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Emerging Satellite Communication Links of Incompatible Polarization via Wavefront Multiplexing Techniques Donald Chang, Joe Lee Spatial Digital Systems Camarillo, CA USA {dcdchang, joelee}@spatialdigital.com Tzer-Hso Lin Spatial Digital Systems Camarillo, CA USA [email protected] Abstract—Many fixed satellite service (FSS) transponders in Ku band belong to the family of linearly polarized (LP) space assets. Therefore the terminals in the FSS-covered service areas also use linear polarization. In this paper, we propose, on the other hand, that circularly polarized (CP) terminals are more economical in manufacturing and installations as comparing to compatible LP terminals. The presented techniques will enable satellite operators to cost-effectively service Ku band VSAT users, either fixed or mobile, via LP space assets in Ku band. A method that makes possible the emergence of multiple g r o u p e d LP satellite transponders through Wave-Front (WF) Multiplexing (muxing) techniques is presented. Grouped LP transponders become accessible efficiently by CP ground terminals and vice versa. This method consists of a polarization converting processor in a ground hub with our modifications of ground user equipment and satellite assets. The received waveforms are processed in the digital domain in order to further service intended ground terminals. A low cost test bed is developed to emulate satellite links and implement WF muxing and WF demultiplexing (demuxing). We present both simulation and experimental results to demonstrate the satellite communication links of transponders and ground terminals using incompatible polarization respectively. Keywords—linear polarization; circular polarization; wavefront multiplexing; wavefront demultiplexing; antenna I. INTRODUCTION High-Speed Satellite Communications (SATCOM) technologies have seen increasing demand for improved capacity. The driving force emerges from net-centric operations, which motivate the SATCOM transition to IP- based services [1]. In response to the proliferation of IP- based services, the SATCOM market calls for novel development of IP-based products [1] for satellite back- bone or transportation applications. Compatible polarization configurations between terminals and space assets have been essential to efficient SATCOM links. Such premise leads to the use of two separate SATCOM link families: LP terminals using LP transponders and CP terminals using CP transponders. For a ground terminal to switch services from a provider with CP satellites to another one with LP satellites, the antenna polarizations requires reconfiguration accordingly in order 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. To avoid the need of reconfiguration, we have developed an approach very different from those of polarization switching, and would not require users to switch polarizations based on their equipment. Our approach enables CP users to use their existing terminals to relay data to CP destinations via linearly polarized (LP) transponders without losses due to the incompatibility in space asset. Two SATCOM services may benefit from the proposed techniques. In one example, we envision the opportunities in the space assets for Ku band and C band. For Ku band, there are many LP space assets covering different service areas for fixed satellite services (FSS) [2]. There are also Ku CP transponders for broadcasting satellite services (BSS). On the other hand, CP terminals are more economical in manufacturing and installations as comparing to compatible LP terminals. The proposed techniques will enable satellite operators to cost-effectively manage LP space assets in Ku band and service Ku band VSAT users, either fixed or mobile. For C-band, though a majority of transponders are in CP formats, there are many C-band LP space assets with near global coverage, which shall be accessible to CP terminals when empowered by the proposed techniques. In another example for mobile VSAT service, the proposed techniques enable a ship-borne CP VSAT to traverse an ocean equally independent of the transponder polarization formats. Whether the satellite assets are in Ku band or C-band, the mobile terminal would be linked to a ground hop. Utility of satellite assets will be efficiently sustained with the proposed techniques. In this paper, we discuss a variety of SATCOM services that can be made possible by the polarization incompatible links. The communication links entail transmitting terminals using CP format, transponders using LP format and ground hubs using LP (or CP) formats. The size of CP terminals may be as small as one or two users, or as extensive as N users. In general, the proposed techniques may also deal 978-1-4799-4912-0/14/$31.00 ©2014 IEEE 2014 IEEE 25th International Symposium on Personal, Indoor and Mobile Radio Communications 978-1-4799-4912-0/14/$31.00 ©2014 IEEE 2056

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Page 1: Emerging Satellite Communication Links of Incompatible ...l.b5z.net/i/u/10112509/f/p2056-chang.pdf · Emerging Satellite Communication Links of Incompatible Polarization via Wavefront

