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An antenna array (e.g., microstrip patch antenna) operates in a manner that exploits the particular susceptibility of the mutual coupling effects between radiating elements in the array. Various differential-mode excitation schemes are provided for determining optimal differential-mode voltages or o

An antenna array (e.g., microstrip patch antenna) operates in a manner that exploits the particular susceptibility of the mutual coupling effects between radiating elements in the array. Various differential-mode excitation schemes are provided for determining optimal differential-mode voltages or optimal differential-mode currents that are applied to the radiating elements (e.g., microstrip patches) to thereby achieve certain desirable radiation characteristics including, for example, aiming a radiated beam in a prescribed direction, steering the beam, shaping the radiated beam, and/or optimizing the gain of the antenna in a specified direction.

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1. An antenna system, comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements

1. An antenna system, comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, wherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array,wherein the control system comprises a computer for performing the steps of(i) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array, wherein the matrix describes radiation in a far field and reflects mutual coupling effects of each radiating element in the array among all of the other radiating elements in the array, and(ii) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents fed at each of the radiating elements in the array. 2. The antenna system of claim 1, wherein the control system comprises a radiation model that exploits the mutual coupling among the radiating elements and uses the calculated matrix to determine optimal differential-mode voltages or differential-mode currents for one of steering the beam, shaping the beam and optimizing a gain of the antenna in a desired direction, based on at least one input parameter. 3. The antenna system of claim 1, further comprising an input to the computer for inputting geometric parameters of the antenna system including at least one of the number of the radiating elements, a separation distance between the radiating elements, an elevation angle of the radiation beam to be emitted from the antenna system, and an azimuth angle of the radiation beam to be emitted from the antenna system to be used by the computer to calculate the matrix of complex numbers. 4. The antenna system of claim 1, wherein the antenna system is a microstrip patch antenna or a monolithic microwave integrated circuit (MMIC) antenna array that is caused to radiate from its entire top surface of the radiating elements in the array. 5. The antenna system of claim 1, wherein the array is planar or non-planar. 6. The antenna system of claim 1, wherein a spacing between the radiating elements in the array is regular. 7. The antenna system of claim 1, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:at least one probe for feeding one of the radiating elements with one of the voltages or currents, wherein the one of the radiating elements has an aperture through which a top end of the at least one probe passes from the bottom side of the one of the radiating elements to the top side of the one of the radiating elements such that a top end of the probe extends above the aperture to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 8. The antenna system of claim 7, wherein the probe comprises a center conductor of a coaxial cable. 9. The antenna system of claim 7, wherein the probe may be centered on the respective patches to exploit the mutual coupling among the radiating elements. 10. The antenna system of claim 1, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:at least one probe for feeding one of the radiating elements with one of the voltages or currents, wherein the one of the radiating elements has an aperture through which a top end of the at least one probe passes from th e bottom side of the one of the radiating elements to the top side of the one of the radiating elements such that a top end of the probe extends above the aperture and is looped over to contact the top side of the respective radiating element to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 11. The antenna system of claim 1, wherein at least some of the radiating elements in the array comprise one or more apertures; andwherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that utilizes and exploits mutual coupling among the radiating elements in the array, wherein the device feeds the voltages or currents from below the radiating elements and wherein the mutual coupling is generated by electromagnetic fields below the radiating elements extending through the one or more apertures in the radiating elements. 12. The antenna system of claim 1, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:a plurality of probes for feeding at least some of the radiating elements with different voltages or currents, wherein a plurality of the radiating elements to which voltages or currents are fed each have an aperture through which a top end of one of the probes passes from the bottom side of the radiating elements to the top side of the radiating elements such that top ends of the probes extend above the apertures to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 13. The antenna system of claim 1, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:a plurality of probes for feeding at least some of the radiating elements with different voltages or currents, wherein a plurality of the radiating elements to which voltages or currents are fed each have an aperture through which a top end of one of the probes passes from the bottom side of the radiating elements to the top side of the radiating elements such that top ends of the probes extend above the apertures and are looped over to contact the top side of the respective radiating element to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 14. An antenna system, comprising:an array of radiating elements;control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, wherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that accounts for mutual coupling among the radiating elements in the array,wherein the control system comprises a computer for performing the steps of(i) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array, and(ii) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents fed at each of the radiating elements in the array, wherein the computer further performs the step of calculating the radiation intensity dP/dΩ proportional to the following expression: f=c·QQ′·c′/c·c′ where c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements c′ is the Herm itian conjugate of the c vector, Q is the matrix of complex numbers, and Q′ is the Hermitian conjugate of the Q matrix. 