Abstract:
Presented are methods that utilize wavefront multiplexing for enabling linearly-polarized terminals to access circularly-polarized satellite transponders. The methods disclosed herein feature (1) polarization formation capability that renders transmitted signal conditioned on circularly-polarized channels through multiple linearly-polarized feeds, and (2) polarization-conversion capability that compensate path differentials introduced by electromagnetic wave propagation channels. Data streams to be transmitted are pre-processed by a wavefront multiplexer into multiple wavefront components in linear polarization formats, where signals from respective data streams are replicated into linearly-polarized sub-channels. These replicated data streams are linked via a unique complex weighting vector (amplitude and phase or their equivalents), or “wavefront”, which are also linked by various spatially independent wavefronts. Additionally, a probing signal is sent on the transmitting side and linked via some of the independent wavefronts. Aggregated signals in linearly-polarized sub-channels are unique linear combinations of all input data streams. Aggregated signals in turn appear in circularly-polarized formats and propagate through circularly-polarized channels including circularly-polarized satellite transponders and a circularly-polarized teleport on the receiving side. Correlation between the circularly-polarized signal and the probing signal is sent back to the transmitting side that drives the polarization-conversion function toward the optimal state such that this correlation is lower than a pre-defined level. Accordingly, an optimally configured satellite communication system either (1) enables the linearly-polarized terminal on the transmitting side to access right-hand circularly-polarized satellite transponder without interfering the left-hand circularly-polarized satellite transponder, or (2) enables the linearly-polarized terminal on the transmitting side to access left-hand circularly-polarized satellite transponder without interfering the right-hand circularly-polarized satellite transponder.

Description:
CROSS REFERENCE TO RELATED PATENTS 
       [0001]    This application is related to U.S. patent application Ser. No. 13/172,620, filed on Jun. 29, 2011. 
     
    
       [0002]    Presented is are methods that enable linearly-polarized ground terminals to access circularly-polarized channels through wavefront multiplexing techniques. This invention comprises conventional ground terminals, a unique polarization alignment processor on the transmitting side and feedback channel. As a result of this invention, teleport operators can gain greater flexibility in how they manage their assets, and so can users in how they access available communication resources. 
         [0003]    This invention also relates to methods that anneal the interference of undesired circularly-polarized signals to the intended channel. A probing signal known to feedback terminals is exploited such that the differentials in signal propagation paths can be equalized by the unique polarization alignment processor and the interference due to undesired signals is annealed. 
       BACKGROUND OF THE INVENTION 
       [0004]    1. Field of the Invention 
         [0005]    The present invention relates to methods for enabling linearly-polarized (LP) ground terminals to access circularly-polarized (CP) channels. It is also related to wavefront multiplexing/de-multiplexing (WF muxing/demuxing) technologies. 
         [0006]    The present invention relates to radio frequency communication devices and communication architectures that comprises ground terminals, communication assets and channels. More specifically, this invention allows ground terminals with linear polarization format to communication with communication assets of circular polarization format via wavefront multiplexing techniques. This offers tremendous advantages including, but not limited to, improved flexibility and increased efficiency of existing assets. 
         [0007]    2. Description of the Prior Art 
         [0008]    It is common practice in utilization of communication links to equip terminals and communication assets with antennas of compatible polarization formats. It is generally true that LP terminals access LP channels, and CP terminals access CP channels. One says that linear polarization and circular polarization are incompatible polarization formats. As the asset changes its polarization format, so does the terminal accordingly. This happens, for instance, when LP terminals switch services from a provider with LP satellites to another one with CP satellites. Then the antenna polarization formats require reconfiguration from LP to CP. One main reason to reconfigure polarization formats is to prevent 3 dB signal-to-noise ratio (SNR) loss due to polarization incompatibility between the ground terminals and the communication assets. The radiation patterns emanating from LP terminals and incident on CP assets have also been treated “unintelligible”, or interference/noise, which also serves as a second reason that the polarization formats of terminals and transponders remain compatible in conventional communication architectures. 
         [0009]    Linear polarization has two complimentary formats, one of which is vertical polarization (VP) and another is horizontal polarization (HP). Signals conditioned on these two formats have 90 degree difference in space. Specifically, a signal with VP format has electrical field aligning with the vertical direction; and a signal with HP format has electrical field aligning with the horizontal direction. The vertical direction represents 90 degree difference with respect to the horizontal one. One should note that the vertical and horizontal directions are both defined with respect to the direction of electromagnetic wave propagation. In free space, the wave moves along the line perpendicular to said vertical and horizontal directions. 
         [0010]    Due to the particular said configuration of electromagnetic wave propagation directions, it is essential for ground terminals and communication assets in conventional architectures to be aligned in their polarization. In other words, for LP ground terminals and LP assets to communicate successfully, their VP directions need to be aligned and so do their HP directions. 
