RELATED APPLICATION DATA 
       [0001]    This application is a continuation of application Ser. No. 13/231,681, filed Sep. 13, 2011, now pending, 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates generally to a terrestrial communications system for mobile and portable devices, with possible applications in peer-to-peer communication systems. More specifically, the present invention relates to a spoke-and-hub communications system with increased user capacity by allowing frequency re-use through the use of multiple polarities, frequency slots, and directions organized through “unique waveforms” to radiate one signal. 
         [0004]    2. Description of Related Art 
         [0005]    Recent demand for terrestrial wireless communications methods such as WiFi and WiMax through portable devices such as iphones, ipods, bluetooth have increased dramatically. The increased use of such devices has resulted in a proliferation of IP-based products using fibers and satellites for back-bone or transport applications. On the other hand, high-speed access communications to handheld devices typically emanate from small wireless antennas that basically radiate and receive in broad beams with near omni-directional radiation patterns. Effective spectrum utilization becomes more and more important because of the expeditious increase of demand for wireless “access” communications. 
         [0006]    Ever increasing demand for a finite amount of spectrum has made it one of the most important resources in wireless communications. Therefore, there have been schemes to increase spectrum utilization efficiency, such as orthogonal frequency-division multiplexing (OFDM) [1]-[3], cellular frequency reuse, and dual-polarization frequency reuse [4], [5]. OFDM is an attractive technique for digital transmission, as spectrum utilization efficiency can be increased by the orthogonal frequency spacing and signal bands&#39; overlapping. Dual-polarization frequency reuse systems, which utilize both linear and circularly polarized electromagnetic (EM) waves that are orthogonal to each other, have been demonstrated in many satellite communications applications to double system capacity for fixed wireless (i.e. Wi-Fi, WiMax) and mobile (i.e. 3G and 4G systems for cell phones) systems. However, these polarization diversity systems are subject to system performance degradation due to cross polarizations and signal fading. 
         [0007]    Linear-polarized (LP) systems feature two polarization directions of vertical polarity (VP) and horizontal polarity (HP). Similarly, circular-polarized systems also feature two polarization directions of right hand circular polarity (RHCP) and left hand circular polarity (LHCP). 
         [0008]    In principle, transmission through orthogonal polarization carriers doubles the system capacity. However, practical use for portable devices is hard to achieve due to a user&#39;s dynamic motions, propagation impairments, antenna imperfections, among other things. The propagation impairments, such as rainfall attenuation, depolarization, and cross-polarization interference (CPI), deteriorate the signal transmission in the satellite-earth station links. Some compensation methods were reported in the literature [4]. Furthermore, the problems will become complicated by multipath fading effects when transmitting in a terrestrial environment. Although some schemes such as equalization and diversity are proposed to overcome such problems, their complicated nature prevents them from being a practical solution. The present invention aims to adopt the concept of wavefront multiplexing to more efficiently utilizing spectrum in polarization diversity. 
         [0009]    Since the advent of low cost integrated Global Navigation Satellite Systems (GNSS) receivers such as the Global Positioning System (GPS) in addition to the usage of commercial off-the-shelf Micro-Electro-Mechanical Sensor (MEMS) accelerometers and gyroscopes, estimation of the “orientations” and motion trends of individual personal portable devices with respect to a fixed coordination system has become practical and affordable, as evidenced by their proliferation to the previously mentioned portable devices. GNSS and related technologies are satellite-based geo-location systems. There are other non-satellite based geo-location systems which may become cost effective, with small size, weight and power (SW&amp;P) to be implemented in portable devices. The small-sized MEMS inertial measurement unit (IMU) provides the raw IMU data through a serial interface to a processor board where the inertial navigation solution and integrated GNSS/IMU with a Kalman filter is generated. Thus, polarizations diversity for better spectrum utility can be implemented with low cost and reliable processing techniques for consumer wireless communications markets, such as those featuring 3g and 4g mobile devices as well as WiFi and WiMax fixed devices. 
         [0010]    Wavefront multiplexed frequency re-use methods via polarization diversity take advantage of incompatibilities among the two polarity formats (such as LP versus CP) to implement “orthogonality” among multiple waveforms used by different user signals that are sharing the same frequency assets. The conventional performance degradations such as cross polarizations of a CP waveform to a LP hub therefore become part of the WF muxed waveforms and operational features. The orthogonality among multiple user signals is no longer solely dependent on orientations of the portable user devices. 
