Patent Publication Number: US-2010123618-A1

Title: Closed loop phase control between distant points

Description:
BACKGROUND OF THE INVENTION 
     1. Statement of the Technical Field 
     The invention concerns communication systems. More particularly, the invention concerns communication systems and methods for controlling the phase between distant points using a closed loop configuration. 
     2. Description of the Related Art 
     Multiple element antenna arrays are widely used in wireless communications systems to enhance the transmission and reception of signals. In particular, the enhanced performance is generally provided by using such antenna arrays in conjunction with beamforming techniques. In conventional beamforming, the naturally occurring interference between the different antenna elements in the antenna array is typically used to change the overall directionality for the array. For example, during transmission, the phase and relative amplitude of the transmitted signal at each antenna element is adjusted, in order to create a desired pattern of constructive and destructive interferences at the wavefront of the transmitted signal. During signal reception, the different antenna elements are modified in phase and amplitude in such a way that a pre-defined pattern of radiation is preferentially observed by the antenna elements. 
     In general, such antenna arrays typically include a system controller, a plurality of antenna controllers, and a plurality of antenna elements (e.g., dish antennas). Each of the antenna elements is communicatively coupled to the system controller and a respective one of the antenna controllers via cables. During transmission and reception, each antenna element converts electrical signals into electromagnetic waves, and vice versa. The system controller, using conventional beamforming techniques, varies the configuration of the various components in the antenna array to provide a particular radiation pattern during transmission or reception. However, as the dimensions of the array, the number of antenna elements, and the precision required in certain beamforming application increase, properly concerting the actions of the various components becomes more difficult. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention concern methods for compensating for phase shifts of a communication signal. The methods involve determining a first reference signal at a first location along a transmission path and a second reference signal at a second location along the transmission path. The second reference signal is the same as the first reference signal. The methods also involve determining at the first location a first phase offset using the first reference signal and a first communication signal. A second phase offset is determined at the second location using the second reference signal and a second communication signal. A phase of a third communication signal is adjusted at the second location using the first and second phase offsets to obtain a modified communication signal. More particularly, a weight is computed at the second location using the first and second phase offsets. The weight is then combined with the third communication signal to obtain the modified communication signal. The first, second, and third communication signals are the same communication signal obtained at different locations along the transmission path. 
     According to an aspect of the invention, the first reference signal is determined by sensing at the first location a transmit signal propagated over a transmission media in a forward direction and a reverse signal propagated over the transmission media in a reverse direction opposed from the forward direction. The reverse signal being a reflected version of the transmit signal. A first sum signal is computed by adding the transmit and reverse signals together. A first difference signal is computed by subtracting the reverse signal from the transmit signal. Thereafter, a first exponentiation signal is determined using the first sum signal and a second exponentiation signal is determined using the first difference signal. The first exponentiation signal is subtracted from the second exponentiation signal to obtain the first reference signal. The first reference signal can have a first frequency equal to a second frequency of the transmit signal. Alternatively, the first reference signal can have a first frequency different than a second frequency of the transmit signal. In such a scenario, the first reference signal can be processed to obtain an adjusted reference signal with a third frequency equal to the second frequency of the transmit signal. 
     The second reference signal is determined by sensing at the second location the transmit and reverse signals. Thereafter, the second reference signal is determined using the transmit and reverse signals sensed at the second location. More particularly, the second reference signal is determined by computing a second sum signal by adding the transmit and reverse signals sensed at the second location together and a second difference signal by subtracting the reverse signal sensed at the second location from the transmit signal sensed at the second location. A third exponentiation signal is determined using the second sum signal and a fourth exponentiation signal using the second difference signal. The third exponentiation signal is subtracted from the fourth exponentiation signal to obtain the second reference signal. 
     Embodiments of the present invention also relate to methods for compensating for phase shifts of received communication signals. The methods generally involve determining a third reference signal at a third location along the transmission path and a fourth reference signal at a fourth location along the transmission path. At the third location, the communication signal is combined with the third reference signal to obtain a modified received communication signal. At the fourth location, a third phase offset is determined using the modified received communication signal and the fourth reference signal. Thereafter, a phase of the modified received communication signal is adjusted using the third phase offset to obtain a phase adjusted received signal. 
     Embodiments of the present invention further relate to systems implementing at least one of the above described methods. The systems generally include at least one reference signal generator and at least one closed loop operator communicatively coupled to the reference signal generator. The reference signal generator is configured for determining the first reference signal at the first location along a transmission path and the second reference signal at the second location along the transmission path. The closed loop operator is configured for determining at the first location the first phase offset using the first reference signal and the first communication signal. The closed loop operator is also configured for determining at the second location the second phase offset using the second reference signal and the second communication signal. The closed loop operator is further configured for adjusting at the first location the phase of a third communication signal using the first and second phase offsets to obtain the modified communication 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 schematic illustration of an exemplary communications system configured according to an embodiment of the present invention. 
         FIG. 2  is a block diagram of the antenna control system shown in  FIG. 1 . 
         FIG. 3  is a block diagram of the transmit side of the antenna control system shown in  FIGS. 1-2  communicatively coupled to the RF equipment shown in  FIG. 1 . 
         FIG. 4  is a more detailed block diagram of the phase comparator of  FIG. 3 . 
         FIG. 5  is a block diagram of the receive side of the antenna control system shown in  FIGS. 1-2  communicatively coupled to the RF equipment shown in  FIG. 1 . 
         FIG. 6A  is a more detailed block diagram of the communication system of  FIG. 1  that is useful for understanding the phase and/or amplitude adjustment functions thereof. 
         FIG. 6B  is a more detailed block diagram of the communication system of  FIG. 1  that is useful for understanding the phase and/or amplitude adjustment functions thereof. 
         FIG. 7  is a more detailed block diagram of the communication system of  FIG. 1  that is useful for understanding the phase and/or amplitude adjustment functions thereof. 
         FIG. 8  is a schematic view of a computer system within which a set of instructions operate according to an embodiment of the present invention. 
         FIG. 9  is a block diagram of a communication system that is useful for understanding how a reference signal is determined. 
         FIG. 10  is a conceptual diagram of a first method embodiment for determining a reference signal that is useful for understanding the present invention. 
         FIG. 11  is a conceptual diagram of a second method embodiment for determining a reference signal that is useful for understanding the present invention. 
         FIG. 12  is a block diagram of a first system embodiment implementing a method of  FIGS. 10 and 11 . 
         FIG. 13  is a block diagram of a second system embodiment implementing the method of  FIG. 10 . 
         FIG. 14  is a block diagram of a third system embodiment implementing the method of  FIG. 10 . 
     
    
    
     DETAILED DESCRIPTION 
     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 operation 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. 
     In conventional multi-beam antenna systems, the phases of the signals to be transmitted from the antenna elements can be shifted as a result of environmental effects on hardware components of the system including the antenna, Radio Frequency (RF) components and the cables connecting the antenna elements to the controllers. These phase shifts typically result in the steering of the radiated main beam in the wrong direction. 
