Abstract:
The invention is about a method and apparatus for grouping multiple satellite transponders with both (LP) polarization formats in different frequencies through Wave-Front (WF) Multiplexing (muxing) techniques for ground terminals with incompatible (CP) polarization formats. As a result of this invention, linear polarized (LP) transponders can be accessed and efficiently utilized by circularly polarized (CP) ground terminals and vice versa. This invention consists of conventional ground terminals, a unique organization of space assets, and a unique polarization alignment processor. The applications of wavefront multiplexing techniques to satellite communications offer many potential advantages, including improved flexibility and utility efficiency of existing space assets. Our proposed “Polarization Utility Waveforms” is an entirely new concept in VSAT and Earth Station Antenna diversity. The implementation enables antennas to switch between different polarization formats at the press of a button, and provides tele-port operators with greater flexibility in how they manage their assets.

Description:
RELATED APPLICATION DATA 
       [0001]    This application, pursuant to 35 U.S.C. §119(e), is a continuation of U.S. patent application Ser. No. 12/847,997 Filing on Jul. 30, 2010. This application, pursuant to 35 U.S.C. §119(e), also claims the benefit of U.S. provisional patent application 61/497,852 filed Jun. 16, 2011. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to radio frequency communications devices. More particularly, it relates to allowing satellite transponders and ground terminals that utilize one polarization method (linear or circular polarization) to be able to cross-communicate with each other via wavefront multiplexing techniques. This offers many potential advantages, including but not limited to improved flexibility and increased efficiency of existing assets. 
         [0004]    2. Description of Related Art 
         [0005]    Satellite Communications (SATCOM) technologies have increased dramatically and have transitioned to IP-based services consistent with concepts for net-centric operations. Their increased use has resulted in a proliferation of IP-based products using satellites for back-bone or transport applications. On the other hand, high-speed satellite communications for access typically emanate from reflector antennas that basically radiate and receive in narrow beams. 
         [0006]    Compatible polarization configurations between terminals and space assets are essential to efficient satcom links. It is generally true that the LP polarized terminals will use LP transponders, and CP terminals relay data via CP transponders. When ground terminals switch services from a provider with CP satellites to another one with LP satellites, their antenna polarizations are reconfigured accordingly, to prevent 3 dB SNR losses in receiving (Rx) functions on the one hand, and to avoid generating unwanted radiations in transmit (Tx) functions on the other hand. Our approach is very different than those of polarization switching, and would not require users to switch polarizations based on their equipment. Circularly Polarized (CP) users can use their existing terminals to relay data to CP destinations via linearly polarized (LP) transponders. There are no space asset losses due to the incompatibility. The method of LP space asset reorganization is the key for operationally circumventing the “incompatibility” issue. 
         [0007]    A concept of the virtual-link concurrently utilizes N communications links organized by Wavefront (WF) Multiplexing (Muxing). A WF carrying a signal stream features a fixed spatial phase distribution among selected N parallel links, which support up to N orthogonal WFs carrying N independent signals concurrently from a source to a destination. The virtual link techniques are referred to as Orthogonal Wave-Front Diversity Multiplex (OWFDM), and the enabling signal structures as OWFDM waveforms. 
         [0008]    Virtual links can be applied for satellite communications transporting data within a field of views common to selected transponders. Our proposed “Polarization Utility Waveforms” can successfully deliver signals via LP transponding satellites using CP ground terminals, and vice versa. They are engineered via techniques of signals spreading over multiple transponders. The waveforms may look like OFDM waveforms and also may appear as MIMO formats, but they are not. They are subsets of OWFDM waveforms and may feature unique format interconnecting OFDM and MIMO through an orthogonal signal structure. 
         [0009]    WF muxing/demuxing techniques are powerful tools for path length equalizations among parallel paths/channels. SDS has applied these techniques for various applications; (1) Power combining from multiple transponders from the same satellites and/or different transponding satellites [ 1 ], (2) back channel equalization for ground based beam forming process in satellite applications [ 2 ], and (3) Distributed data storage [ 3 ]. 
