Performance of combinations of projectors and receivers

It has been shown previously that two different configurations of three transducers each can be used to estimate the angle to an object with the same accuracy. The configurations are: 1) one projector and two receivers, and 2) two projectors (transmitting orthogonal waveforms) and one receiver. The second configuration is desirable in the case where the receiver is complex. This communication demonstrates that the results obtained previously can be extended to the case of four transducers. That is, the three possible combinations of four transducers, namely: 1) three receivers, one projector, 2) two receivers, two projectors, and 3) one receiver, three projectors, can be made to have identical performance in terms of angle estimation. It is well known that an array of three receivers can be used to steer a null in the direction of an interfering object, thus allowing the angle of an object of interest to be estimated. The fact that the three configurations treated herein are equivalent means that one can, for example, form a null in the direction of an interfering object using only one receiver and three projectors.