*3.1.3 The weight function*

Defining *wn* equal to 1 if the sensor is present at grid location *nd*, and 0 for the case of a missing sensor, the weight function is defined as the auto-correlation of *wn*. In simple terms, the weight function gives the number of times a given spatial lag is generated or the number of sensor pairs that can generate a given spatial lag. This weight function should not be confused with the weight vector that defines element currents and phases during beamforming.

A unit spacing corresponds to a spatial lag of one and can be generated by any pair of sensors that are adjacent to each other. In other words, any two sensors that are half-wavelength apart from each other are said to have unit spacing. The concept of unit spacing is important in determining the role of mutual coupling on the array's performance. Empirically, arrays that have a large number of adjacent sensors are more susceptible to the effects of mutual coupling than those with fewer unit spacings.
