## 3 The Proposed S-LCMV Cost Function
 \tag{15}\]  
which multiply to give  
\[\mathbf{A}\mathbf{B}_{j}=\mathbf{A}_{j}-^{1}\times\mathbf{B}_{j}= \begin{bmatrix} a_{j}^{\prime}&a_{j}^{\prime\prime}\\ a_{j}^{\prime}&a_{j}^{\prime}\end{bmatrix}\begin{bmatrix}b_{j}^{\prime}& \beta_{j}^{\prime}\\ b_{j}^{\prime}&\beta_{j}^{\prime}\end{bmatrix} = \begin{bmatrix}a_{j}^{\prime }b_{j}^{\prime}+a_{j}^{\prime\prime}b_{j}^{\prime\prime}&\alpha_{j}^{\prime} \beta_{j}^{\prime}+a_{j}^{\prime\prime}\beta_{j}^{\prime\prime}\\ a_{j}^{\prime}b_{j}^{\prime}+a_{j}^{\prime}b_{j}^{\prime}&a_{j}^{\prime}\beta_{j} ^{\prime}+a_{j}^{\prime}\beta_{j}^{\prime}\end{bmatrix}  \tag{16}\]  
Accordingly, we have \(\mathbf{Y}_{1}=\mathbf{A}\mathbf{B}_{1}\times\mathbf{A}\mathbf{B}_{2}\times \mathbf{A}\mathbf{B}_{3}\times\mathbf{A}\mathbf{B}_{4}\times\mathbf{A}\mathbf{B }_{5}\times\mathbf{A}\mathbf{B}_{6}\). Since \(a_{j}^{\prime},\,a_{j}^{\prime\prime},\,\beta_{j}^{\prime}\), and \(\beta_{j}^{\prime\prime}\) are all infinitesimals, their products are also infinitesimals. To simplify the subsequent expres  
Figure 2: Distribution of Bessel functions. sions, let \(\gamma^{\prime}_{j^{\prime}}\), \(\gamma^{\prime^{\prime\prime}}_{j}\), and \(\gamma^{\prime\prime^{\prime\prime}}_{j}\) denote the three infinitesimals in \(\mathbf{AB}_{j}\), and let \(c_{j}\) denote the constant term in \(\mathbf{AB}_{j}\), then we have  
\[\mathbf{AB}_{1}\times\mathbf{AB}_{2}= \begin{bmatrix}\gamma^{\prime}_{1}& \gamma^{\prime\prime}_{1}\\ c_{1}&\gamma^{\prime}_{1}\end{bmatrix}\begin{bmatrix}\gamma^{\prime}_{2}& \gamma^{\prime\prime}_{2}\\ c_{2}&\gamma^{\prime\prime}_{2}\end{bmatrix} = \begin{bmatrix}\gamma^{\prime}_{1 }\gamma^{\prime}_{2}+\gamma^{\prime\prime}_{1}c_{2}&\gamma^{\prime}_{1}\gamma^ {\prime\prime}_{2}+\gamma^{\prime\prime}_{1}\gamma^{\prime\prime}_{2}\end{bmatrix}  \tag{17}\]  
\[\mathbf{AB}_{3}\times\mathbf{AB}_{4}= \begin{bmatrix}\gamma^{\prime}_{3}\gamma^ {\prime}_{4}+\gamma^{\prime\prime}_{3}c_{4}&\gamma^{\prime}_{3}\gamma^{ \prime\prime}_{4}+\gamma^{\prime\prime}_{3}\gamma^{\prime\prime}_{4}\\ c_{3}\gamma^{\prime}_{4}+\gamma^{\prime\prime}_{3}c_{4}&c_{3}\gamma^{\prime \prime}_{4}+\gamma^{\prime\prime}_{3}\gamma^{\prime\prime}_{4}\end{bmatrix}  \tag{18}\]  
\[\mathbf{AB}_{5}\times\mathbf{AB}_{6}= \begin{bmatrix}\gamma^{\prime}_{5}\gamma^ {\prime}_{6}+\gamma^{\prime\prime}_{5}c_{6}&\gamma^{\prime}_{5}\gamma^{\prime \prime}_{6}+\gamma^{\prime\prime}_{5}\gamma^{\prime\prime\prime}_{6}\\ c_{5}\gamma^{\prime}_{6}+\gamma^{\prime\prime}_{5}c_{6}&c_{5}\gamma^{\prime}_{6}+ \gamma^{\prime\prime}_{5}\gamma^{\prime\prime}_{6}\end{bmatrix}  \tag{19}\]  
Furthermore, we can obtain  
\[ \begin{array}{rl}\mathbf{Y}_{1}(1,2)&=\begin{bmatrix}(\gamma^{\prime}_{1} \gamma^{\prime}_{2}+\gamma^{{}^{\prime\prime}_{1}}c_{2})(\gamma^{\prime}_{3} \gamma^{\prime}_{4}+\gamma^{{}^{\prime\prime}_{3}}c_{4})+(\gamma^{\prime}_{1} \gamma^{\prime\prime}_{2}+\gamma^{\prime\prime}_{1}\gamma^{{}^{\prime\prime \prime}_{2}})(c_{3}\gamma^{\prime}_{4}+\gamma^{{}^{\prime\prime\prime}_{3}}c_{4 })\end{bmatrix}(\gamma^{\prime}_{5}\gamma^{\prime\prime}_{6}+\gamma^{\prime \prime}_{5}\gamma^{{}^{\prime\prime\prime}_{6}}_{6})\\ &+\begin{bmatrix}(c_{1}\gamma^{\prime}_{2}+\gamma^{\prime\prime}_{1}c_{2})( \gamma^{\prime}_{3}\gamma^{\prime}_{4}+\gamma^{\prime\prime}_{3}\gamma^{ \prime\prime}_{4})+(c_{1}\gamma^{\prime}_{2}+\gamma^{\prime\prime}_{1}\gamma^ {\prime\prime}_{2})(c_{3}\gamma^{\prime}_{4}+\gamma^{\prime\prime}_{3}\gamma^ {\prime\prime}_{4})\end{bmatrix}(c_{5}\gamma^{\prime\prime}_{6}+\gamma^{\prime \prime}_{5}\gamma^{{}^{\prime\prime\prime}_{6}}_{6})\end{array}  \tag{20}\]  
According to Equation (20), it can be seen that \(\mathbf{Y}_{1}(1,2)\) is an infinitesimal quantity. Similarly, as the multiplication product of the modified Bessel functions of the first and second kinds approaches zero when \(\lambda\) is large, the elements in \(\mathbf{Y}_{2}(1,1)\) and \(\mathbf{Y}_{3}(1,1)\) are also infinitesimal.