       Uniqueness of the OWFDM 
       [0010]    Unlike OFDM for commercial wireless communications feature waveforms with multiple orthogonal sub-carriers uniformly distributed in a frequency band, our proposed OWFDM techniques will spread transmitting (Tx) signals into multiple channels with a unique phase distribution pattern, referred to as a wavefront (WF). These channels may be assigned to different frequency slots, time slices, polarizations, and/or orbital positions when these space assets are available. The selected multi-dimensional waveforms may be dynamic, and reconfigurable. There will always be embedded pilot signal streams through the same propagating paths, but distributed in phase distribution patterns orthogonal to the one which carries the desired signal stream. In short, the WFs are orthogonal to one another. 
         [0011]    In general, the OWFDM waveforms must meet existing SATCOM polarization and frequency convention restrictions. At a ground station, transmitting (Tx) signals may be preprocessed by a WF multiplexer (muxer), which spreads coherent signals into multiple channels concurrently in the form of an orthogonal structure in a selected N-dimensional domain. The generated orthogonality is among multiple wavefronts (WFs). With N parallel propagating channels, there are N-orthogonal WFs available. Probing signal streams will be attached to at least one of them. The remaining WFs are available for various Tx signal streams. 
         [0012]    Signals originated from a ground terminal propagating through various uplink carriers/paths, including multiple transponders on a satellite or among many satellites, and different down link frequencies/paths arriving at a destination feature differential phase delays, Doppler drifts, and amplitude amplifications/attenuations. 
         [0013]    Post processing implemented at receiving (Rx) sites will equalize the differential phase delays, frequency drifts and amplitude attenuations among signals through propagating paths. Calibrations and equalizations take advantages of embedded probe signals and iterative optimization loops. There are no feedbacks required through back channels. As a result of the equalizations, the Rx WFs become orthogonal, and the attached signals streams are then precisely reconstituted by the WF demuxer. 
       SUMMARY OF THE INVENTION 
       [0014]    This invention presents a subset of OWFDM waveforms taking advantage of polarization incompatibility (CP vs. LP) to access available space assets when the ground terminals are not polarization compatible. We will present the operation concepts and associated mechanisms for CP-equipped terminals to access LP satellites without sacrificing space asset utility efficiencies and capacity. Similar methods can be implemented for LP terminals to access CP satellites. In addition, these techniques also enable sources with CP terminals to communicate sinks with LP terminals via satellite assets with either CP or LP polarization formats as long as the sources and sinks are within the field of view of the selected satellite assets. 
         [0015]    Special OWFM waveforms are constructed under the constraints that all the user terminals feature only one of the two available CP options while the space assets in geostationary satellites feature both LP channels of separated transponders in an orbital slot. As a result, the targeted LP space assets support not only regular LP users but also additional CP customers without power and bandwidth capacity losses due to the polarization incompatibility. 
         [0016]    We will use SCPC (single channel per carrier) channels as examples for illustrations. However, the concepts can be extended for scenarios such as MSPC cases. SCPC refers to using a single signal at a given frequency and bandwidth so the satellite bandwidth is dedicated to a single source. Multiple channels per carrier (MCPC), on the other hand, uses several subcarriers that are combined into a single bitstream before being modulated onto a carrier transmitted from a single location to one or more remote sites. 
         [0017]    Among additional benefits, these techniques will provide means for dynamic space resource allocations such as down link power, or equivalently D/L EIRP. Various channels, such as SCPCs in different transponders, are grouped and utilized by multiple users via OWFDM, therefore, the combined “power” assets can be dynamically assigned to any of the users as long as the total power outputs are constant. For example, two independent CP users accessing a two convention 5 W CP SCPC channels separately, both user may only draw a maximum of 5 W. On the other hand, when the same independent CP users accessing two 5 W LP SCPC channels organized by OWFDM concurrently, the first user may draw 8 W while the second user only need 2 W, and at a later time the first user may not need to transmit any more while the second user can access both transponders coherently to get 10 W equivalent “transponder power”; or a 3 dB more gain on equivalent EIRP. 