         [0011]    Compatible polarization configurations between user terminals and hub and/or cell tower assets are essential to efficient wireless links. It is generally true to efficiently utilizing polarization diversity that the LP polarized user terminals will use LP hubs and/or cell towers, and CP user terminals relay data via CP hubs and/or cell towers. When LP wireless portable terminals communicating to and from a CP hub and/or cell tower, their antenna polarizations must be configured accordingly emulating CP terminals, to prevent 3 dB SNR losses in receiving (Rx) functions on the one hand, and not to generate unwanted radiations in transmitting (Tx) functions on the other hand. 
         [0012]    Our approaches to these issues are very different than those of polarization re-configuration, and may not require users to switch polarizations on their equipment at all. Linearly Polarized (LP) users can use their existing terminals to relay data to CP hubs and/or cell towers. There are no spectrum asset losses due to the incompatibility. It is how we re-organize the CP spectrum assets via operation of hubs and/or cell towers to make the “incompatibility” operationally possible. It is therefore a result of our invention that linearly polarized hubs or cell towers can be accessed and efficiently utilized by circularly polarized user terminals, and vice versa. We will illustrate how to use LP hubs to access CP portable devices efficiently in this application. It would be obvious that a person with ordinary skills in the art can derive similar techniques using CP hubs to access LP portable devices. 
         [0013]    The invention relates to grouping two orthogonally polarized communications channels (e.g. HP and VP in linear polarities) with a common frequency slot on a hub or cell tower through Wave-Front (WF) Multiplexing (muxing) techniques for user portable terminals with incompatible polarization formats (e.g. RHCP and LHCP in circular polarities). The grouping method is extendable to multiple pairs of communications channels assets with both (LP) polarization formats with various frequency slots on different hubs or cell towers. 
         [0014]    One of the approaches utilized by the present invention is the concept of virtual link, which 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. 
         [0015]    Virtual links can also be applied for satellite communications transporting data within a fields of view 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 may also appear as MIMO formats, but are not. They are subsets of OWFDM waveforms and may feature unique format interconnecting OFDM and MIMO through an orthogonal signal structure. 
         [0016]    Virtual links can also be applied for terrestrial communications for last mile connectivity as well as transporting means from N sources to M destinations. Our proposed “Polarization Utility Waveforms” can successfully uploading signals to CP hubs and/or cell towers using LP portable devices terminals, and vice versa. They are engineered via techniques of signals spreading over multiple communications channels in the selected hubs and/or cell towers. The waveforms may look like OFDM waveforms and also appear as MIMO formats, but they are not. 
         [0017]    It can be shown that 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 [6], (2) back channel equalization for ground based beam forming process in satellite applications [7], and (3) Distributed data storage [8]. 
       Uniqueness of the OWFDM 
       [0018]    Unlike OFDM for commercial wireless communications which 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 directions when these “communications assets” become 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. 
         [0019]    In general, the OWFDM waveforms must meet existing polarization and frequency convention restrictions. At a portable device, transmitting (Tx) signals may be preprocessed by a WF multiplexer (muxer), which coherently spread signals into multiple channels concurrently in a form of 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 may be attached to at least one of them. The remaining WFs are available for various Tx signal streams. 
         [0020]    Signals that originate from a portable device propagating through various uplink carriers/paths, and arriving at designated hubs and/or cell towers feature differential phase delays, Doppler drifts, and amplitude amplifications/attenuations. 
         [0021]    Post processing implemented at receiving (Rx) site 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 not feedbacks required through back channels, As a result of equalizations, the Rx WFs become orthogonal, and the attached signals streams are then precisely reconstituted by the WF demuxer. 
       SUMMARY OF THE INVENTION 
       [0022]    The present invention pertains to a set of waveforms taking advantage of polarization incompatibilities between CP and LP signals, allowing portable devices to access available hub (and/or cell tower) communications assets when user portable or fixed terminals are not polarization-compatible. We will present the operational concepts and associated mechanisms to allow CP user terminals to access LP spectrum assets in hubs and/or cell towers (as well as LP user terminals to access CP spectrum assets) without sacrificing spectrum utility efficiencies and capacity. 
