Abstract:
System and method for signal processing and beam forming. A system for processing signals includes a first phase shifter, a second phase shifter, a first variable time delay system, and a second variable time delay system. Additionally, the system includes a first signal processing system and a sampling system. Moreover, the system includes a switching system and a measuring system.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
   The application claims priority to U.S. Provisional Application No. 60/426,453 filed Nov. 15, 2002, which is incorporated by reference herein. 

   BACKGROUND OF THE INVENTION 
   The present invention relates in general to detecting objects and/or areas. More particularly, the invention provides a method and system for adaptive variable true time delay beam forming. Merely by way of example, the invention is described as it applies to a phased array antenna, but it should be recognized that the invention has a broader range of applicability. 
   A phased array antenna has been widely used for communications and radar systems. The phased array antenna usually does not mechanically steer antenna directions, and can provide rapid beam scanning. The directivity of the phased array antenna can be achieved by properly adjusting the relative phases between signals transmitted or received by different antenna elements. These antenna elements can reinforce the transmitted or received radiation in a desired direction. 
     FIG. 1  is a simplified diagram for a conventional phased array antenna. An arrival signal  140  with a center wavelength λ 0  arrives at an array of antenna elements  110 . The angle of arrival is θ 0 . Phase shifters  120  are applied to the outputs of the antenna elements  110  and generate phase delayed signals. The sum of the phase delayed signals forms an output beam  130 . The phase shifters  120  are usually adequate for forming the output beam  130  if the 3 dB bandwidth of the arriving signal  140  is narrow and the scan angle θ 0  is small. Otherwise, a time delay circuit is usually needed for beam formation. For example, the time delay is needed when 
             B   &gt;     0.886     τ   0               (     Equation   ⁢           ⁢   1     )                 τ   0     =         Nd   x     ⁢   sin   ⁢           ⁢     θ   0           f   0     ⁢     λ   0                 (     Equation   ⁢           ⁢   2     )               
   where B is the 3 dB bandwidth of the arriving signal  140 , and τ 0  is the total time delay across the array of antennal elements  110 . Additionally, f 0  is the center frequency of the arriving signal  140 , N is the total number of antenna elements  110 , d x , is the distance between two adjacent antenna elements  110 , and θ 0  is the angel of arrival. As another example, if the total time delay, τ 0 , across the array of antenna elements  110  is greater than the reciprocal of the 3 dB bandwidth, the time delay is usually needed for beam forming. 
   In certain beam forming applications, the received or transmitted signals need to maintain phase continuity and avoid any abrupt phase transition. Phase continuous variable true time delay circuits are usually used. The phase continuous variable true time delay circuits can be implemented by switching in and out of a plurality of RF cables or optical fibers of different lengths. But during the switching of cables, an abrupt phase transition may be introduced into the processed signals. As the size of the antenna aperture and the number of antenna elements become large, testing and calibration of the entire antenna system also become difficult. 
   Hence it is highly desirable to improve techniques for adaptive variable true time delay beam forming. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention relates in general to detecting objects and/or areas. More particularly, the invention provides a method and system for adaptive variable true time delay beam forming. Merely by way of example, the invention is described as it applies to a phased array antenna, but it should be recognized that the invention has a broader range of applicability. 
   According to a specific embodiment of the present invention, a system for processing signals includes a first phase shifter configured to receive or generate a first signal, a second phase shifter configured to receive or generate a second signal, a first variable time delay system coupled to the first phase shifter and configured to generate or receive a third signal, and a second variable time delay system coupled to the second phase shifter and configured to generate or receive a fourth signal. Additionally, the system includes a first signal processing system coupled to the first variable time delay system and the second variable time delay system and configured to generate or receive a fifth signal, and a sampling system configured to sample at least the third signal and the fourth signal and generate at least a sixth signal and a seventh signal respectively. Moreover, the system includes a switching system configured to receive the at least a sixth signal and a seventh signal and output an eighth signal and a ninth signal. The eighth signal is the same as one of the at least a sixth signal and a seventh signal, and the ninth signal is the same as one of the at least a sixth signal and a seventh signal. Also, the system includes a measuring system configured to receive the eighth signal and the ninth signal and process at least information associated with the eighth signal and the ninth signal. 
   According to another embodiment of the present invention, a system for providing a time delay to a signal includes a first signal processing system configured to receive or generate a first combined signal and to generate or receive at least a first divided signal and a second divided signal, a first time delay system configured to receive or generate the first divided signal, generate or receive a third divided signal, and provide a first time delay to the first divided signal or the third divided signal, and a second time delay system configured to received or generate the second divided signal, generate or received a fourth signal, and provide a second time delay to the second divided signal or the fourth divided signal. Additionally, the system includes a first phase shifter configured to receive or generate the third divided signal, generate or receive a fifth divided signal, and provide a first phase shift to the third divided signal or the fifth divided signal, and a second phase shifter configured to receive or generate the fourth divided signal, generate or receive a sixth divided signal, and provide a second phase shift to the fourth divided signal or the sixth divided signal. Moreover, the system includes a first attenuator configured to receive or generate the fifth divided signal and generate or receive a seventh divided signal, and a second attenuator configured to receive or generate the sixth divided signal and generate or receive an eighth divided signal. Also, the system includes a second signal processing system configured to receive or generate the seventh divided signal and the eighth divided signal and generate or receive a second combined signal. 
   According to yet another embodiment of the present invention, a method for processing signals includes selecting a reference signal, selecting a first signal, and processing information associated with the reference signal and the first signal. Additionally, the method includes determining a first phase shift based on at least information associated with the reference signal and the first signal, applying the first phase shift to the first signal, determining a first time delay based on at least information associated with the reference signal and the first signal, and applying the first time delay to the first signal. The applying the first phase shift to the first signal is associated with the first phase-shifted signal. The first phase-shifted signal is substantially free from any phase difference with respect to the reference signal at a predetermined frequency. The applying the first time delay to the first signal is associated with the first phase-shifted and time-delayed signal. The first phase-shifted and time-delayed signal is substantially free from any phase difference with respect to the reference signal within a frequency range. The frequency range includes the predetermined frequency. 
   According yet another embodiment of the present invention, a method for processing signals includes selecting a first signal from a plurality of signals. A sum of the plurality of signals is a combined signal. The combined signal is associated with a first phase difference with respect to the first signal at a predetermined frequency. Additionally, the method includes processing information associated with the combined signal and the first signal, determining a first phase shift and a first time delay based on at least information associated with the combined signal and the first signal, and applying the first phase shift and the first time delay to the first signal to generate the first phase-shifted and time-delayed signal. The first phase-shifted and time-delayed signal is associated with a second phase difference at the predetermined frequency with respect to a first combined phase-shifted and time-delayed signal. The first combined phase-shifted and time-delayed signal is equal to a sum of the first phase-shifted and time-delayed signal and the plurality of signals other than the first signal. The second phase difference is smaller than the first phase difference at the predetermined frequency. 
   According to yet another embodiment of the present invention, a method for processing signals includes receiving a first combined signal, and generating a first divided signal and a second divided signal based on at least information associated with the first combined signal. Additionally, the method includes applying a first time delay to the first divided signal, applying a second time delay to the second divided signal, applying a first phase shift to the first divided time-delayed signal, and applying a second phase shift to the second divided time-delayed signal. Moreover, the method includes applying a first attenuation to the first divided time-delayed and phase-shifted signal, applying a second attenuation to the second divided time-delayed and phase-shifted signal, generating a second combined signal based on at least information associated with the first attenuated divided time-delayed and phase-shifted signal and the second attenuated divided time-delayed and phase-shifted signal. 