         [0011]    As the VP and HP signals have identical strength but exactly 90 degree difference in time, the overall effect stimulates an electrical field that rotates in space with respect to the propagation direction. The VP signal may have 90 degree in advance of or behind the HP one, which results in right-hand circularly polarized (RHCP) or left-hand circularly polarized (LHCP) formats. RHCP and LHCP are two complimentary formats of circular polarization. 
         [0012]    The main property of a CP signal is its handed-ness, which can be RHCP or LHCP. For CP ground terminals and CP assets to communicate successfully, their VP and HP directions need not be aligned respectively. In other words, there is no stringent requirement of aligned polarization in CP communication links as seen in LP ones. On the contrary, there are tremendous advantages of enabling LP ground terminals to access CP communication assets, thanks to the considerable reduction in the cost of mechanically realigning polarization. 
       SUMMARY OF THE INVENTION 
       [0013]    This invention presents methods taking advantage of polarization incompatibility (LP v.s. CP) to access available communication assets when the ground terminals are not polarization compatible. Disclosed herein are the operation concepts and associated mechanisms for LP terminals to access CP communication assets whose availability is limited. 
         [0014]    Essential to this invention is the class of wavefront muxing techniques that make the following scenarios possible: (1) a LP ground terminal successfully accesses a RHCP channel and introduces low interference to adjacent LHCP channel in the same frequency slot; (2) a LP ground terminal successfully accesses a LHCP channel and introduces low interference to adjacent RHCP channel in the same frequency slot; and (3) a LP ground terminal successfully and concurrently carries two signals, one of which can access a RHCP channel and another can access an adjacent LHCP channel in the same frequency slot, without undesired mutual interference. 
         [0015]    For LP ground terminals to successfully access CP channels via wavefront muxing techniques, these terminals transmit probing signals, monitor the level of leakage in authorized channels through feedback terminals and then optimize the transmitted waveforms on the transmitting side. The optimized waveforms introduce no interference of significant level to unauthorized channels. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0016]    The drawings disclose illustrative embodiments of the present disclosure. They do not set forth all embodiments. Other embodiments may be used in addition or instead. Details that may be apparent or unnecessary may be omitted to save space or for more effective illustration. Conversely, some embodiments may be practiced without all of the details that are disclosed. When the same reference number or reference indicator appears in different drawings, it may refer to the same or like components or steps. 
           [0017]    Aspects of the disclosure may be more fully understood from the following description when read together with the accompanying drawings, which are to be regarded as illustrative in nature, and not as limiting. The drawings are not necessarily to scale, with emphasis instead being placed on the principles of the disclosure. In the drawings: 
           [0018]      FIG. 1  illustrates conventional techniques that (1) enable CP ground terminals to access CP channels, through which the signals reach a remote CP receiving device, or (2) enable LP ground terminals to access LP channels, through which the signals reach a remote LP receiving device. 
           [0019]      FIG. 2  illustrates a communication system in an ideal scenario, in which a LP ground terminal accessing CP channels transmits RHCP waveforms via wavefront muxing to a remote RHCP receiving device only through the RHCP channel while causing no interference to the LHCP channel. 
           [0020]      FIG. 3  illustrates one LP ground terminal that transmits VP and HP waveforms, and another LP ground terminal that transmits RHCP and LHCP waveforms. The second LP ground generate CP waveforms through a wavefront muxing processor that has function of 3 dB-hybrid. 
           [0021]      FIG. 4  depicts a wavefront muxing processor that has function of 3 dB-hybrid and conditions two signals in VP and HP formats concurrently. 
           [0022]      FIG. 5  depicts a LP ground terminal equipped with a wavefront muxing processor servicing as 3 dB-hybrid followed by an element that adjusts the amplitude (A) and phase (Φ) of signal. This A &amp; Φ adjustment element ensures that the LP ground terminal transmits RHCP and LHCP waveforms. 
           [0023]      FIG. 6  depicts (1) a LP ground terminal that transmits CP waveforms and has 3 dB-hybrid and optimization elements for facilitating A &amp; Φ adjustment, (2) CP transponders and (3) feedback receiving terminal sending RHCP data stream to the transmitting LP ground terminal through separate dedicated channels. 
           [0024]      FIG. 7  depicts one configuration of the polarization-conversion element, which comprises a wavefront muxing processor serving as 3 dB-hybrid, A &amp; Φ adjustment element and optimization element. This polarization-conversion element is configured to ensure that its host LP ground terminal, while receiving data stream from the feedback terminal, transmits LHCP waveform that has low interference to the RHCP channel. 
           [0025]      FIG. 8  depicts an A &amp; Φ adjustment element that (1) multiplies the input data stream with a complex-valued weight, (2) sends current complex-valued weight to the optimization element, and (3) receives updated complex-valued weight from the optimization element. 
           [0026]      FIG. 9  depicts (1) a LP ground terminal that transmits CP waveforms and has 3 dB-hybrid and optimization elements for facilitating A &amp; Φ adjustment, (2) CP transponders and (3) feedback receiving terminal sending RHCP data stream to the transmitting LP ground terminal through one dedicated channel and sending LHCP data stream to the transmitting LP ground terminal through another dedicated channel. 
