Abstract:
A method is provided for using an antenna array to create two beams (a first beam and a second beam). In one aspect, the method uses dual polarization beam forming, which allows for many degrees of freedom in designing a desired power pattern. The method is well suited for systems with multiple radio chains (e.g., systems with active antennas). The method is also well suited for multi-port systems such as TD-SCDMA. In some embodiments, the method produces two beams where
   (a) the shape of the power beam pattern for the first beam and the shape of the power beam pattern for the second beam are the same (or substantially the same) in a plurality of directions of interest and (b) the beams have orthogonal (or substantially orthogonal) polarizations in the coverage area.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 13/095,426, filed on Apr. 27, 2011 (status pending), which is incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The invention relates to the field of beam forming. 
     BACKGROUND 
     Methods exist for using an antenna array to attempt to create beams having a desired beam shape. In many cases, however, the match between the actual beam shape and the desired beam shape is poor. In addition, the power utilization achieved is often poor. 
     What is desired, therefore, are improved apparatuses and methods for using an antenna array to create beams. 
     SUMMARY 
     Antenna arrays for producing at least two beams (a first beam and a second beam) and methods for using the antenna arrays are provided. In one aspect, a method for using an antenna array employs dual polarization beam forming, which allows for many degrees of freedom in designing a desired power pattern. The provided methods are well suited for systems with multiple radio chains (e.g., systems with active antennas). The methods are also well suited for multi-port systems such as TD-SCDMA. In some embodiments, two beams are produced where each beam has (a) substantially the same power pattern as the other beam in a plurality of directions of interest (or “user equipment (UE) coverage area”), as opposed to in only a single direction of interest, such as the direction of a specific UE location, and (b) a substantially orthogonal polarization with respect to the other beam in the UE coverage area. Some advantages gained from implementing a method according to some embodiments of the invention include: (1) better possibility to realize beams with patterns that match desired beam shapes; (2) better power utilization; and (3) less sensitivity to amplitude and phase errors. 
     In some embodiments, an antenna array apparatus is provided, where the antenna array apparatus includes a first antenna element (AE 1 - a ) and a second antenna element (AE 1 - b ). The first antenna element includes a first antenna (A 1 ) and an antenna element port (S 1a ) connected to the first antenna. The second antenna element includes a second antenna (A 2 ) and an antenna element port (T 1b ) connected to the second antenna. The antenna array apparatus also includes a first beam forming circuit for applying beam weights W b1,S1a  and W b2,S1a  to port S 1a  and a second beam forming circuit for applying beam weights W b1,T1b  and W b2,T1b  to port T 1b . 
     In some embodiments, W b2,S1a  is a function of W b1,T1b  and W b2,T1b  is a function of W b1,S1a . For example, W b2,S1a  may be a function of the complex conjugate of W b1,T1b  and W b2,T1b  is a function of the complex conjugate of W b1,S1a . In some embodiments, W b2,S1a  is determined by phase shifting and amplitude scaling the complex conjugate of W b1,T1b . In some embodiments, the phase shift creates a sign shift. In some embodiments, the complex conjugate of W b1,T1b  is shifted by (β+pi). For instance, in some embodiments, W b2,S1a  equals or substantially equals e i(β+π) (W b1,T1b )*α 1 . In some embodiments, α 1  is a function the power of a signal emitted by the first antenna and the power of a signal emitted by the second antenna. In some embodiments, α 1 =1. 
     In some embodiments, W b2,T1b  is determined by multiplying the complex conjugate of W b1,S1a  by the inverse of the amplitude scaling factor. In some embodiments, W b2,T1b  is determined by phase shifting the complex conjugate of W b1,S1a  by β. For instance, in some embodiments, W b2,T1b  equals or substantially equals e iβ (W b1,S1a )*1/α 1 . 
     In some embodiments, the first antenna (A 1 ) has a first polarization, the second antenna (A 2 ) has a second polarization, and the first polarization is orthogonal (or substantially orthogonal) to the second polarization. In some embodiments, the first antenna (A 1 ) and the second antenna (A 2 ) have the same (or substantially the same) power pattern. 
     In some embodiments, the first antenna element (AE 1 - a ) further comprises a second antenna element port (T 1a ) connected to a third antenna (A 3 ) having a polarization and a power pattern and the second antenna element (AE 1 - b ) comprises a second antenna element port (S 1b ) connected to a fourth antenna (A 4 ) having a polarization and a power pattern. 
