Complex numbers in $\tt ifft$ of an MMSE amplitude estimator
Note that the MMSE estimator gives you a real-valued gain function with which the noisy signal amplitude is modified. Equation (7) is actually

$$\hat{A}_k=G_kR_k\tag{1}$$

where the gain $G_k$ is a function of $v_k$ and $\gamma_k$. You want to reconstruct the original signal as

$$\hat{X}_k=\hat{A}_ke^{j\phi_k}\tag{2}$$

where $\phi_k$ is the phase of the noisy signal $Y_k=R_ke^{j\phi_k}$. Combining (1) and (2) gives

$$\hat{X}_k=G_kR_ke^{j\phi_k}=G_kY_k\tag{3}$$

So you can simply multiply the complex spectral component of the noisy signal with the gain $G_k$ to get the estimation of the spectral component of the input signal.

In Matlab this is easily done. You just have to extend the gain vector to satisfy the symmetry condition for real-valued signals:

X = Y.*[gain; gain(N-1:-1:2];


where I assume that the vector gain has elements $G_k$, and that N is its length. The relation between the FFT length and N is N = Nfft/2+1.