       
    
    
     DETAILED DESCRIPTION 
       [0027]    The present invention relates to a communication system that comprises LP ground terminal on the transmitting side, CP channels in RHCP and LHCP formats and CP feedback channels. Due to the agreement between communication service providers and users, the LP ground terminal may only be allowed to either (1) access the RHCP channel without interfering the adjacent LHCP channel in the same frequency slot, or (2) access the LHCP channel without interfering the adjacent RHCP channel in the same frequency slot. 
         [0028]    We shall use CP transponders on satellites on many examples, exemplifying operational principles and associated methods and apparatus. They can be applied to UAV based communications systems, terrestrial based point-to-point links, point-to-multipoint links, or links via relays. 
         [0029]    The present invention relates to LP ground terminals that have VP and HP feeds. The LP ground terminals are equipped with wavefront muxing processor and polarization-conversion element or polarization realignment element. The input signals of the wavefront muxing processor are transformed and then conditioned in VP and HP formats in the ideal case, thus yielding either RHCP or LHCP waveforms. 
         [0030]    In reality, signals conditioned in VP and HP formats may be amplified in magnitude and shifted in phase, yielding right-hand elliptically-polarized (RHEP) or left-hand elliptically-polarized (LHEP) waveforms. Using RHEP waveforms immediately introduces undesired interference to the LHCP channel if the ground terminal is only permitted to access the RHCP channel. Similarly, using LHEP waveforms immediately introduces undesired interference to the RHCP channel if the ground terminal is only permitted to access the LHCP channel. Therefore, the LP ground terminal requires adjustment, namely “polarization-realignment”, to re-format the elliptically-polarized waveforms toward circularly-polarized waveforms. 
       Embodiment 1 
       [0031]      FIG. 1  illustrates conventional techniques of enabling ground terminals to access communication assets. Panel  108  shows a communication link, in which a CP ground terminal  100  accessing a CP asset establishes communication with the CP receiving device  102  through the RHCP channel  104  and/or the LHCP channel  106 . 
         [0032]    Panel  118  shows another communication link, in which a LP ground terminal  110  accessing an LP asset establishes communication with the LP receiving device  112  through the VP channel  114  and/or the HP channel  116 . 
         [0033]    If users of the ground terminal  100  intend to switch service from CP assets to LP assets, the conventional techniques require change of polarization formats, which indicates transformation of ground terminal  100  with CP formats to ground terminal  110  with LP formats. 
         [0034]    If users of the ground terminal  110  intend to switch service from LP assets to CP assets, the conventional techniques require change of polarization formats, which indicates transformation of ground terminal  110  with LP formats to ground terminal  100  with CP formats. 
         [0035]    The present invention relates to a class of novel solutions to communication service switching and other pertinent applications.  FIG. 2  illustrates an ideal scenario, in which a LP ground terminal  210  that not only resembles the LP ground terminal  110 , but also has additional features that can be made possible by wavefront muxing. The LP ground terminal  210  transmits RHCP waveform S 1  through tis LP feeds. The LP ground terminal  210  can access a CP asset identical to the one in  FIG. 1 . The transmitted RHCP waveform only occupies the RHCP channel  104 , but has no appearance in the LHCP channel  106 . The transmitted RHCP waveform S 1  is received by the RHCP device  102 . 
         [0036]      FIG. 3  depicts two LP ground terminals in different configurations. Depicted in panel  300  is LP ground terminal  110  that has a horn with VP and HP feeds. Signal through the VP path experiences the amplification and phase delay identical to that experienced by the signal through the HP path. There is no requirement on adjustment of amplitude (A) and phase (Φ) of signals S v  and S h . 
         [0037]      FIG. 3  also depicts panel  302  that shows LP ground terminal  210  comprising a wavefront muxing processor with 3 dB-hybrid function and a horn with VP and HP feeds. The wavefront muxing processor takes two signals S RHCP  and S LHCP  as input. Let  v  denote the VP direction and  h  denote the HP direction. One output of the wavefront muxing processor represents the superposition (S RHCP +iS LCHP )/√{square root over (2)} v , and another output of the wavefront muxing processor represents the superposition (S LHCP +iS RHCP )/√{square root over (2)} h . Therefore, the signal S RHCP  has a VP component S RHCP /√{square root over (2)} v  and a HP component iS RHCP /√{square root over (2)} h . Both components have identical magnitude, but the HP component has phase 90 degrees ahead of that of the VP component. This indicates that the LP ground terminal effectively converts and transmits the signal S RHCP  in RHCP format. Similarly, the signal S LHCP  has a VP component iS LHCP /√{square root over (2)} v  and a HP component S LHCP /√{square root over (2)} h . Both components have identical magnitude, but the VP component has phase 90 degrees ahead of that of the HP component. This indicates that the LP ground terminal effectively converts and transmits the signal S LHCP  in LHCP format. Effectively, an aggregated waveform is thus formed such that (1) it has a first component in RHCP format, which only occupies the RHCP channel but has no appearance in the LHCP channel, and (2) it also has a second component in LHCP format, which only occupies the LHCP but has no appearance in the RHCP channel. 
