## 4 Computer Simulation Results
### Evaluation Metrics
#### 4.4.1 Beamformer Baselines for Performance Comparison
DOA-Based MVDR Beamformer Baseline  
The DOA_MVDR system computes the steering vector from the DOA information which can be expressed as follows:  
\[\mathbf{h}_{\mathbf{t}\mathbf{t}}=[\mathbf{e}]^{\frac{2\pi\mathbf{t}}{\mathbf{\tau}_{1}}}\mathbf{e}]^{\frac{ 2\pi\mathbf{t}}{\mathbf{\tau}_{2}}}\mathbf{\tau}_{2}\ldots\mathbf{e}]^{\frac{2\pi\mathbf{t}}{\mathbf{ \tau}_{C}}}\mathbf{\tau} \tag{46}\]  
In (46), \(\mathbf{h}_{\mathbf{t}\mathbf{t}}\) denotes the beam steering vector, \(v\) the speed of sound waves, and \(\mathbf{\tau}_{C}\) the propagation delay w.r.t origin for microphone indexed \(C\). The steering vector is constructed from the DOA information and can be used to construct SCM corresponding to speech signal, which can be utilized in the MVDR beamformer formulation. A baseline beamformer can be constructed utilizing the a priori known DOA information with which performance of other beamformers may be compared in acoustic scenarios involving speech sources in motion. Mask-Based MVDR Beamformer Baseline Based on Attention Mechanism  
The details of this work can be obtained from [8]. In this sub-section, a brief overview of the approach behind this baseline beamformer is included. The baseline beamformer in [8] involves a generalized approach to the computation of SCMs for moving speech sources, which can be interpreted as the weighted sum of ISCMs, weighted by attention weights. A self-attention-based neural architecture is utilized to predict these attention weights. The procedure to compute the attention weights involves processing the vectorized ISCMs by a neural network architecture, which can be expressed as follows:  
\[\{\mathbf{c}_{\mathbf{v}}^{t}\}_{\mathbf{t}=\mathbf{1}}^{T}=\mathbf{\mathcal{F}}^{v}(\{\mathbf{\Psi }_{\mathbf{t}\mathbf{t}}^{\mathbf{v}}\}_{\mathbf{t}=\mathbf{1}}^{\mathbf{T}};\mathbf{\mathcal{ P}}_{\mathbf{v}}) \tag{47}\]  
In (47), \(\{\mathbf{c}_{\mathbf{v}}^{t}\}_{\mathbf{t}=\mathbf{1}}^{T}\) represents the attention weights, \(\mathbf{\mathcal{F}}^{v}(. )\) the neural architecture operation, \(\left\{\mathbf{\Psi}_{\mathbf{t}\mathbf{t}}^{\mathbf{v}}\right\}_{\mathbf{t}=\mathbf{1}}^{T}\) the ISCMs and \(\mathbf{\mathcal{P}}_{\mathbf{v}}\) the parameters of the neural architecture. Once the attention weights are constructed, they are utilized to compute the SCMs which then help to compute the MVDR beamformer weights. In [8], it has been pointed out that the efficacy of this approach lies in the ability of the self-attention-based neural architecture to predict the attention weights which facilitate the accumulation of ISCMs from a similar direction while making it possible to track a speech source. Apart from the abovementioned baseline beamformers, the 'gcn_mvdr' baseline beamformer is presented in [29], which involves the incorporation of a GCN module within the neural architecture. Such an approach helps in the exploitation of spatio-temporal and spectral information in a flexible manner. Performance comparisons between the proposed approach and other state-of-the-art neural approaches on simulated RIRs are presented in Tables 7 and 8. Table 7 presents the performance comparison in terms of speech dereverberation, whereas Table 8 presents the performance comparison in terms of speech separation on simulated RIRs. Moreover, evaluation of the proposed approach on recorded RIRs is also presented in Table 9.