       REFERENCES 
       [0000]    
       
         1. U.S. patent application Ser. No. 12/462,145; “Communication System for Dynamically Combining Power from a Plaurality of Propagation Channels in order to Improve Power Levels of Transmitted Signals without Affecting Receiver and Propagation Segments,” by D. Chang, initial filing on Jul. 30, 2009. 
         2. U.S. patent application Ser. No. 12/122,462; “Apparatus and Method for Remote Beam Forming for Satellite Broadcasting Systems,” by Donald C. D. Chang; initial filing May 16, 2008 
         3. U.S. patent application Ser. No. 12/848,953. “Novel Karaoke and Multi-Channel Data Recording/Transmission Techniques via Wavefront Multiplexing and Demultiplexing,” by Donald C. D. Chang, and Steve Chen Initial Filing on Aug. 2, 2010 
         4. U.S. patent application Ser. No. 12/847,997; “Polarization Re-alignment for Mobile Satellite Terminals,” by Frank Lu, Yulan Sun, and Donald C. D. Chang; Filing on Jul. 30, 2010 
       
     
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0022]      FIG. 1  depicts simplified block diagram of a LP satellite accessed by two CP terminals to relay independent data streams to a CP hub station. It displays return-links from two users to a hub. 
           [0023]      FIG. 2  illustrates three sets of selected SCPC channels on a LP satellite to accommodate CP users. Each set features two SCPC channels on a common frequency slot. 
           [0024]      FIG. 3  illustrates the corresponding forward links for the two users in  FIG. 1 . 
           [0025]      FIG. 4  illustrates the corresponding forward links for the two users in  FIG. 1  but from a LP hub. 
           [0026]      FIG. 5   a  depicts two mathematic matrixes, with one on the left a 2-to-2 Wavefront muxing matrix for two-signal processing, while the one on the right is a 4-to-4 math matrix. The symmetric matrix on the left is constructed under the constraints that all the user terminals feature only one of the two available CPs. The symmetric matrix on the right is constructed under the constraints that all the user terminals feature only one of the two available CPs but with both frequency slots. 
           [0027]      FIG. 5   b  depicts the two mathematic matrix equations converting CP signals into LP channels as they are captured by LP satellite. The differential propagation effects are not included. The one on the left represents the conversions of two CP signals, s 1  in RHCP and s 2  in LHCP, into two aggregated LP signals in an HP and a VP SCPC channels. The one on the right is a 4-to-4 mathematic matrix equation representing signal conversions in four LP SCPC channels; two in HP and two in VP at two identical frequency slots. The symmetric matrix is constructed under the constraints that all the user terminals feature only one of the two available CPs but with both frequency slots. 
           [0028]      FIG. 5   c  illustrates a simplified block diagram of a LP satellite accessed by four CP terminals to relay independent data streams back to a CP hub station utilizing the same matrix conversion assumptions in  FIG. 5   b . It displays return-links from four users to a hub. The architecture is constructed under the constraints that all the user terminals feature only one of the two available CPs but with both frequency slots. 
           [0029]      FIG. 5   d  illustrates a simplified block diagram of an implementation technique for  FIG. 5   c . Standard low-noise amplifiers (LNAs) and high power amplifiers (HPAs) are not shown. Diagnostic signals (pilots) are imbedded to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions. 
           [0030]      FIG. 6  illustrates a simplified block diagram of an implementation technique similar to for  FIG. 5   d . It is for scenarios with multiple LP channels in two satellites at a common frequency slot, instead of multiple LP channels in two common frequency slots in a satellite. Standard low-noise amplifiers (LNAs) and high power amplifiers (HPAs) are not shown. Diagnostic signals (pilots) are embedded to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0031]      FIG. 1   100  illustrates examples of our proposed techniques assuming that CP satcom ground terminals are within a common field of view of both transponding satellites. They are return-links (RL) examples depicting communications from 2 remotes to a hub through transponding satellites. 