         [0038]    If there is imbalance between the HP and the VP paths, there is a requirement of compensation on amplification and phase delay of both paths. Let a complex-valued parameter α denote the relative imbalance of amplification and phase delay on the HP path with respect to the VP path. Without loss of generality, the VP-output of the wavefront muxing processor can still be treated as (S RHCP +iS LHCP )/√{square root over (2)} v , and the HP-output of the wavefront muxing processor can be represented by α(S LHCP +iS RHCP )/√{square root over (2)} h . Effectively, the S RHCP  signal appears in the format S RHCP   v +iαS RHCP   h , which indicates a right-hand elliptically-polarized (RHEP) waveform. Concurrently, the S LHCP  signal appears in the format iαS LHCP   v +S LHCP   h , which indicates a left-hand elliptically-polarized (LHEP) waveform. The RHEP waveform not only occupies the RHCP channel as the primary signal but also appears in the LHCP channel as leakage. Concurrently, the LHEP waveform not only occupies the LHCP channel as the primary signal but also appears in the RHCP channel as leakage. If users of the LP ground terminal are only authorized to access the RHCP channel, the RHEP signal without being compensated appropriately would likely cause unwanted interference to the LHCP channel, which commits unauthorized access. Likewise, if users of the LP ground terminal are only authorized to access the LHCP channel, the LHEP signal without being compensated appropriately would likely cause unwanted interference to the RHCP channel, which also commits unauthorized access. Hence, it is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure authorized access. 
         [0039]      FIG. 4  depicts a wavefront muxing processor  408  that has function of 3 dB-hybrid. A first output  404  of processor  408  comprises a first input S 1  and a phase-shifted (through device  400  increasing phase by 90 degrees) version of a second input S 2 . A second output  406  of processor  408  comprises S 2  and a phase-shifted (through device  400  increasing phase by 90 degrees) version of S 1 . In the context of wavefront muxing, the signal S 1  resides on a distribution pattern, or “wavefront”, by “1” in output  404  and “i” in output  406 . Concurrently, the signal S 2  resides on another distribution pattern, or “wavefront”, by “1” in output  406  and ‘i’ in output  404 . Wavefront muxing takes place through processor  408  through two wavefronts [1 i] T  and [i 1] T , in which “T” represents matrix transposition and the 1 st  (2 nd ) entry in each vector represents the weighting factor introduced in output  404  ( 406 ). Hence, output  404  constitutes a weighted sum of two input signals S 1  and S 2 , and output  406  constitutes another weighted sum of these two input signals. We say that the two signals S 1  and S 2  are wavefront muxed by the processor  408 , and the output  404  and  406  constitute two wavefront muxed signals, respectively. 
         [0040]    Suppose the input signal S 1 , after proper transformation, is authorized to access the RHCP channel, and the signal S 2 , after proper transformation, is authorized to access the LHCP channel. By the same arguments illustrated in  FIG. 3 , the output signal  404  shall feature VP formats and the output signal  406  shall feature HP formats. Specifically, output signal  404  represents the superposition (S 1 +iS 2 )√{square root over (2)} v , and output signal  406  represents the superposition (S 2 +iS 1 )/√{square root over (2)} h . 
         [0041]      FIG. 5  depicts a LP ground terminal  510  that comprises a wavefront muxing processor with function of 3 dB-hybrid, amplitude (A) and phase (Φ) adjustment element (namely, an equalizer) and a horn with VP and HP feeds. Due to the relative differential amplifications and phase delays between HP path and those in VP path, amplitude (A) and phase (Φ) adjustment (namely, equalization) is required. The A and Φ adjustment ensures that CP waveforms, one of which is RHCP and another is LHCP, are transmitted. Without A and Φ adjustment, RHCP and LHCP waveforms would become RHEP and LHEP ones, which would further introduce unwanted interference in LHCP and RHCP channels, respectively. 
         [0042]      FIG. 6  depicts an application of the invention disclosed herein. A LP ground terminal  510  comprises a wavefront muxing processor with function of 3 dB-hybrid, amplitude (A) and phase (Φ) adjustment element (namely, an equalizer), an optimization element and a horn with VP and HP feeds. The LP ground terminal  510  is configured to (1) access CP space segment with RHCP transponder  104  and LHCP transponder  106 , and to (2) receive RHCP signal  602  from a feedback aperture  610  co-located with the terminal  510 . The terminal  510  resembles conventional LP terminals, but has additional function “Polverter” that (1) serves as a polarization-conversion element, and (2) comprises a wavefront muxing processor with function of 3 dB-hybrid, amplitude (A) and phase (Φ) adjustment element (namely, an equalizer) and an optimization element. The “Polverter” function may be implemented in, for instance, software. “Polverter” can be configured, as shown in  FIG. 6 , such that (1) two signals S RHCP  and S LHCP  are transformed and conditioned in VP and HP formats via wavefront muxing, (2) the relative differential amplifications and phase delays between HP path and those in VP path are compensated by the A and Φ adjustment element, and (3) the optimization element computes the optimal weight for A and Φ adjustment. 
