The distribution of the 2-norm based on non-zero mean complex Gaussian variable

Question

Assume a $N$-dimensional vector $a \sim {\rm{{\cal C}{\cal N}}}\left( {\mu ,{\sigma ^2}{I_N}} \right)$ and also define a $N$-dimensional complex vector $b$, what is the distribution of $\left| {{a^T}b} \right|_2^2$, where $T$ is transpose.