     To overcome the various limitations of the conventional multi-beam antenna systems, embodiments of the present invention provide systems implementing an improved beam forming solution. The improved beam forming solution is facilitated by novel methods for determining a reference signal at any location along a transmission media. The methods generally involve determining a first reference signal at a first location along a transmission path and a second reference signal at a second location along the transmission path. The second reference signal must be substantially the same as the first reference signal. At the first location, the first reference signal is combined with a communications signal to obtain a first phase adjusted signal. At the second location, a phase offset is determined using the second reference signal and the first phase adjusted signal. The phase of the first phase adjusted signal is subsequently adjusted using the phase offset to obtain a modified communications signal. 
     Before describing the systems and methods of the present invention, it will be helpful in understanding an exemplary environment 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 phases of transmit signals need to be adjusted so as to counteract the environmental effects on hardware components of communication systems. Such applications include, but are not limited to, mobile/cellular telephone applications, military communication applications, and space communication applications. Accordingly, the present invention will be described in relation to space communication 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. 
     Communication System Architecture 
       FIG. 1  shows an exemplary communication system  100  according to an embodiment of the present invention. As shown in  FIG. 1 , the communication system  100  comprises a multi-element antenna system (MEAS)  150  for transmitting signals to and receiving signals from at least one object of interest  108  remotely located from the MEAS  150 . In  FIG. 1 , the object of interest  108  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  150  can also be used for transmitting and receiving signals from objects of interest  108  that are not airborne or spaceborne but are still remotely located with respect to MEAS  150 . For example, a ground-based MEAS  150  can be used to provide communications with objects of interest  108  at other ground-based or sea-based locations. 
     In  FIG. 1 , the ACS  102  is shown as controlling the operation of antenna elements  106   a,    106   b,    106   c  and associated RF equipment  104   a,    104   b,    104   c.  The antenna elements  106   a,    106   b,    106   c  provide wireless communications. For example, if the MEAS  150  is in a transmit mode, then each antenna element  106   a,    106   b,    106   c  converts electrical signals into electromagnetic waves. The radiation pattern  111  resulting from the interference of the electromagnetic waves transmitted by the different antenna elements  106   a,    106   b,    106   c  can then be adjusted to a central beam  112  in the radiation pattern  111  aimed in the direction  116  of the object of interest  108 . The radiation pattern  111  of the antenna elements  106   a,    106   b,    106   c  also generates smaller side beams (or side lobes)  114  pointing in other directions with respect to the direction of the central beam  112 . However, because of the relative difference in magnitude between the side beams  114  and the central beam  112 , the radiation pattern  111  preferentially transmits the signal in the direction of the central beam  112 . Therefore, by varying the phases and the amplitudes of the signals transmitted by each antenna element  106   a,    106   b,    106   c,  the magnitude and direction of the central beam  112  can be adjusted. If the MEAS  150  is in a receive mode, then each of the antenna elements  106   a,    106   b,    106   c  captures energy from passing waves propagated over transmission media (not shown) in the direction  120  and converts the captured energy to electrical signals. In the receive mode, the MEAS  150  can be configured to combine the electrical signals according to the radiation pattern  111  to improve reception from direction  120 , as described below. 
     In  FIG. 1 , the antenna elements  106   a,    106   b,    106   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  106   a,    106   b,    106   c,  the azimuth and elevation of each antenna element  106   a,    106   b,    106   c  can also be used to further steer the central beam  112  and adjust the radiation pattern  111 . However, embodiments of the present invention are not limited on this regard. The antenna elements  106   a,    106   b,    106   c  can comprise directional or omni-directional antenna elements. 
     Although three (3) antenna elements  106   a,    106   b,    106   c  are shown in  FIG. 1 , the various embodiments of the present invention are not limited in this regard. Any number of antenna elements  106   a,    106   b,    106   c  can be used without limitation. Furthermore, the spacing between the antenna elements  106   a,    106   b,    106   c  with respect to each other is not limited. Accordingly, the antenna elements  106   a,    106   b,    106   c  can be widely spaced or closely spaced. However, as the spacing between the antenna elements  106   a,    106   b,    106   c  increases, the central beam  112  generally becomes narrower and the side beams (or side lobes)  114  generally become larger. The antenna elements  106   a,    106   b,    106   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. 1 ) to form a three dimensional (3D) array of antenna elements. As shown in  FIG. 1 , the arbitrary spacing of the antenna elements  106   a,    106   b,    106   c  can include locations having different altitudes and locations having different distances between each other. 
     As shown in  FIG. 1 , each of the antenna elements  106   a,    106   b,    106   c  is communicatively coupled to a respective RF equipment  104   a,    104   b,    104   c  via a respective cable assembly  110   a,    110   b,    110   c  (collectively  110 ). Each of the cable assemblies  110   a,    110   b,    110   c  can have the same or different lengths. As used herein, the phrase “cable assembly” 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  110   a,    110   b,    110   c  can be bundled or unbundled. 
     Notably, the cables  110   a,    110   b,    110   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  100  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  104   a,    104   b,    104   c  control the antenna elements  106   a,    106   b,    106   c,  respectively. For example, for the directional antenna elements  106   a,    106   b,    106   c  shown in  FIG. 1 , the RF equipment  104   a,    104   b,    104   c  are configured to control antenna motors (not shown), antenna servo motors (not shown), and antenna rotators (not shown). The RF equipment  104   a,    104   b,    104   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  104   a,    104   b,    104   c.  These phase shifts can result in the steering of the radiated central beam  112  in a direction other than the direction  116  of the object of interest  108 . The RF equipment  104   a,    104   b,    104   c  will be described in more detail below in relation to  FIGS. 3 and 5 . 
     As shown in  FIG. 1 , each of the RF equipment  104   a,    104   b,    104   c  is communicatively coupled to the ACS  102  via a respective communications link  118   a,    118   b,    118   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  118   a,    118   b,    118   c  can comprise wireline, optical, or wireless communication links. The cable assemblies for the communications links  118   a,    118   b,    118   c  can have the same or different lengths. Although the communications links  118   a,    118   b,    118   c  are shown to couple the RF equipment  104   a,    104   b,    104   c  to the ACS  102  in parallel, embodiments of the present invention are not limited in this regard. The RF equipment  104   a,    104   b,    104   c  can also be coupled to the ACS  102  in a series arrangement, such as that shown by communication links  119   a,    119   b,    119   c.    
     Notably, the cable assemblies of the communication links  118   a,    118   b,    118   c,    119   a,    119   b,    119   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  100  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. 
     In operation, the ACS  102  modulates signals to be transmitted by the antenna elements  106   a,    106   b,    106   c.  The ACS  102  also demodulates signals received after beamforming. The ACS  102  further controls beam steering. Notably, the interconnecting cables and/or elements can be affected by surrounding environmental conditions (e.g., heat). Such phase shifts can result in the steering of the radiated central beam  112  in a direction other than the direction  116  of the object of interest  108 . As such, the communication system  100  implements a closed loop method to counteract phasing errors due to environmental effects on ACS  102 . The closed loop method will become more evident as the discussion progresses. The ACS  102  will be described in more detail below in relation to  FIGS. 2-3  and  5 . 