         [0043]    In  FIG. 6 , the optimal state (1) allows the S RHCP  signal to only pass through the RHCP transponder  104  without introducing significant interference to the LHCP transponder  106 , and (2) allows the S LHCP  signal to only pass through the LHCP transponder  106  without introducing significant interference to the RHCP transponder  104 . Before the optimal state is attained, the differential amplitude (A) and phase (Φ) have not been compensated appropriately, and leakage can appear at the transponders such that (1) the S RHCP  signal introduces significant interference to the LHCP transponder, and (2) the S LHCP  signal also introduces significant interference to the RHCP transponder. 
         [0044]    To lower the interference of S LHCP  to the RHCP transponder, the LP ground terminal  510  can be configured such that the input of the wavefront muxing processor for the signal S RHCP  is grounded. Before the optimal state is attained, the signal S LHCP  appears at the LHCP transponder as the primary signal and also becomes interference at the RHCP transponder. The leakage of S LHCP  then appears at the feedback aperture  610  and the feedback signal  602 . When the leakage of S LHCP  is significant, the correlation between the feedback signal  602  and the signal S LHCP  by itself, cached by the optimization element, becomes high. Adaptive A and Φ adjustment (namely, equalization) is required to compute the optimal weight for A and Φ adjustment that (1) minimizes the leakage of S LHCP  at the RHCP transponder  104  and the feedback aperture  610  and (2) further minimizes the correlation between the feedback signal  602  and the signal S LHCP  by itself, which is cached by the optimization element. This procedure not only calibrates the leakage effect introduced by the differential amplitude (A) and phase (Φ), but also minimizes this leakage through computation of optimal weight for A and Φ adjustment. 
         [0045]      FIG. 7  depicts the diagram within the “Polverter” function for those applications alike that in  FIG. 6 . The wavefront muxing processor  408  has one grounded input S 1  that resembles the signal S RHCP , and a second input S 2  that resembles the signal S LHCP . The wavefront muxing processor  408  has function of 3 dB-hybrid equipped with phase-shifting devices  400 . If there is imbalance between the HP and the VP paths, there is a requirement of compensation on amplification and phase delay of both paths. Let a complex-valued parameter α denote the relative imbalance of amplification and phase delay on the HP path with respect to the VP path. Before the optimal state is attained, without loss of generality, the VP-output  404  can still be treated as (S 1 +iS 2 )/√{square root over (2)} v , and the HP-output  406  can be represented by α(S 2 +iS 1 )/√{square root over (2)} h . Effectively, the S 1  signal appears in the format S 1   v +iαS 1   h , which indicates a right-hand elliptically-polarized (RHEP) waveform. Concurrently, the S 2  signal appears in the format iαS 2   v +S 2    h , which indicates a left-hand elliptically-polarized (LHEP) waveform. It is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , and (2) the feedback signal  602  diminishes such that its correlation with the S 2  signal is significantly lower than a level. 
         [0046]      FIG. 8  depicts the functional relation between the amplitude (A) and phase (Φ) adjustment element  700  and the optimization element  704 . The input B of the A and Φ adjustment element  700  represents one weighted sum α(S 2 +iS 1 )/√{square root over (2)} h . The main function of the A and Φ adjustment element  700  is to produce an output C that equals the multiplication of B and a weighting factor w, namely C=B×w. In the optimal state, the weighting factor w shall eliminates the effect of the imbalance parameter α completely, which implies w=1/α. However, α is a unknown parameter, and hence needs to be learned in an engineered process. As a matter of fact, in its optimal state, the optimization element  704  shall have zero or significantly low feedback signal  602 , which shall also bear extremely low correlation with the S 2  signal if the host LP ground terminal is designed to only access the RHCP channel. 
         [0047]    The optimization element  704  carries out the following routines iteratively. (1) An objective function ƒ o  is evaluated to quantify the correlation between the feedback signal  602  and the S 2  signal if the host LP ground terminal is designed to only access the RHCP channel; (2) the current weighting factor w n  sent through interface  800  at the n-th iteration is perturbed by some variation term δw multiplied by a control factor β n ; (3) perturbed weight w n +β n  δw is computed and then sent through interface  802  to the A and Φ adjustment element  700 ; (4) the gradient of ƒ o , ∇ w ƒ o , is approximated in terms of the change of ƒ o  and δw; and (5) updated weight w n+1  for the (n+1)-th iteration is computed by w n+1 =w n +γ n ∇ w ƒ o , where γ n  is a control factor. 
