Blind equalization and system identification by Chi C.-Y., Feng C.-C., Chen C.-H., Chen C.-Y.

By Chi C.-Y., Feng C.-C., Chen C.-H., Chen C.-Y.

The absence of teaching indications from many sorts of transmission necessitates the common use of blind equalization and procedure identity. there were many algorithms constructed for those reasons, operating with one- or two-dimensional indications and with single-input single-output or multiple-input multiple-output, genuine or advanced structures. it truly is now time for a unified remedy of this topic, declaring the typical features of those algorithms in addition to studying from their varied views. "Blind Equalization and method identity" offers any such unified therapy offering thought, functionality research, simulation, implementation and functions. it is a textbook for graduate classes in discrete-time random procedures, statistical sign processing, and blind equalization and procedure identity. It includes fabric so one can additionally curiosity researchers and engineers operating in electronic communications, resource separation, speech processing, and different, comparable purposes.

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N (x)} be a set of real or complex orthogonal functions in L2 [xL , xU ] where xU xL φk (x)φ∗m (x)dx = Eφ , k = m, 0, k = m. e. , θn such that the following mean-square-error (MSE) is minimum: xU JMSE (θk ) = |f (x) − sn (x)|2 dx. 2 Mathematical Analysis xU JMSE (θk ) = 37 n |f (x)|2 dx + Eφ xL |θk |2 k=−n n xU θk∗ − xL k=−n xU = xU f (x)φ∗k (x)dx + θk n |f (x)| dx + Eφ 2 xL k=−n xU 1 θk − Eφ n − Eφ k=−n 1 Eφ f ∗ (x)φk (x)dx xL xL 2 f (x)φ∗k (x)dx 2 xU f (x)φ∗k (x)dx . 67) and the corresponding minimum value of JMSE (θk ) is given by n xU |f (x)|2 dx − Eφ min{JMSE (θk )} = xL |θk |2 .

84) k=−∞ and make use of this in many applications. In other words, the theory of Fourier series should be broadened for more extensive applications. The extended theory of Fourier series is, however, beyond the scope of this book; refer to [23, 24] for the details. , θL are real or complex unknown parameters to be determined. An optimization problem is to find (search for) a solution for θ which minimizes or maximizes the function J(θ), referred to as the objective function. There are basically two types of optimization problems, constrained optimization problems and unconstrained optimization problems [12, 25, 26].

132) . 134) θ = θ [i] where C[i] = A[i] − B[i] D[i] = B[i] A[i] A[i] ∗ −1 ∗ −1 B[i] ∗ −1 , . 134) by forcing B[i] = 0 for all iterations, and obtain the following “approximate” update equation for complex θ: θ[i+1] = θ[i] − μ[i] A[i] −1 · ∂J(θ) ∂θ∗ . 137) as the approximate Newton method.

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Blind equalization and system identification by Chi C.-Y., Feng C.-C., Chen C.-H., Chen C.-Y.
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