On the Effect of Tap Length on LMS Adaptive Echo Canceller Performance

Simultaneous data transmission in both directions (full-duplex) over two-wired circuits can be achieved using two-wire to four-wire hybrid couplers. Transmission signal leakage through the near-end hybrid (near-end echo) and transmission signal reflection by the far-end hybrid (far-end echo) ending up in its own receiver due to imperfect hybrid isolation can greatly affect the correct detection of data from the other end. Adaptive echo cancellers are therefore used to nullify this effect using a finite impulse response (FIR) adaptive digital filter for which the number of coefficients must be quite large in order to cancel the far-end echo. In this paper, the data transmission system comprising the combined echo effect is simulated and an expression for the residual echo power is derived from which the relationship between adaptive echo canceller length and residual echo power can be deduced for a specified echo path. Apart from the uncancellable signal due to the far-end signal plus communication channel additive noise, the residual echo power is found to be made up of two components when the adaptive echo canceller length is smaller than that of the actual echo path. The first component represents another uncancellable signal resulting from the truncated terms in the echo path impulse response that are not modeled by the adaptive filter and therefore appear as additional error. The second component results from mismatch between the echo path impulse response and the adaptive canceller coefficients upon convergence due to using the least mean square (LMS) adaptation algorithm. This latter component is influenced by the LMS step size, the length of the adaptive filter and by both the afore-mentioned uncancellable signal powers. Simulation results were found to support the theoretical findings quite accurately. It is also found that, in general, when the tap length is reduced, the LMS step size can be more freely set for fast convergence with little perceptible increase in residual echo power