     Referring now to  FIG. 2 , there is provided a block diagram of the ACS  102  shown in  FIG. 1 . As shown in  FIG. 2 , the ACS  102  includes a transmit side  202  and a receive side  204 . Furthermore, the ACS  102  is configured to manage both transmission and reception operations of the MEAS  150  based on signals for transmission and control signals. In particular, the transmit side  202  can generate signals to be transmitted by the antenna elements  106   a,    106   b,    106   c.  Additionally or alternatively, the transmit side  202  can receive one or more signals from one or more signal generators (not shown). The transmit side  202  is also configured for modulating each of the generated or received signals and communicating the modulated signals to the RF equipment  104   a,    104   b,    104   c  for transmission of the same over a transmission media (not shown). The transmit side  202  will be described in more detail below in relation to  FIG. 3 . 
     The receive side  204  is configured for receiving signals received by the transmission elements. The receive side  204  is also configured for demodulating the electrical signal and communicating the demodulated electrical signal to an output device (not shown). The receive side  204  will be described below in more detail in relation to  FIG. 5 . 
     Although the transmit side  202  and receive side  204  can operate separately or independently in some embodiments of the present invention, in other embodiments, operation of the transmit side  202  can be further adjusted based on one or more signals generated in the receiver side  204  of the ACS  102 , as shown in  FIG. 2 . 
     Referring now to  FIG. 3 , there is provided a block diagram of the transmit side  202  of  FIG. 2  communicatively coupled to the RF equipment  104   a,    104   b,    104   c  of  FIG. 1 . As shown in  FIG. 3 , the transmit side  202  is comprised of a Transmit Radio Signal Generator (TRSG)  302 , hardware entities  304   a,    304   b,    304   c,  beamformers  308   a,    308   b,    308   c,    395   a,    395   b,    395   c,  phase/amplitude controllers  326   a,    326   b,    326   c,  and phase comparators  340   a,    340   b,    340   c.  Each RF equipment  104   a,    104   b,    104   c  comprises hardware entities  328   a,    328   b,    328   c,  high power amplifiers (HPAs)  330   a,    330   b,    330   c,  and phase comparators  332   a,    332   b,    332   c.    
     The TRSG  302  of the transmit side  202  can generate signals to be transmitted from the array of antenna elements  106   a,    106   b,    106   c.  The TRSG  302  is communicatively coupled to the hardware entities  304   a,    304   b,    304   c.  The phrase “hardware entities”, as used herein, refers to signal processing devices, including but not limited to, filters and amplifiers. Each of the hardware entities  304   a,    304   b,    304   c  is communicatively coupled to a respective one of the beamformers  308   a,    308   b,    308   c.    
     Each of the beamformers  308   a,    308   b,    308   c  can be utilized to control the phase and/or the amplitude of transmit signals. In general, the phase and/or amplitude of the transmit signal can be used to adjust formation of the central beam  112 , the side beams (or side lobes)  114 , and nulls in the radiation pattern  111 . 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  112  and the side beams  114 . The combined amplitude a 1 , a 2 , a 3  and phase shift φ 1 , φ 2 , φ 3  is referred to herein as a complex weight w 1 , w 2 , w 3 , respectively. Each of the beamformers  308   a,    308   b,    308   c  combines a respective complex weight w 1 , w 2 , w 3  with the transmit signals to be provided to a respective RF equipment  104   a,    104   b,    104   c.  For example, as shown in  FIG. 3 , each beamformer  308   a,    308   b,    308   c  includes a respective amplitude adjuster  310   a,    310   b,    310   c  for adjusting the amplitude of the transmit signals from respective hardware entities  304   a,    304   b,    304   c  based on an amplitude a 1 , a 2 , a 3 . Each beamformer  308   a,    308   b,    308   c  includes a respective phase adjuster  312   a,    312   b,    312   c  for adjusting the phases of transmit signals from respective hardware entities  304   a,    304   b,    304   c  based on a phase shift φ 1 , φ 2 , φ 3 . 
     Each beamformer  308   a,    308   b,    308   c  is communicatively coupled to a respective closed loop operator  350   a,    350   b,    350   c.  The closed loop operators  350   a,    350   b,    350   c  will be described below. However, it should be understood that the closed loop operators  350   a,    350   b,    350   c  are 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 entity  328   a,    328   b,    328   c  of the RF equipment  104   a,    104   b,    104   c.  The hardware entities  328   a,    328   b,    328   c  are communicatively coupled to a respective HPA  330   a,    330   b,    330   c.  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 HPAs  330   a,    330   b,    330   c  communicate signals to the antenna elements  106   a,    106   b,    106   c  for transmission therefrom in the direction  116  of an object of interest  108 . 
     Each closed loop operator  350   a,    350   b,    350   c  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  102 ,  104   a,    104   b,    104   c  of a communication system  100 . Accordingly, each closed loop operator  350   a,    350   b,    350   c  includes a phase comparator  332   a,    332   b,    332   c,  a phase comparator  340   a,    340   b,    340   c,  a phase/amplitude controller  326   a,    326   b,    326   c,  and a beamformer  395   a,    395   b,    396   c.    
     The phase comparator  332   a,    332   b,    332   c  is configured to receive a transmit signal from the antenna element  106   a  and a reference signal V ref  from a first reference signal generator (not shown). In this regard, it should be understood that each of the antenna elements  106   a,    106   b,    106   c  has a transmit (Tx) signal sensor disposed thereon for sensing the transmit signal. Each of the antenna elements  106   a,    106   b,    106   c  also has a reference radiator disposed thereon for sensing a receive signal. A schematic illustration of the antenna element  106   a  having a transmit (Tx) signal sensor  608  positioned on its reflector  604  is provided in  FIG. 6 . It should be noted that a sensing location on the reflector  604  enables signal path phase compensation over a maximum extent of components subject to variation. However in some applications, the sensing location may, for operational convenience, reside instead within the feed or on a transmission line leading to the feed. The result of such a sensing location is the exclusion of the omitted components from closed loop phase compensation. The first reference signal generator (not shown) and the manner in which the reference signal V ref  is determined will be described below in relation to  FIGS. 9-14 . 
     Subsequent to receiving the transmit signal and the reference signal V ref , the phase comparator  332   a,    332   b,    332   c  performs a comparison operation to determine a phase offset between the signals. The phase offset can be represented in terms of an imaginary part Q and a real part I. After determining the phase offset, the phase comparator  332   a,    332   b,    332   c  communicates the phase offset value(s) to the phase/amplitude controller  326   a,    326   b,    326   c.  The phase comparators  332   a,    332   b,    332   c  will be described in more detail below in relation to  FIG. 4 . 
     The phase comparator  340   a,    340   b,    340   c  is configured to receive a transmit signal from the beamformer  308   a,    308   b,    308   c.  The phase comparator  340   a,    340   b,    340   c  is also configured to receive a reference signal V ref  from a second reference signal generator (not shown). The manner in which the reference signal V ref  is determined will be described below in relation to  FIGS. 9-14 . 
     The second reference signal generator (not shown) is the same as or substantially similar to the first reference signal generator (not shown) that provided the reference signal V ref  to the phase comparator  332   a,    332   b,    332   c.  However, the first and second signal generators (not shown) are positioned at different locations within the communication system  100 . For example, the first signal generator (not shown) can reside in the RF equipment  104   a,    104   b,    104   c.  In contrast, the second signal generator (not shown) can reside in the transmit side  202  of the ACS  102 . The first and second reference signal generators (not shown) will be described below in relation to  FIGS. 9-14 . 