   According to yet another embodiment of the present invention, a method for using a system includes providing a system. The system includes a first signal processing system, a first time delay system coupled to the first signal processing system and configured to provide a first time delay, a second time delay system coupled to the first signal processing system and configured to provide a second time delay, and a third time delay system coupled to the first signal processing system and configured to provide a third time delay. Additionally, the system includes a first phase shifter coupled to the first time delay system and configured to provide a first phase shift within a first phase shift range, a second phase shifter coupled to the second time delay system and configured to provide a second phase shift within a second phase shift range, and a third phase shifter coupled to the third time delay system and configured to provide a third phase shift within a third phase shift range. Moreover, the system includes a first attenuator coupled to the first phase shifter and configured to provide a first attenuation within a first attenuation range, a second attenuator coupled to the second phase shifter and configured to provide a second attenuation within a second attenuation range, and a third attenuator coupled to the third phase shifter and configured to provide a third attenuation within a third attenuation range. Also, the system includes a second signal processing system coupled to the first attenuator, the second attenuator and the third attenuator. The first time delay is shorter than or equal to the second time delay and the second time delay is shorter than or equal to the third time delay. Additionally, the method includes inputting a first signal to the first signal processing system, measuring a second signal from the second signal processing system, processing information associated with the first signal and the second signal, and determining a reference time delay between the second signal and the first signal based on at least information associated with the first signal and the second signal. Moreover, the method includes establishing a first phase synchronization between a first output of the first attenuator and a second output of the second attenuator at a predetermined frequency, establishing a second phase synchronization between a third output of the third attenuator and the second output of the second attenuator at the predetermined frequency, and adjusting at least one of the first attenuation, the second attenuation, and the third attenuation. Also, the method includes measuring a third signal from the second signal processing system, processing information associated with the first signal and the third signal, and determining a relative time delay between the third signal and the first signal with respect to the reference time delay based on at least information associated with the first signal and the third signal. 
   According to yet another embodiment of the present invention, a method for using a system includes providing a system. The system includes a first phase shifter configured to provide a first phase shift, a second phase shifter configured to provide a second phase shift, a first variable time delay system coupled to the first phase shifter and configured to provide a first time delay, and a second variable time delay system coupled to the second phase shifter and configured to provide a second time delay. Additionally, the system includes a signal processing system coupled to the first variable time delay system and the second variable time delay system, a sampling system configured to sample at least a first output of the first variable time delay system and a second output of the second variable time delay system, a switching system configured to receive the at least a first output and a second output and output a third signal and a fourth signal. The third signal is the same as one of the at least a first output and a second output, and the fourth signal is the same as one of the at least a first output and a second output. Moreover, the system includes a measuring system configured to process at least information associated with the third signal and the fourth signal. Additionally, the method includes inputting a fifth signal to the first phase shifter, and inputting a sixth signal to the second phase shifter. The sixth signal and the fifth signal are associated with substantially the same phase and the same time delay. Moreover, the method includes adjusting the first output and the second output. The adjusted first output and the adjusted second output are associated with substantially the same phase and the same time delay. Also, the method includes processing information associated with the third signal and the fourth signal. The third signal is related to the fifth signal, and the fourth signal is related to the sixth signal. Additionally, the method includes determining a phase difference based on at least information associated with the third signal and the fourth signal. 
   According to yet another embodiment of the present invention, a system for processing signals includes a first signal processing system, a first time delay system coupled to the first signal processing system and configured to provide a first time delay, and a second time delay system coupled to the first signal processing system and configured to provide a second time delay. Additionally, the system includes a first phase shifter coupled to the first time delay system and configured to provide a first phase shift, a second phase shifter coupled to the second time delay system and configured to provide a second phase shift, a first attenuator coupled to the first phase shifter and configured to provide a first attenuation, and a second attenuator coupled to the second phase shifter and configured to provide a second attenuation. Moreover, the system includes a second signal processing system coupled to the first attenuator and the second attenuator. 
   According to yet another embodiment of the present invention, a system for processing signals includes a first phase shifter configured to provide a first phase shift, a second phase shifter configured to provide a second phase shift, a first variable time delay system coupled to the first phase shifter and configured to provide a first time delay, and a second variable time delay system coupled to the second phase shifter and configured to provide a second time delay. Additionally, the system includes a signal processing system coupled to the first variable time delay system and the second variable time delay system, a sampling system configured to sample at least a first output of the first variable time delay system and a second output of the second variable time delay system, a switching system configured to receive the at least a first output and a second output and output a third signal and a fourth signal. The third signal is the same as one of the at least a first output and a second output, and the fourth signal is the same as one of the at least a first output and a second output. Also, the system includes a measuring system configured to process at least information associated with the third signal and the fourth signal. 
   Many benefits may be achieved by way of the present invention over conventional techniques. For example, certain embodiments of the present invention reduce complexity of calibration process that usually involves physical manipulation of a large phased array antenna. Some embodiments of the present invention reduce the amount of time required for system integration in the factory. After system deployment, periodic maintenance procedures for periodic test, calibration and performance verifications can be simplified. Certain embodiments of the present invention can make real time measurements and estimate relative time delays and phase delays between received signals. Some embodiments of the present invention can lower the costs of making and using phased array antenna systems. 
   Depending upon the embodiment under consideration, one or more of these benefits may be achieved. These benefits and various additional objects, features and advantages of the present invention can be fully appreciated with reference to the detailed description and accompanying drawings that follow. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a simplified diagram for a conventional phased array antenna; 
       FIGS. 2–5  are simplified diagrams for response of a phased array antenna as a function of number of antenna elements, scan angle and signal frequency; 
       FIG. 6  is a simplified diagram for an adaptive variable true time delay beam forming system according to one embodiment of the present invention; 
       FIG. 7  is a simplified block diagram for an adaptive variable true time delay beam forming method according to one embodiment of the present invention; 
       FIG. 8  is a simplified diagram for phase and time delay differences between two signals according to one embodiment of the present invention; 
       FIG. 9  is a simplified block diagram for an adaptive variable true time delay beam forming method according to one embodiment of the present invention; 
       FIG. 10  is a simplified diagram for phase delay differences among signals according to one embodiment of the present invention; 
       FIG. 11  is a simplified diagram for phase delay differences among signals with adjustments according to one embodiment of the present invention; 
       FIG. 12  is a simplified diagram for phase delay differences among signals with adjustments according to one embodiment of the present invention; 
       FIG. 13  is a simplified diagram for phase delay differences among signals with adjustments according to one embodiment of the present invention; 
       FIG. 14  is a simplified diagram for a variable true time delay system according to one embodiment of the present invention; 
       FIG. 14A  is a simplified block diagram for a variable true time delay method according to one embodiment of the present invention; 
       FIG. 14B  is a simplified diagram for delaying signal according to an embodiment of the present invention; 
       FIG. 15  is a simplified diagram for relative time delay as a function of attenuation levels according to an embodiment of the present invention; 
       FIG. 16  is a simplified block diagram for an antenna system according to one embodiment of the present invention; 
       FIG. 17  is a simplified circuit diagram for an antenna system as describe in  FIG. 16  according to one embodiment of the present invention; 
       FIG. 18  is a simplified block diagram for a method of calibrating a variable true time delay system according to one embodiment of the present invention; 
       FIG. 19  is a simplified diagram for a calibrating system for an adaptive variable true time delay beam forming system according to one embodiment of the present invention; 
       FIG. 20  is a simplified block diagram for a method of calibrating an adaptive variable true time delay beam forming system according to one embodiment of the present invention; 
       FIG. 21  is a simplified diagram for a phased array antenna system; 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present invention relates in general to detecting objects and/or areas. More particularly, the invention provides a method and system for adaptive variable true time delay beam forming. Merely by way of example, the invention is described as it applies to a phased array antenna, but it should be recognized that the invention has a broader range of applicability. 
   As shown in  FIG. 1 , the bandwidth of a phased array antenna can be limited by the bandwidth of the antenna elements  110  and the use of the phase shifters  120  for beam forming. For example, the antenna elements  110  form a linear array with N elements and element spacing d x . The beam former uses the following set of complex weights 
       {     1   ,     exp   ⁡     (     j   ⁢           ⁢       2   ⁢   π       λ   o       ⁢           ⁢   1   ⁢     d   x     ⁢   sin   ⁢           ⁢     θ   o       )       ,     exp   ⁢     (     j   ⁢           ⁢       2   ⁢   π       λ   o       ⁢           ⁢   2   ⁢     d   x     ⁢   sin   ⁢           ⁢     θ   o       )       ,     …   ⁢           ⁢   exp   ⁢     (     j   ⁢           ⁢       2   ⁢   π       λ   o       ⁢           ⁢     (     N   -   1     )     ⁢     d   x     ⁢   sin   ⁢           ⁢     θ   o       )         }       
 
