Patent Publication Number: US-2010124263-A1

Title: Systems for determining a reference signal at any location along a transmission media

Description:
BACKGROUND OF THE INVENTION 
     1. Statement of the Technical Field 
     The invention concerns systems implementing methods for determining a reference signal at any location along a transmission media. 
     2. Description of the Related Art 
     There are many systems and applications known to those having ordinary skill in the art that can benefit from an ability to determine a reference signal at any location along a transmission media. Such systems include, but are not limited to, radar systems and communication systems. For example, a conventional wireless communication system typically includes a system controller, a plurality of antenna controllers, and a plurality of antenna elements (e.g., a plurality of dish antennas). Each of the antenna elements is communicatively coupled to the system controller and a respective one of the antenna controllers via a cable assembly. During transmission and reception, each antenna element converts electrical signals into electromagnetic waves, and vice versa. The phases of the signals to be transmitted from and received by the antenna elements can be shifted as a result of environmental effects on hardware components of the system controller, hardware components of the antenna controllers, and the cable assemblies connecting the antenna elements to the controllers. These phase shifts typically result in the steering of the radiated main beam in the wrong direction. In order to overcome the various limitations of the communication system, it needs to implement a beamforming solution that counter acts the phase shifts resulting from environmental effects on the hardware components and cables thereof. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention concern systems implementing methods for determining one or more reference signals V ref . The systems comprise one or more sensing devices, a first signal combiner communicatively coupled to a first one of the sensing devices (hereinafter referred to as the “first sensing device”), and a first signal subtractor communicatively coupled to the first sensing device. The first sensing device is configured for sensing, at a first location along a transmission media, a first signal propagated over the transmission media in a forward direction. The first sensing device is also configured for sensing a second signal propagated over the transmission media in a reverse direction opposed from the forward direction. The first sensing device can include, but is not limited to, a transducer, a directional coupler, and a fiber demodulator. The transmission media can include, but is not limited to, free space, a waveguide, a coaxial transmission line, an optical fiber, and an acoustic media. The second signal is a reflected version of the first signal. 
     The first signal combiner is configured for computing a first sum signal by adding the first and second signals together. The first signal subtractor is configured for computing a first difference signal by subtracting the second signal from the first signal. The first signal combiner and the first signal subtractor can collectively form a sum-diff hybrid circuit. The sum-diff hybrid circuit can include, but is not limited to, a 180 degree hybrid coupler. 
     The systems also comprise a first signal multiplier, a second signal multiplier, and a second signal subtractor. The first signal multiplier is communicatively coupled to the first signal combiner. The first signal multiplier is configured for computing a first exponentiation signal using the first sum signal. The second signal multiplier is communicatively coupled to the first signal subtractor. The second signal multiplier is configured for computing a second exponentiation signal using the first difference signal. The second signal subtractor is communicatively coupled to the first and second signal multipliers. The second signal subtractor is configured for subtracting the first exponentiation signal from the second exponentiation signal to obtain a first reference signal. The second signal subtractor can include, but is not limited to, a 180 degree hybrid coupler. 
     According to an aspect of the present invention, the first reference signal has a frequency equal to or different than the frequency of the first signal. If the first reference signal has a frequency different than the frequency of the first signal, then one or more post processing devices process the first reference signal to obtain an adjusted reference signal with a frequency equal to the frequency of the first signal. The post processing device can include, but is not limited to, a phase lock loop and a frequency divider. The systems can further include one or more phase and amplitude trimmers. 
     According to another aspect of the present invention, the systems include a reference signal generator. A second one of the sensing devices (hereinafter referred to as the “second sensing device”) is configured for sensing, at a second location different from the first location along the transmission media, the first and second signal. The reference signal generator is configured for computing a second reference signal using the first and second signals sensed at the second location. The second reference signal is the same as the first reference signal. 
     Embodiments of the present invention also concern communication systems. The communication systems include a sensing device and a reference signal generator communicatively coupled to the sensing device. The second sensing device is configured for sensing, at the first location along the transmission media, the first and second signals. The reference signal generator is configured for computing a sum signal by adding the first and second signals together and a difference signal by subtracting the second signal from the first signal. The reference signal generator is also configured for computing a first exponentiation signal using the first sum signal and a second exponentiation signal using the first difference signal. The reference signal generator is further configured for subtracting the first exponentiation signal from the second exponentiation signal to obtain a first reference signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments will be described with reference to the following drawing figures, in which like numerals represent like items throughout the figures, and in which: 
         FIG. 1  is a block diagram of a system that is useful for understanding the present invention. 
         FIG. 2  is a conceptual diagram of a first exemplary method (or process) for determining a reference signal that is useful for understanding the present invention. 
         FIG. 3  is a conceptual diagram of a second exemplary method (or process) for determining a reference signal that is useful for understanding the present invention. 
         FIG. 4  is a block diagram of a first exemplary embodiment of a system configured to generate a reference signal. 
         FIG. 5  is a block diagram of a second exemplary embodiment of a system configured to generate a reference signal. 
         FIG. 6  is a block diagram of a third exemplary embodiment of a system configured to generate a reference signal. 
         FIG. 7  is a block diagram of a fourth exemplary system configured to generate a reference signal. 
         FIG. 8  is a more detailed block diagram of the reference signal generator shown in  FIG. 7 . 
         FIG. 9  is a block diagram of a communication system configured to generate reference signals. 
         FIG. 10  is more detailed block diagram of the communication system of  FIG. 9 . 
         FIG. 11  is a schematic view of a computer system within which a set of instructions operate according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention is described with reference to the attached figures, wherein like reference numbers are used throughout the figures to designate similar or equivalent elements. The figures are not drawn to scale and they are provided merely to illustrate the instant invention. Several aspects of the invention are described below with reference to example applications for illustration. It should be understood that numerous specific details, relationships, and methods are set forth to provide a full understanding of the invention. One having ordinary skill in the relevant art, however, will readily recognize that the invention can be practiced without one or more of the specific details or with other methods. In other instances, well-known structures or operations are not shown in detail to avoid obscuring the invention. The present invention is not limited by the illustrated ordering of acts or events, as some acts may occur in different orders and/or concurrently with other acts or events. Furthermore, not all illustrated acts or events are required to implement a methodology in accordance with the present invention. 
