Patent Publication Number: US-2021190895-A1

Title: Method for Finding Signal Direction Using Modal Antenna

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit of priority with U.S. Provisional Ser. No. 61/954,506, filed Mar. 17, 2014, titled “METHOD FOR FINDING SIGNAL&#39;S DIRECTION USING MODAL ANTENNA”; the contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND 
     Field of the Invention 
     This invention relates generally to wireless communications; and more particularly, to methods for finding direction of a signal using an active multi-mode antenna. 
     Description of the Related Art 
     As new generations of wireless communication devices become smaller and embedded with increased applications, new antenna designs, system configurations and controlling algorithms are required to enable new capabilities and to improve QOS. For example, geolocation is a function to identify the geographic location of a mobile device, such as a cellular phone, a smart phone, a laptop, a tablet, an internet-connected computer terminal and other wireless communication device. These devices are expected to incorporate the location-determining function because of emergency “911” services, public safety and law enforcement concerns. Furthermore, in the emerging vehicle-to-vehicle communication protocols, the location-determining function enables one car to steer the communication signal following the movement of the other car, thereby improving the quality of the communication link and reducing electromagnetic interferences. Such geolocation or location-determining functions can be achieved by configuring an antenna system to find the direction of RF signals. 
     Direction finding, a.k.a. the angel of arrival (AOA) estimation, generally refers to a method of determining the direction of arrival of incoming signals, and plays an important role in spectrum monitoring as well as in reconnaissance and surveillance applications. Typically, the direction finding utilizes an array of antennas that detect incoming RF signals, wherein phase and amplitude information is correlated to calculate the direction of arrival of the signals. In such a conventional direction finding system, one receiver is provided for each antenna, in particular when high resolution is needed in situations where multipath interferences or co-channel signals exist. This configuration allows for continuous sampling of information received by each antenna. However, the drawback is that it is costly and requisite of a large space to provide multiple antennas and receive chains. As is typically the case when a multi-antenna system is used, electromagnetic coupling among the antennas as well as between the antennas and nearby electronics often deteriorates transmission and reception qualities. Additionally, efficiency may deteriorate in many instances where multiple RF chains are energized and power consumption increases. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates an example of a modal antenna. 
         FIG. 2( a )  illustrates a radiation pattern associated with the modal antenna of  FIG. 1  in the first state. 
         FIG. 2( b )  illustrates a radiation pattern associated with the modal antenna of  FIG. 1  in the second state. 
         FIG. 3  is a flowchart illustrating a first direction finding algorithm to obtain the angle that gives the minimum of Err(Θ,Φ) as the AOA of the signal. 
         FIG. 4  is a flowchart illustrating a second direction finding algorithm to obtain the angle that gives the minimum of Err K (Θ,Φ) as the AOA of the signal for the K-th mode, where the angle (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria. 
         FIG. 5  is a flowchart illustrating the procedure for taking signal strength changes into account. 
         FIG. 6  is a flowchart illustrating the procedure for taking signal strength changes into account, which can be incorporated in the second algorithm. 
         FIG. 7  illustrates an example schematically showing multipath signals and a communication device receiving them. 
         FIG. 8  is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the first algorithm. 
         FIG. 9  is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the second algorithm. 
         FIG. 10  is a flowchart illustrating the process of updating the gain variations based on the AOA information previously obtained. 
         FIG. 11  is a table illustrating an example of gain variations and signal strength variations used for the decision making. 
         FIG. 12  schematically illustrates the measurement of the phase shift of the signal strength during the transition between modes of the antenna. 
         FIG. 13  illustrates a portion of the look-up table showing the phase data of the gain according to the angles and the modes, i.e., radiation patterns of the antenna. 
     
    
    
     DETAILED DESCRIPTION 
     In view of the above problems associate with direction finding based on a multi-antenna system, this document provides a new type of direction finding methods based on a single antenna capable of producing multiple radiations patterns. 
     A modal antenna, also referred to as a null-steering antenna, can generate multiple modes corresponding to multiple radiation patterns, equivalent to having a set of antennas with the same feed. By using the modal antenna capable of generating different radiation patterns, it is possible to exploit a priori knowledge of antenna nulls and lobes in the different modes for steering the beam to have nulls in dominant interference directions while keeping gain in desired directions. Accordingly, implementation of a modal antenna may allow for pattern diversity with one antenna, thereby requiring less volume and area than using multiple antennas. Examples of structures and implementations of the modal antennas are provided in U.S. Pat. No. 7,911,402, entitled “ANTENNA AND METHOD FOR STEERING ANTENNA BEAM DIRECTION,” issued on Mar. 22, 2011; the contents of the which are hereby incorporated by reference and are summarized as follows: 
       FIG. 1  illustrates an example of a modal antenna  100 , which includes an Isolated Magnetic Dipole™ (IMD) element  104  placed on a ground plane  108 , a first parasitic element  112  coupled to an first active element  113 , and a second parasitic element  116  coupled to a second active element  117 . The active elements  113  and  117  may include switches that either electrically connect (short) or disconnect (open) the parasitic elements  112  and  116  to the ground plane  108 . This structure allows for two different modes of operation with a common frequency corresponding to a first state where the parasitic elements  112  and  116  are shorted to the ground and a second state where the parasitic elements  112  and  116  are open. 
