposed. Through Monte Carlo simulations, the great performance improvement of the proposed AcR is verified by comparing it with the conventional TR AcR under non-ideal DL conditions. The proposed receiver framework is simple enough to enable a tractable analysis, and provides valuable insights for designing a practical TR UWB AcR that experiences GDR.