15. The antenna system of claim 14, wherein the Q matrix is an M×2 matrix where M is the number of the radiating elements in the array. 16. An antenna system, comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, wherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that accounts for mutual coupling among the radiating elements in the array,wherein the control system comprises a computer for performing the steps of(i) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array, and(ii) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents fed at each of the radiating elements in the array, wherein a spacing between the radiating elements in the array is irregular. 17. An antenna system, comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, wherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array,wherein the control system comprises a computer for performing the steps of(i) calculating a first matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(ii) multiplying the first matrix by its Hermitian conjugate matrix to obtain a second matrix;(iii) determining eigenvalues and eigenvectors of the second matrix, and(iv) selecting the voltages or currents to be fed to each of the radiating elements in the array based on one of the eigenvectors to achieve an optimal radiation intensity in the direction of observation. 18. The antenna system of claim 17, wherein the computer is designed to perform the step of selecting the voltages or currents to achieve the optimal radiation intensity by selecting the voltages or currents to be the row eigenvector of the second matrix that corresponds to the largest eigenvalue of the second matrix. 19. The antenna system of claim 17, wherein the computer further performs the step of calculating the radiation intensity dP/dΩ proportional to the following expression: f=c·QQ′·c′/c·c′ where c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements, c′ is the Hermitian conjugate of the c vector, Q is the matrix of complex numbers, and Q′ is the Hermitian conjugate of the Q matrix. 20. The antenna system of claim 17, wherein the first matrix is an M×2 matrix wherein M is the number of the radiating elements. 21. The antenna system of claim 17, wherein the calculation of the first matrix is based at least in part on the number of the radiating elements, the separation distance between the radiating elements, the elevation angle of the radiation beam to be emitted from the antenna system, and the azimuth angle of the radiation beam to be emitted from the antenna system. 22. The antenna system of claim 17, wherein the antenna system is a microstrip patch antenna or a monolithic microwave integrated circuit (MMIC) antenna array. 23. The antenna system of claim 17, wherein the array is planar or non-planar. 24. The antenna system of claim 17, wherein a spacing between the radiating elements in the array is regular. 25. The antenna system of claim 17, wherein a spacing between the radiating elements in the array is irregular. 26. The antenna system of claim 17, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:at least one probe for feeding one of the radiating elements with one of the voltages or currents, wherein the one of the radiating elements has an aperture through which a top end of the at least one probe passes from the bottom side of the one of the radiating elements to the top side of the one of the radiating elements such that a top end of the probe extends above the aperture to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 27. The antenna system of claim 26, wherein the probe comprises a center conductor of a coaxial cable. 28. The antenna system of claim 26, wherein the probe may be centered on the respective patches to exploit the mutual coupling among the radiating elements. 29. The antenna system of claim 17, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:at least one probe for feeding one of the radiating elements with one of the voltages or currents, wherein the one of the radiating elements has an aperture through which a top end of the at least one probe passes from the bottom side of the one of the radiating elements to the top side of the one of the radiating elements such that a top end of the probe extends above the aperture and is looped over to contact the top side of the respective radiating element to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 30. The antenna system of claim 17, wherein at least some of the radiating elements in the array comprise one or more apertures; andwherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that utilizes and exploits mutual coupling among the radiating elements in the array, wherein the device feeds the voltages or currents from below the radiating elements and wherein the mutual coupling is generated by electromagnetic fields below the radiating elements extending through the one or more apertures in the radiating elements. 31. The antenna system of claim 17, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises;a plurality of probes for feeding at least some of the radiating elements with different voltages or currents, wherein a plurality of the radiating elements to which voltages or currents are fed each have an aperture through which a top end of one of the probes passes from the bottom side of the radiating elements to the top side of the radiating elements such that top ends of the probes extend above the apertures to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 32. The antenna system of claim 17, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:a plurality of probes for feeding at least some of the radiating elements with different voltages or currents, wherein a plur ality of the radiating elements to which voltages or currents are fed each have an aperture through which a top end of one of the probes passes from the bottom side of the radiating elements to the top side of the radiating elements such that top ends of the probes extend above the apertures and are looped over to contact the top side of the respective radiating element to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 33. An antenna system, comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, wherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array,wherein the control system comprises a computer for performing the steps of(i) calculating a first matrix Q of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(ii) multiplying the first matrix by its Hermitian conjugate matrix Q′ to obtain a second matrix QQ′;(iii) calculating a gain matrix G by averaging the second matrix over all solid angles;(iv) determining an optimal generalized eigenvalue and eigenvector obtained from a ratio of c·QQ′·c′/c·G·c′, wherein c represents a matrix of voltages or currents to be applied to the radiating elements, c′ represents the Hermitian conjugate of the c matrix; and(v) determining an optimal gain which corresponds to the optimal generalized eigenvalue and determining the voltages or currents to be fed to each of the radiating elements in the array from the corresponding generalized eigenvector to achieve an optimal gain function in the direction of observation. 