     After receiving the transmit signal and the reference signal V ref , the phase comparator  340   a,    340   b,    340   c  performs a comparison operation to determine a phase offset between the signals. The phase offset can be represented in terms of an imaginary part Q and a real part I. The phase comparators  340   a,    340   b,    340   c  will be described in more detail below in relation to  FIG. 4 . 
     The phase/amplitude controller  326   a,    326   b,    326   c  determines a phase and/or amplitude adjustment value Δw 1 , Δw 2 , Δw 3  that is to be used by a beamformer  395   a,    395   b,    395   c  to control the phase and/or amplitude of transmit signals. The phase and/or amplitude adjustment value Δw 1 , Δw 2 , Δw 3  is determined using the phase offset values received from the phase comparators  332   a,    332   b,    332   c,    340   a,    340   b,    340   c.    
     Referring now to  FIG. 4 , there is provided a detailed block diagram of the phase comparator  332   a.  Each of the phase comparators  332   b,    332   c,    340   a,    340   b,    340   c  is the same as or substantially similar to the phase comparator  332   a.  As such, the following description of the phase comparator  332   a  is sufficient for understanding the phase comparators  332   b,    332   c,    340   a,    340   b,    340   c.    
     As shown in  FIG. 4 , the phase comparator  332   a  comprises a balanced phase detector  402 , operational amplifiers (or comparators)  404   a,    404   b,  low power filters (LPFs)  406   a,    406   b,  and analog to digital converters (ADC)  408   a,    408   b.  The balanced phase detector  402  is configured to receive a transmit signal from the antenna element  106   a  and a reference signal V ref  from a reference signal generator (not shown in  FIG. 4  and will be described below in relation to  FIGS. 8-13 ). The balanced phase detector  402  is also configured to generate a +SIN output, a −SIN output, a +COS output, and a −COS output using the received signals. The SIN outputs represent the real parts I of the phases of the signals. In contrast, the COS outputs represent the imaginary parts Q of the phases of the signals. The SIN outputs are communicated from the balanced phase detector  402  to the operational amplifier (or comparator)  404   a.  Similarly, the COS outputs are communicated from the balanced phase detector  402  to the operational amplifier (or comparator)  404   b.    
     Operational amplifiers (or comparators) 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 operational amplifiers (or comparators)  404   a,    404   b  compares the values of the signals received from the balanced phase detector  402 . Each of the operational amplifiers (or comparators)  404   a,    404   b  also outputs an analog signal and communicates the same to the LPFs  406   a,    406   b,  respectively. After performing filtering operations, the LPFs  406   a,    406   b  forward the filtered analog signals to the ADCs  408   a,    408   b.  The ADCs  408   a,    408   b  convert the filtered analog signals to digital signals. The output of ADC  408   a  represents a real part I of a phase offset value. The output of ADC  408   b  represents an imaginary part Q of the phase offset value. 
     Referring now to  FIG. 5 , there is provided a block diagram of the receive side  204  of  FIG. 2  communicatively coupled to the RF equipment  104   a,    104   b,    104   c  of  FIG. 1 . As shown in  FIG. 5 , each of the RF equipment  104   a,    104   b,    104   c  further comprises a Radio Frequency (RF) translator  502   a,    502   b,    502   c,  a Low Noise Amplifier (LNA)  532   a,    532   b,    532   c,  and a portion of a closed loop operator  550   a,    550   b,    550   c.  The portion of a closed loop operator  550   a,    550   b,    550   c  includes a signal adder  530   a,    530   b,    530   c.  Each of the RF translators  502   a,    502   b,    502   c  performs signal frequency translation of received signals from a respective antenna element  106   a,    106   b,    106   c  in the respective RF equipment  104   a,    104   b,    104   c.  The translation function of the RF translators  502   a,    502   b,    502   c  generally converts the received signal at a respective antenna element  106   a,    106   b,    106   c  from an RF to an intermediate frequency (IF). The RF translators  502   a,    502   b,    502   c  communicate the IF signals to the signal adders  530   a,    530   b,    530   c,  respectively. 
     At the signal adders  530   a,    530   b,    530   c,  the IF signals are combined with a reference signal V ref  or a spread reference signal (not shown) generated using the reference signal V ref . The reference signals V ref  can be generated by reference signal generators (not shown). The reference signal generator (not shown) will be described below in relation to  FIGS. 8-13 . The combined signals (or spread spectrum signals) formed at the signal adders  530   a,    530   b,    530   c  are then communicated to the LNAs  532   a,    532   b,    532   c,  respectively. The LNAs  532   a,    532   b,    532   c  generally amplify the IF signals output from the RF translators  502   a,    502   b,    502   c,  respectively. Each of the LNAs  532   a,    532   b,    532   c  is communicatively coupled to the receive side  204  of the ACS  102 . 
     As shown in  FIG. 5 , the receive side  204  comprises a plurality of filters  534   a,    534   b,    534   c,  portions of the closed loop operators  550   a,    550   b,    550   c,  a plurality of beamformers  508   a,    508   b,    508   c,  hardware entities  512   a,    512   b,    512   c,    516 , and a signal combiner  514 . Embodiments of the present invention are not limited in this regard. For example, the receive side  204  can be absent of the filters  534   a,    534   b,    534   c  and hardware entities  512   a,    512   b,    512   c,    516 . 
     As shown in  FIG. 5 , the filters  534   a,    534   b,    534   c  are communicatively coupled between the LNAs  532   a,    532   b,    532   c  and beamformers  508   a,    508   b,    508   c.  Each of the beamformers  508   a,    508   b,    508   c  can generally include a down converter  506   a,    506   b,    506   c,  a filter  540   a,    540   b,    540   c,  and a combiner  510   a,    510   b,    510   c.  Embodiments of the present invention are not limited in this regard. For example, the beamformers  508   a,    508   b,    508   c  can be absent of the down converters  506   a,    506   b,    506   c  and filters  540   a,    540   b,    540   c.    
     Each down converter  506   a,    506   b,    506   c  converts a digitized real signal centered at an IF to a baseband complex signal centered at zero (0) frequency. The down converters  506   a,    506   b,    506   c  share a common clock (not shown), and therefore receive the same clock (CLK) signal. The CLK signal can be generated within the receive side  204 , elsewhere in the ACS  102 , or external to the ACS  102 . The down converters  506   a,    506   b,    506   c  can be set to the same center frequency and bandwidth. The down converters  506   a,    506   b,    506   c  can also comprise local oscillators that are in-phase with each other. This in-phase feature of the down converters  506   a,    506   b,    506   c  ensures that the down converters  506   a,    506   b,    506   c  shift the phases of signals by the same amount. After converting the digitized real signals to baseband complex signals, the down converters  506   a,    506   b,    506   c  communicate the baseband complex signals to the filters  540   a,    540   b,    540   c,  respectively. The filters  540   a,    540   b,    540   c  filter the baseband complex signals and forward the same to the combiners  510   a,    510   b,    510   c.    
     Each of the combiners  510   a,    510   b,    510   c  combines a baseband complex signal with a complex weight w 1 , w 2 , w 3  for a particular antenna element  106   a,    106   b,    106   c.  The complex weights w 1 , w 2 , w 3  are selected to combine the receive signals according to a particular radiation pattern  111 . That is, the complex weights w 1 , w 2 , w 3  are selected to provide a central beam  112 , side beams  114 , and nulls, as described above, so as to preferentially receive signals from one or more predefined directions. The values of the complex weights w 1 , w 2 , w 3  are controlled by closed loop operators  550   a,    550   b,    550   c.  The closed loop operators  550   a,    550   b,    550   c  will be described below. 