Emerging Satellite Communication Links of Incompatible Polarization via Wavefront

Multiplexing Techniques

Donald Chang, Joe Lee Spatial Digital Systems

Camarillo, CA USA

{dcdchang, joelee}@spatialdigital.com

Tzer-Hso Lin Spatial Digital Systems

Camarillo, CA USA

[email protected]

Abstract—Many fixed satellite service (FSS) transponders in Ku band belong to the family of linearly polarized (LP) space assets. Therefore the terminals in the FSS-covered service areas also use linear polarization. In this paper, we propose, on the other hand, that circularly polarized (CP) terminals are more economical in manufacturing and installations as comparing to compatible LP terminals. The presented techniques will enable satellite operators to cost-effectively service Ku band VSAT users, either fixed or mobile, via LP space assets in Ku band. A method that makes possible the emergence of multiple g r o u p e d LP satellite transponders through Wave-Front (WF) Multiplexing (muxing) techniques is presented. Grouped LP transponders become accessible efficiently by CP ground terminals and vice versa. This method consists of a polarization converting processor in a ground hub with our modifications of ground user equipment and satellite assets. The received waveforms are processed in the digital domain in order to further service intended ground terminals. A low cost test bed is developed to emulate satellite links and implement WF muxing and WF demultiplexing (demuxing). We present both simulation and experimental results to demonstrate the satellite communication links of transponders and ground terminals using incompatible polarization respectively.

Keywords—linear polarization; circular polarization; wavefront multiplexing; wavefront demultiplexing; antenna

I. INTRODUCTION

High-Speed Satellite Communications (SATCOM) technologies have seen increasing demand for improved capacity. The driving force emerges from net-centric operations, which motivate the SATCOM transition to IP-based services [1]. In response to the proliferation of IP-based services, the SATCOM market calls for novel development of IP-based products [1] for satellite back-bone or transportation applications.

Compatible polarization configurations between terminals and space assets have been essential to efficient SATCOM links. Such premise leads to the use of two separate SATCOM link families: LP terminals using LP transponders and CP terminals using CP transponders. For a ground terminal to switch services from a provider with CP satellites to another one with LP satellites, the antenna

polarizations requires reconfiguration accordingly in order 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. To avoid the need of reconfiguration, we have developed an approach very different from those of polarization switching, and would not require users to switch polarizations based on their equipment. Our approach enables CP users to use their existing terminals to relay data to CP destinations via linearly polarized (LP) transponders without losses due to the incompatibility in space asset.

Two SATCOM services may benefit from the proposed techniques. In one example, we envision the opportunities in the space assets for Ku band and C band. For Ku band, there are many LP space assets covering different service areas for fixed satellite services (FSS) [2]. There are also Ku CP transponders for broadcasting satellite services (BSS). On the other hand, CP terminals are more economical in manufacturing and installations as comparing to compatible LP terminals. The proposed techniques will enable satellite operators to cost-effectively manage LP space assets in Ku band and service Ku band VSAT users, either fixed or mobile. For C-band, though a majority of transponders are in CP formats, there are many C-band LP space assets with near global coverage, which shall be accessible to CP terminals when empowered by the proposed techniques.

In another example for mobile VSAT service, the proposed techniques enable a ship-borne CP VSAT to traverse an ocean equally independent of the transponder polarization formats. Whether the satellite assets are in Ku band or C-band, the mobile terminal would be linked to a ground hop. Utility of satellite assets will be efficiently sustained with the proposed techniques.

In this paper, we discuss a variety of SATCOM services that can be made possible by the polarization incompatible links. The communication links entail transmitting terminals using CP format, transponders using LP format and ground hubs using LP (or CP) formats. The size of CP terminals may be as small as one or two users, or as extensive as N users. In general, the proposed techniques may also deal

978-1-4799-4912-0/14/$31.00 ©2014 IEEE

2014 IEEE 25th International Symposium on Personal, Indoor and Mobile Radio Communications

978-1-4799-4912-0/14/$31.00 ©2014 IEEE 2056

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with N communications links managed by Wavefront (WF) Multiplexing (Muxing) and Wavefront De-multiplexing (WF Demuxing). A WF, a “space-distribution” pattern, carrying a signal stream features a fixed spatial pattern among selected N parallel links, which support up to N orthogonal WFs carrying N independent signals concurrently from a source to a destination. The links emerge from polarizat ion incompatible assets enabled by WF muxing, namely the use of multiple WFs, and the enabling signal structures, the ‘WF muxing waveforms’. We present a special case of N = 4, though the construction of general “N-grouping” case is omitted due to page limit.