       FIG. 2( a )  illustrates a radiation pattern  204  associated with the antenna  100  in the first state; and  FIG. 2( b )  illustrates a radiation pattern  208  in the second state, which shows a ninety-degree shift in direction as compared to the radiation pattern  204 . Thus, by controlling the active elements  113  and  117  of the modal antenna  100 , the operation of two modes can be obtained at the same frequency. The control scheme can be extended for three or more multi-mode operations by incorporating, for example, tunable elements in the active elements for variable control and additional active elements for matching. Examples of these active elements include switches, tunable capacitors, tunable phase shifters, diodes, micro-electro-mechanical system (MEMS) switches, MEMS tunable capacitors, and transistors including a metal oxide semiconductor field effect transistor (MOSFET), a metal semiconductor field effect transistor (MESFET), a pseudomorphic high electron mobility transistor (pHEMT), a heterojunction bipolar transistor (HBT) or of other suitable technologies. 
     Direction finding algorithms according to embodiments, to estimate the angle of arrival (AOA) of RF signals by using a modal antenna having multiple radiations patterns, are explained below with reference to the subsequent figures. 
     In these algorithms, the modal antenna is configured to have multiple (N) antenna modes, corresponding to multiple radiation patterns K=0, 1 . . . and N−1; i.e. the modal antenna produces a distinct radiation pattern in each distinct antenna mode of the N modes. The spherical coordinate is used to estimate the AOA of the signal, which is denoted as (Θ 0 ,Φ 0 ). The (Θ,Φ)-space is spanned prior to the direction finding procedure, and all possible discrete values of Θ and Φ to consider according to the required resolution are listed in the group, or a set, Set {Θ,Φ}. G K (Θ,Φ) denotes the gain in dB of the modal antenna with the K-th radiation pattern at the angle (Θ,Φ), which can be premeasured and stored in a memory. E K (Θ,Φ) denotes the difference in gain in dB between the current mode having the K-th radiation pattern and the previous mode having the (K−1)-th radiation pattern at the angle (Θ,Φ), and is defined as follows: 
         E   K (Θ,Φ)= G   K (Θ,Φ)− G   K−1 (Θ,Φ),  Eq. (1)
 
     where K=1, 2 . . . and N, and EN(Θ,Φ) is defined as [G0(Θ,Φ)−GN−1(Θ,Φ)]. S K  denotes the signal strength in dBm in the configuration with the K-th radiation pattern, where K=0, 1 . . . and N−1. Δ K  denotes the difference in signal strength in dB between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, and is defined as follows: 
       Δ K=S   K   −S   K−1 ,  Eq. (2)
 
     where K=1, 2 . . . and N, and Δ N  is defined as [S 0 −S N−1 ]. 
     Having defined the above parameters, computation can be made to obtain the difference between the gain variation E K (Θ,Φ) and the signal strength variation Δ K  at each angle (Θ,Φ) as follows: 
       Err K (Θ,Φ)=[ E   K (Θ,Φ)−Δ K ] 2 ,  Eq. (3)
 
     where K=1, 2 . . . and N, and the power of 2 is taken for having a positive number for the sake of computational convenience. Accordingly, the contributions from all configurations with different radiation patterns can be obtained as follows: 
       Err(Θ,Φ)=Σ K=1   N Err K (Θ,Φ).  Eq. (4)
 
     Therefore, the AOA (Θ 0 ,Φ 0 ) of the signal may be obtained by finding the minimum of the above quantity in Eq. (4) over all pairs of (Θ,Φ) in Set{Θ,Φ} as follows: 
       Err(Θ 0 ,Φ 0 )=min[Err(Θ,Φ)],  Eq. (5)
 
     where (Θ 0 ,Φ 0 )ϵSet {Θ,Φ}. 