         [0023]    The Wavefront multiplexed (WF muxed) polarization diversity methods as described with the present invention may be utilized for peer-to-peer communications to enhance capacity so long as user terminals on both ends of a link are not compatible in polarization formats. For example, when a transmitting device on a Bluetooth link uses a RHCP format, the device on the receiving side of the Bluetooth link will use both HP and VP (two components of LP format). The same transmitting device may use both RHCP and LHCP, therefore capturing additional 100% channel capacity and delivering 100% more data to the receiving side using the polarization diversity methods as described with the present invention. 
         [0024]    Additionally, special OWFM waveforms are constructed under the constraints that all the user terminals feature only one of the two available CP options, while the hub and/or cell tower spectrum assets feature both LP channels of separated transceivers (transmitters and receivers) in a hub and/or cell tower. As a result, the targeted LP hub and/or cell tower spectrum assets support not only regular LP users but also additional CP customers without power and bandwidth capacity loss due to the polarization incompatibility. 
         [0025]    Additional benefits include providing for dynamic resource allocation capability such as downlink power, or equivalently D/L EIRP (equivalent isotropically radiated power). Various user frequency channels in different transceivers are grouped and utilized by multiple users via OWFDM. The combined “power” assets can be dynamically assigned to any of the users as long as the total power output is constant. Current systems allow for two independent CP users to access conventional 100 mW CP channels separately, with the constraint that each user may only draw a maximum of 100 mW. However, with the present invention, when the same users access 100 mW LP channels organized by OWFDM, the first user may draw 160 mW while the second user may only need to draw 40 mW. Dynamic power requirements may mean that the first user no longer needs to transmit, allowing the second user to effectively use all 200 mW of equivalent power, or a 3 dB gain on equivalent EIRP. 
         [0026]    These and other features of the present invention will become apparent from the following description of the invention, when viewed in accordance with the accompanied drawings and appended claims. 
       REFERENCES 
       [0000]    
       
         1. Ramjee Prasad, “OFDM for wireless communications systems” (Google eBook) Artech House, 2004 
         2. Ming Jiang, “Multiuser MIMO-OFDM for Next-Generation Wireless Systems,” Proceedings of the IEEE, Volume: 95 Issue: 7 Jul. 2007 
         3. Ye G. Li, Jack H. Winters, and Nelson R. Sollenberger, “MIMO-OFDM for Wireless Communications: Signal Detection with Enhanced Channel Estimation,” IEEE Trans. On Communications, vol. 50, no. 9, September 2002 
         4. T. S. Chu, “Restoring the orthogonality of two polarizations in radio communication systems I,”  Bell Syst. Tech. J ., vol. 50, no. 9, pp. 3063-3069, November 1971. 
         5. 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. 
         6. 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. 
         7. 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 
         8. 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 
       
     
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0035]      FIG. 1  depicts a block diagram of a LP hub accessed by two CP terminals for independent data stream relay to terrestrial communications networks. It also displays return-links from two users to a hub. 
           [0036]      FIG. 2A  depicts a handheld device in a receiving mode with a digital beam forming (DBF) process capable of performing dynamic polarization realignment, which is based on the knowledge of orientation and location of the handheld device and potential hub locations with respect to common local fixed coordinates. 
           [0037]      FIG. 2B  illustrates a handheld device in a transmitting mode with a digital beam forming (DBF) process capable of performing dynamic polarization realignment, which is based on the knowledge of orientation and location of the handheld device and potential hub locations with respect to common local fixed coordinates. 
           [0038]      FIG. 3  illustrates the corresponding forward links for the two users in  FIG. 1 . 
           [0039]      FIG. 4  illustrates the corresponding forward links for one user in  FIG. 1  but utilizing both RHCP and LHCP. 
           [0040]      FIG. 5A  depicts two mathematic matrixes: a 2-to-2 wavefront muxing matrix for two signals processing and a 4-to-4 mathematic matrix. The symmetric 2-to-2 matrix is constructed under the constraints that support user terminals featuring only one of the two available CPs. The symmetric 4-to-4 matrix is constructed under the constraints that support user terminals featuring only one of the two available CPs but with both frequency slots. However, there are many different applicable combinations of various users sharing the resources via the “matrixes”. For instance, the symmetric 2-to-2 matrix is applicable for a user terminal featuring both two CPs with doubled channel capacity. Similarly the symmetric 4-to-4 matrix is also applicable to a user terminal featuring both two CPs and two frequency slots for quadrupled channel capacity. These two matrixes are functional mechanisms for wavefront multiplexing and de-multiplexing. 
