1. EE-608 Course project Adaptive Echo Cancellation By LMS Algorithm Pannir Selvam E Vikram Mehta Praveen Goyal (05307810) Guided By Prof. U.B. Desai

2. AIM Echo Cancellation by minimizing the Echo Cancellation by minimizing the “ratio of mean square value of the residual “ratio of mean square value of the residual echo to the variance of the echo signal” using Dual LMS algorithm. echo to the variance of the echo signal” using Dual LMS algorithm. That is, to minimize That is, to minimize R 2 (k) = σ 2 ε (k)/σ 2 u = E {[e(k)- e(k)] 2 }/ σ 2 u R 2 (k) = σ 2 ε (k)/σ 2 u = E {[e(k)- e(k)] 2 }/ σ 2 u ^

3. Basic Configuration of an Echo-Canceller Source Impulse Response of Echo path G Trans Path Adaptive Digital Filter Coeff. Vector Of Digital FIR Filter C(k) Receiver ∑ ∑ a(k) r(k) e ^ (k) e(k) u(k)+ + +-

4. Cascaded LMS Algorithm e(k) = A (k) * G e(k) = A (k) * G e(k) = A (k) * C(k) e(k) = A (k) * C(k) r(k) = u(k) + e(k) – e(k) r(k) = u(k) + e(k) – e(k) r(k) = u(k) + A (k) * (G-C(k)) r(k) = u(k) + A (k) * (G-C(k))Where G is Echo Path vector with length N a(k) is transmitted Vector C(k) is coeff. Vector of the digital FIR filter u(k) is the received signal T ^ T ^ T

5. References 1.“On the optimum size for the adaptive sign and LMS algorithms”. R.-Y. Chen and C.-L. Wang 2.“Dual LMS Algorithm for adaptive Echo Cancellation”, R.-Y. Chen and C.-L. Wang. 3.“Adaptive Noise Cancelling: Principles and Applications”, Bernard Widrow et al. IEEE, Vol. 63 No. 12 pp. 1692-1716 Dec 1975