       Embodiment 2 
       [0048]    In another embodiment, the “Polverter” function is configured to enable transmitting LP ground terminal  510  with access only to LHCP channels while limiting the interference to RHCP channels. The “Polverter” function is configured in a way similar to  FIG. 7 , but its wavefront muxing processor  408  has one grounded input S 2  that resembles the signal S LHCP , and a second input S 1  that resembles the signal S RHCP . It is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , and (2) the feedback signal  602  diminishes such that its correlation with the S 1  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall have zero or significantly low feedback signal  602 , which shall also bear extremely low correlation with the S 1  signal if the host LP ground terminal is designed to only access the LHCP channel. 
         [0049]    The optimization element  704  carries out the following routines iteratively. (1) An objective function ƒ o  is evaluated to quantify the correlation between the feedback signal  602  and the S 2  signal if the host LP ground terminal is designed to only access the LHCP channel; (2) the current weighting factor w n  sent through interface  800  at the n-th iteration is perturbed by some variation term δw multiplied by a control factor β n ; (3) perturbed weight w n +β n  δw is computed and then sent through interface  802  to the A and Φ adjustment element  700 ; (4) the gradient of ƒ o , ∇ w ƒ o , is approximated in terms of the change of ƒ o  and δw; and (5) updated weight w n+1  for the (n+1)-th iteration is computed by w n+1 =w n +γ n ∇ w ƒ o , where γ n  is a control factor. 
       Embodiment 3 
       [0050]    In another embodiment, the CP channels comprise (1) communication links between the transmitting LP ground terminals  510  and CP satellites, (2) CP satellites with RHCP and LHCP transponders, (3) communication links between the CP satellites and receiving CP devices, (4) communication links between the CP satellites and the receiving feedback CP aperture  610  and (5) communication links between the receiving feedback CP terminals and the LP ground terminals  510 . 
         [0051]    The “Polverter” function is configured to enable transmitting LP ground terminal  510  with access only to RHCP transponder while limiting the interference to LHCP transponder. The “Polverter” function is configured in a way as shown in  FIG. 7 , in which wavefront muxing processor  408  has one grounded input S 1  that resembles the signal S RHCP , and a second input S 2  that resembles the signal S LHCP . It is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , and (2) the feedback signal  602  diminishes such that its correlation with the S 2  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall have zero or significantly low feedback signal  602 , which shall also bear extremely low correlation with the S 2  signal if the host LP ground terminal is designed to only access the RHCP transponder. 
       Embodiment 4 
       [0052]    In another embodiment, the “Polverter” function is configured to enable transmitting LP ground terminal  510  with access only to LHCP transponder while limiting the interference to RHCP transponder. The “Polverter” function is configured in a way similar to  FIG. 7 , in which wavefront muxing processor  408  has one grounded input S 2  that resembles the signal S LHCP , and a second input S 1  that resembles the signal S RHCP . It is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , and (2) the feedback signal  602  diminishes such that its correlation with the S 1  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall have zero or significantly low feedback signal  602 , which shall also bear extremely low correlation with the S 1  signal if the host LP ground terminal is designed to only access the LHCP transponder. 
       Embodiment 5 
       [0053]    In another embodiment, the “Polverter” function is configured to enable transmitting LP ground terminal  510  with separate access to RHCP and LHCP transponders independently. The “Polverter” function  910  is configured in a way as shown in  FIG. 9 , in which wavefront muxing processor  408  has one input S 1  that resembles the signal S RHCP , and a second input S 2  that resembles the signal S LHCP . Without the amplitude (A) and phase (Φ) adjustment element  700 , the signal S RHCP  would become RHEP and introduce interference to the LHCP transponder, and likewise the signal S LHCP  would become LHEP and introduce interference to the RHCP transponder. It is necessary to minimize the leakage effects introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , (2) the feedback signal  602   a  sent by the CP feedback unit  920  diminishes such that its correlation with the S 2  signal is significantly lower than a level, and, (3) the feedback signal  602   b  sent by the CP feedback unit  920  diminishes such that its correlation with the S 1  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall (1) have zero or significantly low feedback signal  602   a , which shall also bear extremely low correlation with the S 2  signal if the S 1  signal is authorized to only pass through the RHCP transponder, and (2) have zero or significantly low feedback signal  602   b , which shall also bear extremely low correlation with the S 1  signal if the S 2  signal is authorized to only pass through the LHCP transponder. 
       Embodiment 6 
       [0054]    In another embodiment, the CP channels comprise (1) communication links between the transmitting LP ground terminals  510  and CP unmanned aerial vehicles (UAVs), (2) CP UAVs with RHCP and LHCP communication assets, (3) communication links between the CP UAVs and receiving CP devices, (4) communication links between the CP UAVs and the receiving feedback CP terminals  610  and (5) communication links between the receiving feedback CP terminals and the LP ground terminals  510 . 