       FIG. 3  is a flowchart illustrating a first direction finding algorithm to obtain the angle that gives the minimum of Err(Θ,Φ) as the AOA of the signal according to the above procedure. The initialization is carried out in step  304 , to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ,Φ) to span in the spherical coordinate are determined according to the required resolution, and stored in Set {Θ,Φ}. In step  308 , the signal strength in the configuration with the 0-th radiation pattern, S 0 , is measured. Steps  312 - 328  represent the do-loop to compute Err K (Θ,Φ) iteratively from K=1 to K=N. Specifically, after the radiation pattern is changed to the next pattern in step  312 , the signal strength in the new configuration with the K-th radiation pattern, S K , is measured in step  316 . Using the previous measurement value S K−1 , the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, i.e., the signal strength variation, can be computed as in Eq. (2), i.e., Δ K =S K −S K−1 , in step  320 . Using the measured signal strength variation Δ K  and the premeasured and stored G K (Θ,Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step  324  proceeds to compute Err K (Θ,Φ) as in Eq. (3), i.e., Err K (Θ,Φ)=[E K (Θ,Φ)−Δ K ] 2 , where E K (Θ,Φ)=G K (Θ,Φ)−G K−1 (Θ,Φ), which is the gain variation, as in Eq. (1). In step  324 , this computation is carried out for each pair of (Θ,Φ) values in Set {Θ,Φ}. After the computation of Err K (Θ,Φ) for each pair of (Θ,Φ) values for K=1 through N, in step  332 , Err K (Θ,Φ) for all configurations with different radiation patterns is summed as in Eq. (4) to obtain Err(Θ,Φ) for each pair of (Θ,Φ) values in Set {Θ,Φ}. In step  336 , among Err(Θ,Φ) values for all pairs of (Θ,Φ) in Set {Θ,Φ}, Err(Θ,Φ) that gives the minimum is found. If the process is determined to be terminated in step  340 , the (Θ,Φ) value that gives the minimum Err(Θ,Φ) is outputted as the AOA (Θ 0 ,Φ 0 ) in step  344 . If the process is determined to be continued in step  340 , the process goes back to step  304  for initialization, and the subsequent steps are repeated. 
     In the above algorithm, the AOA (Θ 0 ,Φ 0 ) is obtained as the angle that gives the minimum of Err(Θ,Φ) over all pairs of (Θ,Φ) in Set {Θ,Φ}. Alternatively, the AOA (Θ 0 ,Φ 0 ) may be obtained as the angle that gives the minimum of Err K (Θ,Φ) for the configuration with the K-th radiation pattern, except that the pair of (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria. 
       FIG. 4  is a flowchart illustrating a second direction finding algorithm to obtain the angle that gives the minimum of Err K (Θ,Φ) as the AOA of the signal for the K-th mode, where the angle (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria. The initialization is carried out in step  404 , to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ,Φ) to span in the spherical coordinate are determined according to certain criteria, and stored in Subset {Θ,Φ}. The angles (Θ,Φ) in the initial Subset {Θ,Φ} may be selected from the original Set {Θ,Φ} according to an empirical judgment based on the prior computational results or measured data or other sound engineering judgment. In step  408 , the signal strength in the configuration with the 0-th radiation pattern, S ° , is measured. Steps  412 - 464  represent the do-loop to compute Err K (Θ,Φ) iteratively from K=1 to K=N. After the radiation pattern is changed to the next pattern in step  412 , the signal strength in the new configuration with the K-th radiation pattern, S K , is measured in step  416 . Using the previous measurement value S K−1 , the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, i.r., the signal strength variation, can be computed as in Eq. (2), i.e., Δ K =S K  S K−1 , in step  420 . In step  424 , the first pair of (Θ,Φ) is selected from Subset {Θ,Φ}. Using the measured signal strength variation Δ K  and the premeasured and stored G K (Θ,Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step  428  proceeds to compute Err K (Θ,Φ) as in Eq. (3), i.e., Err K (Θ,Φ)=[E K (Θ,Φ)−Δ K ] 2 , where E K (Θ,Φ)=G K (Θ,Φ)−G K−1 (Θ,Φ), which is the gain variation, as in Eq. (1). After the computation of Err K (Θ,Φ) for the pair of (Θ,Φ), it is judged in step  436  if the Err K (Θ,Φ) value is smaller than a predetermined threshold, Tshld, which is related to a tolerance in judging the accuracy of the final AOA. If Yes, in step  440 , the angle (Θ,Φ) that gives the relationship, Err K (Θ,Φ)&lt;Tshld, is stored in Temp-Subset {Θ,Φ}. If No in step  436  as well as after step  440 , the process proceeds to step  444 , where it is judged if all the angles (Θ,Φ) in Subset {Θ,Φ} have been exhausted. If No in step  444 , the next pair of angles (Θ,Φ) in Subset {Θ,Φ} is selected in step  432 , and the process from step  428  through step  432  is repeated until all the angles (Θ,Φ) in Subset {Θ,Φ} are exhausted. In step  448 , Subset {Θ,Φ} is replaced with Temp-Subset {Θ,Φ}, which means only the angles (Θ,Φ) that satisfy the relationship, Err K (Θ,Φ)&lt;Tshld, are selected and stored as the updated Subset {Θ,Φ}. In step  452 , among Err K (Θ,Φ) values for all pairs of (Θ,Φ) in Subset {Θ,Φ}, Err(Θ,Φ) that gives the minimum is found. If the process is determined to be terminated in step  456 , the (Θ,Φ) value that gives the minimum Err K  (Θ,Φ) is outputted as the AOA (Θ 0 ,Φ 0 ) for the given K in step  460 . If the process is determined to be continued in step  456 , the process goes to step  464  to judge if K=N has been reached. If No, the next K is selected in  412  and the process at step  416  and afterward is repeated. If Yes, the process goes back to step  404  for initialization, and the subsequent step are repeated. 
