In a previous correspondence [1], we have studied an echo canceller (EC) compensating far-end echos affected by frequency offset. It has been shown that the sensitivity of the loop gain versus the powerPof the echo and the powerSof the signal, can be reduced by adoption of a normalized gain multiplied by the echo power. In this correspondence a novel and very simple algorithm is described that further reduces this sensitivity and yields an optimum phase loop gain proportional to(S/ p)^{1/6}.

In an echo canceller (EC) compensating far-end echos affected by frequency offset, the phase loop gain is highly dependent on the echo and signal powers. Adoption of a normalized gain multiplied by the echo power yields an improved robustness. It is shown that the latter gain depends only on the echo-to-signal ratio. Practical implementation of this idea is realized by generating a first unitary echo replica, on which the DPLL will act, and then controlling the output power. The system has the additional advantage of a reduced binary size for the canceller taps.

It is well known that implementation of adaptive digital filters for echo cancellation in full-duplex transmission over telephone lines requires a large number of bits for the tap representation. This is due to the large dynamic ranges of the echo and far-end signal. In this paper, we introduce a new echo canceller: the "controlled gain echo canceller" (CGEC) which uses an adaptive gain control at the output of the classical echo canceller (CEC). A feedback loop permits approximate regulation of the front-edge CEC output power at a nominal level, independently of the echo and far-end signal levels. By this means, the precision required for adaptation is reduced to a minimum value. The analysis of adaptation, convergence, residual echo power, and computational complexity is given for the CGEC and compared to the similar quantities in a CEC; computer simulation results are presented. As an example, a 64 taps CGEC with only 16 bits instead of 20 can achieve secure binary data transmission (with bit error rate less than10 ^{-6}) for a far-end signal-to-noise ratio of 16 dB and for an echo to far-end signal ratio of 20 dB, independently of the echo and far-end signal powers.