         [0032]    Panel (a)  110  illustrates a conventional technique accessing a CP space asset  112  via CP terminals  111  and  113 . Terminals  1   111   a  and  2   111   b  are relaying independent data streams s 1 ( t ) and s 2 ( t ) to a hub through a CP satellite  112 . The terminal  1   111   a  in right-hand circularly-polarized (RHCP) is allocated for RHCP SCPC channel  112   a  at a frequency slot, fo, on the CP satellite. SCPC stands for Single channel per carrier and refers to using a single signal stream at a given frequency and bandwidth. Similarly, the terminal  2   111   b  in left-hand circularly-polarized (LHCP) is allocated for a second SCPC channel  112   b  at the same frequency slot, fo, but in LHCP on the satellite. As a result, s 1 ( t ) goes through a RHCP transponder while s 2 ( t ) is independently conditioned by another transponder in LHCP, respectively. Hub  113  receives both s 1 ( t ) and s 2 ( t ) independently through separated antenna ports; s 1 ( t ) from a RHCP port and s 2 ( t ) a LHCP port. 
         [0033]    Panel (b)  120  depicts an operational scenario where CP terminals  111  relay data through a LP satellite  122 . Specifically, SCPC channels  122   a  and  112   b  are used in the LF satellite, with 1 HP and 1 VP channels on an identical frequency slot. 
         [0034]    Mathematically, we select a set of 2-dimensional orthogonal Wave-Front (WF) vectors [1, i] and [1, −i] to match with the signal structures of polarizers for RHCP and LHCP signals. The 2-to-2 WF muxers and demuxers are implemented by analog polarizers in RF instead of 2-to-2 FFT digital processors. 
         [0000]        S 1( t )=+[ v+hi]s 1( t )  (1a)
 
         [0000]        S 2( t )=[ v−hi]s 2( t )  (1b)
 
         [0000]    S 1  radiated by terminal  111   a  feature RHCP while S 2  by terminal  111   b  is in a LHCP format. Equivalently, S 1  in RHCP is transmitted in both HP and VP with a fixed phase distribution, where the phase in HP is always 90° ahead of that in VP. 
         [0035]    As the S 1  signals in RHCP arrive at LP satellite  122 , both VP and HP components will be picked up concurrently by two SCPC channels at a common frequency slot with one in VP  122   a  and the other in HP  122   b  transponders accordingly as depicted. 
         [0036]    Similarly, S 2  is also transmitted in both HP and VP concurrently with a fixed phase distribution, with the phase in HP is always 90° behind that in VP. As the S 2  signals in LHCP arrive at LP satellite  122 , both VP and HP components will be picked up “concurrently” by two SCPC channel; one in VP  122   a  and the other in HP  122   b  transponders accordingly as depicted. 
         [0037]    Each LP SCPC channel is occupied by two independent signals s 1  and s 2  concurrently. As far as each SCPC channel is concerned, the two signals are not separable since they are not multiplexed by code, time or frequency. On the other hand, there are “relationships” between the two s 1  signals in both SCPC channels, and similarly but different relationships for s 2  signals. The two sets of relationships are two orthogonal “wavefronts” (WFs). Because the unique relationship, s 1  and s 2  can be separated and recovered when both SCPC channels are processed simultaneously. 
         [0038]    The conditioned signals by VP SCPC  112   a  and HP SCPC  122   b  are designated as Yh (t) and Yv(t), respectively. The amplitude attentuations and phased delays due to propagation and on board electronics for the HP and VP paths are identified as (Ah and Av) and (α and β) respectively. 