to form a beam in the direction of θ o , and provides the optimal signal to noise gain for a signal at the center frequency f o . λ o  denotes the wavelength corresponding to f o . The output of the beam former for a signal at f o +Δf and from the same direction θ 0  may be expressed by 
               sin   ⁢     {         π   ⁢           ⁢     Nd   x     ⁢   sin   ⁢           ⁢     θ   o         λ   o       ⁢     (       Δ   ⁢           ⁢   f       f   o       )       }         sin   ⁢     {         π   ⁢           ⁢     d   x     ⁢   sin   ⁢           ⁢     θ   o         λ   o       ⁢     (       Δ   ⁢           ⁢   f       f   o       )       }               (     Equation   ⁢           ⁢   3     )             
 
   where N is the total number of antenna elements, d x  is the distance between two adjacent antenna elements, θ 0  is the angel of arrival or scan angle, and Δf is the frequency away from f o . As the factor N×d x ×Δf×sin θ 0  increases, the attenuation of a signal at (f o +Δf) and θ o  increases rapidly. 
     FIGS. 2–5  are simplified diagrams for response of a phased array antenna as a function of number of antenna elements, scan angle and signal frequency. The phased array antenna has a linear array of antenna elements. These diagrams are merely examples, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. 
     FIG. 2  is a simplified diagram for response of a phased array antenna as a function of frequency with N equal to 48 elements and d x  equal to 2.6 inches. The frequency responses for scan angles of 25° and 60° are shown as curves  210  and  220  respectively.  FIG. 3  is a simplified diagram for response of a phased array antenna as a function of frequency with N equal to 48 elements and d x  equal to 3.0 inches. The frequency responses for scan angles of 15° and 40° are shown as curves  310  and  320  respectively. 
     FIG. 4  is a simplified diagram for response of a phased array antenna as a function of frequency with N equal to 4 elements and d x  equal to 2.6 inches. The frequency responses for scan angles of 25° and 60° are shown as curves  410  and  420  respectively.  FIG. 5  is a simplified diagram for response of a phased array antenna as a function of frequency with N equal to 4 elements and d x  equal to 3.0 inches. The frequency responses for scan angles of 15° and 40° are shown as curves  510  and  520  respectively. The comparisons between  FIGS. 2 and 4  and between  FIGS. 3 and 5  show that reduction of array size can significantly improve the frequency response near the band edges. For example, at 2.2 GHz and 25°, the frequency response improves from about −3 dB as shown by the curve  210  to about −0.02 dB as shown by the curve  410 . As another example, for the curve  510 , the drop off in the frequency response is probably hardly measurable. 
   As shown in  FIGS. 2–5 , as the factor (N×d x Δf×sin θ 0 ) increases, the attenuation of a signal at (f o +Δf) and θ o  increases rapidly. In order to compensate the large attenuation, a time delay circuit can be used in the beam forming process. 
     FIG. 6  is a simplified diagram for an adaptive variable true time delay beam forming system according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A time delay beam forming system  600  includes phase shifters  610 ,  612 ,  614  and  616 , amplifiers  620 ,  622 ,  624  and  626 , a combiner and divider system  640 , a divider systems  650 ,  652 ,  654  and  656 , switches  660 ,  662 ,  670  and  672 , a correlative receiver  680 , and signal couplers  690 ,  692 ,  694 ,  696  and  698 . Although the above has been shown using various systems, there can be many alternatives, modifications, and variations. For example, some of the systems may be expanded and/or combined. Additional phase shifters, amplifiers, and variable true time delay systems may be added to generate additional inputs to the combiner and divider system  640 , or receive additional outputs from the combiner and divider system  640 . Other systems may be inserted to those noted above. One or both of the switches  670  and  672  may be removed. One of the switches  660  and  662  can be removed. Depending upon the embodiment, the specific systems may be replaced. The time delay beam forming system  600  can be used to transmit signals, receive signals, or transmit and receive signals. To transmit signals, the direction of the amplifiers  620 ,  622 ,  624  and  626  may be reversed. Further details of these systems are found throughout the present specification and more particularly below. 
   The phase shifters  610 ,  612 ,  614  and  616  receive or generate signals  611 ,  613 ,  615  and  617  respectively. These signals are substantially identical except for their relatively time delay and phase delay differences. In the reception mode, these differences are compensated by the phase shifters  610 ,  612 ,  614  and  616  and variable true time delays systems  620 ,  622 ,  624  and  626 . In the transmission mode, these differences are generated by the phase shifters  610 ,  612 ,  614  and  616  and variable true time delays systems  620 ,  622 ,  624  and  626 . 
   The variable true time delay systems  630 ,  632 ,  634  and  636  generate or receive signals  642 ,  644 ,  646  and  648  respectively. The combiner and divider system  640  generates or receives a signal  641 . These signals  642 ,  644 ,  646 ,  648  and  641  are sampled by signal couplers  690 ,  692 ,  694 ,  696  and  698  respectively, and routed to the correlative receiver  680  for measurement. The routing system includes switches  660 ,  662 ,  670  and  672 . The switch  660  receives the signals  642 ,  644 ,  646  and  648  and selects one of them as its output signal  661 . The switch  670  receives the signals  661  and  641  and selects one of them as its output signal  671 . Similarly, the switch  662  receives the signals  642 ,  644 ,  646  and  648  and selects one of them as its output signal  663 . The switch  672  receives the signals  663  and a test signal  664  and selects one of them as its output signal  673 . As discussed above, the signals  642 ,  644 ,  646 ,  648  and  641  received by the routing system and its components refer to samples of the signals  642 ,  644 ,  646 ,  648  and  641  that are obtained through the signal couplers  690 ,  692 ,  694 ,  696  and  698  respectively. 
   The correlative receiver  680  receives the signals  671  and  673  and measure information related to the phase and time delay differences of these signals. See U.S. patent application Ser. No. 10/693,321, in the name of Lawrence K. Lam, et al., titled, “System and Method for Cross Correlation Receiver,”. This patent application is incorporated by reference herein for all purposes. These phase and time delay differences can be reduced to substantially zero by iteratively adjusting the phase shifters  610 ,  612 ,  614  and  616  and variable true time delay systems  630 ,  632 ,  634  and  636 . 
     FIG. 7  is a simplified block diagram for an adaptive variable true time delay beam forming method according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A time delay beam forming method  700  includes a process  710  for selecting a reference signal, a process  720  for selecting a comparison signal, a process  730  for processing the reference signal and the comparison signal, a process  740  for adjusting a phase shifter, a process  750  for adjusting a variable true time delay system, and a process  760  for determining whether additional signal processing should be performed. Although the above has been shown using a selected sequence of processes, there can be many alternatives, modifications, and variations. For example, some of the processes may be expanded and/or combined. The processes  740  and  750  can be combined. Other processes may be inserted to those noted above. Depending upon the embodiment, the specific sequence of steps may be interchanged with others replaced. Further details of these elements are found throughout the present specification and more particularly below. 
   At the process  710 , a reference signal is selected from the signals  642 ,  644 ,  646  and  648 . For example, the switch  660  receives the signals  642 ,  644 ,  646  and  648  and selects the signal  642  as its output signal  661 . The switch  670  receives the signals  641  and  642  and selects the signal  642  as its output signal  671 . The signal  642  is the reference signal. 
   At the process  720 , a comparison signal is selected from the signals  642 ,  644 ,  646  and  648 . For example, the switch  662  receives the signals  642 ,  644 ,  646  and  648  and selects the signal  644  as its output signal  663 . The switch  672  receives the signals  644  and  664  and selects the signal  644  as its output signal  673 . The signal  644  is the comparison signal. 
   At the process  730 , the reference signal and the comparison signal are processed. For example, the correlative receiver  680  receives the signals  642  and  644  from the switches  670  and  672  respectively. The correlative receiver  680  processes the signals  642  and  644  and measures information related to their phase and time delay differences.  FIG. 8  is a simplified diagram for phase and time delay differences between two signals according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A curve  810  represents the phase difference between two input signals to the correlative receiver  680  as a function of frequency. The curve  810  is substantially a straight line, and its slope represents the time delay between the two input signals. 
