# Questions tagged [complex-random-variable]

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### nature of output of the addition of white noise with colord noise

I want to know that the addition of a uncorrelated time series x with a correlated time series, say y generates a time series ...
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### Detecting complex signal within complex AWGN using Neyman Pearson statistic

I need to construct a Neyman Pearson statistic for detecting a complex signal with known amplitude and unknown phase in additive complex Gaussian noise. My hypotheses are: \begin{align} \mathcal{H}_0 &...
164 views

### Signal with Complex Gaussian noise

If I have: $$y = x_r+jx_i + n_r +j n_i$$ with $n_r$ and $n_i$ Gaussian with mean 0 and variance $\sigma^2$, what is the pdf of the envelope |y| and phase(y)? Is it still Rayleigh-distributed and ...
151 views

### Characteristic function of a random Gaussian variable

I have to find the characteristic function of a random Gaussian variable of $$\sigma_z (w) = E e^{i w z }$$. This is the variable and I know , from the theory that the characteristic function of ...
I have a Rayleigh channel that transmits discrete values according to the following: $$y(n) = h(n) * s_n + \omega_n$$ Where $y$ is the received message, $s_n$ is the symbol sent (constellation 2-PSM), ...