           [0041]      FIG. 5B  depicts the two mathematic matrix equations converting CP signals into LP channels as they are captured by a LP hub. The differential propagation effects are not included. The one on the left represents the conversions of two CP signals, s1 in RHCP and s2 in LHCP, into two aggregated LP signals in an HP and a VP channel. The one on the right is a 4-to-4 mathematic matrix equation representing signal conversions in four LP channels; two in HP and two in VP at two common frequency slots. The symmetric matrix is constructed under the constraints that can support user terminals featuring only one of the two available CPs but with both frequency slots. 
           [0042]      FIG. 5C  illustrates a simplified block diagram of a LP hub accessed by four CP terminals for independent data stream relay back to the hub station utilizing the same matrix conversion assumptions in  FIG. 5B . It also displays return-links from the four users to a hub. The architecture is constructed under the constraints that support user terminals featuring only one of the two available CPs but with both frequency slots. 
           [0043]      FIG. 5D  depicts a simplified block diagram for implementation of technique as shown in  FIG. 5C . The WF muxing are for CP to LP conversions. Standard low-noise amplifiers (LNAs) and high power amplifiers (HPAs) are not shown. Diagnostic signals (pilots) are embedded for phase and amplitude differential equalization among multiple paths for orthogonal WF reconstructions. WF demuxing is used to separate the signals from two portable devices. 
           [0044]      FIG. 6  illustrates a simplified block diagram for implementation of technique as shown in  FIG. 5D , for scenarios with multiple LP channels in two hubs at a common frequency slot, instead of multiple LP channels in two common frequency slots in a hub. 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. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0045]      FIG. 1   100  illustrates particular embodiments of our proposed techniques, assuming that portable CP terminals are within a common field-of-view of both hubs. The terminals are return-links (RL) examples depicting communications from 2 portable devices to a hub. 
         [0046]    Panel (a)  110  illustrates a conventional technique for accessing a CP communications hub asset  112  via CP terminals  111   a  and  111   b . Terminals  111   a  and 2  111   b  relay independent data streams s1(t) and s2(t) to CP hub  112 . Terminal 1  111   a  in right-hand circularly-polarized (RHCP) waveforms is allocated for RHCP channel  112   a  at frequency slot “fo” on the CP hub. Similarly, terminal 2  111   b  in left-hand circularly-polarized (LHCP) waveforms is allocated for second CP channel  112   b  at the same frequency slot “fo” but in LHCP on the hub. As a result, s1(t) goes through a RHCP active channel while s2(t) is independently conditioned by another active channel in LHCP. The “active channel” performs low-noise amplifications, proper filtering processing, frequency translations, etc. Hub receiving processor  113  will receive both s1(t) and s2(t) independently through two separated antenna ports: s1(t) from a RHCP and s2(t) a LHCP port. 
         [0047]    Panel (b)  120  depicts an operational scenario where CP terminals  111  relay data through LP hub  122 . Specifically, active LP channels  122   a  and  122   b  are used in the LP hub. 1 HP and 1 VP channels are on a common frequency slot. 
         [0048]    Mathematically, we select a set of 2-dimensional orthogonal Wave-Front (WF) vectors, [1, i] and [1, −i], to match 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, such that 
         [0000]        S 1( t )=[ v+h i]s 1( t )  (1a)
 
         [0000]        S 2( t )=[ v−h i]s 2( t )  (1b)
 
         [0049]    S1 is radiated by terminal 1  111   a  in RHCP while S2 by terminal 2  111   b  is in LHCP format. Equivalently, S1 in RHCP is transmitted in both HP and VP with a fixed phase distribution, in that the phase in HP is always 90° ahead of that in VP. 
         [0050]    As the S1 signals in RHCP arrive at selected LP hub  122 , both VP and HP components will be picked up “concurrently” by two LP channels at a common frequency slot. As depicted, one is in VP  122   a  and the other in HP  122   b  active channel. 
         [0051]    Similarly S2 is also concurrently transmitted in both HP and VP with a fixed phase distribution, in that the phase in HP is always 90° behind that in VP. As the S2 signals in LHCP arrive at selected LP hub  122 , both VP and HP components will be picked up “concurrently” by two LP active channels. As depicted, one in VP  122   a  and the other in HP  122   b.    