   At the process  740 , a phase shifter is adjusted. The phase shifter corresponds to the comparison signal. For example, the phase shifter  612  corresponds to the signal  644 . The phase shifter  612  is adjusted so that the phase difference between the signals  642  and  644  becomes zero at a predetermined frequency. As shown in  FIG. 8 , the curve  810  is moved up in parallel and becomes a curve  820 . The curve  820  represents a zero phase difference at a predetermined frequency fa. For example, the frequency f a  is the center frequency of the signals  642  and  644 . 
   At the process  750 , a variable true time delay system is adjusted. For example, the variable true time delay system  632  corresponds to the signal  644 . The variable true time delay system  632  is adjusted so that the phase difference between the signals  642  and  644  becomes zero within a frequency range. As shown in  FIG. 8 , the curve  820  is rotated with a pivot point  822  and becomes a curve  830 . The curve  830  represents a zero phase difference at a frequency range from f 1  to f h . For example, the frequency range from f 1  to f h  is the 3 dB bandwidth of the signals  642  and  644 . 
   At the process  760 , whether additional signal processing should be performed is determined. For example, the processes  730 ,  740  and  750  should be performed between the reference signal and each of all other signals. As another example, the processes  730 ,  740  and  750  should be performed between any two signals of the signals  642 ,  644 ,  646  and  648 . In these two examples, if the processes  730 ,  740  and  750  are performed between signals  642  and  644  but not any other pair of signals, the process  760  determines additional signal processing should be performed. 
   If additional signal processing should be performed, some or all of the processes  710  through  760  are repeated. The process  710  may be skipped. For example, the signals  642  and  648  are selected and processed, the phase shifters  610  and  616  are adjusted, and the variable true time delay systems  630  and  636  are also adjusted. If additional signal processing does not need to be performed, the signal  641  is used as the output in the reception mode. If the time delay beam forming system  600  is configured to transmit signals, the signals  611 ,  613 ,  615  and  617  are used as the outputs in the transmission mode. 
   As discussed above and further emphasized here,  FIG. 7  is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. For example, the method  700  also adjusts a phase shifter and a variable true time delay system corresponding to the selected reference signal. 
     FIG. 9  is a simplified block diagram for an adaptive variable true time delay beam forming method according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A time delay beam forming method  900  includes a process  910  for selecting a reference signal, a process  920  for selecting a comparison signal, a process  930  for processing the comparison signal and combined signal, a process  940  for adjusting a phase shifter and a variable true time delay system, and a process  950  for determining whether additional signal processing should be performed. Although the above has been shown using a selected sequence of processes, there can be many alternatives, modifications, and variations. For example, some of the processes may be expanded and/or combined. Other processes may be inserted to those noted above. Depending upon the embodiment, the specific sequence of steps may be interchanged with others replaced. Further details of these elements are found throughout the present specification and more particularly below. 
   At the process  910 , a reference signal is selected from the signals  642 ,  644 ,  646  and  648 . At the process  920 , a comparison signal is selected from the signals  642 ,  644 ,  646  and  648 . For example, the switch  662  receives the signals  642 ,  644 ,  646  and  648  and selects the signal  648  as its output signal  663 . The switch  672  receives the signals  648  and  664  and selects the signal  648  as its output signal  673 . The signal  648  is the comparison signal. 
   At the process  930 , the comparison signal and the combined signal are processed. For example, the switch  670  receives the signals  641  and  661  and selects the signal  641  as its output signal  671 . The signal  641  is the combined signal. The correlative receiver  680  receives the signals  641  and  648  from the switches  670  and  672  respectively. The correlative receiver  680  processes the signals  641  and  648  and measures information related to their phase and time delay differences.  FIG. 10  is a simplified diagram for phase differences among signals according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A vector  1010  represents the combined signal  641 . The length of the vector  1010  represents the magnitude of the combined signal  641  and the direction of the vector  1010  represents the phase of the combined signal  641 . Similarly, vectors  1020 ,  1030 ,  1040  and  1050  represent the signals  648 ,  646 ,  644  and  642  respectively. The vector lengths represent magnitudes of these signals and the vector directions represent phases of these signals respectively. An angle  1022  represents the phase difference between the combined signal  641  and the comparison signal  648 . 
   At the process  940 , a phase shifter and a variable true time delay system are adjusted. The phase shifter and the variable true time delay system correspond to the comparison signal. For example, the phase shifter  616  and the variable true time delay system  636  corresponds to the signal  648 . The phase shifter  616  and the variable true time delay system  636  are adjusted so that the phase difference between the signals  641  and  648 , i.e., the angel  1022 , is minimized.  FIG. 11  is a simplified diagram for phase differences among signals with adjustments according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. The vector  1020  is moved and rotated into a vector  1024 . With the change to the vector  1020 , the vector  1010  becomes a vector  1014 . The vector  1014  is a sum of the vectors  1024 ,  1030 ,  1040  and  1050 . 
   At the process  950 , whether additional signal processing should be performed is determined. For example, the processes  930  and  940  should be performed between the combined signal and each of the divided signals other than the reference signal. The divided signals may include the signals  642 ,  644 ,  646  and  648 . If the processes  930  and  940  are performed between signals  641  and  648  but not any other pair of signals, the process  950  determines additional signal processing should be performed. 
   If additional signal processing should be performed, some or all of the processes  910  through  950  are repeated. The process  910  may be skipped. For example, the signal  642  remains as the reference signal, the signal  646  is selected as the comparison signal, the signals  641  and  646  are processed, the phase shifters  614  and the variable true time delay systems  634  are adjusted.  FIG. 12  is a simplified diagram for phase differences among signals with adjustments according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. The vector  1030  is moved and rotated into a vector  1032 . With the change to the vector  1030 , the vector  1014  becomes a vector  1016 . The vector  1016  is a sum of the vectors  1024 ,  1032 ,  1040  and  1050 . 
   As another example, the signal  642  remains as the reference signal, the signal  644  is selected as the comparison signal, the signals  641  and  644  are processed, the phase shifters  612  and the variable true time delay systems  632  are adjusted.  FIG. 13  is a simplified diagram for phase differences among signals with adjustments according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. The vector  1040  is moved and rotated into a vector  1042 . With the change to the vector  1040 , the vector  1016  becomes a vector  1018 . The vector  1018  is a sum of the vectors  1024 ,  1032 ,  1042  and  1050 . As shown in  FIG. 13 , the vectors  1024 ,  1032 ,  1042  and  1050  have substantially the same direction. 
   If additional signal processing does not need to be performed, the signal  641  is used as the output in the reception mode. If the time delay beam forming system  600  is configured to transmit signals, the signals  611 ,  613 ,  615  and  617  are used as the outputs in the transmission mode. 
   As discussed above and further emphasized here,  FIG. 9  is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. For example, the method  700  also adjusts a phase shifter and a variable true time delay system corresponding to the selected reference signal. 
   As shown in  FIGS. 7 and 9 , the time delay beam forming methods adjust and maintain the phase of a comparison signal to be substantially the same as the reference signal over a predetermined band of frequency. For example, the phases of the comparison signal and the reference signal are within ±10°. As a phased array antenna scans its beams, the phase difference between the comparison signal and the reference signal also changes. The adjustments of the phase shifter and the variable true time delay system should be fast enough to accommodate the dynamics of beam formation. 
   In one embodiment of the present invention, a phased array antenna system with the adaptive variable true time delay beam forming system  600  scans its beams at a rate of 2 degrees of elevation angle per second. The rate of change of the phase difference between two panel array antennas separated vertically by 75 inches is
 