     Embodiments of the present invention provide systems implementing methods for determining a reference signal at any location along a transmission media. The methods generally involve sensing at a first location along the transmission media a first signal (V f ) propagated over the transmission media in a forward direction and a second signal (V r ) propagated over the transmission media in a reverse direction opposed from the forward direction. The second signal V r  is a reflected version of the first signal V f . The methods also involve computing a sum signal (S) by adding the first and second signals (V f +V r ) together and a difference signal (D) by subtracting the second signal from the first signal (V r −V f ). A first exponentiation signal (S 2 ) is computed using the sum signal (S). Similarly, a second exponentiation signal (D 2 ) is computed using the difference signal (D). The first exponentiation signal is subtracted from the second exponentiation signal (D 2 −S 2 ) to obtain a reference signal (V ref ). Notably, the reference signal V ref  is defined by a mathematical equation that is not dependant on “z”, the location along the transmission media. As such, the reference signal V ref  can be determined at any location along the transmission media and/or at multiple different locations along the transmission media. The reference signal V ref  will exhibit the same phase at all locations. Notably, the reference signal(s) V ref  can be used in a variety of applications. For example, the reference signal(s) V ref  can be used to adjust a phase of transmit and/or receive signals so as to counteract the environmental effects on hardware components of a communication system. 
     Before describing the systems and methods of the present invention, it will be helpful in understanding exemplary environments in which the invention can be utilized. In this regard, it should be understood that the systems and methods of the present invention can be utilized in a variety of different applications where a reference signal needs to be determined at any location along a transmission media. Such applications include, but are not limited to, mobile/cellular telephone applications, military communication applications, space communication applications, phased array calibration and timing applications, radar signal distribution applications, radar calibration applications for large radar arrays, radar calibration applications for cooperative radar installations, time synchronization applications for sensors, time synchronization applications for digital systems, time synchronization applications for clocks, time synchronization applications for events, and large area (e.g., from several meters to interplanetary) metrology applications. 
     The word “exemplary” is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the word exemplary is intended to present concepts in a concrete fashion. As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context, “X employs A or B” is intended to mean any of the natural inclusive permutations. That is if, X employs A; X employs B; or X employs both A and B, then “X employs A or B” is satisfied under any of the foregoing instances. 
     Systems and Methods For Determining One or More Reference Signals V ref    
     Referring now to  FIG. 1 , there is provided a block diagram of a system  100  that is useful for understanding the present invention. As shown in  FIG. 1 , the system  100  can comprise a signal source  102 , a sensor  116 , a reflective termination  114 , and a non-reflective termination  104 . Each of these components  102 ,  104 ,  114 ,  116  is well known to those having ordinary skill in the art, and therefore will not be described in detail herein. However it should be understood that in order to determine a reference signal V ref , a forward propagated signal V f  and a reverse propagated signal V r  need to be sensed at a location “z” along the transmission media  108 . Although, the transmission media  108  is shown in  FIG. 1  to include a coaxial transmission line, embodiments of the present invention are not limited in this regard. For example, the transmission media  108  can also include free space, a waveguide, an optical fiber, and an acoustic media. 
     In operation, the signal source  102  generally communicates a signal V f  to the reflective termination  114 . A reflected version of the transmitted signal V r  is communicated from the reflective termination  114  to the non-reflective termination  104 . The sensor  116  senses the presence of the forward propagated signal V f  and the reverse propagated signal V r  on the transmission media  108 . The sensor  116  may also adjust the gain of the signals V f , V r  so that they have equal arbitrarily defined amplitudes “a”. This gain adjustment can involve performing Automatic Gain Control (AGC) operations which are well known to those having ordinary skill in the art. Thereafter, the sensor  116  outputs signals representing the forward propagated signal V f  and the reverse propagated signal V r . These output signals can subsequently be used to compute the reference signal V ref . 
     It should be noted that the forward propagated signal V f  generated by the signal source  102  can be stronger (i.e., have a greater power or intensity) than the reverse propagated signal V r  received at the non-reflective termination  104 . As a result, coupling of the signals V f , V r  can occur making it difficult to distinguish the signals from each other. In order to resolve this signal coupling issue, the signal source  102  and the non-reflective termination  104  can be spaced apart (e.g., a few hundred yards). Alternatively or additionally, the reflective termination  114  can derive a frequency offset of the forward propagated signal V f , adjust the frequency thereof utilizing the frequency offset, and communicating a reflected version V r  of the forward propagated signal V f  with the adjusted frequency to the non-reflective termination  104 . Embodiments of the present invention are not limited in this regard. The reflective termination  114  can implement any method for ensuring that the signals V f , V r  have the same or substantially similar power or intensity. 
     A conceptual diagram of a first exemplary process  200  for determining the reference signal V ref  is provided in  FIG. 2 . As shown in  FIG. 2 , the process  200  begins by ( 202 ,  204 ) sensing a forward propagated signal V f  and a reverse propagated signal V r . It should be appreciated that the sensing processes ( 202 ,  204 ) can involve gain adjustments as necessary so that the resulting signals have an arbitrarily defined amplitude “a”. The gain adjustments can involve performing AGC operations. The forward propagated signal V f  can be defined by the following mathematical equation (1). Similarly, the reverse propagated signal V r , for the exemplary case of a short circuit reflection, can be defined by the following mathematical equation (2). 
         V   f   =ae   j(ωt+φ−βz)    (1) 
         V   r   =−ae   j(ωt+φ+βz)    (2) 
     where a is a signal amplitude. j the is square root of minus one (j=(−1) 1/2 ). ω is a radian frequency. φ is a phase angle. β is a wave number that is equal to 2π/λ, where λ is a wavelength. z is a location along a transmission media measured from the reflective end of the transmission media. 
     Thereafter, a signal combination operation  206  is performed where the signals V f , V r  are combined to obtain a Sum signal (S). This signal combination operation  206  generally involves adding the signals V f , V r  together. The signal combination operation  206  can be defined by the following mathematical equation (3). 
         S=ae   j(ωt+φ−βz)   −ae   j(ωt+φ+βz) =−2 aje   j(ωt+φ) [sin(β z )]  (3) 
     As evident from mathematical equation (3), the Sum signal S is a signal that depends on the location “z” at which the sensor  116  is placed along the transmission media  108 . 
     The process  200  also involves performing a subtraction operation  208 . The subtraction operation  208  generally involves subtracting the reverse propagated signal V r  from the forward propagated signal V f  to obtain a Difference signal (D). The subtraction operation  208  can be defined by the following mathematical equation (4). 
         D=ae   j(ωt+φ−βz)   +ae   j(ωt+φ+βz) =2 ae   j(ωt+φ) [cos(β z )]  (4) 
     As evident from mathematical equation (4), the Difference signal D is a signal that depends on the location “z” at which the sensor  116  is placed along the transmission media  108 . 
