Acoustic echo cancellation (AEC) is a signal processing technique that is used in telecommunication systems with acoustic coupling between the loudspeaker and microphone to achieve echo-free full-duplex communication. Line echo cancellation is used in a telecommunication system to reduce the echo by subtracting an estimated echo from the circuit echo resulting from the impedance mismatch of the hybrid. The system notation for this paper is as follows: let x(n), y(n), (n) and e(n) represent the far-end, near-end, estimated echo and error signals, respectively. The cross-correlation between various signal components can be revealing to the state of the echo canceller and can be useful to the control of an echo canceller double-talk detectors).

The cross-correlation between the near-end and the estimated echo signals, γyd̂, and the cross-correlation between the near-end and error signals, γye, are referred to as the open-loop correlations. They reveal similar aspects of the echo cancellation system. For example, when γyd̂ is highly correlated the system is converged. Inversely, when γye is low thesystem has convergence. Using these correlations for double-talk detection can lead to some misleading results. For example, when the near-end and error signals are highly correlated, it is difficult to distinguish whether the two signals are correlated because you do not know if the system has not converged, or because the near-end signal contains mostly near-end speaker. Therefore, in order to determine whether the correlation is high because of a double-talk scenario, an additional statistic is required to ensure the echo canceller has achieved a convergent state.

The cross-correlation between the far-end and near-end signal, γxy, is referred to as the closed-loop correlation. Since it can be relatively safe to assume that far-end and near-end speaker signals are uncorrelated. Thus, when γxy is high, the echo canceller is in a echo-only scenario. When γxy is low, the system is either in a double-talk scenario or near-end only scenario. The downfall to this correlation over the open-loop correlations is it requires more computational complexity. The range of a series of cross-correlations with various delays in excitation signal need to be taken. The delay that produces the maximum cross-correlation represents the delay in the echo path. This delay estimate can be useful in systems in which the bulk delay of the echo path cannot be determined a priori or is variable throughout the communication. For example, in centralized network implementations of an acoustic echo canceller.

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