     In some embodiments, the antenna array apparatus further includes a third beam forming circuit for applying beam weights W b1,S1b  and W b2,S1b  to port S 1b  and a fourth beam forming circuit for applying beam weights W b1,T1a  and W b2,T1a  to port T 1a . 
     In some embodiments, W b2,S1b  is a function of W b1,T1a  and W b2,T1a  is a function of W b1,S1b . For example, W b2,S1b  may be a function of the complex conjugate of W b1,T1a  and W b2,T1a  is a function of the complex conjugate of W b1,S1b . In some embodiments, W b2,S1b  is determined by phase shifting and amplitude scaling the complex conjugate of W b1,T1a . In some embodiments, the phase shift creates a sign shift. In some embodiments, the complex conjugate of W b1,T1a  is shifted by pi (π). For instance, in some embodiments, W b2,S1b  equals or substantially equals e i(β+π) (W b1,T1a )*α 2 . In some embodiments, α 2  is a function the power of a signal emitted by the third antenna and the power of a signal emitted by the fourth antenna. In some embodiments, α 2 =1. 
     In some embodiments, the polarization of the first antenna (A 1 ) is orthogonal (or substantially orthogonal) to the polarization of the third antenna (A 3 ), the polarization of the fourth antenna (A 4 ) is orthogonal (or substantially orthogonal) to the polarization of the second antenna (A 2 ), and the third antenna (A 3 ) and the fourth antenna (A 4 ) have the same (or substantially the same) power pattern. 
     In some embodiments, the antenna array apparatus further includes a third antenna element (AE 2 - a ) and a fourth antenna element (AE 2 - b ) that together form a second pair of antenna elements (AE 2 - a ,AE 2 - b ), wherein the third antenna element (AE 2 - a ) comprises an antenna element port (S 2a ) connected to a fifth antenna (A 5 ) and the fourth antenna element (AE 2 - b ) comprises an antenna element port (T 2b ) connected to a sixth antenna (A 6 ). In this embodiment, the antenna array apparatus may further include a fifth beam forming circuit for applying beam weights W b1,S2a  and W b2,S2a  to port S 2a  and a sixth beam forming circuit for applying beam weights W b1,T2b  and W b2,T2b  to port T 2b . 
     In some embodiments, W b2,S2a  is a function of W b1,S2b  and W b2,T2b  is a function of W b1,S2a . For example, W b2,S2a  may be a function of the complex conjugate of W b1,T2b  and W b2,T2b  is a function of the complex conjugate of W b1,S2a . In some embodiments, W b2,S2a  is determined by phase shifting and amplitude scaling the complex conjugate of W b1,T2b . In some embodiments, the phase shift creates a sign shift. In some embodiments, the complex conjugate of W b1,S2b  is shifted by pi (π). For instance, in some embodiments, W b2,S2a  equals or substantially equals e i(β+π) (W b1,T2b )*α 3  and W b2,T2b  equals or substantially equals e iβ (W b1,S2a )*1/α 3 . 
     In some embodiments, the first antenna element and the second antenna element are located symmetrically with respect to a symmetry point, and the third antenna element and the fourth antenna element are located symmetrically with respect to the symmetry point. 
     In some embodiments, the shape of the power beam pattern for the first beam and the shape of the power beam pattern for the second beam are the same or substantially the same in a plurality of directions of interest and the first beam and the second beam have orthogonal or substantially orthogonal polarizations in the coverage area. 
     In some embodiments, the antenna array apparatus further includes a weight determining unit configured to determine W b2,S1a  and W b2,T1b . In some embodiments, the weight determining unit is configured to determine W b2,S1a  by obtaining the complex conjugate of W b1,T1b  and (a) phase shifting the complex conjugate of W b1,T1b  or (b) multiplying the complex conjugate of W b1,T1b  by an amplitude scaling factor, thereby producing an amplitude scaled complex conjugate of W b1,T1b , and phase shifting the amplitude scaled complex conjugate of W b1,T1b . In some embodiments, the weight determining unit is configured to determine W b2,T1b  by obtaining the complex conjugate of W b1,S1a  and multiplying the complex conjugate of W b1,S1a  by the inverse of the amplitude scaling factor. In some embodiments, the weight determining unit is configured to determine W b2,S1a  by phase shifting the obtained complex conjugate of W b1,T1b , thereby producing a phase shifted complex conjugate of W b1,T1b , and multiplying the phase shifted complex conjugate of W b1,T1b  by the amplitude scaling factor. In some embodiments, the weight determining unit is configured to phase shift the complex conjugate of W b1,T1b  by phase shifting the complex conjugate of W b1,T1b  by pi. 