34. The antenna system of claim 33, wherein the computer further performs the step of calculating the radiation intensity dP/dΩ proportional to the following expression: f=c·QQ′·c′/c·c′ wherein c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements. 35. The antenna system of claim 33, wherein the Q matrix is an M×2 matrix wherein M is the number of the radiating elements. 36. The antenna system of claim 33, wherein the computer further comprises an input for inputting at least one of the number of the radiating elements, a separation distance between the radiating elements, an elevation angle of the radiation beam to be emitted from the antenna system, and an azimuth angle of the radiation beam to be omitted from the antenna system for use by the computer in calculating the Q matrix. 37. The antenna system of claim 33, wherein the antenna system is a microstrip patch antenna or a monolithic microwave integrated circuit (MMIC) antenna array. 38. The antenna system of claim 33, wherein the array is planar or non-planar. 39. The antenna system of claim 33, wherein a spacing between the radiating elements in the array is regular. 40. The antenna system of claim 33, wherein a spacing between the radiating elements in the array is irregular. 41. The antenna system of claim 33, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:at least one probe for feeding one of the radiating elements with one of the voltages or currents, wherein the one of the radiating elements has an aperture through which a top en d of the at least one probe passes from the bottom side of the one of the radiating elements to the top side of the one of the radiating elements such that a top end of the probe extends above the aperture to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 42. The antenna system of claim 41, wherein the probe comprises a center conductor of a coaxial cable. 43. The antenna system of claim 41, wherein the probe may be centered on the respective patches to exploit the mutual coupling among the radiating elements. 44. The antenna system of claim 41, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:at least one probe for feeding one of the radiating elements with one of the voltages or currents, wherein the one of the radiating elements has an aperture through which a top end of the at least one probe passes from the bottom side of the one of the radiating elements to the top side of the one of the radiating elements such that a top end of the probe extends above the aperture and is looped over to contact the top side of the respective radiating element to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 45. The antenna system of claim 33, wherein at least some of the radiating elements in the array comprise one or more apertures; andwherein the differential-mode voltages or differential-mode currents are applied to the radiating elements to generate a radiation beam that utilizes and exploits mutual coupling among the radiating elements in the array, wherein the device feeds the voltages or currents from below the radiating elements and wherein the mutual coupling is generated by electromagnetic fields below the radiating elements extending through the one or more apertures in the radiating elements. 46. The antenna system of claim 33, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:a plurality of probes for feeding at least some of the radiating elements with different voltages or currents, wherein a plurality of the radiating elements to which voltages or currents are fed each have an aperture through which a top end of one of the probes passes from the bottom side of the radiating elements to the top side of the radiating elements such that top ends of the probes extend above the apertures to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 47. The antenna system of claim 33, wherein the array of radiating elements has a top side and a bottom side; and wherein the device for feeding the differential-mode voltages or differential-mode currents to the radiating elements comprises:a plurality of probes for feeding at least some of the radiating elements with different voltages or currents, wherein a plurality of the radiating elements to which voltages or currents are fed each have an aperture through which a top end of one of the probes passes from the bottom side of the radiating elements to the top side of the radiating elements such that top ends of the probes extend above the apertures and are looped over to contact the top side of the respective radiating element to generate the mutual coupling of the radiating elements from the top side of the radiating elements. 48. A method for controlling differential-mode operation of an antenna system, the antenna system comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, the method comprising the ste ps of(a) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array, wherein the matrix describes radiation in a far field and reflects mutual coupling effects of each radiating element in the array among all of the other radiating elements in the array,(b) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents fed at each of the radiating elements in the array; and(c) applying the differential-mode voltages or differential-mode currents to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array. 49. A method for controlling differential-mode operation of an antenna system, the antenna system comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, the method comprising the steps of(a) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(b) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents fed at each of the radiating elements in the array; and(c) applying the differential-mode voltages or differential-mode currents to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array, wherein the radiation intensity dP/dΩ is proportional to the following expression: f=c·QQ′·c′/c·c′ where c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements, c′ is the Hermitian conjugate of the c vector, Q is the matrix of complex numbers, and Q′ is the Hermitian conjugate of the Q matrix. 