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For each couple [��z, woR(��z)], the related directivity is computed by Equation (14). The couple [��z, woR(��z)] that provides the highest directivity is selected, and the related directivity value represents the maximum for the constrained directivity. 4. Results and Discussion 4.1. Directivity Versus Spacing Initially, a linear array composed of eight ES sensors is considered, and the WNG is imposed to be always �� 0 dB. The directivity of this array is evaluated as a function of the normalized spacing (i.e., the ratio between d and ��, d/��) considering spacing values smaller than ��/2. Regarding oversteering, Epigenetics Compound Library three different real weighting windows are considered: uniform, Taylor��s, and the optimum window computed by solving BMS-777607 molecular weight Equation (28). First, we assess the performance of the end-fire array without oversteering when complex or real weight coefficients are used. For a given value of d/��, the optimum complex weights are computed by setting �� = 0 and solving Equation (23). The optimum real weights are computed by setting �� = 0 and solving Equation (28). CVX software is employed for convex programming [20] on a common PC equipped with an Intel? Core i5 CPU with 2.60 GHz of clock and 12 Gbyte of RAM, and the solution is found in less than 0.2 s. Figure 4 compares the maximum constrained directivities and illustrates the directivity obtainable with uniform weights. In this specific case, the optimum real weights only provide a directivity higher than that obtained by uniform weights for d/�� Evodiamine obtained for an end-fire array of N = 8 sensors by imposing WNG �� 0 dB using complex weights (solid line) or real weights (dashed line); the directivity obtained using uniform weights (dotted line) is included for ... Figure 5 compares the performances obtained by the oversteering technique when the uniform and Taylor��s weighting windows are applied. The optimum value for the oversteering amount ��, where �� ? (0, ��/d ? 2), is computed by the algorithm described in Section 3.3 using a predefined weight vector (uniform or Taylor��s) instead of woR(��z). A discretization step for �� of 0.01 is established and a Matlab? script is run on the previously mentioned PC, which results in a computation time that does not exceed 5 s.