     In another aspect, a method for creating two beams (a first beam and a second beam) is provided. In some embodiments, the method includes: using an antenna array to create said first beam and said second beam, wherein the array antenna comprises: a first antenna element (AE 1 - a ) and a second antenna element (AE 1 - b ) that together form a pair of antenna elements (AE 1 - a ,AE 1 - b ), the first antenna element (AE 1 - a ) comprises an antenna element port (S 1a ) connected to a first antenna (A 1 ) and the second antenna element (AE 1 - b ) comprises an antenna element port (T 1b ) connected to a second antenna (A 2 ). In some embodiments, the step of using the antenna array to create said first beam and said second beam comprises: applying beam weights W b1,S1a  and W b2,S1a  to antenna element port S 1a  and applying beam weights W b1,T1b  and W b2,T1b  to antenna element port T 1b . In some embodiments, W b2,S1a  equals or substantially equals e i(β+π) (W b1,T1b )*α 1 , and W b2,T1b  equals or substantially equals e iβ (W b1,S1a )*1/α 1 . 
     The above and other aspects and embodiments are described below with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated herein and form part of the specification, illustrate various embodiments of the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the invention. In the drawings, like reference numbers indicate identical or functionally similar elements. 
         FIG. 1  illustrates an example antenna array. 
         FIG. 2  further illustrates a first portion of the example antenna array. 
         FIG. 3  further illustrates a second portion of the example antenna array. 
         FIG. 4  further illustrates a third portion of the example antenna array. 
         FIG. 5  illustrates an example 2-dimensional antenna array. 
         FIGS. 6A, 6B  are graphs showing beam power patterns. 
         FIGS. 7A, 7B  are graphs showing beam power patterns. 
         FIG. 8  is a graph showing that the polarizations for two beams are orthogonal in all directions. 
         FIG. 9  is a flow chart illustrating a process according to an embodiment of the invention. 
         FIG. 10  is a flow chart illustrating a process for determining a beam weight according to an embodiment of the invention. 
         FIG. 11  illustrates a weight determining unit according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Described herein are embodiments of an antenna array apparatus that can be used to create two beams (a first beam and a second beam) where (a) the shape of the power beam pattern for the first beam and the shape of the power beam pattern for the second beam are the same or substantially the same in a plurality of directions of interest (or UE coverage area), as opposed to in only a single direction of interest, and (b) each beam has an orthogonal or substantially orthogonal polarization with respect to the other beam in the UE coverage area. In some embodiments, the antenna array includes one or more of (1) a pair of single port elements, which may be located symmetrically with respect to a symmetry point for the antenna array, (2) a pair of dual port antenna elements, which may be located symmetrically with respect to the symmetry point for the antenna array, and/or (3) a single dual port antenna element, which may be centered on the symmetry point. 
       FIG. 1  illustrates an example of such an antenna array apparatus  100 . Example antenna array apparatus  100  includes: (1) a pair of dual port antenna elements (i.e., antenna elements AE 1 - a  and AE 1 - b ); (2) a pair of single port antenna elements (i.e., antenna elements AE 2 - a  and AE 2 - b ); and (3) a single dual port antenna element AE 3 . As shown in  FIG. 1 , antenna element pair AE 1 - a ,AE 1 - b  and antenna element pair AE 2 - a ,AE 2 - b  are each located symmetrically (or substantially symmetrically) with respect to a symmetry point  104  for antenna array apparatus  100 . That is, for example, each antenna of antenna element AE 1 - a  (i.e., antennas A 1  and A 3 —see  FIG. 2 ) and the corresponding antennas of antenna element AE 1 - b  (i.e., antennas A 2  and A 4 , respectively) are equidistant from symmetry point  104 , a straight line going from the phase center of antenna A 1  to the phase center of antenna A 2  passes through symmetry point  104 , and a straight line going from the phase center of antenna A 3  to the phase center of antenna A 4  passes through symmetry point  104 . Likewise, the antenna of antenna element AE 2 - a  (i.e., antenna A 5 —see  FIG. 3 ) and the antenna of antenna element AE 2 - b  (i.e., antenna A 6 ) are equidistant from symmetry point  104  and a straight line going from the phase center of antenna A 5  to the phase center of antenna A 6  passes through symmetry point  104 . Antenna element AE 3  is centered on symmetry point  104  (e.g., the phase centers of the antennas of element AE 3  are equidistant from the symmetry point and a straight line going from the phase centers of the antennas passes through symmetry point  104 ). 