         [0055]    The “Polverter” function has various configurations to enable transmitting LP ground terminal  510  with access to CP UAVs. In a first configuration, the “Polverter” function is configured in a way as shown in  FIG. 7 , in which wavefront muxing processor  408  has one grounded input S 1  that resembles the signal S RHCP , and a second input S 2  that resembles the signal S LHCP . It is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , and (2) the feedback signal  602  diminishes such that its correlation with the S 2  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall have zero or significantly low feedback signal  602 , which shall also bear extremely low correlation with the S 2  signal if the host LP ground terminal is designed to only access the RHCP communication assets of UAVs. 
         [0056]    In a second configuration, the “Polverter” function is configured in a way similar to  FIG. 7 , in which wavefront muxing processor  408  has one grounded input S 2  that resembles the signal S LHCP , and a second input S 1  that resembles the signal S RHCP . It is necessary to minimize the leakage effect introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , and (2) the feedback signal  602  diminishes such that its correlation with the S 1  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall have zero or significantly low feedback signal  602 , which shall also bear extremely low correlation with the S 1  signal if the host LP ground terminal is designed to only access the LHCP communication assets of UAVs. 
         [0057]    In a third configuration, the “Polverter” function is configured in a way as shown in  FIG. 9 , in which wavefront muxing processor  408  has one input S 1  that resembles the signal S RHCP , and a second input S 2  that resembles the signal S LHCP . Without the amplitude (A) and phase (Φ) adjustment element  700 , the signal S RHCP  would become RHEP and introduce interference to the LHCP transponder, and likewise the signal S LHCP  would become LHEP and introduce interference to the RHCP transponder. It is necessary to minimize the leakage effects introduced by the imbalance parameter α in order to ensure (1) the amplitude (A) and phase (Φ) adjustment element  700  makes use of the optimal weighting factor computed by the optimization element  704 , (2) the feedback signal  602   a  diminishes such that its correlation with the S 2  signal is significantly lower than a level, and, (3) the feedback signal  602   b  diminishes such that its correlation with the S 1  signal is significantly lower than a level. As a matter of fact, in its optimal state, the optimization element  704  shall (1) have zero or significantly low feedback signal  602   a , which shall also bear extremely low correlation with the S 2  signal if the S 1  signal is authorized to only pass through the RHCP communication assets of UAVs, and (2) have zero or significantly low feedback signal  602   b , which shall also bear extremely low correlation with the S 1  signal if the S 2  signal is authorized to only pass through the LHCP communication assets of UAVs. 
       Embodiment 7 
       [0058]    Referring to  FIG. 9 , a communications system comprises of mainly (1) a linearly-polarized (LP) transmitting terminal  510  transmitting a horizontally polarized (HP) signal through a HP port and a vertically polarized (VP) signal through a VP port at a common frequency slot through circularly-polarized (CP) channels  104  and  106 ; (2) a polarization-conversion element  910 , or “Polverter” function, in the transmitting LP terminal modifying the relative amplitude and phase of the HP and the VP signals by the amplitude (A) and phase (Φ) adjustment element  700 ; and (3) a circularly-polarized (CP) feedback unit  920  with a receiving aperture  610  receiving feedback signals from said CP channels  602   a  and  602   b . In a perfect world, the output of a RHCP transponder  104  and that of a LHCP transponder  106  for a CP transponding satellite  930  should feature, respectively, only amplified and frequency translated signals from S RHCP  and S LHCP , namely the two CP inputs in the ground transmitter  510 . In a real world, both transponders will have leakages from the other CP channel in a common frequency slot due to propagation differentials both in amplitudes and phases among devices and in-space in the two CP channels. The “Polverter” function  910  on the ground transmitting site will perform pre-compensation iteratively to equalize the propagation amplitude and phase differentials, minimizing or eliminating the leakage signals or interferences. 
         [0059]    The communications system may become a terminal with combining functions of the CP feedback unit  920  and those of the transmitting LP terminal  910 . The terminal with combined function will be transmitting the LP signals to the CP channels  104  and  106  while receiving feedback signals from the CP channels  602   a  and  602   b . It is also possible to have a separated terminal, which may have a mode for performing all functions of the CP feedback unit  920 , which will be relayed back to the terminal  510  with all transmitting functions. 
         [0060]    The communications system further comprises of methods of transmitting a first signal S RHCP  in right-hand circularly-polarized (RHCP) formats through a 3 dB hybrid with functions of multiplying the first signal by a first complex weighting factor and transmitting the first weighted first signal through said VP feed port; and multiplying the first signal by a second complex weighting factor and transmitting the second weighted first signal through said HP feed port. Similarly the communications system also comprises methods of transmitting a second signal S LHCP  in left-hand circularly-polarized (LHCP) formats through the same 3-dB hybrid with functions of multiplying the second signal by a third complex weighting factor and transmitting the first weighted second signal through the VP feed port; and multiplying the second signal by a fourth complex weighting factor and transmitting the second weighted second signal through the HP feed port. 
         [0061]    It is also possible to configure the communications system to further comprise of methods of concurrently transmitting a first signal S RHCP  in RHCP and a second signal S LHCP  in LHCP formats through the same 3 dB hybrid with functions of (1) multiplying said first signal S RHCP  by a first complex weighting factor and the second signal S LHCP  by a third complex weighting factor, then transmitting the first weighted sum of the first weighted first signal and the third weighted second signal through said VP feed port; and (2) multiplying the first signal S RHCP  by a second complex weighting factor and the second signal S LHCP  by a fourth complex weighting factor, then transmitting a second weighted sum of the second weighted first signal and the fourth weighted second signal through the HP feed port. 
         [0062]    Furthermore in the communications system, it is also possible to transmit a first signal S RHCP  at a normal power level P 0  radiating through a RHCP channel and transmitting a second signal S LHCP  at a power level less than P 0 -10 dB through a LHCP channel among the CP channels from the transmitting LP ground terminal at said common frequency slot. The communications system further comprises of methods of radiating signal from the transmitting LP ground terminal to a desired CP satellite. 
         [0063]    The 3-dB hybrid in the polarization-conversion element in the transmitting LP ground terminal may be implemented by software functions comprising methods of processing a first input S RHCP  and a second input S LHCP , and outputting a first output signal for HP port transmitting and a second output signal for VP port transmitting. In addition, following the 3 dB hybrid, its two outputs are subjected for further processing by an equalizer preprocessing for equalization of path differentials. The first output signal of the equalizer comprised a weighted sum from said first input VP weighted by a first complex weight and said second input HP weighted by a second complex weight; and the second output comprising another weighted sum from said first input VP weighted by a third complex value and said second input HP weighted by a fourth complex value. In  FIG. 9 , the equalizer shown features a single complex multiplication on the HP output arm of an idealized 3-dB hybrid. It is also using the VP arm for signal amplitude and phase references in the equalization process by assigning the first  3  from the 4 complex weights to zero. 
         [0064]    The methods for said polarization-conversion element further comprise of methods of calculating and optimizing the first, the second, the third, and the fourth complex weights by an optimization processor by (1) inputting a third input in a RHCP format, received by a feedback CP unit  920  and duplicating said second input S LHCP , and then performing correlation calculation between the third input and the duplicated second input, (2) then converting the correlation calculation results into a current total cost through a mapping process, (3) measuring gradient of said total cost, and finally deriving new weights according to optimization algorithms for next weighting update. The mapping process can be implemented as a table look-up, converting sets of “observable” into sets of “measurable.” The weight optimization in the polarization-conversion element further comprises of methods of minimizing the total cost between the second and the third inputs for iteratively updating and optimizing the complex weights. 
         [0065]    The polarization-conversion element may also comprises of methods of calculating correlation between a third input in a LHCP format sent by the CP feedback channel  602   b , and the duplicated second input data stream S LHCP , wherein methods of duplication further comprising of caching said second to-be-LHCP-formatted-input S LHCP  in the transmitting LP ground terminal 
         [0066]    The communications system will allow a transmitting terminal  510  radiating a desired communications signal to a LHCP channel as a desired channel and radiating a low intensity probing reference signal to a RHCP channel among the CP channels  104  and  106  in the common frequency slot. The communications system further comprises of methods of radiating low power level interference through the transmitting LP ground terminal  510  to a RHCP channel  104  or a LHCP channel  106  among many CP channels. 
         [0067]    The polarization-conversion element  910  may further comprise of methods of (1) receiving a first input S RHCP  through replicating RHCP components of transmitting signals of the LP transmitting terminal  510 , (2) receiving a second input S LHCP  by replicating LHCP components of transmitting signals of the LP transmitting terminal  510 , (3) receiving a third input via replicating received RHCP signals  602   a  of the CP feedback unit  920 , (4) receiving a fourth input by replicating LHCP received signals  602   b  of said CP feedback unit  920 . The polarization-conversion element  910  then calculates current first correlations between the first input and the third input, and second correlations between the first input and the fourth input. The polarization-conversion element  910  also calculates third correlations between the second input and the third input, and fourth correlations between the second input and the fourth input. 
         [0068]    The communications system transmits through many CP channels; some of the CP channels may go through CP satellite transponders  104  and  106  for satellite communications. The methods of receiving feedback signals from the CP channels  602   a  and  602   b  will comprise of methods of receiving signals through CP satellite transponders  104  and  106 . 
         [0069]    The proposed systems are applicable to many terrestrial applications. The methods for transmitting through CP channels may comprising methods of transmitting to CP ground terminals via terrestrial based or airborne CP channels. The communications system for transmitting through CP channels may further comprise of methods of transmitting through transponders in UAVs. The UAVs may feature RHCP and LHCP communication assets. On the other hand, the communications system of transmitting through CP channels may further comprise methods of transmitting through multiple LP transponders in UAVs, wherein each of said UAVs comprising VP or HP communication assets. 
       REFERENCE 
       [0000]    
       
         1. U.S. Pat. No. 8,538,326 B2, “Accessing LP Transponders with CP Terminals via Wavefront Multiplexing Techniques,” published on Sep. 17, 2013.