     After determining the Sum signal S and the Difference signal D, the process  200  continues with a plurality of multiplication operations  210 ,  212 . A first one of the multiplication operations  210  generally involves multiplying the Sum signal S by itself to obtain a first Exponentiation signal E S . The first multiplication operation  210  can generally be defined by the following mathematical equation (5). 
         E   S   =S·S=S   2    (5) 
     where E S  is the first Exponentiation signal. S is the Sum signal. S 2  is the Sum signal S raised to the second power. 
     A second one of the multiplication operations  212  generally involves multiplying the Difference signal D by itself to obtain a second Exponentiation signal E D . The second multiplication operation  212  can generally be defined by the following mathematical equation (6). 
         E   D   =D·D=D   2    (6) 
     where E D  is the second Exponentiation signal. D is the Difference signal. D 2  is the Difference signal D raised to the second power. 
     Subsequent to determining the first and second Exponentiation signals, the process continues with a subtraction operation  214 . The subtraction operation  214  generally involves subtracting the first Exponentiation signal E S  from the second Exponentiation signal E D . The subtraction operation  214  can be defined by the following mathematical equation (7). 
         V   doubled   =D   2   −S   2 =4 a   2   e   j2(ωt+φ) [sin 2 (β z )+cos 2 (β z )]=4 a   2   e   j2(ωt+φ)    (7) 
     where V doubled  represents a signal obtained as a result of performing the subtraction operation  214 . As evident from mathematical equation (7), the resulting signal V doubled  does not depend on the location “z” at which the sensor  116  is placed along the transmission media  108 . As such, the signal V doubled  can be determined at one or more locations along a transmission media. This location “z” independence is a significant and highly desirable result. 
     The resulting signal V doubled  has twice the frequency relative to that of each propagated signal V f , V r . As such, the resulting signal V doubled  can be further processed to increase its frequency to a desired value or to reduce its frequency to a desired value (e.g., the value of the frequency of a propagated signal V f , V r ). If the resulting signal V doubled  is further processed to increase its frequency, then the process  200  can include a multiplication operation (not shown). If the resulting signal V doubled  is further processed to reduce its frequency, then the process  200  can include a frequency reduction operation  216 . 
     The optional frequency reduction operation  216  can generally involve performing a phase locked loop operation and a frequency division operation. Phase locked loop operations are well known to those having ordinary skill in the art, and therefore will not be described herein. The frequency division operation can involve dividing the frequency of the resulting signal V doubled  by two (2). The output signal from the frequency reduction operation is the reference signal V ref . The reference signal V ref  can be defined by the following mathematical equation (8): 
       V ref   =±e   j(ωt+φ)    (8) 
     for any line position “z”. As evident from mathematical equation (8), the reference signal V ref  is a signal that does not depend on the location “z” at which the sensor  116  is placed along the transmission media  108 . As such, the reference signal V ref  can be determined at one or more locations along a transmission media. This location “z” independence is a significant and highly desirable result. 
     Embodiments of the present invention are not limited to the process  200  described above in relation to  FIG. 2 . For example, if the frequency of each propagated signal V f , V r  is reduced by exactly half, then the optional frequency reduction operation  216  need not be performed. A conceptual diagram of a process  300  for determining the reference signal V ref  absent of the frequency reduction operation  216  is provided in  FIG. 3 . As shown in  FIG. 3 , the propagated signals with half the frequency of the signals V f , V r  have the following designations V′ f , V′ r , respectively. 
     As shown in  FIG. 3 , the process  300  generally involves performing sensing operations  302 ,  304  to sense propagated signals V′ f , V′ r , a signal combination operation  306 , subtraction operations  308 ,  314 , and multiplication operations  310 ,  312 . These listed operations  302 ,  304 , . . . ,  314  are the same as or substantially similar to the operations  202 ,  204 , . . . ,  214  of  FIG. 2 , respectively. As such, the operations  302 ,  304 , . . . ,  314  of process  300  will not be described herein. 
     Referring now to  FIG. 4 , there is provided a block diagram of an exemplary system  400  implementing a method for determining a signal V doubled  and/or a reference signal V ref . As shown in  FIG. 4 , the system  400  comprises a sensing device  402 , a signal adder  406 , signal subtractors  408 ,  414 , and signal multipliers  410 ,  412 . The system  400  can also comprise an optional phase lock loop  416  and an optional frequency divider  418 . The sensing device  402  is generally configured for sensing the presence of a forward propagated signal V f  or V′ f  and a reverse propagated signal V r  or V′ r  on the transmission media  108 . The sensing device  402  may also adjust the gain of the signals V f  or V′ f , V r  or V′ r  so that they have equal arbitrarily defined amplitudes “a”. This gain adjustment can involve performing AGC operations. The sensing device  402  can also generate output signals representing the forward propagated signal V f  or V′ f  and the reverse propagated signal V r  or V′ r . These output signals can subsequently be used to determine the signal V doubled  or the reference signal V ref . As such, the sensing device  402  can further communicate the signals representing the forward propagated signal V f , or V′ f  and the reverse propagated signal V r  or V′ r  to the following components  406 ,  408 . 
     The signal adder  406  is generally configured for performing a signal combination operation  206 ,  306  (described above in relation to  FIGS. 2 and 3 ) to obtain a Sum signal S or S′. The signal subtractor  408  is generally configured for performing a subtraction operation  208 ,  308  (described above in relation to  FIGS. 2 and 3 ) to obtain a Difference signal D or D′. The output signals of the components  406 ,  408  are forwarded to the signal multipliers  410 ,  412 . Each of the multipliers  410 ,  412  is configured to perform a multiplication operation  210 ,  212 ,  310 ,  312  (described above in relation to  FIGS. 2 and 3 ) to obtain a respective Exponentiation signal E S , E′ S , E D , or E′ D . The Exponentiation signals E S  and E D  or E′ S  and E′ D  are then communicated from the signal multipliers  410 ,  412  to the signal subtractor  414 . At the signal subtractor  414 , a subtraction operation  214 ,  314  (described above in relation to  FIGS. 2 and 3 ) is performed to obtain a signal V doubled  or a reference signal V ref . 
     If the result of the subtraction operation is the signal V doubled , then the signal V doubled  can be further processed to reduce the value of its frequency. In such a scenario, the signal V doubled  can be forwarded to an optional phase lock loop  416  and an optional frequency divider  418 . The signal V doubled  can be forwarded to a multiplier (not shown). The components  416 ,  418  collectively act to reduce the frequency of the signal V doubled  to a desired value (i.e., the value of the frequency of a propagated signal V f , V r ). In contrast, the multiplier (not shown) can act to increase the frequency of the signal V doubled  to a desired value. The output of the frequency divider  418  is the reference signal V ref . It should be noted that the signals V f , V′ f , V r , V′ r , V doubled , and V ref  of  FIG. 4  have the same phase. 