         [0052]    Each LP channel is occupied by an aggregated signal stream consisting of two concurrent, independent signals s1 and s2. A caveat is that s1 and s2 cannot be seperated from the associated aggregatted signal stream as they are not multiplexed by code, time, or frequency. Rather, there are special relationships, also called “wavefronts” (WFs) between the two s1 signals in both LP channels, with something similar for s2 signals. s1 and s2 can be separated and recovered with both aggregated signals from the LP channels are processed simultaneously. The two signals are therefore multiplexed spatially while propagating through both paths. 
         [0053]    The conditioned signals by VP channel  112   a  and HP channel  122   b  are designated as Yh (t) and Yv(t) respectively. The amplitude attentuations and phased delays due to propagation and electronics for the HP and VP paths are identified as (Ah and Av) and (a and I) respectively, where 
         [0000]        Yv ( t )= s 1( t )+ s 2( t )  (1a)
 
         [0000]        Yh ( t )= i[s 1( t )− s 2( t )]  (1b)
 
         [0054]    As the signals arrive at a LP hub  112 , polarization alignment processor  124  and a RF polarizer from a Rx CP antenna will serve as the WF demuxer functions, where the two concurrent CP antenna outputs will be: 
         [0000]        Z rhcp ( t )=[ Av exp( j α)* Yv ( t )− i Ah exp( j β)* Yh ( t )]/2  (2a)
 
         [0000]        Z lhcp ( t )=[ Av exp( j α)* Yv ( t )+ i Ah exp( j β) Yh ( t )]/2  (2b)
 
         [0055]    Furthermore, in terms of s1 and s2 Equation (1) can be re-written as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
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         [0056]    In general, the two wavefronts will not be orthogonal when they arrive at polarization alignment processor  124 . Diagnostic and compensation circuits (not shown) are present for amplitude and phase differential adjustment among the HP and VP paths. As the amplitude and phase effects of the two paths are equalized, the WFs regain orthogonality, wherein the associated signals can then be precisely reconstituted. 
         [0057]    For hub operators, the LP hub assets (RF power and frequency bandwidth) from channels  122   a  and  122   b  are grouped together and shared by two seperated users via unique orthogonal waveforms which happen to be conventional RHCP and LHCP. Each LP channel “serves” only one of the aggregated wavefront components (wfc). It always takes two components to re-construct relayed signals 
         [0058]    It should be noted that the linear channels need not be from the same hub. There may be situations that call for LP hubs to cover the same service areas. 
         [0059]      FIG. 2A   200   a  depicts a receiving beam-forming block diagram for portable device  210  with receiving/radiating elements  211  distributed as depicted. Signals received by elements  211  are conditioned (amplified, and filtered) by LNAs (low noise amplifiers)  222 , frequency down-converted by down converters  223 , then digitized by A/Ds (analog-to-digital converters)  224  before processing via digital beam forming (DBF) networks  225 . DBF processors  225  dynamically generate two CP beams, one in RHCP and one in LHCP. DBF  225  performs weighted summations of all received signals captured by N individual elements, where N is an integer and N&gt;2. Complex weightings are then performed by N complex digital multipliers  2251 , with the summing via digital combiners  2252 . The multiplicands are the N captured received signals and the multipliers are beam weight vectors (BWV), of which the components feature complex parameters dynamically controlled by controller  226  based on the knowledge of the device current positions and orientation with respect to the designated hubs locations and orientations. The data is gained from embedded inertial reference devices such as MEM IMU  227 , and other stored information  228  such as array geometries of the remote device, the directions of intended hubs, etc. The controller will “calculate” or “derive” the proper BWV such that the composite receiving patterns from distributed array  211  will feature adequate antenna gains and excellent polarization orientations toward the intended base-stations or communications hubs. 
         [0060]    Additional circuits (not shown) may be added to enhance the polarization isolations between the RHCP and LHCP channels. The additional diagnostic circuits may be based on correlations between RHCP and LHCP assuming these are completely independent and therefore completely uncorrelated. An optimization loop may be incorporated as one of the drivers for altering the two sets of BWVs. The optimization goals are to minimize the cross-correlations between RHCP and LHCP channels. 