     In the above first and second algorithms, the E K (Θ,Φ) values are obtained by using the gain values of the modal antenna, G K (Θ,Φ), which can be premeasured and stored in the memory. In addition to the antenna gain in free space, antenna gains under various use conditions or environments can also be premeasured and stored in the memory. For example, the radiation patterns may be disturbed because of placement of a head, a hand, laps, wood, metal, or other interference-causing objects, with different positions and angles, in the proximity of the antenna. The antenna gains under such different conditions or environments can be premeasured and stored in the memory. Furthermore, one or more sensors may be included in the device to detect the use conditions or environments. Such sensors may include a proximity sensor, a motion sensor, a light sensor, a pressure sensor or other types of sensors. During the actual operation, the sensor is configured to detect the use condition or the environment during each time interval, and send the detected information to a controller, which is configured to select the gain values corresponding to the detected condition or environment. These premeasured G K (Θ,Φ) values that are stored in the memory according to conditions or environments can then be used to obtain the E K (Θ,Φ) values in the first and second algorithms. 
     In the actual application of the above two algorithms, there is a possibility that the actual signal strength changes during the time between measurements for the configurations with the K-th and (K−1)-th radiation patterns, giving rise to an inaccurate estimation of the AOA. To take into account such changes, the signal strength can be measured over a predetermined time period, and the time average of the signal strength can be used in the direction finding algorithms.  FIG. 5  is a flowchart illustrating the procedure for taking signal strength changes into account, which can be incorporated in each of the first and second algorithms described with reference to  FIGS. 3 and 4 , respectively. After step  304  in the first algorithm or step  404  in the second algorithm, the process may proceed to step  508 . In step  508 , the signal strength in the configuration with the 0-th radiation pattern, S 0 , is measured over a certain time period Δt, and the average of S 0  over Δt is obtained as Sav 0 . After the radiation pattern is changed to the next pattern in step  512 , the signal strength in the new configuration with the K-th radiation pattern, S K , is measured over a certain time period Δt, and the average of S K  over Δt is obtained as Sav K  in step  516 . Using the previous measurement value Say K−1 , the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed as in Eq. (2), i.e., Δav K =Sav K −Sav K−1 , in step  520 . Thereafter, the process proceeds to step  324  in the first algorithm or step  424  in the second algorithm. 
     Additionally or alternatively, the change of signal strength between measurements can be taken into account by varying the parameter Tshld in the second algorithm according to the magnitude of the signal strength change over a certain time period.  FIG. 6  is a flowchart illustrating the procedure for taking signal strength changes into account, which can be incorporated in the second algorithm described with reference to  FIG. 4 . After the radiation pattern is changed to the next pattern in step  412 , the signal strength in the new configuration with the K-th radiation pattern, S K , is measured over a certain time period Δt, and the minimum and maximum of S K  during Δt is obtained as S K  min and S K  max, respectively, in step  616 . The parameter Tshld is then determined according to the magnitude of |S K  max−S K  min| in step  620 . In general, the larger the |S K  max−S K  min| is, the larger the Tshld value is to accommodate the variation. The process may proceed to step  420  to compute Δ K =S K −S K−1  by using the S K  and S K−1  values, each measured at a predetermined representative time point during Δt. Alternatively, by combining the time average procedure described with reference to  FIG. 5 , Δav K =Sav K −Sav K−1 , may be computed by using the Sav K  and Sav K−1  values, each representing the average of the signal strength over Δt. Furthermore, instead of changing the parameter Tshld according to the magnitude of the signal strength change for each K, a weight factor for Err K  (Θ,Φ) may be determined according to the magnitude of the signal strength change for each K, and multiplied to Err K  (Θ,Φ) for the comparison with a fixed Tshld in step  436  of  FIG. 4 . 
