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There are also methods that do not require a training sequence; these methods are referred to as blind equalization (e.g. constant modulus algorithm). …

The mapping from $z_n$ to $s_n$ is not bijective, so it can't be inverted. This means that even in the transmitter, $z_n$ cannot be recovered from $s_n$. This is why the constant modulus algorithm (CM …

If I'm not mistaken the only solution for $\mathbf{T}$ which is independent of the vector $\mathbf{X}$ is a diagonal (complex) matrix, where the diagonal satisfies the complex conjugate symmetry. EDI …

The formula you need, which I don't see in the scanned pages, is the N-dimensional Gaussian distribution of the received vector given that the signal $s_m$ was transmitted: $$f(\vec{r}|s_m)=\frac{1}{ …

Also, perfect equalization of the channel is not always desired if the channel is not only dispersive (i.e., acts a filter) but if it also introduces noise. …

If $F^*(1/z)$ is supposed to denote $[F(1/z)]^*$, then the book would be wrong. Note that $$\big[F(1/z)\big]^*=\left[\sum_{n=-\infty}^{\infty}f[n]z^n\right]^*=\sum_{n=-\infty}^{\infty}f^*[n](z^*)^n$$ …

In practice you can design an approximate equalization filter by choosing the filter coefficients of the equalizer such that the error $$\epsilon=\sum_i\left|H(e^{j\omega_i})E(e^{j\omega_i})-e^{-j\omega_i …

Note that what you're trying to do is equalization, as opposed to channel estimation. …

The generalized eigenvalue problem is given by $$Bw=\lambda Cw\tag{1}$$ where $\lambda$ is the generalized eigenvalue of the matrices $B$ and $C$. Multiplying $(1)$ from the left with $w^H$ (with $^ …

This problem is related to deconvolution and equalization. …

If the channel just adds noise and does not cause any distortion (as in the first figure), you can design the transmit filter $g(t)$ such that, when combined with its matched filter at the receiver, t …

signal), and in such noisy conditions the CMA cannot perform properly. you have a channel with $3$ taps, and your equalizer length is also only $3$ taps; this is much too short to achieve any reasonable equalization …