         [0061]      FIG. 2B   200   b  depicts a transmitting beam-forming block diagram for portable device  210 , with receiving/radiating elements  211  distributed as depicted. The transmitting signals are sent to transmitting digital beam forming (DBF) networks  235 , dynamically generating two CP beams for the N-element distributed arrays, one in RHCP and the other LHCP, where N is an integer and N&gt;2. DBF functions  235  for a CP beam perform signal replications by first re-generating N-identical components, and then weight replicating streams individually by N components of a BWV. The weighted N signals from the RHCP DBF and those from the LHCP DBF for individual radiating elements are summed together before conversion to analogue format by D/As  234 , frequency up-converted by up-converters  233  and power amplified by power-amplifiers  232  before being radiated individually to free space by distributed array elements  211 . The complex weightings are performed by N complex digital multipliers  2351  and the duplications are via digital replicators  2352 . The multiplicands are the N captured received signals and the multipliers are the beam weight vectors (BWV). The components featuring complex parameters that are dynamically controlled by controller  226  are based on the knowledge of the device&#39;s current positions and orientations with respect to the designated hubs locations and orientations. This knowledge is derived from embedded inertial reference devices  227 , and other stored information  228  such as array geometries of the remote device, and the directions of intended hubs. The controller will “calculate” and/or “derive” the proper BWV such that the composite receiving patterns from the distributed array  211  will feature adequate antenna gains and excellent polarization orientations toward the intended base-stations or communications hubs. 
         [0062]      FIG. 3300  depicts the same scenario as that in  FIG. 1 , except it is for “forward links” communications flows from a LP hub  312  to CP remotes  311 . A preprocessing unit  324  in the hub is used to “pre-compensate” for the amplitude and phase differentials among the two LP propagation paths. Signals in the corresponding forward-link channels for terminal-1  311   a  and terminal-2  311   b  are available locally at the source location  312 . These signals can be used as feedback for the pre-compensation processing  324 . 
         [0063]      FIG. 4   400  depicts the similar scenario as that in  FIG. 3  in that both are for “forward links” communications flows.  FIG. 4   400  depicts flow from LP hub  412  to CP remotes  411 . LP hub  412  must feature both HP and VP polarization transmission functions. The desired signals to the first remote terminal s1(t) is decomposed into two sub streams s1a(t) and s1b(t). The decomposition process may be a 2-to-2 FFT or a 1-to-2 TDM demuxing switch. Pre-processor  424  performs two linear combinations, combining s1a (the first signals stream for terminal-1  411   a ), and s1b (the second signals stream also for terminal-1  411   a ). The weightings among the two linear combinations are for generating two equivalent CP signals at anticipated destinations  411 , and shall include effects from propagations and unbalanced electronics. Signals in both forward-link channels for terminal-1 are available locally at the source location  412 . These signals will be used as feedback to optimize the pre-compensation processing  424 . At the destination, the first remote terminal  411   a  will re-combine the two received substreams s1a(t) and s1b(t) into the reconstituted signal stream s1(t). 
         [0064]      FIG. 5A  depicts wavefront multiplexing matrixes  512  and  522  for CP user terminals to access multiple communications channels in LP hubs. 2-by-2 matrix  512  is for conversion of two independent CP signals (one at RHCP  512   a  and the other at LHCP  512   b ) into two signal streams in LP (one in HP and the other in VP). All the signal streams (two inputs and two outputs) are at same frequency slot f1. 
         [0065]    Similarly, 4-by-4 matrix  522  on the right converts 4 independent CP signals (two at RHCP  522   a  and  522   c  and the other two at 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. 
         [0066]      FIG. 5B  depicts the mathematic matrix equations  510  and  520  for conversion of CP signals into LP channels as they are captured by an LP satellite. The differential propagation effects are not included. 2-by-2 matrix equation  510  represents the conversions of two CP signals  513 , s1 in RHCP and s2 in LHCP, into two aggregated LP signals  511  in an HP and a VP channels in a LP hub. The symmetrical conversion matrix  512  is the WF muxing processor and is referred as Mf2. 
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         [0000]    It should be noted that Mf2 can be used to convert two CP signals into two LP signals, and can also convert two LP signals into two CP signals. Furthermore, 
         [0000]      ½ ·Mf 2 ·Mf 2* T=I   (4b)
 
         [0000]    Mf2 can be used as a WF muxer and its corresponding WF demuxer will be Mf2* T . The two resulting wavefronts (WFs)  512   a  and  512   b  as depicted in  FIG. 5A  are orthogonal to each other. 
         [0067]    Matrix equation  520  is a 4-by-4 mathematic matrix equation representing signal conversions from 4 CP signals  523  in four LP channels  521  of a communications hub, where two in HP and two in VP are at two identical frequency slots. 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. 