ΔΦ=2 π×D×R ×cos θ/λ  (Equation 4)
 
   where ΔΦ represents the rate of change of the phase difference, D represents the distance between two panel array antennas, R represents the rate of change of beam angle, θ represents the beam pointing angle, and λ represents the wavelength of the beam signal. With D equal to 75 inches, R equal to 2 degrees per second, θ equal to zero degree, and λ corresponding to 2.3 GHz, ΔΦ equals about 183.5 degrees per second. In order to keep the phase difference between divided signals less than 10°, the phase adjustments should be performed once every about 50 msec. 
     FIG. 14  is a simplified diagram for a variable true time delay system according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A variable true time delay system  1400  includes a combiner and divider system  1410 , time delay systems  1420 ,  1422  and  1424 , phase shifters  1430 ,  1432  and  1434 , variable attenuators  1440 ,  1442  and  1444 , and a combiner and divider system  1450 . Although the above has been shown using various systems, there can be many alternatives, modifications, and variations. For example, some of the systems may be expanded and/or combined. Additional time delay systems, phase shifters, and variable attenuators may be added to generate additional inputs to the combiner and divider system  1450 , or receive additional outputs from the combiner and divider system  1450 . Other systems may be inserted to those noted above. Depending upon the embodiment, the specific systems may be replaced. Further details of these systems are found throughout the present specification and more particularly below. The variable true time delay system  1400  may be used as each of the variable true time delay systems  630 ,  632 ,  634  and  636  as shown in  FIG. 6 . 
   The combiner and divider system  1410  receives a signal  1460  and generates signals  1462 ,  1464  and  1466  respectively. For example, the signal  1460  has a 3 dB bandwidth from f 1  to f h . The time delay systems  1420 ,  1422  and  1466  receive the signals  1462 ,  1464  and  1466  and generate signals  1472 ,  1474  and  1476  respectively. For example, the time delay systems  1420 ,  1422  and  1426  include cables, optical fibers, or transmission lines respectively. The time delay systems  1420 ,  1422  and  1426  can provide predetermined time delays τ 1 , τ 2  and τ 3  respectively. The phase shifters  1430 ,  1432  and  1434  receive the signals  1472 ,  1474  and  1476  and generate signals  1482 ,  1484  and  1486  respectively. The variable attenuators  1440 ,  1442  and  1444  receives the signals  1482 ,  1484  and  1486  and generates signals  1492 ,  1494  and  1496  respectively. The combiner and divider system  1450  receives the signals  1492 ,  1494  and  1496  and generates a signal  1498 . By controlling the attenuation levels of the variable attenuators  1440 ,  1442  and  1444 , the effective time delay between the signal  1498  and the signal  1460  can be varied from the minimum of τ 1 , τ 2  and τ 3  to the maximum of τ 1 , τ 1  and τ 3  in a phase continuous manner. For example, the time differences between τ 1 , τ 2  and τ 3  are selected such that the phase differences over a frequency band from f 1  to f h  between any one of the time delayed signals are small, such as less than 30 degrees. These selections are usually acceptable for beam-forming purpose without significant loss of signal processing gain. 
   In another embodiment, the combiner and divider system  1410  generates the signal  1460  and receives the signals  1462 ,  1464  and  1466  respectively. The time delay systems  1420 ,  1422  and  1466  generates the signals  1462 ,  1464  and  1466  and receive the signals  1472 ,  1474  and  1476  respectively. The time delay systems  1420 ,  1422  and  1426  can provide the predetermined time delays τ 1 , τ 2  and τ 3  respectively. The phase shifters  1430 ,  1432  and  1434  generate the signals  1472 ,  1474  and  1476  and receive the signals  1482 ,  1484  and  1486  respectively. The variable attenuators  1440 ,  1442  and  1444  generates the signals  1482 ,  1484  and  1486  and receives signals  1492 ,  1494  and  1496  respectively. The combiner and divider system  1450  generates the signals  1492 ,  1494  and  1496  and receives the signal  1498 . By controlling the attenuation levels of the variable attenuators  1440 ,  1442  and  1444 , the relative time delay between the signal  1460  and the signal  1498  can be varied from the minimum of τ 1 , τ 2  and τ 3  to the maximum of τ 1 , τ 1  and τ 3  in a phase continuous manner. 
     FIG. 14A  is a simplified block diagram for a variable true time delay method according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A variable true time delay method  1401  includes a process  1402  for receiving signal, a process  1403  for dividing signal, a process  1404  for delaying divided signals, a process  1405  for phase shifting divided signals, a process  1406  for attenuating divided signals, a process  1407  for combining divided signals, and a process  1408  for outputting combined signal. Although the above has been shown using a selected sequence of processes, there can be many alternatives, modifications, and variations. For example, the method  1401  can be modified for transmission mode. Some of the processes may be expanded and/or combined. Other processes may be inserted to those noted above. Depending upon the embodiment, the specific sequence of steps may be interchanged with others replaced. Further details of these elements are found throughout the present specification and more particularly below. 
   At the process  1402 , the signal  1460  is received by the combiner and divider system  1410 . At the process  1403 , the combiner and divider system  1410  divides the signal  1460  into several signals, such as the signals  1462 ,  1464  and  1466 . At the process  1404 , the divided signals are delayed for the predetermined periods of time. For example, the signal  1462  is delayed by the time delay system  1420  by τ 1  nsec. At the process  1405 , the divided signals are phase shifted by the phase shifters  1430 ,  1432  and  1434 . At the process  1406 , the divided signals are attenuated by the variable attenuators  1440 ,  1442  and  1444 . At the process  1407 , the divided signals are combined by the combiner and divider system  1450 . At the process  1408 , a combined signal  1498  is generated. 
   For example, the method  1401  can rotate a frequency phase response around a pivot point.  FIG. 14B  is a simplified diagram for delaying signal according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A curve  1410  represents the phase difference between the signal  1460  and the signal  1498  as a function of frequency. The curve  1410  is substantially a straight line, and its slope represents a relative time delay between the two signals. The relative time delay is measured with respect to a reference time delay. By adjusting the phase shifters  1430 ,  1432  and  1434  and the variable attenuators  1440 ,  1442  and  1444  in the processes  1405  and  1406 , the curve  1410  rotates around a point  1420  and becomes a curve  1430 . Usually, the settings of the phase shifters  1430 ,  1432  and  1434  affect the location of the pivot point  1420  and the settings of the variable attenuators  1440 ,  1442  and  1444  affect the slope of the curve  1430 . The slope of the curve  1430  is related to the relative time delay between the signal  1460  and the signal  1498 . 
     FIG. 15  is a simplified diagram for relative time delay as a function of attenuation levels according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. The time delay systems  1420 ,  1422  and  1426  provide the predetermined time delays τ 1 , τ 2  and τ 3  respectively, and τ 1 , τ 2  and τ 3  equal to 0.00, 2.25 and 4.50 nsec respectively. A vertical axis  1510  measures attenuation levels of the variable attenuators  1440 ,  1442  and  1444 , and a horizontal axis  1520  measures relative time delay relative to τ 2 . Curves  1530 ,  1532  and  1534  represent the attenuation levels of the variable attenuators  1440 ,  1442  and  1444  corresponding to relative time delay values. For example, to achieve an relative time delay of −0.75 nsec, the attenuation levels of the variable attenuators  1440 ,  1442  and  1444  should be adjusted to about −4 dB, −1 dB, and less than −21 dB respectively. 
   According to an embodiment of the present invention, the design of a variable true time delay system is explained as follows. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. The variable true time delay system is designed to provide a phase delay of φ=2×π×τ×f radian, where τ denotes an relative time delay, and f=f 1 , f 2 , or f 3  within a bandwidth from f 1  to f h . The center of f 1  and f h  is denoted by f o . 
   For example, the variable true time delay system  1400  is designed. The variable true time delay system  1400  has signal channels  1 ,  2  and  3  corresponding to the signals  1462 ,  1464  and  1466  respectively. To describe the operation of the system  1400  based on two signal channels, one of the three channels is assumed to have its variable attenuator programmed at the maximum attenuation. 
   The transfer function of the system  1400  is represented by
 
 a   1 *exp { jφ   o   +j 2πτ 1   f+jφ   1   }+a   2 *exp {+ jφ   o   +jπτ   2   f+jφ   2 }=exp { jφ   o   +j 2πτ 2   f}×[a   2  exp { jφ   2   }+a   1  exp { j 2π(τ 1 −τ 2 ) f+jφ   1 }]  (Equation 5)
 
 a   2 *exp { jφ   o   +j 2πτ 2   f+jφ   2   }+a   3 *exp {+ jφ   o   +jπτ   3   f+jφ   3 }=exp { jφ   o   +j 2πτ 2   f}×[a   2  exp { jφ   2   }+a   3  exp { j   2π(τ   3 −τ 2 ) f+jφ   3 }]  (Equation 6)
         where a 1 , a 2  and a 3  denote the amplitudes of the signals in signal channels  1 ,  2  and  3 , φ o  represents the value of the common phase delay, τ 1 , τ 2  and τ 3  represents the time delays in signal channels  1 ,  2  and  3 , and φ 1 , φ 2  &amp; φ 3  represents the phase delays in channels  1 ,  2  and  3  respectively. For example, a 1 , a 2  and a 3  are determined at least in part by the variable attenuators  1440 ,  1442  and  1444 . As another example, τ 2 −τ 1=2.25  nsec and τ 3 −τ 2=2.25  nsec.       

   The variable true time delay system  1400  has three frequency calibration points, 2.25, 2.30 and 2.35 GHz. At a calibrated frequency point f o , the system is calibrated to produce φ 2 = 0 , and the phase shifters of channels  1  and  3  are calibrated such that  2 π(τ 2 −τ 1 )f o +φ 1 = 2 π(τ 3 −τ 2 )f o +φ 3  equal an integral multiple of 2π. Therefore, the expressions for the transfer function of the variable time delay system become exp {jφ o +j2πτ 2 (f o +Δf)}×[a 2 +a 1  exp{−j 2π(τ   2 −τ 2 )Δf}] or exp {jφ o +j2πτ 2 (f o +Δf)}×[a 2 +a 3  exp {j2π(τ 3 −τ 2 )Δf}] where f=f o +Δf. 
   For example, the calibrated values of φ 1  and φ 3  are show in Table 1. The values for φ 1  and φ 3  may be different from ones listed in Table 1 due to differences in cable lengths used for time delays systems in various signal channels. 
   
     
       
             
             
             
           
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
               Calibration frequency 
               φ 1  (degrees) 
               φ 3  (degrees) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               2250.0 MHz 
               −22.5 
               −22.5 
             
             
               2300.0 MHz 
               −63.0 
               −63.0 
             
             
               2350.0 MHz 
               −103.5 
               −103.5 
             
             
                 
             
           
        
       
     
   
   The theoretical transmission coefficient s 21  for the system  1400  is described in Tables 2 and 3 as a function of a 1 , a 2  and a 3 . The transmission coefficient also varies with frequency measured from the center frequency f 0 . For example, f o  equals 2250, 2300 or 2350 MHz. For each combination of a 1 , a 2  and a 3 , s 21  is listed for the relative frequency values of −50, −40, −30, −20, −10, 0, 10, 20, 30, 40 and 50 MHz, and the relative frequency values are measured with respect to the center frequency f 0 . The magnitude of s 21  is described in Table 2, and the phase of s 21  in degrees is described in Table 3. The system  1400  has an electrical length compensation of τ 2  and a phase compensation of φ o . 
   