     Some protocols such as WCDMA use an architecture including a RAKE receiver, which can be utilized in the above algorithms to increase the accuracy of the AOA estimation. In many instances of RF communication, the line of sight between a transmitter and a receiver becomes blocked or shadowed with obstacles such as walls, trees and other objects. Each signal bounce may introduce phase shifts, time delays, attenuations and distortions, giving rise to multipath components of the signal. The multipath components are delayed copies of the original signal travelling through different echo paths, each with a different magnitude and time of arrival at the receiver. Since each component contains original information, the information can be obtained reliably by taking into account the magnitude and time of arrival (phase) of each component. 
     A RAKE receiver has multiple “fingers,” each assigned to receive a different multipath component. The information obtained by all fingers is correlated to make the best use of the different characteristics of the multipath signals.  FIG. 7  illustrates an example schematically showing multipath signals and a communication device receiving them. In this example, the communication device is equipped with a modal antenna coupled with a RAKE receiver. The modal antenna is set with the K-th radiation pattern, and the RAKE receiver is receiving the main signal S K   1 , the first copy S K   2  of S K   1 , and the second copy S K   3  of S K   1 . The first copy S K   2  is a multipath component of the main signal with a bounce before incoming to the communication device, and the second copy S K   3  is a multipath component of the main signal with a different bounce before incoming to the communication device. The time of arrival of S K   2  is delayed later than S K   1 , and the time of arrival of S K   3  is further delayed than S K   2  in this example. 
     It is known to those skilled in the art that most of the channel propagation based on the 3GPP standard includes at least one multipath component that arrives at an angle close to the main signal, e.g., within 15 degrees. This fact indicates that if at least one of the components has the incident angle that is close within a certain tolerance to the incident angle of the main signal, the probability is high for the incident angle to be indeed the AOA. Thus, detection of multipath component signals can be utilized to enhance the accuracy, or the confidence level, of the AOA estimation in direction finding algorithms. 
       FIG. 8  is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the first algorithm described earlier with reference to  FIG. 3 , where the angle that gives the minimum of Err(Θ,Φ) is obtained as the AOA of the signal. This example is based on a device including a modal antenna having N modes corresponding to N radiation patterns, and a RAKE receiver coupled to the modal antenna and configured to receive a main signal and two multipath components, i.e., two copies of the main signal. It should be understood that he RAKE receiver can be configured to receive a main signal and one or more copies of the main signal, depending on computation time and other factors. In  FIG. 8 , the initialization is carried out in step  804 , to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ,Φ) to span in the spherical coordinate are determined according to the required resolution, and stored in Set {Θ,Φ}. In step  808 , the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the configuration with the 0-th radiation pattern, S 0   1 , S 0   2 , S 0   3 , are measured. Steps  812 - 828  represent the do-loop to compute Err K   1 (Θ,Φ), Err K   2 (Θ,Φ), Err K   3 (Θ,Φ) iteratively from K=1 to K=N, where Err K   1 (Θ,Φ), Err K   2 (Θ,Φ), Err K   3 (Θ,Φ) are defined as in Eq. (3) based on the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal S K   1 , S K   2 , S K   3  in the configuration with the K-th radiation pattern. Specifically, after the radiation pattern is changed to the next pattern in step  812 , the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the new configuration with the K-th radiation pattern, S K   1 , S K   2 , S K   3 , are measured in step  816 . Using the previous measurement values, S K−1   1 , S K−1   2  S K−1   3  the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed for each signal as in Eq. (2), i.e., Δ K   i =S K   i , −S K−1   i  where i=1, 2 and 3, in step  820 . Using the measured signal strength variations Δ K   i  and the premeasured and stored G K (Θ,Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step  824  proceeds to compute Err K   i (Θ,Φ) for each i as in Eq. (3), i.e., Err K (Θ,Φ)=[E K (Θ,Φ)−Δ K   i ] 2 , where i=1, 2 and 3 and E K (Θ,Φ)=G K (Θ,Φ)−G K−1 (Θ,Φ), which is the gain variation, as in Eq. (1). In step  824 , this computation is carried out for each pair of (Θ,Φ) values in Set {Θ,Φ}. After the computation of Err K (Θ,Φ) for each pair of (Θ,Φ) values for K=1 through N, in step  832 , Err K   1 (Θ,Φ), Err K   2 (Θ,Φ), Err K   3 (Θ,Φ) for all configurations with different radiation patterns is summed as in Eq. (4) to obtain Err i (Θ,Φ), Err 2 (Θ,Φ), Err 3 (Θ,Φ) for each pair of (Θ,Φ) values in Set {Θ,Φ}. In step  836 , among Err 1 (Θ,Φ) values for all pairs of (Θ,Φ) in Set {Θ,Φ}, Erri(Θ,Φ) that gives the minimum is found for each of i=1, 2 and 3. Thus, the (Θ,Φ) value that gives the minimum Erri(Θ,Φ) is obtained as the AOA (Θ 0i ,Φ 0i ) for each of i=1, 2 and 3. In step  838 , it is judged if (Θ 01 ,Φ 01 )=(Θ 02 ,Φ 02 ) and (Θ 01 ,Φ 01 )=(Θ 03 ,Φ 03 ) within a certain tolerance. If No in this step, it means there is abnormality, and the process goes back to the initialization in step  804 . If Yes, it can be determined that the angle (Θ 01 ,Φ 01 ) is the AOA with the high confidence level, and the process proceeds to step  840 . If the process is determined to be continued in step  840 , the process goes back to step  804  for initialization, and the subsequent steps are repeated. If the process is determined to end, the angle (Θ 01 ,Φ 01 ) is outputted as the AOA in step  844 . 
