Probability density function (pdf) of $\|{\bf X}{\bf a}\|_{2}^{2}$, given the pdf of the elements of random matrix ${\bf X}$

Question

I am reading some papers regarding Johnson-Lindenstrauss lemma and some proofs of the restricted isometry property (RIP) in compressive sensing.

I have the following problem:

${\bf X} \in \mathbb{C}^{M \times N}$ is a random matrix, whose elements $X_{ij} ~ (1 \leq i \leq M, 1 \leq j \leq N)$ are independently distributed and have the identical probability density function, say $f(x)$.

What is the distribution of $\|{\bf X}{\bf a}\|_{2}^{2}$, where ${\bf a} \in \mathbb{C}^{N}$ is an arbitrary scalar vector? How does it related to $f(x)$?