         [0068]    The symmetrical conversion matrix  522  is the WF muxing processor and is referred as Mf4. 
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         [0000]    It should be noted that Mf4 can be used to convert four CP signals into four LP signals, and it can also convert four LP signals into four CP signals. Furthermore, 
         [0000]      ¼ ·Mf 4· Mf 4* T=I   (5b)
 
         [0000]    Mf4 can be used as a WF muxer and its corresponding WF demuxer will be Mf4* T . The four resulting wavefronts (WFs)  522   a ,  522   b ,  522   c , and  522   d  as depicted in  FIG. 5A  are orthogonal to each other. 
         [0069]    In  FIG. 5C   530 , we have split the two CP pairs 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. 
         [0070]    S1 is a waveform occupying two RHCP channels, one at fa and the other at fb, carrying signal s1 radiated by terminal-1  531   a.    
         [0071]    S2 is a waveform occupying two LHCP channels, one at fa and the other at fb, carrying signal s2 radiated by terminal-2  531   b    
         [0072]    S3 is a waveform occupying two RHCP channels, one at fa and the other at fb, carrying signal s3 radiated by terminal-3  531   c.    
         [0073]    S4 is a waveform occupying two LHCP channels, one at fa and the other at fb, carrying signal s4 radiated by terminal-4  531   d    
         [0074]    When these signals arrive at a LP satellite  532 , the 4 LP channels will feature the following aggregated signals: 
         [0075]    VP channel at fa  532   va : s1+is2+s3+is4 
         [0076]    HP channel at fa  532   ha : is1+s2+is3+s4 
         [0077]    VP channel at fb  532   vb : s1+i s2−s3−is4 
         [0078]    HP channel at fb  532   hb ; is1+s2−is3−s4 
         [0079]    When these signals captured by LP hub  532 , the channels will feature the following aggregated signals, assuming the amplitude attenuations and phase delays among the 4 propagation channels are identical, where 
         [0080]    RHCP channel at fa: y1(t)=is2+is4 
         [0081]    LHCP channel at fa: y2(t)=s1+s3 
         [0082]    RHCP channel at fb: y3(t)=is2−is4 
         [0083]    LHCP channel at fb; y4(t)=s1−s3 
         [0084]    A post processor, not shown, will calculate the s1, s2, s3, and s4 according to the received y1, y2, y3, and y4. In addition, the post processor performs amplitude and phase equalizations among the propagation paths. 
         [0085]    The relative phases between the CP components at two frequencies are critical. When the relative geometries among user  531  and hub  532  are fixed, the cumulative phase difference among signals at two separated frequencies propagating from a source  531  to a destination  532  is constant; therefore, the accumulated phase difference is constant. However when a user  531  is drifting relative to hub  532 , the phase differences between two signals at two frequencies propagating from user source location  531  to hub  532  will vary accordingly. Additional phase differentials may result from Doppler effects. 
         [0086]    At destination  532 , four concurrent receiving functions are present: 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 orthogonality among multiple WFs when they arrive at destination  532 . 
         [0087]      FIG. 5D   540  illustrates a simplified block diagram for an implementation technique for  FIG. 5C . Standard low-noise amplifiers (LNAs) and high power amplifiers (HPAs) are not presently shown.  540  depicts top level implementation concepts for the hub  532  as well as two  531   a  and  531   b  of the four users  531 . Terminal  541 -t1 for user  531   a  features transmissions of an identical signal stream s1 via two RHCP channels at fa and fb simultaneously. Embedded pilots for diagnostics are multiplexed  541 - 1  with a transmission stream x1(t). The mux processing may be a standard technique such as TDM, FDM, or CDM for minimizing bandwidth assets dedicated to probe signals. This in turn supports optimization loop  543 - 5  at the destination. The muxed signals are frequency up-converted  541 - 2  to two predetermined frequency slots before joining by a FDM output mux  541 - 3 . The muxed signals are amplified and radiated by antenna  541 - 0  to designated hub  542 . 
         [0088]    Similarly, terminal  541 -t2 for user  531   b  features transmissions of another identical signal stream s2 via two LHCP channels at fa and fb simultaneously. Embedded pilot signals for diagnostic purposes are multiplexed  541 - 1  with a transmission stream x1(t). The mux processing may be a standard technique such as TDM, FDM, or CDM minimizing bandwidth assets dedicated to probe signals. This in turn supports optimization loop  543 - 5  at the destination. The muxed signals are frequency up-converted  541 - 2  to two predetermined frequency slots before joining by a FDM output mux  541 - 3 . The muxed signals are amplified and radiated by antenna  541 - 0  to designated communications hub  542 . 