     Similar to the above, the multipath component signals can be utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the second algorithm described earlier.  FIG. 9  is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the second algorithm described earlier with reference to  FIG. 4 , where the angle that gives the minimum Err K (Θ,Φ) is obtained as the AOA of the signal for the K-th mode, where the angle (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria. The initialization is carried out in step  904 , to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ,Φ) to span in the spherical coordinate are determined according to certain criteria, and stored in Subset {Θ,Φ}. The angles (Θ,Φ) in the initial Subset {Θ,Φ} may be selected from the original Set {Θ,Φ} according to an empirical judgment based on the prior computational results or measured data or other sound engineering judgment. In step  908 , the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the configuration with the 0-th radiation pattern, S 0   1 , S 0   2 , S 0   3 , are measured. After the radiation pattern is changed to the next pattern in step  912 , the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the new configuration with the K-th radiation pattern, S K   1 , S K   2 , S K   3 , are measured in step  916 . Using the previous measurement values, S K−1   1 , S K−1   2 , S K−1   3 , the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed for each signal as in Eq. (2), i.e., Δ K−1   i =S K   i −S K−1   i , where i=1, 2 and 3, in step  920 . In step  924 , the first pair of (Θ,Φ) is selected from Subset {Θ,Φ}. Using the measured signal strength variations Δ K   i  and the premeasured and stored G K (Θ,Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step  928  proceeds to compute Err K (Θ,Φ) for each i as in Eq. (3), i.e., Err K (Θ,Φ)=[E K (Θ,Φ)−Δ K   i ] 2 , where i=1, 2 and 3 and E K (Θ,Φ)=G K (Θ,Φ)−G K−1 (Θ,Φ), which is the gain variation, as in Eq. (1). After the computation of Err K   i (Θ,Φ) for the pair of (Θ,Φ), it is judged in step  936  if the Err K (Θ,Φ) value is smaller than a certain threshold, Tshldi, which is related to a tolerance in judging the accuracy of the final AOA, where i=1, 2 and 3. If Yes, the angle (Θ,Φ) that satisfies the relationships, Err K   1 (Θ,Φ)&lt;Tshld1, Err K   2 (Θ,Φ)&lt;Tshld2, Err K   3 (Θ,Φ)&lt;Tshld3, may be selected and stored in Temp-Subset1 {Θ,Φ}, Temp-Subset2{Θ,Φ}, Temp-Subset3 {Θ,Φ}, respectively, in step  940 . If No in step  936  as well as after step  940 , the process proceeds to step  944 , where it is judged if all the angles (Θ,Φ) in Subset {Θ,Φ} have been exhausted. If No in step  944 , the next pair of angles (Θ,Φ) in Subset {Θ,Φ} is selected in step  932 , and the procedure from step  928  through step  932  is repeated until all the angles (Θ,Φ) in Subset {Θ,Φ} are exhausted. In step  948 , Subset1{Θ,Φ} is replaced with Temp-Subset1{Θ,Φ}, which means only the angles (Θ,Φ) that satisfy the relationship, Err K   i (Θ,Φ)&lt;Tshldi, are selected and stored as the updated Subseti{Θ,Φ}, where i=1, 2 and 3. In step  950 , among Err K   i (Θ,Φ) values for all pairs of (Θ,Φ) in Subseti{Θ,Φ}, Err K i(Θ 01 ,Φ 0i ) that gives the minimum is found for each of i=1, 2 and 3. Thus, the (Θ 0i ,Φ 0i ) value that gives the minimum Err K   i (Θ,Φ) is obtained as the AOA (Θ 01 ,Φ 0i ) for each of i=1, 2 and 3. In step  952 , it is judged if (Θ 01 ,Φ 01 )=(Θ 02 ,Φ 02 ) and (Θ 01 ,Φ 01 )=(Θ 03 ,Φ 03 ) within a certain tolerance. If No in this step, it means there is abnormality, and the process goes back to the initialization in step  904 ; if Yes, it can be determined that the angle (Θ 01 ,Φ 01 ) is the AOA for the K-th mode with the high confidence level, and the process proceeds to step  956 . If the process is determined to be continued in step  956 , the process proceeds to step  964  to determine if K=N has been reached. If No, the radiation pattern is changed to the next one at step  912 , and the subsequent steps are repeated; if Yes, the process goes back to step  904  for initialization, and the subsequent steps are repeated. If the process is determined to end in step  956 , the angle (Θ 01 ,Φ 01 ) is outputted as the AOA for the K-th mode in step  960 . When the algorithm is repeated from the step  904  or step  912 , angles in Subseti{Θ,Φ} defined in step  948  may be used for each of i=1, 2 and 3 in the subsequent steps. 
