From the application of information theory, it is found that for low signal‐to‐noise ratios, there is no better method of increasing the information content of a signal than to add the outputs of the elements of an array to improve the signal‐to‐noise ratio. When the signal‐to‐noise ratio is already high, however, the array should be designed so that independent information is supplied by each element when associated with a reference element.
The possibility of increasing directionality by nonlinear operations is then discussed. In particular, it is shown that, for the noiseless case, a two element array can be made to yield patterns equivalent to those produced by an n‐element linear array. Linear maximum directivity arrays (in the sense of Pritchard) may also be synthesized with three omnidirectional elements and a number of nonlinear operations which remains invariant as the order of the equivalent linear army is increased.
Finally linear methods designed to minimize the mean squared error are considered and it is found that array rotation is capable of giving optimum results under certain circumstances.