Implementing MVDR beamformer in the STFT domain
In this context $\Phi_y$ often describes the (estimated) power spectral density matrix  of $y(f)$, which is
$$\Phi_y(f) = E\{y(f) y^H(f)\} = 
\begin{bmatrix}
 y_1 \cdot y_1^*(f),&amp; y_1 \cdot y_2^*(f),&amp; \dots    \\
 \vdots        &amp; \ddots    &amp;          \\
 y_M \cdot y_1^*(f),&amp;               &amp; y_M \cdot y_M^*(f)  \\
   \end{bmatrix},$$
where $M$ is the number of channels, and each element of the matrix corresponds to the cross-power spectral density of two channels for this frequency. Consistent estimates of PSDs in blockwise STFT processing can be obtained, for example, using Welch's method (pwelch in MATLAB).

I am also unsure about your steering vectors and complex conjugate transposes (which I assume is the $\cdot^H$ in your notation). They need to make the steering vector compensate the delay for a specific direction.

From my memory, I think the formulas should be

$$ h_\text{MVDR}(f) = \frac{\Phi_y^{-1}(f)d(f)}{d^H(f)\Phi_y^{-1}d(f)}$$

and 

$$ Z(f) = h_\text{MVDR}(f)^T y(f).$$

I think the orginal MVDR paper is this one by Capon. You might want to double-check notations since a complex conjugate does change the beamformer's output quite a bit.

Edit: Thanks to Stanley Pawlukiewicz for pointing out my error!