     
       
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 2 
             
             
                 
                 
             
             
                 
               a 1   
               a 2   
               a 3   
               −50 
               −40 
               −30 
               −20 
               −10 
               0 
               10 
               20 
               30 
               40 
               50 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               1 
               0.88 
               0.00 
               0.00 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
             
             
               2 
               0.87 
               0.10 
               0.00 
               0.95 
               0.96 
               0.96 
               0.97 
               0.97 
               0.97 
               0.97 
               0.97 
               0.96 
               0.96 
               0.95 
             
             
               3 
               0.86 
               0.20 
               0.00 
               1.02 
               1.03 
               1.04 
               1.05 
               1.06 
               1.06 
               1.06 
               1.05 
               1.04 
               1.03 
               1.02 
             
             
               4 
               0.84 
               0.30 
               0.00 
               1.08 
               1.10 
               1.12 
               1.13 
               1.13 
               1.14 
               1.13 
               1.13 
               1.12 
               1.10 
               1.08 
             
             
               5 
               0.80 
               0.40 
               0.00 
               1.14 
               1.16 
               1.18 
               1.19 
               1.20 
               1.20 
               1.20 
               1.19 
               1.18 
               1.16 
               1.14 
             
             
               6 
               0.76 
               0.50 
               0.00 
               1.19 
               1.21 
               1.23 
               1.25 
               1.26 
               1.26 
               1.26 
               1.25 
               1.23 
               1.21 
               1.19 
             
             
               7 
               0.70 
               0.60 
               0.00 
               1.22 
               1.25 
               1.27 
               1.29 
               1.30 
               1.30 
               1.30 
               1.29 
               1.27 
               1.25 
               1.22 
             
             
               8 
               0.63 
               0.70 
               0.00 
               1.24 
               1.27 
               1.30 
               1.31 
               1.32 
               1.33 
               1.32 
               1.31 
               1.30 
               1.27 
               1.24 
             
             
               9 
               0.53 
               0.80 
               0.00 
               1.25 
               1.28 
               1.30 
               1.31 
               1.32 
               1.33 
               1.32 
               1.31 
               1.30 
               1.28 
               1.25 
             
             
               10 
               0.38 
               0.90 
               0.00 
               1.22 
               1.24 
               1.26 
               1.27 
               1.28 
               1.28 
               1.28 
               1.27 
               1.26 
               1.24 
               1.22 
             
             
               11 
               0 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               12 
               0.00 
               0.90 
               0.38 
               1.22 
               1.24 
               1.26 
               1.27 
               1.28 
               1.28 
               1.28 
               1.27 
               1.26 
               1.24 
               1.22 
             
             
               13 
               0.00 
               0.80 
               0.53 
               1.25 
               1.28 
               1.30 
               1.31 
               1.32 
               1.33 
               1.32 
               1.31 
               1.30 
               1.28 
               1.25 
             
             
               14 
               0.00 
               0.70 
               0.63 
               1.24 
               1.27 
               1.30 
               1.31 
               1.32 
               1.33 
               1.32 
               1.31 
               1.30 
               1.27 
               1.24 
             
             
               15 
               0.00 
               0.60 
               0.70 
               1.22 
               1.25 
               1.27 
               1.29 
               1.30 
               1.30 
               1.30 
               1.29 
               1.27 
               1.25 
               1.22 
             
             
               16 
               0.00 
               0.50 
               0.76 
               1.19 
               1.21 
               1.23 
               1.25 
               1.26 
               1.26 
               1.26 
               1.25 
               1.23 
               1.21 
               1.19 
             
             
               17 
               0.00 
               0.40 
               0.80 
               1.14 
               1.16 
               1.18 
               1.19 
               1.20 
               1.20 
               1.20 
               1.19 
               1.18 
               1.16 
               1.14 
             
             
               18 
               0.00 
               0.30 
               0.84 
               1.08 
               1.10 
               1.12 
               1.13 
               1.13 
               1.14 
               1.13 
               1.13 
               1.12 
               1.10 
               1.08 
             
             
               19 
               0.00 
               0.20 
               0.86 
               1.02 
               1.03 
               1.04 
               1.05 
               1.06 
               1.06 
               1.06 
               1.05 
               1.04 
               1.03 
               1.02 
             
             
               20 
               0.00 
               0.10 
               0.87 
               0.95 
               0.96 
               0.96 
               0.97 
               0.97 
               0.97 
               0.97 
               0.97 
               0.96 
               0.96 
               0.95 
             
             
               21 
               0.00 
               0.00 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
               0.88 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 3 
             
             
                 
                 
             
             
                 
               a 1   
               a 2   
               a 3   
               −50 
               −40 
               −30 
               −20 
               −10 
               0 
               10 
               20 
               30 
               40 
               50 
               delay 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               1 
               0.88 
               0.00 
               0.00 
               40.50 
               32.40 
               24.30 
               16.20 
               8.10 
               0.00 
               −8.10 
               −16.20 
               −24.30 
               −32.40 
               −40.50 
               −2.25 
             
             
               2 
               0.87 
               0.10 
               0.00 
               36.58 
               29.20 
               21.86 
               14.55 
               7.27 
               0.00 
               −7.27 
               −14.55 
               −21.86 
               −29.20 
               −36.58 
               −2.03 
             
             
               3 
               0.86 
               0.20 
               0.00 
               33.18 
               26.45 
               19.78 
               13.16 
               6.57 
               0.00 
               −6.57 
               −13.16 
               −19.78 
               −26.45 
               −33.18 
               −1.84 
             
             
               4 
               0.84 
               0.30 
               0.00 
               30.13 
               24.01 
               17.95 
               11.94 
               5.96 
               0.00 
               −5.96 
               −11.94 
               −17.95 
               −24.01 
               −30.13 
               −1.67 
             
             
               5 
               0.80 
               0.40 
               0.00 
               27.31 
               21.77 
               16.28 
               10.83 
               5.41 
               0.00 
               −5.41 
               −10.83 
               −16.28 
               −21.77 
               −27.31 
               −1.52 
             
             
               6 
               0.76 
               0.50 
               0.00 
               24.60 
               19.63 
               14.69 
               9.78 
               4.89 
               0.00 
               −4.89 
               −9.78 
               −14.69 
               −19.63 
               −24.60 
               −1.37 
             
             
               7 
               0.70 
               0.60 
               0.00 
               21.90 
               17.50 
               13.11 
               8.74 
               4.37 
               0.00 
               −4.37 
               −8.74 
               −13.11 
               −17.50 
               −21.90 
               −1.22 
             
             
               8 
               0.63 
               0.70 
               0.00 
               19.08 
               15.28 
               11.47 
               7.65 
               3.83 
               0.00 
               −3.83 
               −7.65 
               −11.47 
               −15.28 
               −19.08 
               −1.06 
             
             
               9 
               0.53 
               0.80 
               0.00 
               15.90 
               12.77 
               9.61 
               6.42 
               3.21 
               0.00 
               −3.21 
               −6.42 
               −9.61 
               −12.77 
               −15.90 
               −0.88 
             
             
               10 
               0.38 
               0.90 
               0.00 
               11.78 
               9.51 
               7.18 
               4.81 
               2.41 
               0.00 
               −2.41 
               −4.81 
               −7.18 
               −9.51 
               −11.78 
               −0.65 
             
             
               11 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               12 
               0.00 
               0.90 
               0.38 
               −11.78 
               −9.51 
               −7.18 
               −4.81 
               −2.41 
               0.00 
               2.41 
               4.81 
               7.18 
               9.51 
               11.78 
               0.65 
             
             
               13 
               0.00 
               0.80 
               0.53 
               −15.90 
               −12.77 
               −9.61 
               −6.42 
               −3.21 
               0.00 
               3.21 
               6.42 
               9.61 
               12.77 
               15.90 
               0.88 
             
             
               14 
               0.00 
               0.70 
               0.63 
               −19.08 
               −15.28 
               −11.47 
               −7.65 
               −3.83 
               0.00 
               3.83 
               7.65 
               11.47 
               15.28 
               19.08 
               1.06 
             
             
               15 
               0.00 
               0.60 
               0.70 
               −21.90 
               −17.50 
               −13.11 
               −8.74 
               −4.37 
               0.00 
               4.37 
               8.74 
               13.11 
               17.50 
               21.90 
               1.22 
             
             
               16 
               0.00 
               0.50 
               0.76 
               −24.60 
               −19.63 
               −14.69 
               −9.78 
               −4.89 
               0.00 
               4.89 
               9.78 
               14.69 
               19.63 
               24.60 
               1.37 
             
             
               17 
               0.00 
               0.40 
               0.80 
               −27.31 
               −21.77 
               −16.28 
               −10.83 
               −5.41 
               0.00 
               5.41 
               10.83 
               16.28 
               21.77 
               27.31 
               1.52 
             
             
               18 
               0.00 
               0.30 
               0.84 
               −30.13 
               −24.01 
               −17.95 
               −11.94 
               −5.96 
               0.00 
               5.96 
               11.94 
               17.95 
               24.01 
               30.13 
               1.67 
             