     Referring now to  FIG. 5 , there is provided a block diagram of another exemplary embodiment of a system  500  implementing a method for determining a reference signal V ref . As shown in  FIG. 5 , the system  500  comprises a sensing device  504  disposed along a transmission media  502 . Although, the transmission media  502  is shown in  FIG. 5  to include a coaxial transmission line, embodiments of the present invention are not limited in this regard. For example, the transmission media  502  can also include free space, a waveguide, and an acoustic media. The system  500  also comprises a sum-diff hybrid circuit  508 , multipliers  510 ,  512 , a signal subtractor  514 , a phase lock loop (PLL)  516 , and a frequency divider  518 . Embodiments of the present invention are not limited to the configuration shown in  FIG. 5 . For example, the system  500  can be absent of the PLL  516  and the frequency divider  518 . The system  500  can also include a phase locked oscillator (not shown) instead of the PLL  516  and the frequency divider  518 . 
     The sensing device  504  is generally configured for sensing the presence of a forward propagated signal V f  and a reverse propagated signal V r  on the transmission media  502 . The sensing device  504  may also adjust the gain of the signals V f , V r  so that they have equal arbitrarily defined amplitudes “a”. This gain adjustment can involve performing AGC operations. The sensing device  504  can also generate output signals representing the forward propagated signal V f  and the reverse propagated signal V r . These output signals can subsequently be used to determine the reference signal V ref . As such, the sensing device  504  can further communicate the signals representing the forward propagated signal V f  and the reverse propagated signal V r  to the sum-diff hybrid circuit  508 . 
     The sum-diff hybrid circuit  508  is generally configured for performing a signal combination operation  206  (described above in relation to  FIG. 2 ) to obtain a Sum signal S and a subtraction operation  208  (described above in relation to  FIG. 2 ) to obtain a Difference signal D. Subsequent to completing the signal combination operation  206  and the subtraction operation  208 , the sum-diff hybrid circuit  508  communicates the signals S, D to the multipliers  510 ,  512 , respectively. Each of the multipliers  510 ,  512  is configured to perform a multiplication operation  210 ,  212  (described above in relation to  FIG. 2 ) to obtain a respective Exponentiation signal E S , E D . The Exponentiation signals E S , E D  are then communicated from the multipliers  510 ,  512  to the signal subtractor  514 . At the signal subtractor  514 , a subtraction operation  214  (described above in relation to  FIG. 2 ) is performed to obtain a signal V doubled . The signal V doubled  is then processed by the PLL  516  and frequency divider  518  to reduce the frequency of the signal V doubled  to a desired value (i.e., the value of the frequency of a propagated signal V f , V r ). The output of the frequency divider  518  is the reference signal V ref . It should be noted that the functions of the PLL  516  and the frequency divider  518  can alternatively be performed by a phase locked oscillator (not shown). 
     Referring now to  FIG. 6 , there is provided a block diagram of another exemplary embodiment of a system  600  implementing the method of  FIG. 2 . As shown in  FIG. 6 , the system  600  comprises transducers  604 ,  620  and a reference signal generator  650 . Transducers are well known to those having ordinary skill in the art, and therefore will not be described herein. However, it should be understood that each of the transducers  604 ,  620  is configured to communicate a signal representing a signal V f , V r  propagated on the transmission media  602  to the reference signal generator  650 . Although, the transmission media  602  is shown in  FIG. 6  to include a coaxial transmission line, embodiments of the present invention are not limited in this regard. For example, the transmission media  602  can also include free space, a waveguide, and an acoustic media. 
     As also shown in  FIG. 6 , the reference signal generator  650  comprises 180 degree hybrid couplers  606 ,  614 , input square devices  608   a ,  608   b , a PLL  616 , and a frequency divider  618 . Embodiments of the present invention are not limited to the configuration shown in  FIG. 6 . For example, the reference signal generator  650  can be absent of the PLL  616  and the frequency divider  618 . The reference signal generator  650  can also place the frequency divider in the feedback path of the PLL to obtain frequencies higher than the frequencies of the reference signal V ref . 
     Hybrid couplers are well known to those having ordinary skill in the art, and therefore will not be described herein. However, it should be understood that the hybrid coupler  606  generally combines incoming signals into a first output signal. The hybrid coupler  606  also generally subtracts a first incoming signal from a second incoming signal to obtain a second output signal. In effect, the hybrid coupler  606  generates the Sum signal S and the Difference signal D using the incoming signals V f , V r . The generated signals S and D are then communicated from the hybrid coupler  606  to the input square devices  608   a ,  608   b , respectively. Each of the input square devices  608   a ,  608   b  generates a respective Exponentiation signal E S , E D . The Exponentiation signals E S , E D  are communicated from the input square devices  608   a ,  608   b  to the hybrid coupler  614 . The hybrid coupler  614  generally subtracts a first incoming signal from a second incoming signal to obtain a second output signal. More particularly, the hybrid coupler  614  performs a subtraction operation  214  (described above in relation to  FIG. 2 ) to obtain a signal V doubled . 
     Next, the signal V doubled  is further processed to reduce the value of its frequency. Accordingly, the signal V doubled  is forwarded from the hybrid coupler  614  to the PLL  616  and the frequency divider  618 . The components  616 ,  618  collectively act to reduce the frequency of the signal V doubled  to a desired value (i.e., the value of the frequency of a propagated signal V f , V r ). The output of the frequency divider  618  is the reference signal V ref . 
     Referring now to  FIG. 7 , there is provided a block diagram of yet another exemplary embodiment of a system  700  implementing the method of  FIG. 2 . As shown in  FIG. 7 , the system  700  is an optical fiber based system. As such, the system  700  comprises a signal source  704 , a fiber modulator  706 , an optical fiber  702 , and a mirrored fiber end  710 . Each of these components  702 ,  704 ,  706 ,  710  is well known to those having ordinary skill in the art, and therefore will not be described herein. 
