There are many systems that require the controlled, directional transmission or reception of radio frequency energy, such as radar systems, radio frequency communication and navigation systems and AM, FM and television broadcast transmitters and receivers. One common technique for the controlled, directional transmission or reception of radio frequency energy in such systems is the use of arrays of radio frequency transmitting and receiving elements, which are often referred to as "phased arrays". In this method, the elements of an array, which are generally but not necessarily identical units, are arranged in a predetermined geometric relationship and the directional pattern or patterns of transmission or reception of the array, often referred to as "beams", are determined by the combination of the patterns of transmission or reception of the individual elements of the array. In particular, the directions and shapes of the beams are determined by the transmission and reception patterns of the individual elements, the geometric relationship between the elements and the phase relationships among the signals used to drive the elements or received from the elements. Of these, the geometric arrangement of the elements and the characteristics of the elements are generally fixed and the phase relationships among the signals driving or received from the elements are typically controlled to form and direct the "beams" of the array.
It is well understood that a phased array in a radio frequency system can form a beam of a desired pattern or shape and can direct the beam in an arbitrary direction by appropriate selection and control of the phase relationships among the transmitted or received signals. In a typical radio frequency phased array system, the selection and control of the phase relationships among the signals is accomplished by selection and control of time delays through the signal channels through which driving signals are provided to the array elements or the received signals are received from the array elements. It is commonly understood that if each element is provided with its own independent signal channel these delays can be chosen optimally to provide the best possible beam, subject to the physical constraints of the geometry of the array, the number and characteristic of the array elements and the signal waveforms. This result can also be achieved where the number of available signal channels is greater than the number of array elements, or when the geometry of the array is symmetric with respect to the desired beam or beams so that the number of required unique delays is reduced to less than the number of signal channels and so that, for example, one channel can be used for more than one array element.
It is a commonly occurring problem, however, that the number of required delays is greater than the number of available signal channels and it is then necessary for at least some of the array elements to share one or more of the channels, that is, to be grouped or wired together and connected to a channel. In such instances, each such group of array elements connected from a single signal channel operates as a single array element and it is often difficult to obtain the optimum beam or beams from the array, or even a close approximation of the optimum beams. It is possible in theory, however, to obtain a beam or beams that are close to the optimum beam or beams if the Nyquist criterion for spatial sampling can be satisfied by the array and if appropriate groupings of the array elements and corresponding signal channel delay times can be determined and implemented in a realizable system.
In general, the methods of the prior art for determining groupings of array elements and sets of signal channel delay times have attempted to find the array element groupings and channel delay times that provide beams that match, as closely as possible, the beams formed in the optimum situation wherein the number of available signal channels is equal to the number of array elements. In those instances wherein the optimum required delays fall into localized clusters of values such that the number of such clusters of values is equal to or less than the number of available signal channels, a reasonable solution is to choose a delay time for each channel that is equal to the center, or average, of a corresponding cluster of delay time values and, thereby, the corresponding group of array elements. In general, however, the set of optimum delay time values will be irregularly scattered between some minimum value and some maximum value and the selection of a set of delay times that optimally approximates the optimum delay time values is unobvious and difficult, at best.
One method that has been used to find a set of delay times that acceptably approximate the optimum delay time values has been to find a set of delay times that minimizes the sum of the squares of the differences between each optimum delay time value and the closest delay of the set of approximate delay times. Determining such a set is a non-linear problem, however, since small changes in the delay times selected to represent the optimum delay time values may cause a change in the correspondence between any given optimum delay time value and the delay time that represents that optimum delay time value, in effect causing an array element to move from one group of array elements to another group of array elements. This non-linearity renders the usual approaches to such problems, such as least squares approximation, ineffective.
The present invention provides a solution to these and other problems of the prior art by providing a method for determining the groupings of array elements and the corresponding signal channel delay times to allow the selectable and arbitrary formation and steering of beams by a radio frequency phased array system, and a mechanism for controlling the distribution of appropriately delayed waveforms to the groups of array elements, assuming that there are no arbitrary array element grouping constraints, that is, that any element may be grouped with any other element or group of elements.