         [0089]    Hub  542  provides two pairs of LP communications channels: the inputs for the first ones  542 - ha  and  542 - va  are at fa, and those for the other set  542 - hb  and  542 - vb  are at fb. The corresponding output frequencies are at fa′ and fb′, respectively. 
         [0090]    At destination  543 , antenna  543 - 0  features independent RHCP and LHCP ports. The received RHCP signals Y1(t) and LHCP signals Y2(t) are conditioned (amplified and filtered), FDM de-muxed  543 - 1  and frequency down converted  543 - 2 , then fed into electronic filters  543 - 3   a  as equalization mechanisms before WF demuxing processor  543 - 3   b . The WF demuxer  543 - 3   b  features  4  output ports dedicated for users  531 . 
         [0091]    The corresponding outputs are de-muxed  543 - 4  separating desired signals x1(t), x2(t) from probe signals. The recovered probing signals are used by the optimization loop  543 - 5  as diagnostic signals to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions. 
         [0092]      FIG. 6   600  illustrates a simplified block diagram of an implementation technique similar to for  FIG. 5D , specifically for scenarios that utilize multiple LP channels in two satellites  642  at a common frequency slot. 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. 
         [0093]    Terminal  641 -t1 for a user  531   a  features transmissions of an identical signal stream s1 via two RHCP channels at fa via two communications hubs concurrently covering a common service area. Embedded pilots for diagnostics are multiplexed  641 - 1  with a transmission stream x1(t). The mux processing may be a standard technique such as TDM, FDM, or CDM minimizing bandwidth assets dedicated to probe signals. this in turn supports optimization loop  643 - 5  at the destination. The muxed signals are frequency up-converted  641 - 2  to a predetermined frequency slot, amplified, power split into two signal paths, then individually radiated by antenna  641 - 0  to two designated satellites  642 . 
         [0094]    Similarly, terminal  641 -t2 for a user  531   b  features transmissions of another identical signal stream s2 via two LHCP channels at fa via two communications hubs simultaneously. Embedded pilots for diagnostics are multiplexed  641 - 1  with a transmission stream x2(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 and then radiated by a multi-beam antenna  641 - 0  to the two designated satellite  642 . 
         [0095]    Selected communications hubs  642  provide two pairs of LP channels: the inputs for channels  642 - ha  and  642 - va  are at hub-1, inputs for channels  642 - hb  and  642 - vb  are at the second hub. The corresponding output frequencies are at fa′ and fb′, respectively. 
         [0096]    At destination  643 , multi-beam antenna  643 - 0  features independent RHCP and LHCP ports aiming at both hubs. The two received RHCP signals Y1(t), Y3(t) and two Rx LHCP signals Y2(t) and Y4(t) are conditioned (amplified and filtered) and frequency down-converted  643 - 2 , then fed into electronic filters  643 - 3   a  as equalization mechanisms before the WF demuxing processor  643 - 3   b . The WF demuxer  643 - 3   b  features  4  output ports dedicated for users  531 . 
         [0097]    The corresponding outputs are de-muxed  643 - 4 , separating desired signals x1(t), x2(t) and two sets of probe signals. The recovered probing signals are used by the optimization loop  543 - 5  as diagnostic signals to equalize phase and amplitude differentials among multiple paths for orthogonal WF reconstructions.
A novel terrestrial wireless communications technique for terrestrial portable terminals including hand-held mobile devices and fixed wireless instruments, utilizing a spoke-and-hub communications system, having a plurality of individual hubs and/or base-stations all in communications with the portable terminals. The portable terminals and the hubs are assigned to use incompatible polarity formats in terms of circularly polarity (CP) and linearly polarity (LP). In forward links, a signal processed by the LP ground telecommunications hubs is radiated through multiple antennas with various LP polarities to an individual CP user simultaneously. The multiple paths are organized via assignments of a plurality of polarities, frequency slots, and directions by wavefront multiplexing/demultiplexing techniques such that the same communications assets including frequency spectrum may be re-used by other users. The same polarity diversity methods can be extended to peer-to-peer communications.