Synthesis of multi-element directional patterns using a two-element single-frequency receiving array

The principle of space-frequency equivalence has been shown elsewhere to permit synthesis of multi-element directional patterns using only two physical elements by employing a multi-frequency carrier in the transmission medium. Disadvantages of the system are the use of more spectrum space and the need for a special transmission. The present paper shows that even if a single-frequency carrier only is used, multi-element receiving patterns can be synthesized from the outputs of two physical elements. By the use of frequency-multipliers at the element outputs, multi-frequency carriers are produced synthetically at the receiver. This makes possible the production by electronic methods of a wide variety of directional patterns at the receiver without the cooperation of the distant transmitter. Penalties are paid in signal/noise ratio and multi-source resolution relative to a physical multi-element array.