50. A method for controlling differential-mode operation of an antenna system, the antenna system comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, the method comprising the steps of(a) calculating a first matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(b) multiplying the first matrix by its Hermitian conjugate matrix to obtain a second matrix;(c) determining eigenvalues and eigenvectors of the second matrix, and(d) selecting the voltages or currents to be fed to each of the radiating elements in the array based on one of the eigenvectors to achieve an optimal radiation intensity in the direction of observation; and(e) applying the selected differential-mode voltages or differential-mode currents to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array. 51. The method of claim 50, wherein the voltages or currents are selected to achieve the optimal radiation intensity by selecting the voltages or currents to be the row eigenvector of the second matrix that corresponds to the largest eigenvalue of the second matrix. 52. The method of claim 50, further comprising calculating the radiation intensity dP/dΩ proportional to the following expression: f=c·QQ′·c′/c·c′ where c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements, c′ is the Hermitian conjugate of the c vector, Q is the matrix of complex numbers, and Q′ is the Hermitian conjugate of the Q matrix. 53. A method for controlling differential-mode operation of an antenna system, the antenna system comprising:an array of radiating elements;a control system for generating differential-mode voltages or differential-mode currents for exciting the radiating elements; anda device for feeding the differential-mode voltages or differential-mode currents to the radiating elements, the method comprising the steps of(a) calculating a first matrix Q of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(b) multiplying the first matrix Q by its Hermitian conjugate matrix Q′ to obtain a second matrix QQ′;(c) calculating a gain matrix G by averaging the second matrix over all solid angles,(d) determining an optimal generalized eigenvalue and eigenvector obtained from a ratio of c·QQ′·c′/c·G·c′, wherein c represents a matrix of voltages or currents to be applied to the radiating elements, c′ represents the Hermitian conjugate of the c matrix;(e) determining an optimal gain which corresponds to the optimal generalized eigenvalue and determining the voltages or currents to be fed to each of the radiating elements in the array from the corresponding generalized eigenvector to achieve an optimal gain function in the direction of observation, and(f) applying the differential-mode voltages or differential-mode currents to the radiating elements to generate a radiation beam that exploits mutual coupling among the radiating elements in the array. 54. The method of claim 53, further comprising calculating the radiation intensity dP/dΩ proportional to the following expression: f=c·QQ′·c′/c·c′ wherein c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements. 55. A computer-readable medium having stored thereon a program for use in calculating a radiation intensity of an array of radiating elements in an antenna system and differential-mode voltages or differential-mode currents to be fed to the radiating elements to exploit mutual coupling among the radiating elements, wherein the program, when executed by the computer, performs the steps of:(i) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array, wherein the matrix describes radiation in a far field and reflects mutual coupling effects of each radiating element in the array among all of the other radiating elements in the array, and(ii) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents to be fed at each of the radiating elements in the array. 56. A computer-readable medium having stored thereon a program for use in calculating a radiation intensity of an array of radiating elements in an antenna system and differential-mode voltages or differential-mode currents to be fed to the radiating elements to exploit mutual coupling among the radiating elements, wherein the program, when executed by the computer, performs the steps of:(i) calculating a matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(ii) calculating a radiation intensity in the direction of observation using the calculated matrix, and actual voltages or currents to be fed at each of the radiating elements in the array, wherein the radiation intensity dP/dΩ is proportional to the following expression: f=c·QQ′·c′/c·c′ where c is a vector representable by a 1×M matrix of either currents or voltages to be applied to each of the radiating elements of the array of which there are M radiating elements, c′ is the Hermitian conjugate of the c vector, Q is the matrix of complex numbers, and Q′ is the Hermitian conjugate of the Q matrix. 57. The computer of claim 56, wherein the Q matrix is an M×2 matrix where M is the number of the radiating elements in the array. 58. A computer-readable medium having stored thereon a program for use in calculating a radiation intensity of an array of radiating elements in an antenna system and differential-mode voltages or differential-mode currents to be fed to the radiating elements to exploit mutual coupling among the radiating elements, wherein the program, when executed by the computer, performs the steps of:(i) calculating a first matrix of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(ii) multiplying the first matrix by its Hermitian conjugate matrix to obtain a second matrix;(iii) determining eigenvalues and eigenvectors of the second matrix, and(iv) selecting the voltages or currents to be fed to each of the radiating elements in the array based on one of the eigenvectors to achieve an optimal radiation intensity in the direction of observation. 59. A computer-readable medium having stored thereon a program for use in calculating a radiation intensity of an array of radiating elements in an antenna system and differential-mode voltages or differential-mode currents to be fed to the radiating elements to exploit mutual coupling among the radiating elements, wherein the program, when executed by the computer, performs the steps of:(i) calculating a first matrix Q of complex numbers that is dependent on a direction of observation of radiation intensity emitted by the antenna system and on a geometry of the array of radiating elements, but is independent of voltage or current excitations of the array,(ii) multiplying the first matrix by its Hermitian conjugate matrix Q′ to obtain a second matrix QQ′;(iii) calculating a gain matrix G by averaging the second matrix over all solid angles;(iv) determining an optimal generalized eigenvalue and eigenvector obtained from a ratio of c·QQ′·c′/c·G·c′, wherein c represents a matrix of voltages or currents to be applied to the radiating elements, c′ represents the Hermitian conjugate of the c matrix; and(v) determining an optimal gain which corresponds to the optimal generalized eigenvalue and determining the voltages or currents to be fed to each of the radiating elements in the array from the corresponding generalized eigenvector to achieve an optimal gain function in the direction of observation.