     Each of the algorithms described so far with reference to  FIGS. 3-9  is configured to obtain the AOA of the incoming signal. After the AOA is found, the algorithm can be repeated for any needed times to update the AOA since the signal incidence may change often or continuously. The information obtained in running the algorithm can be utilized for the next time the same algorithm is driven to run. In particular, the E K (Θ,Φ) values may be updated based on the AOA information previously obtained. 
       FIG. 10  is a flowchart illustrating the process of updating the E K (Θ,Φ) values, i.e., the gain variations, based on the AOA information previously obtained. Namely, this process represents a post AOA process. After obtaining the AOA (Θ 0 ,Φ 0 ) in the first algorithm, the second algorithm or its variation described earlier, the process may proceed to step  1004 , where K=0 and (Θ,Φ)=(Θ 0 ,Φ 0 ) are set. In step  1008 , the signal strength S 0  in the configuration with the 0-th radiation pattern is measured. After the radiation pattern is changed to the next pattern in step  1012 , the signal strength in the new configuration with the K-th radiation pattern, S K , is measured in step  1016 . Using the previous measurement value S K−1 , the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed as in Eq. (2), i.e., Δ K =S K −S K−1 , in step  1020 . The measured signal strength variation Δ K  is then stored as E K (Θ 0 ,Φ 0 ) in step  1024 . Thus, the more accurate E K (Θ 0 ,Φ 0 ) value is obtained based on the measured Δ K  value, and can be used for the next time the first algorithm, the second algorithm or its variation is driven to run. The above steps are repeated for the next K in step  1028 , until all the modes are exhausted. The E K (Θ,Φ) values for the angles (Θ,Φ) other than the angle (Θ 0 ,Φ 0 ) may be obtained by using the premeasured and stored G K (Θ,Φ) values. In this way, the E K (Θ,Φ) values for all K&#39;s as well as for all angles (Θ,Φ) are initialized for running the algorithm for the next time around with better accuracy. The accuracy in direction finding is expected to go up, as the number of runs increases and E K (Θ,Φ) is updated many times by using the present updating algorithm. 
     Another post AOA process may be configured to involve decision making as to whether the whole direction finding process should be restarted. In this process, the difference between the signal strength variation, i.e., Δ K , and the gain variation at the angle (Θ 0 ,Φ 0 ), i.e., E K (Θ 0 ,Φ 0 ), can be checked. If the difference is within a certain threshold, it can be determined that the angle (Θ 0 ,Φ 0 ) is still close to the AOA; if not, the angle (Θ 0 ,Φ 0 ) is no longer the AOA, and thus the complete direction finding process may be restarted.  FIG. 11  is a table illustrating an example of gain variations and signal strength variations used for the decision making. The gain variation at the angle (Θ 0 ,Φ 0 ) can be E K (Θ 0 ,Φ 0 )=G K (Θ 0 ,Φ 0 )−G K−1 (Θ 0 ,Φ 0 ) as in Eq. (1), or an average of E K (Θ 0 ,Φ 0 ) values obtained after running several times the direction finding algorithm with the updating process illustrated in  FIG. 10 . The signal strength variation is Δ K =S K −S K−1  as in Eq. (2), which is a measured value. In the first step of this table, the previous mode 0 and the current mode 1 are selected, the gain variation at (Θ 0 ,Φ 0 ) is obtained to be −2.10 dB, and the Δ K  is measured to be −1.50 dB. In the second step of this table, the previous mode 0 and the current mode 2 are selected, the gain variation at (Θ 0 ,Φ 0 ) is obtained to be −1.05 dB, and the Δ K  is measured to be −3.50 dB. In the third step of this table, the previous mode 1 and the current mode 2 are selected, the gain variation at (Θ 0 ,Φ 0 ) is obtained to be −4.20 dB, and the Δ K  is measured to be −4.10 dB. By using a predetermined threshold value of 0.7 dB, for example, it is observed that the difference between the gain variation and the signal strength variation in the second step is larger than the threshold value. Thus, it can be determined that the signal direction has changed, and the full direction finding process be restarted to find the new AOA. 