     The combiners  510   a,    510   b,    510   c  can include, but are not limited to, complex multipliers. Thereafter, the combiners  510   a,    510   b,    510   c  communicate the signals to the hardware entities  512   a,    512   b,    512   c,  respectively. The hardware entities  512   a,    512   b,    512   c  can further process the signals received from the beamformers  508   a,    508   b,    508   c.  The hardware entities  512   a,    512   b,    512   c  communicate the processed signals to the signal combiner  514 . 
     At the signal combiner  514 , the processed signals are combined to form a combined signal. The signal combiner  514  can include, but is not limited to, a signal adder as shown in  FIG. 5 . Subsequent to forming the combined signal, the signal combiner  514  communicates the same to the hardware entities  516  for further processing. After processing the combined signal, the hardware entities  516  can communicate the same to a demodulator (not shown) for demodulation. 
     Each closed loop operator  550   a,    550   b,    550   c  is generally configured for controlling the phase and/or amplitude of receive signals so as to counteract phasing errors due to cable delay effects, wide antenna spacing effects, and environmental effects on hardware components  102 ,  104   a,    104   b,    104   c  of a communication system  100 . Accordingly, each closed loop operator  550   a,    550   b,    550   c  includes a signal adder  530   a,    530   b,    530   c,  a phase comparator  536   a,    536   b,    536   c,  and the phase/amplitude controller  328   a,    328   b,    328   c.  The phase comparator  536   a,    536   b,    536   c  is configured to receive a received signal from the respective LNA  532   a,    532   b,    532   c  and a reference signal V ref  from a reference signal generator (not shown) located at the RF equipment  104   a,    104   b,    104   c.  The reference signal generator (not shown) will be described below in relation to  FIGS. 9-14 . Subsequent to receiving the signals, the phase comparator  536   a,    536   b,    536   c  performs a comparison operation to determine a phase offset between the signals. The phase offset can be represented in terms of an imaginary part Q and a real part I. 
     After determining the phase offset, the phase comparator  536   a,    536   b,    536   c  communicates the phase offset value(s) to the phase/amplitude controller  538   a,    538   b,    538   c.  The phase/amplitude controller  538   a,    538   b,    538   c  determines a complex weight w 1 , w 2 , w 3  that is to be used by a beamformer  508   a,    508   b,    508   c  to control the phase and/or amplitude of receive signals. The complex weight w 1 , w 2 , w 3  is determined using the received phase offset value(s) and a reference signal V ref  received from a reference signal generator (not shown). More particularly, the phase/amplitude controller  538   a,    538   b,    538   c  adjusts complex weights using the phase offset values. The reference signal generator (not shown) will be described below in relation to  FIGS. 9-14 . 
     Referring now to  FIGS. 6A-6B , there are provided more detailed block diagrams of the communication system  100  that are useful for understanding the phase and/or amplitude adjustment functions thereof. The phase and/or amplitude adjustments functions of the transmit side  202  will be described below in relation to  FIG. 6A . The phase and/or amplitude adjustments functions of the receive side  204  will be described below in relation to  FIG. 6B . Notably, the antenna elements  106   b,    106   c  and RF equipment  104   b,    104   c  are not shown in  FIGS. 6A-6B  to simplify the following discussion. However, it should be understood that the antenna elements  106   b,    106   c  are the same as or substantially similar to the antenna element  106   a.  Similarly, the RF equipment  104   b,    104   c  is the same as or substantially similar to the RF equipment  104   a.    
     As shown in  FIG. 6A , the ACS  102  comprises a station frequency reference  602 , the TRSG  302 , hardware entities  304   a,  beamformers  308   a,    395   a,  a power coupler  604 , the phase/amplitude controller  326   a,  the phase comparator  340   a,  and a reference signal generator  614   a.  As also shown in  FIG. 6A , the RF equipment  104   a  comprises hardware entities  328   a,  the HPA  330   a,  the phase comparator  332   a,  and a reference signal generator  614   b.  As further shown in  FIG. 6A , the MEAS  150  comprises a ½ transmit carrier frequency device  608 , an analog fiber modulator  610 , an optical fiber  616 , and a fiber mirror  628 . 
     The TRSG  302  of the ACS  102  can generate signals to be transmitted from the antenna elements  106   a,    106   b  (not shown),  106   c  (not shown). The TRSG  302  is communicatively coupled to the station frequency reference  602  and the hardware entities  304   a.  The hardware entities  304   a  are communicatively coupled to the beamformer  308   a.    
     As noted above in relation to  FIG. 3 , the beamformer  308   a  can be utilized to control the phases and/or the amplitudes of transmit signals. Accordingly, the beamformer  308   a  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  308   a  is communicatively coupled to power coupler  604 . The power coupler  604  is communicatively coupled to the closed loop operator  350   a.  The closed loop operator  350   a  will be described below. However, it should be understood that the closed loop operator  350   a  is generally configured to adjust the phase and/or amplitude of transmit signals. The closed loop operator  350   a  is also configured to communicate the phase and/or amplitude adjusted transit signals to the hardware entities  328   a  of the RF equipment  104   a.  The hardware entities  328   a  are communicatively coupled to the HPA  330   a.  The HPA  330   a  communicates processed signals to the antenna element  106   a  for transmission therefrom. 
     The closed loop operator  350   a  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  102  and  104   a  of the communication system  100 . Accordingly, the closed loop operator  350   a  includes phase comparators  340   a,    332   a,  a phase/amplitude controller  326   a,  and a beamformer  395   a.    
     The phase comparator  332   a  is configured to receive a transmit signal  624  from the antenna element  106   a  and a reference signal V ref-1  from a reference signal generator  614   b.  In this regard, it should be understood that the antenna element  106   a  has a transmit (Tx) signal probe  622  disposed on its reflector  620  for sensing the transmit signal  624 . In order to avoid the introduction of phase offsets into transmit signals, the communication path between the Tx signal probe  622  and the phase comparator  332   a  can be minimized. At the phase comparator  332   a,  the phase of the sensed transmit signal  624  is compared with the phase of the reference signal V ref-1  to determine a phase offset  626 . The phase offset  626  can be represented in terms of an imaginary part Q and a real part I. The phase offset  626  is then communicated from the phase comparator  332   a  to the phase/amplitude controller  326   a.    
     The reference signal V ref-1  utilized by the phase comparator  332   a  is generated by the reference signal generator  614   b.  The reference signal generator  614   b  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) disposed on the optical fiber  616  at a first location. Additionally or alternatively, the reference signal generator  614   b  is configured to sense signals V f , V r  propagated along the optical fiber  616 . 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 will be described below in relation to  FIGS. 9-11 . The reference signal generator  614   b  can be the same as or substantially similar to any one of the reference signal generators described below in relation to  FIGS. 12-14 . 