We note that Wavefront multiplexing (WF muxing) / demultiplexing (demuxing) process refers to the class of algorithms for allocating wavefronts in space communications where transmissions demand a high degree of power combining, security, reliability and optimization [6], [8], [10]. It covers applications including: (1) coherent power combining [3], [7], [9]; (2) remote beamforming [4]; and (3) distributed data storage [5], [12]. It supports processing in RF and digital domains.

The polarization incompatible links can be applied for satellite communications transporting data within a field of view common to selected transponders. Our proposed "Polarization 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. Unlike OFDM wave-forms or MIMO formats, WF muxing waveforms need not be limited to an orthogonal signal structure.

The rest of this paper is organized as follows. Section II introduces the basic model of the service for single or two users via polarization incompatible links and WF muxing/demuxing. Section III describes the advanced model of the service for multiple users with N = 4 as a special case. Section IV presents the technical results in simulation and experiment. Section V concludes this paper.

II. BASIC MODEL

In this section, we present a basic model of the service for single or two users via polarization in compatible links. WF muxing based on different design concepts may support both cases respectively.

We first use Fig. 1 to illustrate the conventional technique based on polarization compatible links and the premise that portable CP terminals and the CP hub are within the field-of-view of the transponder(s). The return-link (RL) example depicts communications from 2 portable devices to a hub. It represents a technique for connecting to a CP communications hub asset via a CP transponder. Two terminals transmit independent data streams s1(t) and s2(t) to t h e CP hub. One terminal in right-hand circularly-polarized (RHCP) format is allocated for RHCP channel at frequency slot "fo" on the CP hub. Similarly, a second terminal in left-hand circularly-polarized (LHCP) format is allocated for second CP channel at the same frequency slot "fo" on the CP hub. As a result, s1(t) goes through a RHCP channel while s2(t) is independently

conditioned by another channel in LHCP. The CP hub will receive both s1(t) and s2(t) independently through two separated antenna ports: s1(t) from a RHCP port and s2(t) a LHCP port (not shown).

In the sequel, we shall see how WF muxing may be used to support either single user or two users via polarization incompatible links.

Fig. 1. Polarization compatible links: two CP terminals can access a CP hub via CP transponders of different CP formats respectively.

Fig. 2. A polarization incompatible link for single user: two CP terminals of different CP formats communicate with an LP hub via LP transponders.

A. Single User

Fig. 2 depicts an operational scenario where a terminal w i t h t wo p o r t s o f d i f f e r en t C P f o r m a t s transmits data from single user through a LP transponder. Signal goes through a serial-to-parallel device, generating two streams

and .Specifically, one horizontal-polarized (HP) and one vertical-polarized (VP) channel are on a common frequency slot. Mathematically, we select a set of 2-dimensional orthogonal Wave-Front (WF) vectors, [1, 1 ] and [1, -1], to match the signal polarization structures 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 and are carried by different CP formats respectively.

S1 is radiated by a first terminal in RHCP while S2 by a second terminal 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. The distribution of the first input S1(t) in the two outputs is in a first wavefront (WF) vector of [1, 1], while that

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of S2(t) is in a second WF vector [i, -i] or i[1, -1]. These two WF vectors are orthogonal to one another.

As the S1 signals in RHCP arrive at selected LP hub, 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 and the other in HP channel.

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, both VP and HP components will be picked up "concurrently" by two LP channels. As depicted, one is in VP and the other is in HP.

A caveat is that s1 and s2 would not be separated from the associated aggregated signal stream without WF demuxing as they are not multiplexed by code, time, or frequency. Rather, there are special relationships, also called "wavefronts" (WFs) between the two signals in both LP channels. The two signals are therefore multiplexed spatially while propagating through both paths.

