Performance and Stability Analysis of Echo Cancellers Based on Training Sequences

Abstract

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 pseudonoise 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.

Design Criteria for FIR-Based Echo Cancellers

“…This architecture has been presented in our previous works [36], [37], along with an analytical framework aimed at the derivation of the expected performance.…”

“…• Here, a realistic finite-time impulse response of the transmit and receive filters is considered, whereas in [37] we considered ideal filters, with an infinite impulse response. This impacts on the analytical framework that models the echo-cancellation performance, outlined in the following, now better reflecting realistic conditions.…”

“…In [37] only the former issue was investigated, assuming that the impact of the latter is negligible. The dual assumption was made, instead, in [15].…”

“…In this paper, in particular, we develop the work already presented in [36] and [37], where a digital echo-canceller architecture has been proposed and investigated: the estimation of the coupling-channel between the transmitting and the receiving antennas is achieved through the injection in the repeated signal of a training sequence, and the echo is cancelled by a negative feedback constituted by an adaptive digital filter that reproduces the characteristics of the couplingchannel. This kind of echo canceller has been first proposed and implemented for SFN DVB-T repeaters in the second part of the last decade, but its general purpose design makes it independent of the communication technology.…”

“…Starting from the performance and stability analysis carried out in [37] (which is extended in [38] by considering the impact of quantization noise), in this paper we analytically derive the general design criteria for the proposed architecture. In particular, the following aspects are thoroughly investigated:…”