     The phase comparator  340   a  is configured to receive a transmit signal  618  from the power coupler  604  and a reference signal V ref-2  from a reference signal generator  614   a.  At the phase comparator  340   a,  the phase of the transmit signal  618  is compared with the phase of the reference signal V ref-2  to determine a phase offset  606 . The phase offset  606  can be represented in terms of an imaginary part Q and a real part I. The phase offset  606  is then communicated from the phase comparator  340   a  to the phase/amplitude controller  326   a.    
     The reference signal V ref-2  utilized by the phase comparator  340   a  is generated by the reference signal generator  614   a.  The reference signal generator  614   a  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) disposed on the optical fiber  616  at a second location different from the first location. Additionally or alternatively, the reference signal generator  614   a  is configured to sense signals V f , V r  propagated along the optical fiber  616 . The sensed signals V f , V r  are used by the reference signal generator  614   a  to determine the reference signal V ref-2 . The manner in which the reference signal V ref-2  is determined is described below in relation to  FIGS. 9-11 . The reference signal generator  614   a  can be the same as or substantially similar to any one of the reference signal generator described below in relation to  FIGS. 12-14 . The reference signal generator  614   a  can also be the same as or substantially similar to the reference signal generator  614   b.    
     The phase/amplitude controller  326   a  determines a phase and/or amplitude adjustment value Δw N  that is to be used by a beamformer  395   a  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  606 ,  626  values received from the phase comparators  340   a,    332   a,  respectively. 
     As shown in  FIG. 6B , the ACS  102  comprises a station frequency reference  652 , a receiver  670 , the hardware entities  516 ,  512   a,  the signal adder  514 , the beamformer  508   a,  the filter  534   a,  a power coupler  654 , a despreader  672 , the phase/amplitude controller  538   a,  the phase comparator  536   a,  and a reference signal generator  654   a.  As also shown in  FIG. 6B , the RF equipment  104   a  comprises the LNA  532   a,  a reference signal generator  654   b,  and a spreader  676 . As further shown in  FIG. 6B , the MEAS  150  comprises a ½ transmit carrier frequency device  658 , an analog fiber modulator  660 , an optical fiber  656 , and a fiber mirror  668 . 
     During operation, the object of interest  108  communicates a signal to the MEAS  150 . The signal is received at the antenna element  106   a.  The antenna element  106   a  includes a reflector  620  with an Rx signal probe  652  disposed thereon. The Rx signal probe  652  transmits a spread reference signal  624  generated by a spreader  676 . The spreader  676  is provided to ensure that the reference signal V ref-1  does not interfere with receive signals. The spreader  676  can be, but is not limited to, a random number spreader or a pseudo-random number spreader. The spreader  676  can receive a reference signal V ref-1  from the reference signal generator  654   b  and utilize the reference signal V ref-1  to generate the spread reference signal  624 . More particularly, the spreader  676  can combine the reference signal V ref-1  with a random or pseudo-random number sequence to obtain the spread reference signal  624 . Embodiments of the present invention are not limited in this regard. For example, the MEAS  150  can be absent of the spreader  676 . In such a scenario, the MEAS  150  can alternatively include a frequency adjuster configured for offsetting the frequency of the reference signal V ref-1  by a desired amount. The desired amount can be selected for ensuring that the reference signal V ref-1  does not interfere with receive signals. 
     At the antenna element  106   a,  the received signal is combined with the spread reference signal  624  to form a spread spectrum signal. The spread spectrum signal is then communicated to the LNA  532   a  of the RF equipment  104   a.  The LNA  532   a  processes the spread spectrum signal and communicates the processed spread spectrum signal to the power coupler  654  of the ACS  102  or optional hardware entities  674 . 
     The reference signal V ref-1  utilized by the spreader  676  is generated by the reference signal generator  654   b.  The reference signal generator  654   b  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) disposed on the optical fiber  696  at a first location. Additionally or alternatively, the reference signal generator  654   b  is configured to sense signals V f , V r  propagated along the optical fiber  696 . 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 will be described below in relation to  FIGS. 9-11 . The reference signal generator  654   b  can be the same as or substantially similar to any one of the reference signal generators described below in relation to  FIGS. 12-14 . 
     At the ACS  102 , the power coupler  654  receives the spread spectrum signal from the RF equipment  104   a  and processes the same. Thereafter, the power coupler  654  communicates the processed spread spectrum signal to the despreader  672  and the filter  534   a.  At the despreader  672 , operations are performed with a known despreading code sequence to despread the spread spectrum signal. The dispreading code sequence can be the same as the spread reference signal  624 . The despread signal is then communicated from the despreader  672  to the closed loop operator  550   a.    
     The closed loop operator  550   a  is generally configured for controlling the phases and/or amplitudes of receive signals so as to counteract phasing errors due to cable delay effects, wide antenna spacing effects, and environmental effects on hardware components  102  and  104   a  of the communication system  100 . Accordingly, the closed loop operator  550   a  includes a phase comparator  536   a  and a phase/amplitude controller  538   a.    
     The phase comparator  536   a  is configured to receive a despread signal from the despreader  672  and a reference signal V ref-2  from a reference signal generator  654   a.  At the phase comparator  536   a,  the phase of the despread signal is compared with the phase of the reference signal V ref-2  to determine a phase offset  686 . The phase offset  686  can be represented in terms of an imaginary part Q and a real part I. The phase offset  686  is then communicated from the phase comparator  536   a  to the phase/amplitude controller  538   a.    
     The reference signal V ref-2  utilized by the phase comparator  536   a  is generated by the reference signal generator  654   a.  The reference signal generator  654   a  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) disposed on the optical fiber  696  at a first location. Additionally or alternatively, the reference signal generator  654   a  is configured to sense signals V f , V r  propagated along the optical fiber  696 . The sensed signals V f , V r  are used to determine the reference signal V ref-2 . The manner in which the reference signal V ref-2  is determined will be described below in relation to  FIGS. 9-11 . The reference signal generator  654   a  can be the same as or substantially similar to any one of the reference signal generator described below in relation to  FIGS. 12-14 . The reference signal generator  654   a  can also be the same as or substantially similar to the reference signal generator  654   b  described above. 
     The phase/amplitude controller  538   a  determines the complex weight w 1  that is to be used by a beamformer  508   a  to control the phase and/or amplitude of receive signals. The complex weight w 1  is determined using the received phase offset  686  values received from the phase comparator  536   a.    
     Referring now to  FIG. 7 , there is provided a more detailed block diagram of the communication system  100  that is useful for understanding the phase and/or amplitude adjustment functions thereof. Notably, the antenna elements  106   b,    106   c  and RF equipment  104   b,    104   c  are not shown in  FIG. 7  to simplify the following discussion. As shown in  FIG. 7 , the ACS  102  comprises a station frequency reference  702 , the TRSG  302 , hardware entities  304   a,  beamformers  308   a,    735 , and a phase/amplitude controller  726   a.  As also shown in  FIG. 7 , the RF equipment  104   a  comprises hardware entities  328   a,  the HPA  330   a,  the phase comparator  732   a,  and a reference signal generator  714 . As further shown in  FIG. 7 , the MEAS  150  comprises a ½ transmit carrier frequency device  708 , an analog fiber modulator  710 , an optical fiber  716 , and a fiber mirror  728 . 
     The TRSG  302  of the ACS  102  can generate signals to be transmitted from the antenna elements  106   a,    106   b  (not shown),  106   c  (not shown). The TRSG  302  is communicatively coupled to the station frequency reference  702  and the hardware entities  304   a.  The hardware entities  304   a  are communicatively coupled to the beamformer  308   a.    
