asymptotic distribution of quadratic form

Question

I am considering the asymptotic distribution of the following statistics the form $ \ \Gamma =\frac{1}{\sqrt{nm}}\sum_{i=1}^{n}\mathbf{u}_{i}^{T}\mathbf{A}_{m}% \mathbf{u}_{i}, \ $ where $\mathbf{u}_{i}=\left( u_{i1},\ldots ,u_{im}\right) ^{\prime }$ is vector of independently distributed idiosyncratic errors and $\mathbf{A}_{m}$ is a $% m\times m$ bounded matrix. Is there any reference of establishing the limiting distribution of $\Gamma ,$ i.e., the distribution of $\Gamma $ when $n$ and $m$ go to $\infty $ (could be jointly or sequentially)? Any reference on this? Thanks a lot!