The signals conditioned by VP channel and HP channel are denoted as Yh (t) and Yv(t) respectively, where both Yh (t) and Yv(t) consist of and . In fact, it may be seen in Yh (t) and Yv(t) the amplitude attenuations and phased delays due to propagation effects for the HP and VP paths. As the signals arrive at a LP hub, a polarization alignment processor and a RF polarizer from an Rx LP antenna will serve as the WF demuxer functions.

Hence the formal objective of the problem is to solve and based on the signals received by the LP

transponder. In general, the propagation effects complicates the process of recovering s1 and s2 as the above two wavefronts arrive at the polarization re-alignment processor. An equalizer (not shown) is required 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 can then be precisely reconstituted [4]. We note that such reconstitution does not solely rely on the features of signals, but has to be based on the consideration of antenna properties and propagation channel.

Fig. 3. Polarization incompatible links for two users: two CP terminals of different CP formats communicate with an LP hub via LP transponders.

B. Two Users

Fig. 3 depicts similar scenario as that in Fig. 2, except it is for two users communicating using two terminals of different CP formats with a remote L P h u b via a LP transponder. Two source signals may exhibit particular features, which allow degree-of-freedom in the design of polarization alignment.

III. ADVANCED MODEL

The advanced model of the service for more users is closely related to the design concept in a multibeam array using WF muxing. Though implemented in RF domain, it also reveals similar principle behind the design of polarization incompatible links for multiple users.

Fig. 4. WF muxing in a transmitting multibeam array.

A. WF Muxing For Multiple Users

Fig. 4 depicts a multibeam array that generates 4 independent transmitting beams concurrently delivering various signals to 4 different geostationary satellites. These satellites are located at - 48.6°, - 14.5°, 14.5° and 48.6° away from the array boresite direction, respectively. The selected multiple-beam beam-forming-network (BFN) is related to 4-to-4 Butler matrix (BM) [11], which features a 4-to-4 FFT operation in RF mathematically.

The 4 input beam ports of the BM are the four beams B1, B2, B3, and B4 as indicated, where a B1(t) signal stream is input to the BFN via port B1, a B2(t) signal stream is input to the BFN via port B2, a B3(t) signal stream is input to the BFN via port B3, and a B4(t) signal stream is input to the BFN via port B4. There are 4 output element ports of the BM that are connected to the array elements, E1, E2, E3, and E4 as indicated. An E1(t) signal stream is output from the BFN via element port E1, and E2(t) , E3(t), and E4(t) signal streams from ports E2, E3, and E4, respectively. A signal stream Bi(t) shall yield a particular phase delay distribution by connecting to the “ith” input port of the BM. The appearance of B1(t) at the four Ei ports features a phase difference of 135 degrees. The appearance of B2(t) at the four Ei ports features a phase difference of 45 degrees. The appearance of B3(t) at the four Ei ports features a phase difference of -45 degrees. The appearance of B4(t) at the four Ei ports features a phase difference of -135 degrees. A “wavefront” or WF, i.e. the phase-difference pattern, is thus formed: here WF is in a form of a linear slope of phase delays among the 4 adjacent radiating array elements. As far as each of the 4 signal streams is

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concerned, the four array elements effectively “spatially sample” the wavefront of the signal streams, and radiate the signal streams with the unique WF. The four aggregated wavefronts from B1, B2, B3, and B4 are created concurrently by the 4-to-4 BM. We may refer to the aggregation process as “wavefront multiplexing or WF muxing”.

The WF “muxed” signal streams are radiated into free space by the array. Assuming the linear array with an element spacing of 0.5 wavelengths, the radiating B1(t) signal stream from the 4 array elements will coherently transmit to the -48.6° satellite from the array. Similarly signal streams B2(t), B3(t), and B4(t) connected to port B2, B3, and B4 featuring various distributions of linear phase progressions shall arrive at -14.48°, 14.48°, and 48.6°, away from the array boresite individually. A unique common feature exists among the 4 individual beams: the direction of a peak of a beam is always at directions of nulls of other beams. This unique feature has been identified as orthogonal beams (OB) [12]. The WF demuxing function is accomplished via effects of RF propagations from array element apertures to various far field directions. Therefore the propagation effects from array elements separate individual signals streams from a group of the WF muxed signals by directions.

