Chi-squared distribution conjecture for the squared norm of effective channels

Let ${\bf h}^{\textrm{eff}}_i$ denote the effective channel vector for user $i$ in a system with $M$ transmit dimensions and an effective-channel subspace of dimension $N$. Chi-squared distribution conjecture. The squared norm $\lVert {\bf h}^{\textrm{eff}}_i\rVert^2$ is chi-squared distributed with $2(M-N+1)$ degrees of freedom. This conjecture concerns the distribution of the effective channel magnitudes, complementing the preceding characterization of their normalized directions as independent isotropic vectors; the provided text does not establish the claimed distribution or indicate whether it has been resolved.