Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means:

$$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation

The signal $y[n]$ could be complex since we can consider the channel $h[n]$ to be complex too.

In normal case, $h[n]$ should be known in order to estimate $x[n]$ using deconvolution process.

My question what about if I only know that $ \forall n$, $$x[n] \in \left\{ -1, 1 \right\}$$ it means $x[n]$ is either $1$ or $-1$, it's a vector and each value in the vector is $1$ or $-1$ ($x[n]$ is a vector of +1/-1 we means I need to estimate the whole vector).

For example if its length is $4$ , it could be $[1,-1,-1,1]$ or $[1,1,1,1]$ and so on. Is it possible in that case to perform anyway, for example, deconvolution or any other method to estimate $x[n]$?

NP: The maximum length of $x[n]$ can be $256$ and maximum length of $h[n]$ can be $64$

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means:

$$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation

The signal $y[n]$ could be complex since we can consider the channel $h[n]$ to be complex too.

In normal case, $h[n]$ should be known in order to estimate $x[n]$ using deconvolution process.

My question what about if I only know that $ \forall n$, $$x[n] \in \left\{ -1, 1 \right\}$$ it means $x[n]$ is either $1$ or $-1$, it's a vector and each value in the vector is $1$ or $-1$ ($x[n]$ is a vector of +1/-1 we means I need to estimate the whole vector).

For example if its length is $4$ , it could be $[1,-1,-1,1]$ or $[1,1,1,1]$ and so on. Is it possible in that case to perform anyway, for example, deconvolution or any other method to estimate $x[n]$?

NP: The maximum length of $x[n]$ can be $256$ and maximum length of $h[n]$ can be $64$ , and we have a known information about vector $x[n]$ which is the $sum(x[n]) = 0$.

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means:

$$y[n] = h[n] \star x[n]$$ where $\star$ is the convolution operation

The signal $y[n]$ could be complex since we can consider the channel $h[n]$ to be complex too.

In normal case, $h[n]$ should be known in order to estimate $x[n]$ using deconvolution process.

My question what about if I only know that $ \forall n$, $$x[n] \in \left\{ -1, 1 \right\}$$ it means $x[n]$ is either $1$ or $-1$, it's a vector and each value in the vector is $1$ or $-1$ ($x[n]$ is a vector of +1/-1 we means I need to estimate the whole vector).

For example if its length is $4$ , it could be $[1,-1,-1,1]$ or $[1,1,1,1]$ and so on. Is it possible in that case to perform anyway, for example, deconvolution or any other method to estimate $x[n]$?

NP: The maximum length of $x[n]$ can be $256$ and maximum length of $h[n]$ can be $64$

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means:

$$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation

The signal $y[n]$ could be complex since we can consider the channel $h[n]$ to be complex too.

In normal case, $h[n]$ should be known in order to estimate $x[n]$ using deconvolution process.

My question what about if I only know that $ \forall n$, $$x[n] \in \left\{ -1, 1 \right\}$$ it means $x[n]$ is either $1$ or $-1$, it's a vector and each value in the vector is $1$ or $-1$ ($x[n]$ is a vector of +1/-1 we means I need to estimate the whole vector).

For example if its length is $4$ , it could be $[1,-1,-1,1]$ or $[1,1,1,1]$ and so on. Is it possible in that case to perform anyway, for example, deconvolution or any other method to estimate $x[n]$?

NP: The maximum length of $x[n]$ can be $256$ and maximum length of $h[n]$ can be $64$