             
               19 
               0.00 
               0.20 
               0.86 
               −33.18 
               −26.45 
               −19.78 
               −13.16 
               −6.57 
               0.00 
               6.57 
               13.16 
               19.78 
               26.45 
               33.18 
               1.84 
             
             
               20 
               0.00 
               0.10 
               0.87 
               −36.58 
               −29.20 
               −21.86 
               −14.55 
               −7.27 
               0.00 
               7.27 
               14.55 
               21.86 
               29.20 
               36.58 
               2.03 
             
             
               21 
               0.00 
               0.00 
               0.88 
               −40.50 
               −32.40 
               −24.30 
               −16.20 
               −8.10 
               0.00 
               8.10 
               16.20 
               24.30 
               32.40 
               40.50 
               2.25 
             
             
                 
             
           
        
       
     
   
   In Table 3, the last column of data indicates the time delay relative to τ 2  for the system  1400 . For example, τ 2  equals 2.25 nsec. Additional optimization on the parameters a 1 , a 2  and a 3  is required to obtain magnitude responses closer to unity. It should be pointed out that the effectiveness of the variable time delay system in terms of providing the desirable phase is usually tolerant of small errors in its time delay. For example, an relative time delay error of 0.25 nsec translates into a maximum phase error of less than 4.5 degrees within 50 MHz of the calibration point. 
     FIG. 16  is a simplified block diagram for an antenna system according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. As shown in  FIG. 16 , two antennas  1610  and  1612  are separated by a horizontal baseline distance of L equal to 67″. These antennas  1610  and  1612  correspond to signal channels  1620  and  1622  respectively. The signal channels  1620  and  1622  are also called Channel R and Channel L respectively. The arriving signals are two telemetry links, narrow band signals centered at 2200.5 MHz and 2275.5 MHz. The incident angle is θ inc =15 degree relative to antenna baseline normal. The time difference of arrival is Δτ=(L sin θ inc )/c, where c is the speed of light. For a 15 degree incident angle, Δτ=1.4682 nsec. 
     FIG. 17  is a simplified circuit diagram for an antenna system as describe in  FIG. 16  according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. At a cross section  1710 , the signals at Channel L and Channel R are both expressed by x 1 (t)+x 2  (t), where x 1 (t) and x 2 (t) denote the telemetry links. At a cross section  1720 , the signal at Channel L is expressed by x 1 (t)+x 2  (t), and the signal at Channel R is expressed by 
                     x   1     ⁡     (   t   )       ⁢   exp   ⁢     {     j   *   2   ⁢           ⁢   π   *   Δτ   *     f   1       }       +         x   2     ⁡     (   t   )       ⁢   exp   ⁢     {     j   *   2   ⁢           ⁢   π   *   Δτ   *     f   2       }         =             x   1     ⁡     (   t   )       ⁢   exp   ⁢     {     jξ   1     }       +         x   2     ⁡     (   t   )       ⁢   exp   ⁢     {     jξ   2     }         =           x   1     ⁡     (   t   )       ⁢   exp   ⁢     {     j   ⁢           ⁢   65.48   ⁢   °     }       +         x   2     ⁡     (   t   )       ⁢   exp   ⁢     {     j   ⁢           ⁢   165.87   ⁢   °     }                   (     Equation   ⁢           ⁢   7     )               
   where ΔΣ=1.4682 nsec, f 1=2200.5  MHz, and f 2=2275.5  MHz. The signal at Channel R can be approximated to
 
 x   1 ( t ) exp { jφ   o   +j 2πτ 2 f 1   }×[a   2   +a   3  exp { j 2π(τ 3 −τ 2 )Δ f   1   }]+x   2 ( t ) exp { jφ   o   +j 2πτ 2   f   2   }×[a   2   +a   3  exp { j 2π(τ 3 −τ 2 )Δ 2   }]   (Equation 8)
 
   where Δf 1 =−49.5 MHz, and Δf 2=25.5  MHz. With φ o =22.50, a 2=0.5 , and a 3=0.76 , the signal at Channel R can be further approximated to
 
1.25 *x   1 ( t )exp { j 65.36°}+1.06 *x   2 ( t )exp{ j 163.56°}  (Equation 9)
 
   Equations 7 and 9 shows that for both telemetry links the signal in Channel L is close to being in phase with the signal in Channel R. As shown in  FIG. 17 , at a cross section  1730 , the signals at Channel L and Channel R channel are both expressed by x 1 (t)exp{j*2π*(Δτ+τ 2 )*f 1 }+x 2 (t)exp{j*2π*(Δτ+τ 2 )*f 2 }, where Δτ=1.4682 nsec, τ 2=2.25  nsec, f 1=2200.5  MHz, and f 2=2275.5  MHz. 
     FIG. 18  is a simplified block diagram for a method of calibrating a variable true time delay system according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A calibrating method  1800  includes a process  1810  for establishing reference time delay, a process  1820  for phase synchronization, a process  1830  for determining relative time delay. Although the above has been shown using a selected sequence of processes, there can be many alternatives, modifications, and variations. For example, some of the processes may be expanded and/or combined. Other processes may be inserted to those noted above. Depending upon the embodiment, the specific sequence of steps may be interchanged with others replaced. Further details of these elements are found throughout the present specification and more particularly below. 
   At the process  1810 , a reference time delay is established in a network analyzer. The network analyzer is connected between the combiner and divider systems  1410  and  1450 . The network analyzer sends the signal  1460  to the combiner and divider system  1410  and receivers the signal  1498  from the combiner and divider system  1450 . The time delay systems  1420 ,  1422  and  1424  provide the predetermined delays τ 1 , τ 2  and τ 3  respectively. The minimum of τ 1 , τ 2  and τ 3  is τ min , the maximum of τ 1 , τ 2  and τ 3  is τ max , and the middle value of τ 1 , τ 2  and τ 3  is τ mid . The phase shifter associated with τ mid  is adjusted to a mid-point value in terms of the total range of phase shift, and the variable attenuator associated with τ mid  is set to the minimum attenuation. The other two variable attenuators are set to the maximum attenuation. For example, τ 2  equals τ mid . The phase shifter and the variable attenuator associated with τ mid  are the phase shifter  1432  and the variable attenuator  1442 . The network analyzer is set to measure the transmission coefficient S 21  of the variable true time delay system  1400  over a frequency band from f 1 , to f h . S 21  equals a ratio of the signal  1498  to the signal  1460 , and is a complex number with magnitude and phase. Based on the measured magnitude and phase, the network analyzer establishes the reference time delay and phase offset. The reference time delay is used to determined a relative time delay. A time delay equal to the reference time delay has a zero relative time delay. Optionally, the network analyzer may set data averaging factor to 64, use aperture smoothing factor of 10%. 
   At the process  1820 , phase synchronization is performed. When the phases are synchronized, the relative phases of the signals  1492 ,  1494  and  1496  through the three signal channels are the same at a predetermined frequency. This predetermined frequency corresponds to the pivot point  822  in  FIG. 8  and the pivot point  1420  in  FIG. 14B . For example, the control voltages for the phase shifters associated with τ min  and τ max  are adjusted to achieve phase synchronization between each of these two signal channels and the τ mid  signal channel at the predetermined frequency. The predetermined frequency may equal to 2.22 GHz, 2.26 GHz, 2.30 GHz, 2.34 GHz, 2.38 GHz or other value. The control voltage values for phase synchronization may be stored in a table similar to Table 4. Table 4 is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. 
   
     
       
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
                 
               TABLE 4 
             
             
                 
                 
             
             
                 
               2.22 GHz 
               2.26 GHz 
               2.30 GHz 
               2.34 GHz 
               2.38 G 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               τ 1   
               V 11   
               V 12   
               V 13   
               V 14   
               V 15   
             
             
               τ 2   
               V 21   
               V 22   
               V 23   
               V 24   
               V 25   
             
             
               τ 3   
               V 31   
               V 32   
               V 33   
               V 34   
               V 35   
             
             
                 
             
           
        
       
     
   
   At the process  1830 , the relative time delay is determined. The control voltages for the variable attenuators  1440 ,  1442  and  1444  are adjusted with the variable true time delay system  1400  remains phase synchronized at the predetermined frequency. The network analyzer measures the transmission coefficient S 21  of the system  1400  as a function of the control voltages. Based on the measured S 21 , the effective attenuation and the relative time delay are determined with respect to the reference time delay established in the process  1810 . These data can be compiled into a table similar to Table 5. Table 5 is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. For relative time delays at every 0.2 nsec between the range of τ min  and τ max , the values of control voltages can be determined for a predetermined pivot point frequency. τ min  and τ max  are associated with having the τ min  signal channel and the τ max  signal channel being active by themselves one at a time. 
   