     As further shown in  FIG. 1 , antenna elements AE 1 - a , AE 1 - b , and AE 3 , each have two ports: an “S” port and a “T” port. More specifically, antenna element AE 1 - a  has ports S 1   a  and T 1   a , antenna element AE 1 - b  has ports S 1   b  and T 1   b , and antenna element AE 3  has ports S 3  and T 3 . As also shown in  FIG. 1 , antenna elements AE 2 - a  an AE 2 - b  each have a single port. Antenna element AE 2 - a  has a single S port (S 2   a ) and Antenna element AE 2 - b  has a single T port (T 2   b ). 
     While antenna array apparatus  100  may appear to be a 2-dimensional antenna array, the invention is not so limiting. Antenna array apparatus  100  may be a 1, 2 or 3-dimensional array. 
       FIG. 2  further illustrates a portion of antenna array apparatus  100 . That is,  FIG. 2  further illustrates antenna elements AE 1 - a  and AE 1 - b  and shows beam forming circuits  201 - 204  of antenna array apparatus  100 . As shown in  FIG. 2 , each antenna element port of antenna elements AE 1 - a,b  is electrically connected to an antenna. Specifically, antenna element port S 1   a  is connected to antenna A 1 , antenna element port T 1   a  is connected to antenna A 3 , antenna element port S 1   b  is connected to antenna A 4 , and antenna element port T 1   b  is connected to antenna A 2 . 
     The structure of the antennas A 1 -A 4  is not significant. For example, the antennas A 1 -A 4  may consist of a single radiating element or may comprise, among other things, a plurality of radiating elements. Additionally, while the antennas within the antenna elements AE 1 - a  and AE 1 - b  are shown as being spaced apart, this is not a requirement. In some embodiments, however, certain characteristics of antennas A 1 -A 4  are significant. For instance, in some embodiments, antenna A 1  may have an arbitrary polarization, but antennas A 2  and A 3  each have a polarization that is orthogonal or substantially orthogonal to the polarization of antenna A 1 , and antenna A 4  has a polarization that is orthogonal or substantially orthogonal to the polarization of antennas A 2  and A 3 . Similarly, in some embodiments, the power pattern for antenna A 1  is the same or substantially the same as the power pattern for antenna A 2  and the power pattern for antenna A 3  is the same or substantially the same as the power pattern for antenna A 4 . 
     As shown in  FIG. 2 , each antenna element port of antenna elements AE 1 - a  and AE 1 - b  is connected to a beam forming circuit. In some embodiments, as shown, the beam forming circuits  201 - 204  have the same basic structure. In the embodiment shown, each beam forming circuit includes: a first multiplier  221  connected to a first beam port (“beam port  1 ”) of antenna array apparatus  100  for multiplying the signal injected into beam port  1  of antenna array with a beam weight (e.g., a complex beam weight) associated with the first beam; a second multiplier  222  connected to a second beam port (“beam port  2 ”) of antenna array apparatus  100  for multiplying the signal injected into beam port  2  of antenna array with a beam weight associated with the second beam; and a combiner  223 , connected to the antenna element port, for combing the outputs of multipliers  221 , 222  and providing the resulting combined signal to the antenna element port to which combiner  223  is connected. As also shown, a beam forming circuit (e.g., beam forming circuit  201 ) may connect to an antenna element port through one or more circuit elements (e.g., amplifier  224  and/or other circuit element such as a signal processing element). Beam forming circuits  201 - 204  may be implemented using a signal processing element (e.g., a digital signal processor (DSP)) or other processor (e.g., an application specific integrated circuit (ASIC), a microprocessor). In the embodiment shown, for each antenna element port S 1   a , S 1   b , T 1   a  and T 1   b , two beam weights are applied to the antenna element port—a beam weight for the first beam W b1  and a beam weight for the second beam W b2 . More specifically, beam weights W b1,S1a  and W b2,S1a  are applied to antenna element port S 1   a , beam weights W b1,T1a  and W b2,T1a  are applied to antenna element port T 1   a , beam weights W b1,S1b  and W b2,S1b  are applied to antenna element port S 1   b , and beam weights W b1,T1b  and W b2,T1b  are applied to antenna element port T 1   b.    
     In some embodiments, the W b2  beam weight for a particular S antenna element port of a particular antenna element is function of the W b1  beam weight for the T antenna element port corresponding to the particular S antenna element port (a.k.a., the “corresponding” T port)—the corresponding T antenna element port is the T antenna element port of the antenna element that is paired with the particular antenna element that includes the particular S antenna element port in question. Similarly, the W b2  beam weight for a particular T antenna element port of a particular antenna element is function of the W b1  beam weight for the corresponding S antenna element port (i.e., the S antenna element port of the antenna element that is paired with the particular antenna element that includes the particular T antenna element port). For example,
 
