Analytical evaluation of superdirective array sensitivity factor

In this paper, the sensitivity of superdirective end-fire arrays to the precision of the excitation coefficients associated to its elements is studied through the notion of sensitivity factor. Starting from the array factor with optimized coefficients and the general sensitivity factor expression previously defined in the literature, this work provides formulas that can predict the precision requirements for the realization of superdirective arrays. The theoretical formulas are validated through numerical results obtained using an ad-hoc synthesis procedure based on spherical wave expansion.