         [0039]    The signals arriving at a CP hub and the RF polarizer from Rx CP antennas will serve as WF demuxer functions, where the two concurrent CP antenna outputs will be 
         [0000]        Zrhcp ( t )=[ Av exp( j α)* Yv ( t )− iAh exp( j β)* Yh ( t )]/2  (2a)
 
         [0000]        Zlhcp ( t )=[ Av exp( j α)* Yv ( t )+ iAh exp( j β) Yh ( t )]/2  (2b)
 
         [0040]    Furthermore, in terms of s 1  ans s 2 , Equation (1) can be re-written as 
         [0000]        Zrhcp ( t )=[ Av exp( j α)*( s 1 +s 2)− iAh exp( j β)*( is 1 −is 2)]/2 =s 1 [Av exp( j α)+ Ah exp( j β)]/2 +s 2 [Av exp( j α)− Ah exp( j β)]/2,  (3a)
 
         [0000]        Zlhcp ( t )=[ Av exp( j α)*( s 1 +s 2) Yv ( t )+ iAh exp( j β)( is 1 −is 2)]/2 =s 1 [Av exp( j α)− Ah exp( j β)]/2 +s 2 [Av exp( j α)+ Ah exp( j β)]/2.  (3b)
 
         [0041]    The two wavefronts will no longer by orthogonal by the time they arrive at destination  113 . Diagnostic and equalization circuits  124  are implemented to dynamically compensate for the amplitude and phase differentials among the HP and VP paths. As the amplitude and phase effects on the two paths are equalized, the WFs become orthogonal, and the associated signals can then be precisely reconstituted. 
         [0042]    From the point of view of satellite operators, the LP space assets (RF power and frequency bandwidth) from SCPC channels  112   a  and  112   b  are grouped together and shared by two separate users via unique orthogonal waveforms in conventional RHCP and LHCP. Each SCPC channel transponds to one of the aggregated wavefront components (wfc). It always takes two components to re-construct relayed signals 
         [0043]    It should be noted that the two linear transponders may not be from the same satellite. There are occasions where two LP transponders covering the same service areas are from two different satellites. 
         [0044]      FIG. 2   200  depicts a typical uplink frequency plan of a C-band satellite with 24 transponders, 36 MHz bandwidths for individual transponders with a 4 MHz guide band in between adjacent slots. HP transponders  220  are numbered odd, while VP transponders  210  are even-numbered, while the center frequencies of the two sets are offset by 20 MHz. 
         [0045]    Among the total 864 MHz (36 MHz*24) available LP bandwidth, 736 MHz are convertible for serving CP users due to a fixed frequency offset among the HP and VP transponders and 4 MHz guard bands among adjacent transponders. The remaining 128 MHz bandwidth can only serve LP users. 
         [0046]    Three pairs of the communications channels, ( 211   a ,  221   a ), ( 211   b ,  221   b ), and ( 211   c ,  221   c ), at three different frequency slots are identified. Each pair features both HP and VP channels, illustrating two selected SCPC channels on a LP satellite to accommodate two CP users. 
         [0047]      FIG. 3   300  depicts the same scenario as that in  FIG. 1 , except it is for “forward links” communications flows from CP hub  313  to CP remotes  311  through LP satellite  312 . Preprocessing unit  324  in the hub is used to “pre-compensate” for the amplitude and phase differentials among the two propagation paths. Relay satellite  312  covers both source and destinations. Signals in the corresponding down-link channels for terminal- 1   311   a  and terminal- 2   311   b  are available locally at the source location  313 . These signals can be used as those from feedback channels for the pre-compensation processing  324 . 