     As noted above in relation to  FIG. 3 , the beamformer  308   a  can be utilized to control the phases and/or the amplitudes of transmit signals. Accordingly, the beamformer  308   a  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  308   a  is communicatively coupled to the closed loop operator  750   a.  The closed loop operator  750  will be described below. However, it should be understood that the closed loop operator  750   a  is generally configured to adjust the phase and/or amplitude of transmit signals. The closed loop operator  750   a  is also configured to communicate the phase and/or amplitude adjusted transmit signals to the hardware entities  328   a  of the RF equipment  104   a.  The hardware entities  328   a  are communicatively coupled to the HPA  330   a.  The HPA  330   a  communicates processed signals to the antenna element  106   a  for transmission therefrom. 
     The closed loop operator  750   a  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  102  and  104   a  of the communication system  100 . Accordingly, the closed loop operator  750   a  includes the phase comparator  732   a,  a phase/amplitude controller  726   a,  and a beamformer  735 . 
     The phase comparator  732   a  is configured to receive a transmit signal  724  from the antenna element  106   a  and a reference signal V ref-1  from a reference signal generator  714 . In this regard, it should be understood that the antenna element  106   a  has a transmit (Tx) signal probe  722  disposed on its reflector  720  for sensing the transmit signal  724 . At the phase comparator  732   a,  the phase of the sensed transmit signal  724  is compared with the phase of the reference signal V ref-1  to determine a phase offset  726 . The phase offset  726  can be represented in terms of an imaginary part Q and a real part I. The phase offset  726  is then communicated from the phase comparator  732   a  to the phase/amplitude controller  726   a.    
     The reference signal V ref-1  utilized by the phase comparator  732   a  is generated by the reference signal generator  714 . The reference signal generator  714  is configured to receive sensed signals V f , V r  from one or more sensor devices (not shown) disposed on the optical fiber  716  at a first location. Additionally or alternatively, the reference signal generator  714  is configured to sense signals V f , V r  propagated along the optical fiber  716 . 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 will be described below in relation to  FIGS. 9-11 . The reference signal generator  714  can be the same as or substantially similar to any one of the reference signal generators described below in relation to  FIGS. 12-14 . 
     The phase/amplitude controller  726   a  is configured for receiving phase offsets from each of the RF equipments  104   a,    104   b  (not shown),  104   c  (not shown). The phase/amplitude controller  726   a  determines a phase and/or amplitude adjustment value Δw N  that is to be used by a beamformer  735  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  606  values received from the RF equipments  104   a,    104   b  (not shown),  104   c  (not shown). 
       FIG. 8  is a schematic diagram of a computer system  800  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  800  can be implemented to perform the various tasks of the transmit side  202  and/or the receive side  204  the ACS  102 . In some embodiments, the computer system  800  operates as a single standalone device. In other embodiments, the computer system  800  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  800  can operate in the capacity of a server or a client machine in server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. 
     The computer system  800  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  800  can include a processor  802  (such as a central processing unit (CPU), a graphics processing unit (GPU, or both), a main memory  804  and a static memory  806 , which communicate with each other via a bus  808 . The computer system  800  can further include a display unit  810 , 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  800  can include an input device  812  (e.g., a keyboard), a cursor control device  814  (e.g., a mouse), a disk drive unit  816 , a signal generation device  818  (e.g., a speaker or remote control) and a network interface device  820 . 
     The disk drive unit  816  can include a computer-readable storage medium  822  on which is stored one or more sets of instructions  824  (e.g., software code) configured to implement one or more of the methodologies, procedures, or functions described herein. The instructions  824  can also reside, completely or at least partially, within the main memory  804 , the static memory  806 , and/or within the processor  802  during execution thereof by the computer system  800 . The main memory  804  and the processor  802  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  824  or that receives and executes instructions  824  from a propagated signal so that a device connected to a network environment  826  can send or receive data, and that can communicate over the network  826  using the instructions  824 . The instructions  824  can further be transmitted or received over a network  826  via the network interface device  820 . 
     While the computer-readable storage medium  822  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. 
     As noted above, the cable assemblies  110   a,    110   b,    110   c  and the communication links  118   a,    118   b,    118   c  (or  119   a,    119   b,    119   c ) of the communication system  100  delay signals between the ACS  102  and the antenna elements  106   a,    106   b,    106   c.  In effect, the phases of the signals are shifted thereby resulting in phasing errors. Such phasing errors are exacerbated by the spacing between the antenna elements  106   a,    106   b,    106   c.  Phasing errors also occur as a result of environmental effects on the hardware components  102 ,  104   a,    104   b,    104   c  of the communication system  100 . Phasing errors further occur as a result of operation delays between the beamformers  308   a,    308   b,    308   c  or operation delays between beamformers  408   a,    408   b,    408   c.  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  112  in a direction other than the direction  116  of the object of interest  108 . 
     Accordingly, the communication system  100  implements a method for adjusting the phases and/or amplitudes of signals transmitted from and received at each antenna element  106   a,    106   b,    106   c.  The phases and/or amplitudes of the transmit and receive signals are adjusted using a plurality of reference signals V ref . The reference signals V ref  generally represent transmitted signals absent of phase shifts. A first one of the reference signals V ref  is compared with a signal having phase shifts for determining a phase offset between the same. The phase offset and a second one of the reference signals V ref  are then used to control the phase and/or amplitude of a transmit and/or receive signal so as to counteract phasing errors due to cable delay effects, wide antenna spacing effects, and environmental effects on hardware components  102 ,  104   a,    104   b,    104   c  of a communication system  100 . More particularly, the phase offset and a second one of the reference signals V ref  are used to determine the complex weights w 1 , w 2 , w 3  that are subsequently combined with transmit and/or receive signals. Systems and methods for determining the reference signals V ref  will now be described in relation to  FIGS. 9-14 . 
     Systems and Methods for Determining Reference Signals V ref     
     Referring now to  FIG. 9 , there is provided a block diagram of a communication system  900  that is useful for understanding how a reference signal V ref  is determined. As shown in  FIG. 9 , the communication system  900  can comprise a signal source  902 , a sensor  916 , a reflective termination  914 , and a non-reflective termination  904 . Each of these components  902 ,  904 ,  914 ,  916  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  908 . As such, the signal source  902  generally transmits a signal V f  to the reflective termination  914 . A reflected version of the transmitted signal V r  is communicated from the reflective termination  914  to the non-reflective termination  904 . The sensor  916  senses the presence of a forward propagated signal V f  and a reverse propagated signal V r  on the transmission media  908 . The sensor  916  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  916  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 . 
     A conceptual diagram of a first exemplary process  1000  for determining the reference signal V ref  is provided in  FIG. 10 . As shown in  FIG. 10 , the process  1000  begins by ( 1002 ,  1004 ) sensing a forward propagated signal V f  and a reverse propagated signal V r . It should be appreciated that the sensing processes ( 1002 ,  1004 ) 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 signal amplitude. j is the 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. 
     Thereafter, a signal combination operation  1006  is performed where the signals V f , V r  are combined to obtain a Sum signal (S). This signal combination operation  1006  generally involves adding the signals V f , V r  together. The signal combination operation  1006  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 sine signal that depends on the location “z” at which the sensor  916  is placed along the transmission media  908 . 