     As also shown in  FIG. 7 , the system  700  comprises dual directional couplers  708   a ,  708   b ,  708   c , fiber demodulators  712   a ,  712   b ,  712   c ,  712   d ,  712   e ,  712   f , and reference signal generators  714   a ,  714   b ,  714   c.  Dual directional couplers and fiber demodulators are well known to those having ordinary skill in the art, and therefore will not be described herein. However, it should be understood that the fiber demodulators  712   a ,  712   b ,  712   c ,  712   d ,  712   e ,  712   f  are generally configured for communicating signals V f-1 , V r-1 , V f-2 , V r-2 , V f-3 , V r-3  to the reference signal generators  714   a ,  714   b ,  714   c , respectively. It should be noted that the signals V f-1 , V r-1 , V f-2 , V r-2 , V f-3 , V r-3  are unique at each of the three (3) sensor  708   a ,  708   b ,  708   c  locations as they vary in phase and amplitude. 
     Each of the reference signal generators  714   a ,  714   b ,  714   c  is configured to generate a signal V doubled  using the received signals V f-1 , V r-1 , V f-2 , V r-2 , V f-3 , V r-3 , respectively. More particularly, each of the reference signal generators  714   a ,  714   b ,  714   c  is configured for computing a Sum signal S by adding the received signals V f-1 , V r-1 , V f-2 , V r-2 , V f-3 , V r-3  together. Each of the reference signal generators  714   a ,  714   b ,  714   c  is also configured for computing a Difference signal D by subtracting a second one of the received signals V r-1 , V r-2 , V r-3  from a first one of the received signals V f-1 , V f-2 , V f-3 . Each of the reference signal generators  714   a ,  714   b ,  714   c  is also configured for computing a first Exponentiation signal E S  using the Sum signal S and a second Exponentiation signal E D  using the Difference signal D. Each of the reference signal generators  714   a ,  714   b ,  714   c  is further configured for subtracting the first Exponentiation signal E S  from the second Exponentiation signal ED to obtain the reference signal V doubled . The reference signal generators  714   a ,  714   b ,  714   c  will be described in more detail below in relation to  FIG. 8 . 
     Referring now to  FIG. 8 , there is provided a more detailed block diagram of the reference signal generators  714   a.  Notably, the reference signal generators  714   b ,  714   c  are the same as or substantially similar to the reference signal generator  714   a.  As such, the following description of the reference signal generator  714   a  is sufficient for understanding the reference signal generators  714   b  and  714   c.    
     As shown in  FIG. 8 , the reference signal generator  714   a  comprises buffers  802   a ,  802   b , phase/amplitude trimmers  804   a ,  804   b ,  804   c ,  804   d,    180  degree hybrid couplers  806 ,  816 , analog multipliers  808   a ,  808   b , and a filter  810 . Buffers, phase/amplitude trimmers, and hybrid couplers are well known to those having ordinary skill in the art, and therefore will not be described herein. However, it should be understood that the hybrid coupler  806  generates signals representing the Sum signal S and the Difference signal D. The generated signals S and D are then communicated from the hybrid coupler  806  to the analog multipliers  808   a ,  808   b , respectively. Each of the analog multipliers  808   a ,  808   b  generates a respective Exponentiation signal E S , E D . The Exponentiation signals E S , E D  are communicated from the analog multipliers  808   a ,  808   b  to the hybrid coupler  816 . The hybrid coupler  816  performs a subtraction operation  214  (described above in relation to  FIG. 2 ) to obtain a signal V doubled . 
     Next, the signal V doubled  is further processed to eliminate undesired spurious signals. Accordingly, the signal V doubled  is forwarded from the hybrid coupler  816  to the filter  810 . The filter can include, but is not limited to, a bandpass filter. The filter  810  eliminates any unwanted signals generated in the analog multiplication process and leakage of the fundamental signals V f-1 , V r-1 . The output of the filter  810  is the reference signal V doubled  having twice the frequency of signals V f-1 , V r-1 . It should be noted that each of the signals V doubled  of  FIGS. 7-8  have the same phase. 
     Communication System Including A Reference Signal Generator 
       FIG. 9  shows an exemplary communication system  900  implementing the present invention. As shown in  FIG. 9 , the communication system  900  comprises a multi-element antenna system (MEAS)  950  for transmitting signals to and receiving signals from at least one object of interest  908  remotely located from the MEAS  950 . In  FIG. 9 , the object of interest  908  is shown as an airborne or spaceborne object, such as an aircraft, a spacecraft, a natural or artificial satellite, or a celestial object (e.g., a planet, a moon, an asteroid, a comet, etc . . . ). However, embodiments of the present invention are not limited in this regard. The MEAS  950  can also be used for transmitting and receiving signals from objects of interest  908  that are not airborne or spaceborne but are still remotely located with respect to MEAS  950 . For example, a ground-based MEAS  950  can be used to provide communications with objects of interest  908  at other ground-based or sea-based locations. The MEAS  950  can generally include an array control system (ACS)  902  for controlling the operation of multiple antenna elements  906   a ,  906   b ,  906   c.    
     In  FIG. 9 , the ACS  902  is shown as controlling the operation of antenna elements  906   a ,  906   b ,  906   c  and associated RF equipment  904   a ,  904   b ,  904   c.  The antenna elements  906   a ,  906   b ,  906   c  provide wireless communications. For example, if the MEAS  950  is in a transmit mode, then each antenna element  906   a ,  906   b ,  906   c  converts electrical signals into electromagnetic waves. The radiation pattern  911  resulting from the interference of the electromagnetic waves transmitted by the different antenna elements  906   a ,  906   b ,  906   c  can then be adjusted to a central beam  912  in the radiation pattern  911  aimed in the direction  916  of the object of interest  908 . The radiation pattern  911  of the antenna elements  906   a ,  906   b ,  906   c  also generates smaller side beams (or side lobes)  914  pointing in other directions with respect to the direction of the central beam  912 . However, because of the relative difference in magnitude between the side beams  914  and the central beam  912 , the radiation pattern  911  preferentially transmits the signal in the direction of the central beam  912 . Therefore, by varying the phases and the amplitudes of the signals transmitted by each antenna element  906   a ,  906   b ,  906   c , the magnitude and direction of the central beam  912  can be adjusted. If the MEAS  950  is in a receive mode, then each of the antenna elements  906   a ,  906   b ,  906   c  captures energy from passing waves propagated over transmission media (not shown) in the direction  920  and converts the captured energy to electrical signals. In the receive mode, the MEAS  950  can be configured to combine the electrical signals according to the radiation pattern  911  to improve reception from direction  920 , as described below. 