         [0048]      FIG. 4   400  depicts the similar scenario as that in  FIG. 3  in that  FIG. 4  also depicts “forward links” communications flows.  FIG. 3  is from CP hub  313  to CP remotes  311  through LP satellite  312 .  FIG. 4  depicts signals transmit from LP hub  413  to two CP remotes  411  through LP satellite  412 . LP hub  413  requires transmission capabilities for both HP and VP polarization. Pre-processing unit  414  performs two linear combinations combining s 1  (the signals for terminal- 1   411   a ), and s 2  (the signal for terminal- 2   411   b ) signals. The weightings among the two linear combinations are to generate two equivalent CP signals at anticipated destinations  411   a  and  411   b , and shall include effects from propagations and unbalanced electronics on ground and in space. Coverage from relay satellite  412  includes both source  413  and destination locations  411   a  and  411   b . Signals in the corresponding down-link channels for terminal- 1  and terminal- 2  are available locally at source location  413 . These signals will be used as those from feedback channels to optimize pre-compensation processing  414 . 
         [0049]      FIG. 5   a  depicts wavefront multiplexing matrixes  512  and  522  for CP user terminals to access multiple communications channels in LP satellites. The 2-by-2 matrix  512  converts two independent CP signals (RHCP  512   a  and LHCP  512   b ) into two signal streams in LP (one in HP and the other in VP). All signal streams (two inputs and two outputs) are at frequency slot f 1 . 
         [0050]    Similarly, 4-by-4 matrix  522  converts 4 independent CP signals (RHCP  522   a  and  522   c  and LHCP  522   b  and  522   d ). As a result, an input stream is replicated in every output stream, and each output stream consists of all input streams. 
         [0051]      FIG. 5   b  depicts the two mathematic matrix equations  510  and  520  converting CP signals into LP channels as they are captured by LP satellite. Differential propagation effects are not included. Matrix  510  represents the conversions of two CP signals  513 , s 1  in RHCP and s 2  in LHCP, into two aggregated LP signals  511  in HP and VP SCPC channels. Symmetrical conversion matrix  512  is the WF muxing processor and is referred as Mf 2 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0052]    It should be noted that Mf 2  can be used to convert two CP signals into two LP signals, and it can also convert two LP signals into two CP signals. Furthermore, 
         [0000]      ½ ·Mf 2· Mf 2* T   =I   (4b)
 
         [0053]    Mf 2  can be used as a WF muxer and its corresponding WF demuxer will be Mf 2 * T . The resulting wavefronts (WFs)  512   a  and  512   b  as depicted in  FIG. 5   a  are orthogonal to each other. 
         [0054]    Matrix  520  is a 4-to-4 mathematic equation representing signal conversions from 4 CP signals  523  in four LP SCPC channels  521 , with two in HP and two in VP at two identical frequency slots. The symmetric matrix  522  is constructed under the constraints that all the user terminals feature only one of the two available CPs but with both frequency slots. 
         [0055]    Symmetrical conversion matrix  522  is the WF muxing processor and is referred as Mf 4 , where 
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         [0000]    It should be noted that Mf 4  can be used to convert four CP signals into four LP signals, and can also convert four LP signals into four CP signals. Furthermore, 
         [0000]      ¼ ·Mf 4 ·Mf 4* T   =I   (5b)
 
         [0056]    Mf 4  can be used as a WF muxer and its corresponding WF demuxer will be Mf 4 * T . The four resulting wavefronts (WFs)  522   a ,  522   b ,  522   c , and  522   d  as depicted in  FIG. 5   a  are orthogonal to each other. 
         [0057]    In  FIG. 5   c    530 , two CP pairs are split for two common frequency slots; 1 pair of CP at fa and the other pair at fb. Similarly, the two LP pairs are for the same two common frequency slots; 1 pair of LP at fa and the other pair at fb. 
         [0058]    S 1  is a waveform occupying two RHCP channels, one at fa and the other at fb carrying signal s 1  radiated by terminal- 1   531   a.    
         [0059]    S 2  is a waveform occupying two LHCP channels, one at fa and the other at fb carrying signal s 2  radiated by terminal- 2   531   b    
         [0060]    S 3  is a waveform occupying two RHCP channels, one at fa and the other at fb carrying signal s 3  radiated by terminal- 3   531   c.    