B. Multiple Users (N=4)

Fig. 5 shows a construction of link based on WF muxing and polarization diversity that support N = 4 signal streams. Grouped as a “virtual port”, the CP terminals access an LP transponder with two VP ports and two HP ports. For a CP ground hub with WF demuxing capability, four signal streams can be retrieved by their intended user individually. For LP hub, WF demuxing will also enable the service for all four intended users individually, provided that the LP hub is also within the LP transponder’s field-of-view.

The design of the waveforms in Fig. 5 takes advantage of the variation of polarization formats. The RHCP port ‘a’ consists of multiple RHCP signal formats, and the LHCP port ‘a’ consists of multiple LHCP signal formats. Similarly, the RHCP port ‘b’ consists of multiple RHCP signal formats, and the LHCP port ‘b’ consists of multiple LHCP signal formats. However, there are distinct features between two RHCP ports, and so are between two LHCP ports. This construction of polarization incompatible links also supports as little as single user and other suitable number of users.

Fig. 5. Two RHCP ports and two LHCP ports that access an LP

transponder.

IV. SIMULATIONS AND EXPERIMENTS

We evaluate the proposed techniques in simulations and experiments of polarization incompatible links via WF muxing and WF demuxing.

A. Simulations of Polarization diversity via WF Muxing

Fig. 6 depicts a configuration of simulations for a scenario of an LP transponder to service two CP terminals concurrently in a common frequency slot. Two waveforms, S1 and S2, which may represent two ‘users’ using two separated CP VSAT terminals on ground, radiate to a LP satellite in geostationary orbits in return links. S1(t) is in a RHCP format while S2(t) is in a LHCP format.

The LP satellite comprises of two LP transponders with multiple common frequency slots covering same service areas. The first LP transponder is in a vertical polarized (VP) format and the second one in a horizontal polarized (HP) format. The captured signals streams in a teleport, Ox(t) and Oy(t), are processed via an optimization algorithm to recover S1 and S2 accordingly. The differentials for link propagations between two CP terminals to the satellite and those for amplifications and delays in the two transponders are included as input parameters in the simulations. Simulations are performed in baseband with two uncorrelated waveforms. The carriers for both uplinks and downlinks are not addressed. Therefore, Doppler effects are not included, and so are those due to difference in output frequencies for two transponders with non-identical local oscillator frequencies for some of transponding satellites.

Fig. 6. Simulation result of two CP users, an LP transponder, and a teleport with LP receiving antenna and an optimization processor. The polarization incompatible links may service two intended users.

Two return-links signals, as depicted in Fig. 6, are from two separated CP ground terminal users assigned in a common frequency slot: S1(t), a sinusoidal signal, in RHCP from a first user and S2(t), a square-like signal, in LHCP from a second user. Two return-link signals are captured by a LP ground hub in a teleport after amplified and transponded by the two transponders: Ox for received mixed signals in HP and Oy for those in VP. Neither does Ox nor Oy resemble S1(t) or S2(t). Two recovered signals, S1’(t) and S2’(t), after an optimization processing in a teleport, are successfully retrieved by the intended receiving bround hubs with LP antennas. The iterative optimization is based on a

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cost minimization principle, where the “costs” are measured in various observables based on the inherent features in two output S1’(t) and S2’(t).

B. Expeiment of Polarization diversity via WF Muxing

We have emulated the communication link by utilizing commercial satellite communication modems, digital signal processors (DSP) and our proprietary WF demuxing and radio-frequency (RF) circuits. Two highly uncorrelated source signals representing two users are generated in different setting. One is a video stream, which is up-converted to 1.202 GHz, modulated by QPSK, error-correction-coded with code-rate 7/8 and transmitted with -25 dBm Tx-power at 4038.4 kpbs. Another is a sinusoidal signal, which is up-converted to 1.201 GHz and transmitted with -21.5 dBm Tx-power. An analog polarizer operating in the frequency-band of interest (in the vicinity of 1.2 GHz) is chosen to emulate a WF muxing process with the particular phase-shifting distribution featuring polarization diversity. It has been widely used in converting two linearly polarized feeds to function as a circularly polarized feed and vice versa in RF and antenna industries.