     The process  1000  also involves performing a subtraction operation  1008 . The subtraction operation  1008  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  1008  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 cosine signal that depends on the location “z” at which the sensor  916  is placed along the transmission media  908 . 
     After determining the Sum signal S and the Difference signal D, the process  1000  continues with a plurality of multiplication operations  1010 ,  1012 . A first one of the multiplication operations  1010  generally involves multiplying the Sum signal S by itself to obtain a first Exponentiation signal E S . The first multiplication operation  1010  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  1012  generally involves multiplying the Difference signal D by itself to obtain a second Exponentiation signal E D . The second multiplication operation  1012  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  1014 . The subtraction operation  1014  generally involves subtracting the first Exponentiation signal E S  from the second Exponentiation signal E D . The subtraction operation  1014  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 the signal obtained as a result of performing the subtraction operation  1014 . As evident from mathematical equation (7), the resulting signal V doubled  does not depend on the location “z” at which the sensor  916  is placed along the transmission media  908 . 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  is further processed to increase its frequency to a desired value or reduce its frequency to a desired value (i.e., the value of the frequency of a propagated signal V f , V r ). If the frequency of the resulting signal V doubled  is to be increased to the desired value, then a multiplication operation (not shown) can be performed. If the frequency of the resulting signal V doubled  is to be reduced to the desired value, then a frequency reduction operation  1016  can be performed. 
     The frequency reduction operation  1016  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  916  is placed along the transmission media  908 . 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  1000  described above in relation to  FIG. 10 . For example, if the frequency of each propagated signal V f , V r  is reduced by exactly half, then the frequency reduction operation  916  need not be performed. A conceptual diagram of a process  1100  for determining the reference signal V ref  absent of the frequency reduction operation  1016  is provided in  FIG. 11 . The propagated signals with half the frequency of the signals V f , V r  is referred to herein as V′ f , V′ r , respectively. 
     As shown in  FIG. 11 , the process  1100  generally involves performing sensing operations  1102 ,  1104  to sense propagated signals V′ f , V′ r , a signal combination operation  1106 , a subtraction operations  1108 ,  1114 , and multiplication operations  1110 ,  1112 . These listed operations  1102 ,  1104 , . . . ,  1114  are the same as or substantially similar to the operations  1002 ,  1004 , . . . ,  1014  of  FIG. 10 , respectively. As such, the operations  1102 ,  1104 , . . . ,  1114  of process  1100  will not be described herein. 
     Referring now to  FIG. 12 , there is provided a block diagram of a first exemplary system  1200  implementing a method for determining a reference signal V ref , V′ ref . As shown in  FIG. 12 , the system  1200  comprises a sensing device  1202 , a signal adder  1206 , signal subtractors  1208 ,  1214 , and signal multipliers  1210 ,  1212 . The system  1200  can also comprise an optional phase lock loop  1216  and an optional frequency divider  1218 . The sensing device  1202  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  908 . The sensing device  1202  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  1202  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 compute the signal V doubled  and/or the reference signal V ref . As such, the sensing device  1202  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  1206 ,  1208 . 
     The signal adder  1206  is generally configured for performing a signal combination operation  1006 ,  1106  to obtain a Sum signal S or S′. The signal subtractor  1208  is generally configured for performing a subtraction operation  1008 ,  1108  to obtain a Difference signal D or D′. The output signals of the components  1206 ,  1208  are forwarded to the signal multipliers  1210 ,  1212 . Each of the multipliers  1210 ,  1212  is configured to perform a multiplication operation  1010 ,  1012 ,  1110 ,  1112  to obtain a respective Exponentiation signal E S , E′ S , E D , E′ D . The Exponentiation signals E S  and E D  or E′ S  and E′ D  are then communicated to the signal subtractor  1214 . At the signal subtractor  1214 , a subtraction operation  1014 ,  1114  is performed to obtain a signal V doubled  or a reference signal V ref . 
     If the result of the subtraction operation is a 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  is forwarded to an optional phase lock loop  1216  and an optional frequency divider  1218 . The components  1216 ,  1218  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  1218  is the reference signal V ref . 
     Referring now to  FIG. 13 , there is provided a block diagram of a second exemplary system  1300  implementing a method for determining a reference signal V ref . As shown in  FIG. 13 , the system  1300  comprises a sensing device  1304  disposed along a transmission media  1302  and a reference signal generator  1350 . The reference signal generator  1350  comprises a sum-diff hybrid circuit  1308 , multipliers  1310 ,  1312 , a signal subtractor  1314 , a phase lock loop (PLL)  1316 , and a frequency divider  1318 . Embodiments of the present invention are not limited to the configuration shown in  FIG. 13 . For example, the reference signal generator  1350  can be absent of the PLL  1316  and the frequency divider  1318 . 
     The sensing device  1304  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  1302 . The sensing device  1304  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  1304  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 compute the reference signal V ref . As such, the sensing device  1302  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  1308 . 
     The sum-diff hybrid circuit  1308  is generally configured for performing a signal combination operation  1006  to obtain a Sum signal S and a subtraction operation  1008  to obtain a Difference signal D. Subsequent to completing the signal combination operation and subtraction operation, the sum-diff hybrid circuit  1308  communicates the signals S and D to the multipliers  1310 ,  1312 , respectively. Each of the multipliers  1310 ,  1312  is configured to perform a multiplication operation  1010 ,  1012  to obtain a respective Exponentiation signal E S , E D . The Exponentiation signals E S , E D  are then communicated to the signal subtractor  1314 . At the signal subtractor  1314 , a subtraction operation  1014  is performed to obtain a signal V doubled . The signal V doubled  is then processed by the PLL  1316  and frequency divider  1318  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  1318  is the reference signal V ref . 
     Referring now to  FIG. 14 , there is provided a block diagram of a third system embodiment  1400  implementing the method of  FIG. 10 . As shown in  FIG. 14 , the system  1400  comprises transducers  1404 ,  1420  and a reference signal generator  1450 . 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  1404 ,  1420  is configured to communicate a signal representing a signal V f , V r  propagated on the transmission media  1402  to the reference signal generator  1450 . 
     As also shown in  FIG. 14 , the reference signal generator  1450  comprises 180 degree hybrid couplers  1406 ,  1414 , input square devices  1408   a,    1408   b,  a PLL  1416 , and a frequency divider  1418 . Embodiments of the present invention are not limited to the configuration shown in  FIG. 14 . For example, the reference signal generator  1450  can be absent of the PLL  1416  and the frequency divider  1418 . 
     Hybrid couplers  1406  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  1406  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  1406  to the input square devices  1408   a,    1408   b,  respectively. Each of the input square devices  1408   a,    1408   b  generates a respective Exponentiation signal E S , E D . The Exponentiation signals E S , E D  are communicated from the input square devices  1308   a,    1408   b  to the hybrid coupler  1414 . The hybrid coupler  1414  performs a subtraction operation  1014  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  1414  to the PLL  1416  and the frequency divider  1418 . The components  1416 ,  1418  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 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 invention. However, embodiments of the 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 skilled in the art upon the reading and understanding of this specification and the annexed drawings. In addition, while a particular feature of the 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.