Some limiting theorems of some random quadratic forms

In this paper, the random quadratic form s1T(S1D1S1T+σ2I)-1s1 is considered. The main motivation comes from the application to wireless communication. For τ>0, it is shown that s1T(S1D1S1T+σ2I)-1s1 converges to a fixed quantity with convergence rate oa.s(N1/2-τ). Also, convergence in probability is established.