Fig. 7. Emulation of polarization incompatible links via satellite modems, analog polarizer and baseband WF demuxing (DSP/FPGA polarization re-alignment).

Fig. 8. Left: source video stream (left display) is transmitted; Rx side display shows no video when WF demuxing is not used. Right: WF demuxing enables the Rx to show the video.

An analog polarizer can be treated as a 4 port device that performs WF muxing. The two WF muxed signals from the 3dB-hybrid are down-converted (D/C) to baseband and demuxed via a WF demuxing unit implemented in DSP and FPGA. The WF demuxed baseband signals are sent through an up-converter (U/C) and looped back to a demodulator in the modems (Fig. 7). The following observed results verify effectiveness of WF muxing and WF demuxing: (1) Rx modem does not detect the desired signal stream without the use of the WF demuxing unit, hence showing no video on the Rx side display (Fig. 8, left); (2) two baseband WF demuxed signals are observed via the oscilloscope when WF demuxing unit is

enabled; (3) the detected data signal streams exhibit 10-12 bit-error-rate (B.E.R.) with error-correction and 9.4 – 10.4 dB signal-to-noise ratio (SNR); and (4) video stream identical to the original, despite marginal time delay, is observed on the Rx side display (Fig. 8, right) as WF demuxing is performed.

V. CONCLUSION

We present a subset of WF muxing techniques taking advantage of polarization incompatibility (CP vs. LP) to access available space assets when the ground terminals are not polarization compatible. The CP-equipped terminals m a y b e e n a b l e d to access LP transponders while supporting space asset utility efficiency and capacity. Similar methods can be implemented for LP terminals to access CP satellites. These techniques also enable sources with CP terminals to communicate with 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. In addition, applications of WF muxing techniques to satellite communications offer many advantages, including service provision for CP VSAT terminals either through LP or via CP space assets, and for teleport operators with greater flexibility a n d e f f i c i e n c y in how they manage their assets. It is shown that polarization incompatible links may service variable number of users.

REFERENCES [1] J.N. Pelton, S. Madry, and S. Camacho-Lara, “Handbook of Satellite

Applications,” Springer, 2013.

[2] M. R. Chartrand, “Satellite Communications for The Nonspecialist,” SPIE Press, 2003.

[3] D. C. D. Chang, “Communication System for Dynamically Combining Power From A Plurality of Propagation Channels in order to Improve Power Levels of Transmitted Signals without Affecting Receiver and Propagation Segments,” US Patent No. 8,111,646, issued on 02/07/2012.

[4] 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 on May 16, 2008.

[5] 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.

[6] U.S. pattern No. 8538326, “Accessing LP transpoders with CP terminals via wavefront multiplexing techniques,” published on Sept. 17, 2013.

[7] D.C.D. Chang, “Coherent Power Combining via Wavefront Multiplexing on Deep Space Spacecraft,” US Patent Application No 13,367,031, filed on 02/06/2012.

[8] D. C. D. Chang, H. G. Yeh, and P. Wang, “Dynamic power allocation via wavefront multiplexing through multiple base stations,” in Proc. of 2012 IEEE GlobeCom, pp. 3813-3818, Anaheim, CA, Dec. 2012.

[9] D. C. D. Chang, H. G. Yeh, and Q.B. He, “Coherent Power Combining on Spacecraft via Wavefront Multiplexing Techniques,” in Proc. of IEEE ICNC 2013, pp. 268-272, San Diego Jan. 2013.

[10] D. C. D. Chang, H. G. Yeh, and Y. L. Sun, “Orthogonal Wavefront-Multiplexing Architecture for Communications in Non-Contiguous Channels,” Wireless Telecommunications Symposium 2013, Phoenix Arizona, April 17-19, 2013.

[11] http://www.ee.ucla.edu/~harish/Butler%2520Matrix.pdf.

[12] Chang, Donald, Joe Lee, Steve K. Chen, Hen-Geul Yeh, and Kung Yao. "Secured Utility Bill Data Storage via Wavefront-Multiplexing." In Proceedings of the Second International Conference on Innovative Computing and Cloud Computing, p. 193. ACM, 2013.

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