         [0061]    S 4  is a waveform occupying two LHCP channels, one at fa and the other at fb carrying signal s 4  radiated by terminal- 4   531   d    
         [0062]    When these signals arrive at a LP satellite  532 , the 4 LP channels will feature the following aggregated signals: 
         [0063]    VP channel at fa  532   va : s 1 +is 2 +s 3 +is 4   
         [0064]    HP channel at fa  532   ha : is 1 +s 2 +is 3 +s 4   
         [0065]    VP channel at fb  532   vb : s 1 +is 2 −s 3 −is 4   
         [0066]    HP channel at fb  532   hb ; is 1 +s 2 −is 3 −s 4   
         [0067]    When these LP signals are radiated by LP satellite  532  and arrive at a desired destination with CP hub  533 , the 4 CP channels will feature the following aggregated signals, assuming the amplitude attenuations and phase delays among the 4 propagation channels are identical: 
         [0068]    RHCP channel at fa: y 1 ( t )=is 2 +is 4   
         [0069]    LHCP channel at fa: y 2 ( t )=s 1 +s 3   
         [0070]    RHCP channel at fb: y 3 ( t )=is 2 −is 4   
         [0071]    LHCP channel at fb; y 4 ( t )=s 1 −s 3   
         [0072]    A post processor, not shown, will calculate the s 1 , s 2 , s 3 , and s 4  according the received y 1 , y 2 , y 3 , and y 4 , accordingly. In addition, the post processor performs amplitudes and phase equalizations among the propagation paths. 
         [0073]    The relative phases between the CP components at two frequencies are critical. When the relative geometries among user  531 , satellite  532  and hub  533  are fixed, the cumulative phase difference among signals at two separate frequencies propagating from source  531  via satellite  532  to destination  533  is constant. The total accumulated phase difference is therefore a constant. However when targeted satellite  532  is slowly drifting relative to users  531  and hub  533 , the phase differences between two signals at two frequencies propagating from a use source location  531  to hub  533  will vary accordingly. In addition, there will be additional phase differentials due to Doppler effects 
         [0074]    At the destination  533 , there are four concurrent receiving functions; RHCPa, RHCPb, LHCPa, and LHCPb. The associated phase and amplitude differential effects among the 4 propagation channels at different frequencies and polarizations must be continuously calibrated and equalized to assure the orthogonality among multiple WFs when arriving at destination  533 . 
         [0075]      FIG. 5   d    540  illustrates a simplified block diagram of an implementation technique for  FIG. 5   c . Standard low-noise amplifiers (LNAs) and high power amplifiers (HPAs) are not shown. It depicts top level implementation concepts for the hub  533  as well as two  531   a  and  531   b  of the four users  531 . Terminal  541 - t   1  for user  531   a  features transmissions of an identical signal stream s 1  via two RHCP channels at fa and fb simultaneously. Embedded pilots for diagnostics are multiplexed  541 - 1  with a transmission stream x 1 ( t ). The mux processing may be a standard technique such as TDM, FDM, or CDM, minimizing bandwidth assets dedicated to probe signals supporting optimization loop  543 - 5  at the destination. The muxed signals are frequency up-converted  541 - 2  to two predetermined frequency slots before combined by a FDM output mux  541 - 3 . The muxed signals are amplified and radiated by an antenna  541 - 0  to the designated satellite  542 . 
         [0076]    Similarly, the terminal  541 - t   2  for a second user  531   b  features transmissions of another identical signal stream s 2  via two LHCP channels at fa and fb simultaneously. Embedded pilots for diagnostics are multiplexed  541 - 1  with a transmission stream x 1 ( t ). The mux processing may be a standard technique such as TDM, FDM, or CDM, minimizing bandwidth assets dedicated to probe signals supporting the optimization loop  543 - 5  at the destination. The muxed signals are frequency up-converted  541 - 2  to two predetermined frequency slots before combined by a FDM output mux  541 - 3 . The muxed signals are amplified and radiated by an antenna  541 - 0  to the designated satellite  542 . 