     In  FIG. 9 , the antenna elements  906   a ,  906   b ,  906   c  are shown as reflector-type (e.g., a dish) antenna elements, which generally allow adjustment of azimuth (or rotation) and elevation (angle with respect to a ground plane). Therefore, in addition to adjustment of phase and amplitude of the signal transmitted by each of the antenna elements  906   a ,  906   b ,  906   c , the azimuth and elevation of each antenna element  906   a ,  906   b ,  906   c  can also be used to further steer the central beam  912  and adjust the radiation pattern  911 . However, embodiments of the present invention are not limited on this regard. The antenna elements  906   a ,  906   b ,  906   c  can comprise directional or omni-directional antenna elements. 
     Although three (3) antenna elements  906   a ,  906   b ,  906   c  are shown in  FIG. 9 , the various embodiments of the present invention are not limited in this regard. Any number of antenna elements  906   a ,  906   b ,  906   c  can be used without limitation. Furthermore, the spacing between the antenna elements  906   a ,  906   b ,  906   c  with respect to each other is not limited. Accordingly, the antenna elements  906   a ,  906   b ,  906   c  can be widely spaced or closely spaced. However, as the spacing between the antenna elements  906   a ,  906   b ,  906   c  increases, the central beam  912  generally becomes narrower and the side beams (or side lobes)  914  generally become larger. The antenna elements  906   a ,  906   b ,  906   c  can also be regularly spaced (not shown) with respect to one another or arbitrarily spaced (or non-linearly spaced) with respect to one another (as shown in  FIG. 9 ) to form a three dimensional (3D) array of antenna elements. As shown in  FIG. 9 , the arbitrary spacing of the antenna elements  906   a ,  906   b ,  906   c  can include locations having different altitudes and locations having different distances between each other. 
     As shown in  FIG. 9 , each of the antenna elements  906   a ,  906   b ,  906   c  is communicatively coupled to a respective RF equipment  904   a ,  904   b ,  904   c  via a respective cable assembly  910   a ,  910   b ,  910   c  (collectively  910 ). Each of the cable assemblies  910   a ,  910   b ,  910   c  can have the same or different lengths. As used herein, the phrase “cable assemblies” refers to any number of cables provided or interconnecting two different components. In the various embodiments of the present invention, the cables in the cable assemblies  910   a ,  910   b ,  910   c  can be bundled or unbundled. 
     Notably, the cables  910   a ,  910   b ,  910   c  can delay transmit signals. In effect, the phases of the transmit signals can be shifted thereby resulting in phasing errors. As such, the communication system  900  implements a closed loop method to counteract phasing errors due to cable delay effects. The closed loop method will become more evident as the discussion progresses. 
     The RF equipment  904   a ,  904   b ,  904   c  control the antenna elements  906   a ,  906   b ,  906   c , respectively. For example, for the directional antenna elements  906   a ,  906   b ,  906   c  shown in  FIG. 9 , the RF equipment  904   a ,  904   b ,  904   c  can be configured to control antenna motors (not shown), antenna servo motors (not shown), and antenna rotators (not shown). The RF equipment  904   a ,  904   b ,  904   c  can also include hardware entities for processing transmit signals and receive signals. Notably, the phases of transmit signals can be shifted as a result of environmental effects on the cabling, antenna, and/or RF equipment  904   a ,  904   b ,  904   c.  These phase shifts can result in the steering of the radiated central beam  912  in a direction other than the direction  916  of the object of interest  908 . The RF equipment  904   a ,  904   b ,  904   c  will be described in more detail below in relation to  FIG. 10 . 
     As shown in  FIG. 9 , each of the RF equipment  904   a ,  904   b ,  904   c  is communicatively coupled to the ACS  902  via a respective communications link  918   a ,  918   b ,  918   c.  Generally, such communications links are provided via a cable assembly. However, embodiments of the present invention are not limited in this regard. In the various embodiments of the present invention, the communications links  918   a ,  918   b ,  918   c  can comprise wireline, optical, or wireless communication links. The cable assemblies for the communications links  918   a ,  918   b ,  918   c  can have the same or different lengths. Although the communications links  918   a ,  918   b ,  918   c  are shown to couple the RF equipment  904   a ,  904   b ,  904   c  to the ACS  902  in parallel, embodiments of the present invention are not limited in this regard. The RF equipment  904   a ,  904   b ,  904   c  can also be coupled to the ACS  902  in a series arrangement, such as that shown by communication links  919   a ,  919   b ,  919   c.    
     Notably, the cable assemblies of the communication links  918   a ,  918   b ,  918   c ,  919   a ,  919   b ,  919   c  can delay transmit signals. In effect, the phases of the transmit signals can be shifted thereby resulting in phasing errors. Additionally, the RF electronic components  904   a ,  904   b ,  904   c  used in the antennas (such as power amplifiers, filters and feed horns) may also introduce phase errors. All these errors are further subject to changes in phase due to operating environment and signal levels. As such, the communication system  900  implements a closed loop method to counteract phasing errors due to imperfect phase matching. The closed loop method will become more evident as the discussion progresses. 
     In operation, the ACS  902  modulates signals to be transmitted by the antenna elements  906   a ,  906   b ,  906   c.  The ACS  902  also demodulates signals received from other antenna systems. The ACS  902  further controls beam steering. Notably, the interconnecting cables, antenna elements  906   a ,  906   b ,  906   c , and RF equipment  904   a ,  904   b ,  904   c  can be affected by surrounding environmental conditions (e.g., heat). Such phase shifts can result in the steering of the radiated central beam  912  in a direction other than the direction  916  of the object of interest  908 . As such, the communication system  900  implements a closed loop method to counteract phasing errors due to environmental effects on ACS  902 . The closed loop method will become more evident as the discussion progresses. The ACS  902  will be described in more detail below in relation to  FIG. 10 . 
     In view of the forgoing, it should be appreciated that the cables  910   a ,  910   b ,  910   c  and the communications links  918   a ,  918   b ,  918   c  (or  919   a ,  919   b ,  919   c ) of the communication system  900  delay signals between the ACS  902  and the antenna elements  906   a ,  906   b ,  906   c.  In effect, the phases of the signals are shifted thereby resulting in phasing errors. Such errors are exacerbated by the spacing between the antenna elements  906   a ,  906   b ,  906   c.  Phasing errors further occur as a result of environmental effects on the hardware components  902 ,  904   a ,  904   b ,  904   c  of the communication system  900 . The accumulated phasing errors inhibit desirable or adequate beam formation, i.e., the accumulated phasing errors can result in the steering of the radiated central beam  912  in a direction other than the direction  916  of the object of interest  908 . 
     Accordingly, the communication system  900  is configured to adjust the phases and/or amplitudes of signals transmitted from and received at each antenna element  906   a ,  906   b ,  906   c  so as to counteract the errors in phasing. The phases and/or amplitudes of the transmit and receive signals can be adjusted using a reference signal V ref . This phase and/amplitude adjustment function of the communication system  900  will become more evident as the discussion progresses. 