 W   b2,Sxa   =F 1( W   b1,Txb ),
 
 W   b2,Sxb   =F 1( W   b1,Txa ),
 
 W   b2,Txa   =F 2( W   b1,Sxb ), and
 
 W   b2,Txb   =F 2( W   b1,Sxa )
 
     In some embodiments, W b2,Sxa  and W b2,Sxb  may be a function of the complex conjugate of W b1,Txb  and W b2,Txa , respectively. Similarly, W b2,Txa  and W b2,Txb  may be a function of the complex conjugate of W b1,Sxb  and W b2,Sxa , respectively. In some embodiments, W b2,Sxa  an W b2,Sxb  are determined by phase shifting and amplitude scaling the complex conjugate of W b1,Txb  and W b1,Txa , respectively. In some embodiments, the phase shift creates a sign shift. In some embodiments, the complex conjugate of W b1,T1b  is shifted by β+pi and the complex conjugate of W b1,T1a  is shifted by β+pi. In some embodiments, W b2,Txa  and W b2,Txb  are determined by amplitude scaling the complex conjugate of W b1,Sxb  and W b1,Sxa , respectively. 
     In some particular embodiments,
 
 F 1( W   b1,Tx ) equals or substantially equals  e   i(β+π) ( W   b1,Tx )*α 1 , and
 
 F 2( W   b1,Sx ) equals or substantially equals  e   iβ ( W   b1,Sx )*α1/α 1 , where
 
(W b1,Sx ) is the complex conjugate of W b1,Sx  and (W b1,Tx )* is the complex conjugate of W b1,Tx , and α 1  is an amplitude scaling factor.
 
     In some embodiments, the value of beta (β) ranges from 0 to 2π, 0 being preferred. The value α 1  may be a function of the power of the signals emitted by the antennas connected to the corresponding antenna element ports, assuming equal input power on the two antenna element ports. Thus, for example, in the equation W b2,S1a  equals or substantially equals e i(β+π) (W b1,T1b )*α 1 ,α 1  is a function of the power of the signal emitted by antenna A 2  in a direction (d) (i.e., P(d) A2 ) and the power of the signal emitted by antenna A 1  in the direction d (i.e., (P(d) A1 ). In some embodiments, α 1  equals or substantially equals Sqrt(P(d) A2 /(P(d) A1 ). In many cases, in practice α 1 =1. 
     In the example embodiment described above, the vector of W b2  beam weights for the ports shown in  FIG. 2  is as follows:
 
 W   b2,S1a  equals or substantially equals  e   i(β+π) ( W   b1,T1b )*α 1 ,
 
 W   b2,S1b  equals or substantially equals  e   i(β+π) ( W   b1,T1a )*α 1 ,
 
 W   b2,T1a  equals or substantially equals  e   iβ ( W   b1,S1b )*1/α 1 , and
 
 W   b2,T1b  equals or substantially equals  e   iβ ( W   b1,S1a )*1/α 1 .
 
       FIG. 3  further illustrates another portion of antenna array apparatus  100 . That is,  FIG. 3  further illustrates antenna elements AE 2 - a  and AE 2 - b  and shows beam forming circuits  301  and  302  of antenna array apparatus  100 . As shown in  FIG. 3 , each antenna element port of antenna elements AE 2 - a  and AE 2 - b  is electrically connected to an antenna. Specifically, antenna element port S 2   a  is connected to antenna A 5  and antenna element port T 2   b  is connected to antenna A 6 . The structure of the antennas A 5 -A 6  is not significant. However, in some embodiments, certain characteristics of antennas A 5 -A 6  are significant. For instance, in some embodiments, antenna A 5  may have an arbitrary polarization, but antenna A 6  has a polarization that is orthogonal or substantially orthogonal to the polarization of antenna A 5 . Similarly, in some embodiments, the power pattern for antenna A 5  is the same or substantially the same as the power pattern for antenna A 6 . 
     As shown in  FIG. 3 , each antenna element port of antenna elements AE 2 - a  and AE 2 - b  is connected to a beam forming circuit that is used to apply to the antenna element port two beam weights (a W b1  beam weight for beam  1  and a W b2  beam weight for beam  2 ). More specifically, beam weights W b1,S2a  and W b2,S2a  are applied to antenna element port S 2   a  and beam weights W b1,T2b  and W b2,T2b  are applied to antenna element port T 2   b.    
     As described above, in some embodiments, the W b2  beam weight for a particular S antenna element port of a particular antenna element is function of the W b1  beam weight for the corresponding T antenna element port. Similarly, the W b2  beam weight for a particular T antenna element port of a particular antenna element is function of the W b1  beam weight for the corresponding S antenna element port. 
     In the example embodiment described above, the W b2  beam weights for the antenna element ports shown in  FIG. 3  is as follows:
 
 W   b2,S2a  equals or substantially equals  e   i(β+π) ( W   b1,T2b )*α 2 ,
 
 W   b2,T2b  equals or substantially equals  e   iβ ( W   b1,S2a )*1/α 2 .
 
       FIG. 4  illustrates antenna elements AE 3 , according to some embodiments, and shows beam forming circuits  401  and  402  of antenna array apparatus  100 . As shown in  FIG. 4 , each port of antenna element AE 3  is electrically connected to an antenna. Specifically, antenna element port S 3  is connected to antenna A 7  and antenna element port T 3  is connected to antenna A 8 . The structure of the antennas A 7 -A 8  is not significant. However, in some embodiments, certain characteristics of antennas A 7 -A 8  are significant. For instance, in some embodiments, antenna A 7  may have an arbitrary polarization, but antenna A 8  has a polarization that is orthogonal or substantially orthogonal to the polarization of antenna A 7 . Similarly, in some embodiments, the power pattern for antenna A 7  is the same or substantially the same as the power pattern for antenna A 8 . 
     As shown in  FIG. 4 , each antenna element port of antenna element AE 3  is connected to a beam forming circuit that is used to apply to the antenna element port two beam weights (one for beam  1  and one for beam  2 ). More specifically, beam weights W b1,S3  and W b2,S3  are applied to antenna element port S 3  and beam weights W b1,T3  and W b2,T3  are applied to antenna element port T 3 . 
     As described above, in some embodiments, the W b2  beam weight for a particular S antenna element port of a particular antenna element is function of the W b1  beam weight for the corresponding T antenna element port, and the W b2  beam weight for a particular T antenna element port of a particular antenna element is function of the W b1  beam weight for the corresponding S antenna element port. In the example embodiment described above, the W b2  beam weights for the antenna element ports shown in  FIG. 4  is as follows:
 
 W   b2,S3  equals or substantially equals  e   i(β+π) ( W   b1,T3 )*α 3 ,
 
 W   b2,T3  equals or substantially equals  e   iβ ( W   b1,S3 )*1/α 3 .
 
     Referring now to  FIG. 5 ,  FIG. 5  illustrates an example 2-dimensional antenna array  500  for forming two beams (a first beam and a second beam) where (a) the shape of the power beam pattern for the first beam and the shape of the power beam pattern for the second beam are the same or substantially the same in a plurality of directions and (b) each beam has an orthogonal or substantially orthogonal polarization with respect to the other beam in the UE coverage area. In this example, all of the antenna elements  502  of antenna array  500  are dual-port antenna elements that have an S antenna port and a T antenna port. The indexes that are used to name the S antenna ports and T antenna ports is arbitrary, but, as will be seen below, the naming scheme used in  FIG. 5  has the advantage making it easy to show the relationship between beam weights. 
     Antenna array  500  has six pairs of antenna elements. That is, each of the twelve antenna elements  502  of antenna array  500  is paired with another antenna element. More specifically, an antenna element  502  having port Sx (where x&lt;7) is paired with antenna element  502  having port Sy, where y=13−x. Thus, for example, the antenna element having ports S 1  and T 12  is paired with the antenna element having ports S 12  and T 1 . Antenna array  500  also has a symmetry point  501 . In the example embodiment shown, each pair of antenna elements is located symmetrically with respect to symmetry point  501 . 
     Although not shown, antenna array  500  includes a beam forming circuit for each antenna element port. As described above, each beam forming circuit is used to apply two beam weights—a beam weight W b1  for the first beam and a beam weight W b2  for the second beam—to the antenna element port to which the beam forming circuit is connected. 
     Using the same beam weight rule described above, the vector of W b2  beam weights for the ports shown in  FIG. 4  is as follows:
 
 W   b2,Sx  equals or substantially equals  e   i(β+π) ( W   b1,Tx )*α x ,
 
 W   b2,Tx  equals or substantially equals  e   iβ ( W   b1,Sx )*1/α x , where  x= 1,2, . . . ,12.
 
     Example Beam Pattern 
     An example antenna array for producing an example beam pattern is a four column antenna array with five dual port antenna elements per column. Column separation is 0.5 wavelengths and separation within a column is 0.847 wavelengths. All antenna elements are identical, having perfectly orthogonal polarizations in all directions (at least those of interest). The weight vector for the first beam (B 1 ) contains 40 complex beam weights. The beam weight applied to S ports, identical weight in columns 1 through 4, for elevation domain beam forming is here found as 
     
       
         
           
             
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     The weight applied to S ports, identical weight to all 5 ports in the column, for azimuth beam forming is found as. 
     
       
         
           
             
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                   4 
                 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         - 
                         0.9959 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.0786 
                       
                     
                   
                 
                 
                   
                     
                       
                         - 
                         0.2562 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.0786 
                       
                     
                   
                 
                 
                   
                     1 
                   
                 
                 
                   
                     
                       
                         - 
                         0.0861 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.9953 
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     The total weight for the S ports is found by multiplying these weight vectors according to
 
 W   s,B1,1to20   =w   s,B1,El1to5   w   s,B1,Az1to4   T  
 
resulting in a matrix with 20 (5 rows×4 columns) elements. This matrix can then be vectorized by taking the weights, column by column, forming a column vector with 20 elements.
 
     The weights applied to the T ports are found in a similar way. Again, the weight applied to columns 1 through 4, for elevation domain beam forming is identical and here found as 
     
       
         
           
             
               w 
               
                 t 
                 , 
                 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 , 
                 
                   El 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   to 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         - 
                         0.4074 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.2899 
                       
                     
                   
                 
                 
                   
                     
                       
                         - 
                         0.2693 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.4213 
                       
                     
                   
                 
                 
                   
                     
                       0.1121 
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.4873 
                       
                     
                   
                 
                 
                   
                     0 
                   
                 
                 
                   
                     0.500 
                   
                 
               
               ] 
             
           
         
       
     
     The weight applied to T ports, identical weight to all 5 elements in the column, for azimuth beam forming is found as 
     
       
         
           
             
               w 
               
                 t 
                 , 
                 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 , 
                 
                   Az 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   to 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         - 
                         0.2244 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.6154 
                       
                     
                   
                 
                 
                   
                     
                       0.1743 
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.6314 
                       
                     
                   
                 
                 
                   
                     0.6550 
                   
                 
                 
                   
                     
                       0.5353 
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0.3764 
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     The total weight for the T ports is found by multiplying these weight vectors according to
 
 W   t,B1,1to20   =w   t,B1,El1to5   w   t,B1,Az1to4   T  
 
Finally the total weight vector for beam  1 , containing 40 elements, is found as
 
     
       
         
           
             
               w 
               
                 B 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       w 
                       
                         s 
                         , 
                         
                           B 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         , 
                         
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           to 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           20 
                         
                       
                     
                   
                 
                 
                   
                     
                       w 
                       
                         t 
                         , 
                         
                           B 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         , 
                         
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           to 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           20 
                         
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     The weight vector for the second beam is found by applying the method described above and with β set to 0 and α set to 1. 
       FIGS. 6A, 6B  show power patterns for beams  1  and  2 , respectively, for an azimuth cut via beam peak. As can be seen from  FIGS. 6A-6B , the beams have identical power patterns.  FIGS. 7A, 7B  show power patterns for beams  1  and  2 , respectively, for an elevation cut via beam peak. As can be seen from the figures the beams have identical power patterns.  FIG. 8  shows that polarizations for beams  1  and  2  are orthogonal in all directions. 
       FIG. 9  is a flow chart illustrating a process  900  for using an antenna array to produce a first beam (beam  1 ) and a second beam (beam  2 ). Process  900  begins in step  902 , where a vector of beam weights for beam  1  is selected (each beam weight in the vector of beam weights for beam  1  is associated with an antenna element port of the antenna array). In step  904 , the selected vector of beam weights for beam  1  is used to determine a vector of beam weights for beam  2  (each beam weight in the vector of beam weights for beam  2  is associated with one of the antenna element ports). In step  906 , for each beam weight in the vector of beam weights for beam  1 , the beam weight is applied to its associated antenna element port. In step  908 , for each beam weight in the vector of beam weights for beam  2 , the beam weight is applied to its associated antenna element port. In some embodiments, a beam weight for beam  1  is applied to an antenna element port by using a beam forming circuit connected to the antenna element port to multiply the beam weight for beam  1  with a signal injected into beam port  1  of the antenna array, and a beam weight for beam  2  is applied to the antenna element port by using the beam forming circuit to multiply the beam weight for beam  2  with (i) a signal injected into beam port  2  of the antenna array or (ii) the signal injected into beam port  1  of the antenna array, where the beam forming circuit is configured to provide the resulting signals to the antenna element port (e.g., see  FIG. 2 ). 
     Referring now to  FIG. 10 ,  FIG. 10  illustrates a process  1000  for determining the beam weight for beam  2  that is associated with a selected antenna element port. Process  1000  may being in step  1002 , where an antenna element port is selected (e.g., antenna element S 1a  is selected). In step  1004 , the antenna element port that is paired with the selected antenna element port is determined. For example, if antenna element port S 1a  is selected in step  1002 , then antenna element port T 1b  is determined in step  1004 , because that is the port that is paired with antenna element port S 1a . In step  1006 , the beam  1  beam weight associated with the antenna element port that is paired with the selected antenna element port is obtained. In step  1008 , the complex conjugate of the beam weight obtained in step  1006  is obtained. In step  1010 , the obtained complex conjugate is phase shifted. In step  1012 , the phase shifted complex conjugate is multiplied by an amplitude scaling factor. In some embodiments, the obtained complex conjugate is multiplied by the scaling factor prior to being phase shifted. 
     Referring now to  FIG. 11 ,  FIG. 11  illustrates a block diagram of a weight determining unit  1101  according to some embodiments of the invention. As shown in  FIG. 11 , weight determining unit  1101  may include: a data processing system  1102 , which may include one or more processors (e.g., a microprocessor, a DSP) and/or one or more circuits, such as an application specific integrated circuit (ASIC), Field-programmable gate arrays (FPGAs), etc; and data storage system  1106 , which may include one or more non-volatile storage devices and/or one or more volatile storage devices (e.g., random access memory (RAM)). As shown, data storage system  1106  may be used to store a vector of beam weights for a first beam (beam  1 ). In embodiments where data processing system  1102  includes a microprocessor, computer readable program code (CRPC)  1143  may be stored in a computer readable medium  1142 , such as, but not limited, to magnetic media (e.g., a hard disk), optical media (e.g., a DVD), memory devices (e.g., random access memory), etc. In some embodiments, computer readable program code  1143  is configured such that when executed by a processor, code  1143  causes route weight determining unit  1101  to perform steps described above (e.g., steps describe above with reference to the flow chart shown in  FIG. 10 ). In other embodiments, weight determining unit  1101  is configured to perform steps described above without the need for code  1143 . That is, for example, data processing system  1102  may consist merely of one or more ASICs. Hence, certain features of the present invention described above may be implemented in hardware and/or software. For example, in particular embodiments, the functional components of weight determining unit  1101  described above may be implemented by data processing system  1102  executing computer instructions  1143 , by data processing system  1102  operating independent of any computer instructions  1143 , or by any suitable combination of hardware and/or software. 
     While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of the present invention should not be limited by any of the above described exemplary embodiments. Moreover, any combination of the above described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein. 
     Additionally, while the methods described above and/or illustrated in the drawings include a sequence of steps, this was done solely for the sake of illustration. Accordingly, it is contemplated that some steps may be added, some steps may be omitted, the order of the steps may be rearranged, and some steps may be performed in parallel.