         [0077]    The selected satellite  542  provides two pairs of LP SCPC channels; the inputs for channels  542 - ha  and  542 - va  are at fa, and those for channels  542 - hb  and  542 - vb  are at fb. The corresponding output frequencies are at fa′ and fb′ respectively. 
         [0078]    At the destination  543 , antenna  543 - 0  features independent RHCP and LHCP ports. The received RHCP signals Y 1 ( t ) and LHCP signals Y 2 ( t ) after conditioning (amplified and filtered), are FDM de-muxed  543 - 1  and frequency down converted  543 - 2 , then fed into a bank of electronic filters  543 - 3   a  as an equalization mechanism before the WF demuxing processor  543 - 3   b . The WF demuxer  543 - 3   b  features  4  output ports dedicated for users  531 . Only two of the four are using the space asset for this example. 
         [0079]    The corresponding outputs are de-muxed  543 - 4 , separating desired signals x 1 ( t ), x 2 ( t ) and two sets of probe signals. The recovered probing signals are used by optimization loop  543 - 5  as diagnostic signals to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions. 
         [0080]      FIG. 6   600  illustrates a simplified block diagram of an implementation technique similar to  FIG. 5   d . It is for scenarios with multiple LP channels in two satellites  642  at a common frequency slot, instead of multiple LP channels in two common frequency slots in a satellite. Standard low-noise amplifiers (LNAs) and high power amplifiers (HPAs) are not shown. Diagnostic signals (pilots) are imbedded to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions. 
         [0081]    The terminal  641 - t   1  for a first user  531   a  features transmissions of an identical signal stream s 1  via two RHCP channels at fa via two satellites concurrently. The satellites cover a common service area for all users and the hubs from two separated orbital spots. Embedded pilot signals for diagnostics are multiplexed  641 - 1  with a transmission stream x 1 ( t ). The mux processing may be a standard technique such as TDM, FDM, or CDM minimizing bandwidth assets dedicated to probe signals support the optimization loop  643 - 5  at the destination. The muxed signals are frequency up-converted  641 - 2  to a predetermined frequency slot, and then amplified, power split into two signal paths, and then radiated by a multi-beam antenna  641 - 0  to two designated satellites  642  individually. 
         [0082]    Similarly, the terminal  641 - t   2  for a second user  531   b  features transmissions of another identical signal stream s 2  via two LHCP channels at fa via two satellite simultaneously. Embedded pilots for diagnostics are multiplexed  641 - 1  with a transmission stream x 2 ( t ). The mux processing may be a standard technique such as TDM, FDM, or CDM, minimizing bandwidth assets dedicated to probe signals which support the optimization loop  643 - 5  at the destination. The muxed signals are frequency up-converted  641 - 2  to a predetermined frequency slot, amplified, divided into two paths, then radiated by multi-beam antenna  641 - 0  to designated satellites  642 . 
         [0083]    Selected satellites  642  provide two pairs of LP SCPC channels; inputs  642 - ha  and  642 - va  are at satellite- 1 , and inputs  642 - hb  and  642 - vb  are at the second satellite. The corresponding output frequencies are at fa′. 
         [0084]    At the destination  643 , multi-beam antenna  643 - 0  features both RHCP and LHCP ports independently aiming at both satellites. The two received RHCP signals Y 1 ( t ), Y 3 ( t ) and two Rx LHCP signals Y 2 ( t ) and Y 4 ( t ) after conditioning (amplified and filtered), are frequency down converted  643 - 2 , then fed into electronic filters  643 - 3   a  as an equalization mechanism before the WF demuxing processor  643 - 3   b . The WF demuxer  643 - 3   b  features  4  output ports dedicated for users  531 . Only two of the four are using the space asset for this example. 
         [0085]    The corresponding outputs are de-muxed  643 - 4 , separating desired signals x 1 ( t ), x 2 ( t ) and two sets of probe signals. The recovered probing signals are then used by optimization loop  543 - 5  as diagnostic signals to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions.