## 2 Materials and Methods
The input impedance of the patch at a distance \(\mathrm{y_{0}}\), namely inset length (\(\mathrm{L_{inset}}\)) from the patch edge along its length, is as follows:  
\[\mathrm{R_{in}}\left(\mathrm{y_{0}}\right)=\mathrm{R_{in}}(0)\cos^{2}\left( \frac{\pi}{\mathrm{L}}\mathrm{y_{0}}\right) \tag{9}\]  
Many important design parameters and equations must be considered when making a series-fed antenna array. The distance of separation of antenna elements plays a vital role in obtaining the formulation intended in the radiation pattern. For instance, in a uniform linear array, the spacing distance (\(\mathrm{L_{\ell}}\)) is generally set at half-wavelength (\(\mathrm{\Delta g}/2\)) to encourage constructive interference along the main beam direction to facilitate effective beamforming. The array factor explains how the individual elements collaborate with each other to form the complete production of the radiation pattern of the array. For a uniform linear array with N elements, the array factor (AF) can be expressed as:  
\[\mathrm{AF}=\sum\limits_{1}^{N}\mathrm{e}^{\mathrm{i}(n-1)\mathrm{kdcos}( \theta)} \tag{10}\]The array factor (AF) is calculated as a function of off-broadside angles, as the contribution of each element to the overall antenna radiation pattern is expressed. It is good to have an impedance match in an efficient antenna array. Good impedance matching makes an efficient transfer of power inside the array. The antenna elements and feed networks should be impedance matched to system impedance (say 50 \(\Omega\)) to reflect the minimum and increase overall performance. MIMO antenna assessment parameters gauge performance. One of the significant quantifications is the envelope correlation coefficient (ECC), which measures how the signal envelopes received through different antennas correlate with one another. Lower ECC would mean stronger diversity performance because it can mean better reception of uncorrelated signals and better diversity gains. Diversity gain (DG) refers to the improvement in signal reception quality obtained by using multiple antennas to counteract signal fading through spatial diversity. Another critical parameter is the \"mean effective gain\", which describes the power gain of antenna pattern averaged over all the angles in a given scenario, thus giving an idea about the overall capability of the system itself. Combining the Effective Diversity Gain incorporates part diversity gain through antenna correlation, providing better insight into system diversity performance. Channel Capacity Loss (CCL) defines the amount by which the maximum potential data rate is reduced due to interference or noise and provides figures to measure the channel-inherent inefficiencies affecting capacity. In this case, the usefulness of ECC computation is related to signal correlation and its effects on system performance. ECC can be calculated in different ways depending on the purpose. \[\Delta\text{L}=0.412\text{h}\frac{(\epsilon_{\text{reff}}+0.3)\Big{(}\frac{ \text{W}}{\text{h}}+0.264\Big{)}}{(\epsilon_{\text{reff}}-0.254)\Big{(}\frac{ \text{W}}{\text{h}}+0.8\Big{)}} \tag{2}\]0  
where the terms \(\text{S}_{\text{ii}}\), \(\text{S}_{\text{jj}}\), \(\text{S}_{\text{ii}}\)*, and \(\text{S}_{\text{ji}}\)* refer to the complex and conjugate complex elements of the scattering matrix, demonstrating signals received by antennas i and j, respectively. ECC directly affects the DG, measured in dB, as follows:  
\[\Delta\text{L}=0.412\text{h}\frac{(\epsilon_{\text{reff}}+0.3)\Big{(}\frac{ \text{W}}{\text{h}}+0.264\Big{)}}{(\epsilon_{\text{reff}}-0.254)\Big{(}\frac{ \text{W}}{\text{h}}+0.8\Big{)}} \tag{2}\]1  
The CCL metric quantifies the decrease in the highest attainable data rate by considering the logarithm of the magnitude of the received signal coefficients. Thus, it is computed by:  
\[\Delta\text{L}=0.412\text{h}\frac{(\epsilon_{\text{reff}}+0.3)\Big{(}\frac{ \text{W}}{\text{h}}+0.264\Big{)}}{(\epsilon_{\text{reff}}-0.254)\Big{(}\frac{ \text{W}}{\text{h}}+0.8\Big{)}} \tag{2}\]2  
where  
\[\beta^{\text{R}}=