     The direction finding algorithms described thus far utilize the gain of the modal antenna with the K-th radiation pattern at the angle (Θ,Φ), denoted as G K (Θ,Φ), following Eqs. (1)-(3). As explained earlier, the gain value for each radiation pattern at each selected angle can be premeasured and stored in the memory to be used for the algorithms, and updated as the direction finding processes are being carried out. The accuracy of the direction finding may be enhanced by explicitly including the phase information associated with the gain and the measured signal strength. In this case, Eqs. (1)-(3) take their corresponding complex forms, where the phase of the gain with the K-th radiation pattern is denoted by φ K , and j is defined as the imaginary unit. Here, the phase α K  of the gain is a function of two angles, Θ and Φ, in the spherical coordinate, but the notation is simplified in the following equations. The phase φ K  of the gain of the modal antenna can be premeasured and stored in the memory for each radiation pattern and for each selected angle. The complex gain variation E K (Θ,Φ) exp(jφ K ) denotes the difference in gain between the current mode having the K-th radiation pattern and the previous mode having the (K−1)-th radiation pattern at the angle (Θ,Φ), and is defined as follows: 
         E   K (Θ,Φ)exp( jφ   K )= G   K (Θ,Φ)exp( jφ   K )− G   K−1 (Θ,Φ)exp( jφ   K−1 ).  Eq. (6)
 
     The complex signal strength variation Δ K  exp(jβ K ) denotes the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, now including the phase β K  representing the measured phase of the signal S K , and is defined as follows: 
       Δ K  exp( jβ   K )= S   K  exp( jβ   K )− S   K−1 exp( jβ   K−1 ).  Eq. (7)
 
     The difference between the complex gain variation and the complex signal strength variation is expressed as follows: 
       Err K (Θ,Φ)=∥ E   K (Θ,Φ)exp( jφ   K )−Δ K  exp( jβ   K )∥ 2 .  Eq. (8)
 
     Note that because the modulus squared operator (∥ ∥ 2 ) is used for the complex difference in Eq. (8), the Err K (Θ,Φ) becomes entirely real. Thus, the scalar form of the error metric Err K (Θ,Φ) may be used in Eqs. (1)-(3) even for the present complex case; however, in each of the direction finding algorithms, the complex form as expressed in Eqs. (6)-(8) may be substituted. 
     The phase β K  of the signal S K  in Eq. (7) can be obtained from the phase shift measurement.  FIG. 12  schematically illustrates the measurement of the phase shift of the signal strength during the transition from the (K−1)-th mode to the K-th mode. The top figure illustrates an example of a received signal waveform, where the in-phase (I) component and the quadrature-phase (Q) component are measured. The mode transition is occurring at the time point indicated by an arrow, and the phase shift is observed at the point. By carrying out the analog-to-digital conversion, the amount of phase shift is obtained as illustrated in the bottom figure. This information is used to obtain β K  and β K−1  in Eq. (7). 
     Similar to the gain values used in the previous direction finding algorithms, the phase φ K  of the gain of the modal antenna in Eq. (6) can be obtained based on the data that has been premeasured and stored in a memory, such as in the form of a look-up table.  FIG. 13  illustrates a portion of the look-up table showing the phase data of the gain according to the angles (Θ,Φ) and the modes, i.e., radiation patterns, K=0 through (N−1). The stored data can be used to obtain φ K  and φ K−1  in Eq. (6). The phase data can be updated as the direction finding processes are being carried out, and used for the algorithms for enhanced accuracy. 
     While this document contains many specifics, these should not be construed as limitations on the scope of an invention or of what may be claimed, but rather as descriptions of features specific to particular embodiments of the invention. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be exercised from the combination, and the claimed combination may be directed to a subcombination or a variation of a subcombination.