Effects of gain and phase imbalance on sum-difference code tracking loop´s performance in spread spectrum systems

The nonlinear renewal process approach (RPA) is applied to analyze the noncoherent sum-difference loop (SDL) with gain and phase imbalance for spread spectrum systems. In the analysis, the code acquisition boundary is equal to the branch offset, 0<δ⩽1. The results indicate that under phase imbalance, when δ⩾0.5 and with gain balance, the values of the DC bias of the SDL are small and will not change with the loop signal-to-noise ratio (SNR); when δ<0.5 and with a low loop SNR, the DC bias becomes larger which will result in the SDL loss of lock. A larger branch offset may result in a higher mean-time-to-lose-lock (MTLL) for the SDL with gain and phase imbalance; however, the RMS tracking error has not obviously changed with the increasing branch offset. Furthermore, it is shown that in case where the early and late branch of the SDL can not be implemented with equal gain, one can get better performance results by putting the arm with smaller gain in the late branch of the SDL