# Questions tagged [complex-random-variable]

The tag has no usage guidance.

14 questions
Filter by
Sorted by
Tagged with
52 views

### Exact formula for 8-PSK BER

Is there an exact formula for the probability of bit error (or bit error rate, BER) for 8-PSK (in the literature, course slides, etc.)? I am not referring to SEP (Symbol Error Probability) but BER. ...
52 views

### How can I add complex WGN to a complex damped signal for a specified SNR?

I want to add complex wgn to a signal for a specified SNR. I have been using the following lines: ...
49 views

### 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 ...
51 views

### 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 &...
261 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 ...
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 ...