     Referring now to  FIG. 10 , there is provided a more detailed block diagram of the communication system  900  that is useful for understanding the phase and/amplitude adjustment function thereof. Notably, the antenna elements  906   b ,  906   c  and RF equipment  904   b ,  904   c  are not shown in  FIG. 10  to simplify the following discussion. However, it should be understood that the antenna elements  906   b ,  906   c  are the same as or substantially similar to the antenna element  906   a.  Similarly, the RF equipment  904   b ,  904   c  is the same as or substantially similar to the RF equipment  906   a.    
     As shown in  FIG. 10 , the ACS  902  comprises a station frequency reference  1003 , a Transmit Radio Signal Generator (TRSG)  1004 , hardware entities  1006 , beamformers  1008 ,  1035 , a power coupler  1013 , a phase/amplitude controller  1010 , a phase comparator  1012   b , and a reference signal generator  1014   b.  Embodiments of the present invention are not limited in this regard. For example, the ACS  902  can include a set of components  1006 ,  1008 ,  1010 ,  1012   b ,  1013 ,  1014   b , and  1035  for each antenna element  906   a ,  906   b ,  906   c.  As also shown in  FIG. 10 , the RF equipment  904   a  comprises hardware entities  1042 , a high power amplifier (HPA)  1044 , a phase comparator  1012   a , and a reference signal generator  1014   a.  Embodiments of the present invention are not limited in this regard. For example, the RF equipment  904   a  can be absent of hardware entities  1042 . As also shown in  FIG. 10 , the antenna system  950  comprises a ½ transmit carrier frequency device  1015 , an analog fiber modulator  1017 , an optical fiber  1025 , and a fiber mirror  1023 . 
     The TRSG  1004  of the ACS  902  can generate signals to be transmitted from the antenna elements  906   a ,  906   b  (not shown),  906   c  (not shown). The TRSG  1004  is communicatively coupled to the station frequency reference  1003  and the hardware entities  1006 . The phrase “hardware entities”, as used herein, refers to signal processing devices, including but not limited to, filters and amplifiers. The hardware entities  1006  are communicatively coupled to the beamformer  1008 . 
     The beamformers  1008  can be utilized to control the phases and/or the amplitudes of transmit signals. In general, the phases and/or amplitudes of the transmit signal can be used to adjust formation of the central beam  912 , the side beams (or side lobes)  914 , and nulls in the radiation pattern  911 . Nulls correspond to directions in which destructive interference results in a transmit signal&#39;s strength that is significantly reduced with respect to the directions of the central beam  912  and the side beams  914 . The beamformer  1008  combines a complex weight w N  with transmit signals to be provided to the RF equipment  904   a ,  904   b  (not shown),  904   c  (not shown). 
     The beamformer  1008  is communicatively coupled to power coupler  1013 . The power coupler  1013  is communicatively coupled to the closed loop operator  1098 . The closed loop operator  1098  will be described below. However, it should be understood that the closed loop operator  1098  is generally configured to adjust the phase and/or amplitude of transmit signals and communicate the phase and/or amplitude adjusted transmit signals to the hardware entities  1042  of the RF equipment  904   a  to be provided the weighted transmit signals. The hardware entities  1042  are communicatively coupled to the HPA  1044 . HPAs are well known to those having ordinary skill in the art, and therefore will not be described herein. However, it should be understood that the HPA  1044  communicates signals to the antenna element  906   a  for transmission therefrom. 
     The closed loop operator  1098  is generally configured for controlling the phases and/or amplitudes of transmit signals so as to counteract phasing errors due to cable delay effects, wide antenna spacing effects, and environmental effects on hardware components  902  and  904   a  of the communication system  900 . Accordingly, the closed loop operator  1098  includes the phase comparators  1012   a ,  1012   b , the phase/amplitude controller  1010 , and the beamformer  1035 . 
     The phase comparator  1012   a  is configured to receive a transmit signal  1060  from the antenna element  906   a  and a reference signal V ref-1  from a reference signal generator  1014   a.  In this regard, it should be understood that the antenna element  906   a  has a transmit (Tx) signal probe  1028  disposed thereon for sensing the transmit signal  1060 . At the phase comparator  1012   a , the phase of the sensed transmit signal  1060  is compared with the phase of the reference signal V ref-1  to determine a phase offset  1070 . The phase offset  1070  can be represented in terms of an imaginary part Q and a real part I. The phase offset  1070  is then communicated from the phase comparator  1012   a  to the phase/amplitude controller  1010 . 
     The reference signal V ref-1  utilized by the phase comparator  1012   a  is generated by the reference signal generator  1014   a.  The reference signal generator  1014   a  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) dispose on the optical fiber  1025  at a first location. Additionally or alternatively, the reference signal generator  1014   a  is configured to sense signals V f , V r  propagated along the optical fiber  1025 . The sensed signals V f , V r  are used to determine the reference signal V ref-1 . The manner in which the reference signal V ref-1  is determined is described above in relation to  FIGS. 1-3 . The reference signal generator  1014   a  can be the same as or substantially similar to any one of the reference signal generator shown in  FIGS. 4-8 . 
     The phase comparator  1012   b  is configured to receive a transmit signal  1050  from the power coupler  1013  and a reference signal V ref-2  from a reference signal generator  1014   b.  At the phase comparator  1012   b , the phase of the transmit signal  1050  is compared with the phase of the reference signal V ref-2  to determine a phase offset  1016 . The phase offset  1016  can be represented in terms of an imaginary part Q and a real part I. The phase offset  1016  is then communicated from the phase comparator  1012   b  to the phase/amplitude controller  1010 . 
     The reference signal V ref-2  utilized by the phase comparator  1012   b  is generated by the reference signal generator  1014   b.  The reference signal generator  1014   b  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) disposed on the optical fiber  1025  at a second location different from the first location. Additionally or alternatively, the reference signal generator  1014   b  is configured to sense signals V f , V r  propagated along the optical fiber  1025 . The sensed signals V f , V r  are used by the reference signal generator  1014   b  to determine the reference signal V ref-2 . The manner in which the reference signal V ref-2  is determined is described above in relation to  FIGS. 1-3 . The reference signal generator  1014   b  can be the same as or substantially similar to any one of the reference signal generator shown in  FIGS. 4-8 . The reference signal generator  1014   b  can also be the same as or substantially similar to the reference signal generator  1014   a.    
