Performance and stability analysis of echo cancellers based on training sequences

We analyze a two-stage echo cancellation technique for on-channel repeaters (OCRs) based on the reconstruction of the coupling channel impulse response via digital filtering. The estimation of the coupling channel between the transmitting and the receiving antennas is achieved through the injection in the repeated signal of locally generated low-power pseudo-noise sequences or trains of short pulses. The analytical model developed in this paper permits the investigation of some important performance figures, such as the mean rejection ratio, the echo suppression and the echo suppression at nominal position. In addition, a new analytical framework dealing with canceller stability issues, arising due to the non perfect echo cancellation, is derived. Specifically, an upper bound on the probability of instability of the canceller is provided. As shown in the numerical results, this framework permits the identification of the main OCR design guidelines. Finally, we will validate our analytical models by showing their accordance with the experimental measurements realized with the OCR prototypes we developed.