I want to find the distribution of the following random variable:
$v = \| a_1b_1e^{j\theta_1} + a_2b_2e^{j\theta_2} + \dots + a_Mb_Me^{j\theta_M}\|$
where $\theta_i$ is a random variable with known distribution and $a_i$ and $b_i$ are complex deterministic values. We also know that:
$\| a_1b_1 + a_2b_2 + \dots + a_Mb_M\| = 1$
I have done simulations and seen that we can fit a Rice distribution to $v$ with high accuracy, but I cannot figure out the Rice distribution parameters.