     
       
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
                 
               TABLE 5 
             
             
                 
                 
             
             
                 
               τ max   
               τ mid   
               τ min   
               Attenuation (dB) 
               Delay (nsec) 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               1 
               V 11   
               V 12   
               V 13   
               Atten 1   
               Delay 1   
             
             
               2 
               V 21   
               V 22   
               V 23   
               Atten 2   
               Delay 2   
             
             
               3 
               V 31   
               V 32   
               V 33   
               Atten 3   
               Delay 3   
             
             
               4 
               V 41   
               V 42   
               V 43   
               Atten 4   
               Delay 4   
             
             
               5 
               V 51   
               V 52   
               V 53   
               Atten 5   
               Delay 5   
             
             
               . . . 
               . . . 
               . . . 
               . . . 
               . . . 
               . . . 
             
             
               25  
                V 251   
                V 252   
                V 253   
                Atten 25   
                Delay 25   
             
             
               26  
                V 261   
                V 262   
                V 263   
                Atten 26   
                Delay 26   
             
             
               27  
                V 271   
                V 272   
                V 273   
                Atten 27   
                Delay 27   
             
             
               28  
                V 281   
                V 282   
                V 283   
                Atten 28   
                Delay 28   
             
             
                 
             
           
        
       
     
   
   As discussed above and further emphasized here,  FIG. 18  is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. The attenuation corresponding to the variable attenuator set to minimum attenuation may be determined for each signal channel at each pivot point frequency. For example, the minimum attenuation corresponding to the τ 1  signal channel may be determined by setting the variable attenuator  1440  to minimum attenuation and setting the variable attenuators  1442  and  1444  to maximum attenuations. The time delays may be measured for each signal channel at each pivot point frequency. For example, the time delay is measured for the τ 1  signal channel by setting the variable attenuator  1440  to minimum attenuation and setting the variable attenuators  1442  and  1444  to maximum attenuations. 
     FIG. 19  is a simplified diagram for a calibrating system for an adaptive variable true time delay beam forming system according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A calibrating system  1900  includes a signal generator  1910 , a divider system  1920 , amplifiers  1932 ,  1934 ,  1936  and  1938 , and attenuators  1942 ,  1944 ,  1946  and  1948 . Although the above has been shown using various systems, there can be many alternatives, modifications, and variations. For example, some of the systems may be expanded and/or combined. The combiner system  1920  may generate more or less than four output signals. Additional amplifiers and attenuators may be added to generate additional output signals. Other systems may be inserted to those noted above. Depending upon the embodiment, the specific systems may be replaced. Further details of these systems are found throughout the present specification and more particularly below. 
   The signal generator  1910  generates a signal  1912  at a predetermined frequency. The signal  1912  is received by the divider system  1920  and divided into signals  1922 ,  1924 ,  1926  and  1928 . The signals  1922 ,  1924 ,  1926  and  1928  are received by the amplifiers  1932 ,  1934 ,  1936  and  1938  respectively, which generate signals  1933 ,  1935 ,  1937  and  1939  respectively. For example, the amplifiers are set at a gain of 30 dB and the attenuators are set at an attenuation of 6 dB. The signals  1933 ,  1935 ,  1937  and  1939  have substantially the same relative phase and the same relative time delay. Additionally, the signals  1933 ,  1935 ,  1937  and  1939  have substantially the same magnitude with different random noises. 
     FIG. 20  is a simplified block diagram for a method of calibrating an adaptive variable true time delay beam forming system according to one embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. A calibrating method  2000  includes a process  2010  for providing signals to time delay beam forming system, a process  2020  for selecting two signal channels, and a process  2030  for measuring phase difference. Although the above has been shown using a selected sequence of processes, there can be many alternatives, modifications, and variations. For example, some of the processes may be expanded and/or combined. Other processes may be inserted to those noted above. Depending upon the embodiment, the specific sequence of steps may be interchanged with others replaced. Further details of these elements are found throughout the present specification and more particularly below. 
   At the process  2010 , the signals  1952 ,  1954 ,  1956  and  1958  are provided to the time delay beam forming system  600  as the signals  611 ,  613 ,  615  and  617  respectively. The phase shifters  610 ,  612 ,  614  and  616  are adjusted and the variable true time delay system  630 ,  632 ,  634  and  636  are adjusted to provide the signals  642 ,  644 ,  646  and  648  the same relative phase and the same relative time delay. At the process  2020 , two signal channels are selected from the signal channels corresponding to the signals  642 ,  644 ,  646 , and  648 . Switches  660  and  670  both output a signal from one of the two selected signal channels, and switches  662  and  672  both output a signal from the other one of the two selected signal channels. At the process  2030 , the phase difference (PD) is measured by the correlative receiver  680 . The measured phase difference corresponds to two input signals to the correlative receiver  680 , related to the signals  642 ,  644 ,  646  and  648  having the same phase and the same time delay. Processes  2020  and  2030  may be repeated at each desired frequency for all relevant combinations of pair of signals from the inputs of the combiner and divider system  640 . The values of the correlation value may be compiled into a table similar to Table 6. In Table 6, #1, #2, #3 and #4 represent signal channels corresponding to the signals  642 ,  644 ,  646  and  648  respectively. Table 6 is merely an example, which should not unduly limit the scope of the claims. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. 
   
     
       
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
                 
               TABLE 6 
             
             
                 
                 
             
             
                 
               2.20 G 
               2.24 GHz 
               2.28 GHz 
               2.32 GHz 
               2.36 GHz 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               #1 and #1 
               PD 1,1,2.20   
               PD 1,1,2.24   
               PD 1,1,2.28   
               PD 1,1,2.32   
               PD 1,1,2.36   
             
             
               #2 and #2 
               PD 2,2,2.20   
               PD 2,2,2.24   
               PD 2,2,2.28   
               PD 2,2,2.32   
               PD 2,2,2.36   
             
             
               #3 and #3 
               PD 3,3,2.20   
               PD 3,3,2.24   
               PD 3,3,2.28   
               PD 3,3,2.32   
               PD 3,3,2.36   
             
             
               #4 and #4 
               PD 4,4,2.20   
               PD 4,4,2.24   
               PD 4,4,2.28   
               PD 4,4,2.32   
               PD 4,4,2.36   
             
             
               #1 and #2 
               PD 1,2,2.20   
               PD 1,2,2.24   
               PD 1,2,2.28   
               PD 1,2,2.32   
               PD 1,2,2.36   
             
             
               #1 and #3 
               PD 1,3,2.20   
               PD 1,3,2.24   
               PD 1,3,2.28   
               PD 1,3,2.32   
               PD 1,3,2.36   
             
             
               #1 and #4 
               PD 1,4,2.20   
               PD 1,4,2.24   
               PD 1,4,2.28   
               PD 1,4,2.32   
               PD 1,4,2.36   
             
             
               #2 and #3 
               PD 2,3,2.20   
               PD 2,3,2.24   
               PD 2,3,2.28   
               PD 2,3,2.32   
               PD 2,3,2.36   
             
             
               #2 and #4 
               PD 2,4,2.20   
               PD 2,4,2.24   
               PD 2,4,2.28   
               PD 2,4,2.32   
               PD 2,4,2.36   
             
             
               #3 and #4 
               PD 3,4,2.20   
               PD 3,4,2.24   
               PD 3,4,2.28   
               PD 3,4,2.32   
               PD 3,4,2.36   
             
             
                 
             
           
        
       
     
   
   Certain embodiments of the present invention as shown in  FIGS. 1–20  can be applied to a phased array antenna.  FIG. 21  is a simplified diagram for a phased array antenna system. An antenna system  2040  includes four panels  2042 ,  2044 ,  2046  and  2048 . In order to improve the frequency response of the antenna system  2040 , the outputs of the panels  2042 ,  2044 ,  2046  and  2048  are inputted into the time delay beam forming system  600  as shown in  FIG. 6 . As discussed above and further emphasized here, the application of the present invention to  FIG. 21  is merely an example, which should not unduly limit the scope of the present invention. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. 
   The present invention has various advantages. For example, certain embodiments of the present invention reduce complexity of calibration process that usually involves physical manipulation of a large phased array antenna. Some embodiments of the present invention reduce the amount of time required for system integration in the factory. After system deployment, periodic maintenance procedures for periodic test, calibration and performance verifications can be simplified. Certain embodiments of the present invention can make real time measurements and estimate relative time delays and phase delays between received signals. Some embodiments of the present invention can lower costs of making and using phased array antenna systems. 
   Although specific embodiments of the present invention have been described, it will be understood by those of skill in the art that there are other embodiments that are equivalent to the described embodiments. Accordingly, it is to be understood that the invention is not to be limited by the specific illustrated embodiments, but only by the scope of the appended claims.