     The phase/amplitude controller  1010  determines the phase and/or amplitude adjustment value Δw N  that is to be used by the beamformer  1035  to adjust the phase and/or amplitude of transmit signals. The phase and/or amplitude adjustment value Δw N  is determined using the received phase offset  1016 ,  1070  values received from the phase comparators  1012   a ,  1012   b , respectively. 
       FIG. 11  is a schematic diagram of a computer system  1100  for executing a set of instructions that, when executed, can cause the computer system to perform one or more of the methodologies and procedures described above. For example, a computer system  1100  can be implemented to perform the various tasks of the systems  100 ,  400 ,  500 ,  600 ,  700 , and  900 . In some embodiments, the computer system  1100  operates as a single standalone device. In other embodiments, the computer system  1100  can be connected (e.g., using a network) to other computing devices to perform various tasks in a distributed fashion. In a networked deployment, the computer system  1100  can operate in the capacity of a server or a client developer machine in server-client developer network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. 
     The computer system  1100  can comprise various types of computing systems and devices, including a server computer, a client user computer, a personal computer (PC), a tablet PC, a laptop computer, a desktop computer, a control system, a network router, switch or bridge, or any other device capable of executing a set of instructions (sequential or otherwise) that specifies actions to be taken by that device. It is to be understood that a device of the present disclosure also includes any electronic device that provides voice, video or data communication. Further, while a single computer is illustrated, the phrase “computer system” shall be understood to include any collection of computing devices that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. 
     The computer system  1100  can include a processor  1102  (such as a central processing unit (CPU), a graphics processing unit (GPU, or both), a main memory  1104  and a static memory  1106 , which communicate with each other via a bus  1108 . The computer system  1100  can further include a display unit  1110 , such as a video display (e.g., a liquid crystal display or LCD), a flat panel, a solid state display, or a cathode ray tube (CRT)). The computer system  1100  can include an input device  1112  (e.g., a keyboard), a cursor control device  1114  (e.g., a mouse), a disk drive unit  1116 , a signal generation device  1118  (e.g., a speaker or remote control) and a network interface device  1120 . 
     The disk drive unit  1116  can include a computer-readable storage medium  1122  on which is stored one or more sets of instructions  1124  (e.g., software code) configured to implement one or more of the methodologies, procedures, or functions described herein. The instructions  1124  can also reside, completely or at least partially, within the main memory  1104 , the static memory  1106 , and/or within the processor  1102  during execution thereof by the computer system  1100 . The main memory  1104  and the processor  1102  also can constitute machine-readable media. 
     Dedicated hardware implementations including, but not limited to, application-specific integrated circuits, programmable logic arrays, and other hardware devices can likewise be constructed to implement the methods described herein. Applications that can include the apparatus and systems of various embodiments broadly include a variety of electronic and computer systems. Some embodiments implement functions in two or more specific interconnected hardware modules or devices with related control and data signals communicated between and through the modules, or as portions of an application-specific integrated circuit. Thus, the exemplary system is applicable to software, firmware, and hardware implementations. 
     In accordance with various embodiments of the present disclosure, the methods described herein can be stored as software programs in a computer-readable storage medium and can be configured for running on a computer processor. Furthermore, software implementations can include, but are not limited to, distributed processing, component/object distributed processing, parallel processing, virtual machine processing, which can also be constructed to implement the methods described herein. 
     The present disclosure contemplates a computer-readable storage medium containing instructions  1124  or that receives and executes instructions  1124  from a propagated signal so that a device connected to a network environment  1126  can send or receive voice and/or video data, and that can communicate over the network  1126  using the instructions  1124 . The instructions  1124  can further be transmitted or received over a network  1126  via the network interface device  1120 . 
     While the computer-readable storage medium  1122  is shown in an exemplary embodiment to be a single storage medium, the term “computer-readable storage medium” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more sets of instructions. The term “computer-readable storage medium” shall also be taken to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure. 
     The term “computer-readable medium” shall accordingly be taken to include, but not be limited to, solid-state memories such as a memory card or other package that houses one or more read-only (non-volatile) memories, random access memories, or other re-writable (volatile) memories; magneto-optical or optical medium such as a disk or tape; as well as carrier wave signals such as a signal embodying computer instructions in a transmission medium; and/or a digital file attachment to e-mail or other self-contained information archive or set of archives considered to be a distribution medium equivalent to a tangible storage medium. Accordingly, the disclosure is considered to include any one or more of a computer-readable medium or a distribution medium, as listed herein and to include recognized equivalents and successor media, in which the software implementations herein are stored. 
     Although the present specification describes components and functions implemented in the embodiments with reference to particular standards and protocols, the disclosure is not limited to such standards and protocols. Each of the standards for Internet and other packet switched network transmission (e.g., TCP/IP, UDP/IP, HTML, and HTTP) represent examples of the state of the art. Such standards are periodically superseded by faster or more efficient equivalents having essentially the same functions. Accordingly, replacement standards and protocols having the same functions are considered equivalents. 
     In light of the forgoing description of the invention, it should be recognized that the present invention can be realized in hardware, software, or a combination of hardware and software. A method for determining a reference signal V ref  according to the present invention can be realized in a centralized fashion in one processing system, or in a distributed fashion where different elements are spread across several interconnected processing systems. Any kind of computer system, or other apparatus adapted for carrying out the methods described herein, is suited. A typical combination of hardware and software could be a general purpose computer processor, with a computer program that, when being loaded and executed, controls the computer processor such that it carries out the methods described herein. Of course, an application specific integrated circuit (ASIC), and/or a field programmable gate array (FPGA) could also be used to achieve a similar result. 
     Applicants present certain theoretical aspects above that are believed to be accurate that appear to explain observations made regarding embodiments of the present invention. However, embodiments of the present invention may be practiced without the theoretical aspects presented. Moreover, the theoretical aspects are presented with the understanding that Applicants do not seek to be bound by the theory presented. 
     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. Numerous changes to the disclosed embodiments can be made in accordance with the disclosure herein without departing from the spirit or scope of the invention. Thus, the breadth and scope of the present invention should not be limited by any of the above described embodiments. Rather, the scope of the invention should be defined in accordance with the following claims and their equivalents. 
     Although the invention has been illustrated and described with respect to one or more implementations, equivalent alterations and modifications will occur to others having ordinary skill in the art upon the reading and understanding of this specification and the annexed drawings. In addition, while a particular feature of the present invention may have been disclosed with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Furthermore, to the extent that the terms “including”, “includes”, “having”, “has”, “with”, or variants thereof are used in either the detailed description and/or the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.