Method for decoding orthogonal modulation symbols arriving at multiple rectangular antenna arrays and method for correcting Doppler frequency shift

Abstract

A wireless communication method and apparatus enables communication between multiple endpoints and a satellite or terrestrial gateway integrated with multiple rectangular antenna arrays. The wireless communication method utilizes orthogonal modulation of data symbols. This method allows the use of multiple compact rectangular antenna arrays to increase network capacity and reduce endpoint power consumption.

Description

[0001] Cross Reference

[0002] This application claims the benefit of U.S. non-provisional patent application No. 17 / 391,914, filed on August 2, 2021, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present application relates to apparatus and methods for implementing high-capacity satellite and terrestrial low-power wide-area networks for connecting Internet of Things (IoT) devices to the Internet. Background Art

[0004] Low-power wide-area networks (LPWANs) are used to connect battery-powered sensors and other Internet of Things (IoT) devices (collectively referred to herein as "endpoints") to the Internet over long distances. As demand for LPWAN connectivity services grows, the need for (1) low-cost and reliable connectivity worldwide and (2) networks that are scalable to billions of IoT endpoints is increasing. Low-cost connectivity worldwide is challenging due to the cost of installing terrestrial gateways over the vast areas required to cover the world's landmasses. Furthermore, providing connectivity over the oceans using terrestrial gateways is not possible. Scaling to billions of IoT devices at low cost is also challenging due to the high cost of licensed spectrum and the limited amount of available unlicensed spectrum.

[0005] One way to reduce LPWAN construction costs and increase wireless network capacity is to exploit the spatial domain by using multiple antennas at the gateway, where these antennas operate together to transmit or receive a given signal, which is called beamforming. Wireless receive beamforming uses multiple antennas to collect radio energy from one or more specific directions. Wireless transmit beamforming uses multiple antennas to focus radio energy in one or more specific directions. Beamforming antenna arrays are typically arranged as one-dimensional antenna arrays, called linear arrays, or two-dimensional antenna arrays. Two-dimensional antenna arrays are typically arranged as square antenna arrays, but can also be rectangular. Linear antenna arrays are able to focus wireless energy along only one dimension (the dimension along the line formed by the antenna array). Square antenna arrays are able to focus wireless energy along two dimensions of the array. The radio beam formed along a specific dimension of the antenna array has a beam width that is proportional to the size of the antenna array along the corresponding dimension.

[0006] Wireless beamforming technology enables radios to use the spatial domain in addition to the time and frequency domains to improve range, reliability, and capacity. Single-antenna radios are limited to utilizing time and frequency resources within the geographic area pointed by the antenna. Building large antenna arrays typically requires a large footprint, making integration into small satellites difficult.

[0007] Satellites integrated with radio gateways can act as global low-power wide area network platforms for connecting sensors and other IoT endpoints to the Internet. Because satellites typically have an altitude of about 500 km or more, even a single satellite provides considerable coverage. The downside of having considerable coverage is that because satellites cover a larger geographic area, radio gateways mounted on satellites need to handle higher levels of uplink and downlink traffic than ground-based gateways. A second challenge with satellites is the high launch cost, where the cost generally increases linearly with the size of the satellite. Therefore, it is preferable to design the satellite to be as small as possible to minimize cost while providing sufficient network capacity to handle a large number of endpoint traffic. The present disclosure discusses apparatus and methods for minimizing the size of the satellite while maximizing the wireless network capacity of a satellite-based gateway using multiple rectangular antenna arrays, and also discusses applicability to ground-based gateways. Summary of the Invention

[0008] A device for constructing a satellite-based wireless communication gateway is provided. The device includes multiple rectangular antenna arrays that are not parallel to each other. Each antenna array comprises a foldable module that folds into the satellite housing. Each module includes radio beamforming circuitry and solar cells, enabling a compact satellite with high network capacity.

[0009] A method is provided for decoding orthogonally modulated symbols from multiple rectangular antenna arrays mounted on satellites, aircraft, or Earth-based structures. This method allows for higher network capacity and lower endpoint energy consumption compared to a gateway using a single square antenna array of equivalent volume.

[0010] A method is provided for correcting Doppler shift of endpoint radio transmissions arriving at a mobile satellite including a plurality of rectangular antenna arrays.

[0011] A method for estimating the position and attitude of a satellite equipped with multiple rectangular antenna arrays is provided. The method utilizes ground-based transmitters with known positions. The method can supplement or replace other satellite position and attitude estimation methods, such as attitude estimation using magnetic sensors and star trackers and position estimation using the Global Positioning System (GPS).

[0012] Additional features and advantages of the present disclosure will be described below. It will be appreciated by those skilled in the art that the present disclosure can be readily used as a basis for modifying or designing other structures for achieving the same purpose of the present disclosure. It will also be appreciated by those skilled in the art that such equivalent constructions do not depart from the teachings of the present disclosure as set forth in the appended claims. The novel features (both with respect to its organization and method of operation) that are considered to be characteristic of the present disclosure, as well as further objects and advantages, will be better understood from the following description when considered in conjunction with the accompanying drawings. However, it will be clearly understood that each of the figures in the accompanying drawings is provided for illustration and description purposes only and is not intended to be a definition of limitations of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The above and other aspects, features and advantages of the present invention will become more apparent from the following description thereof taken in conjunction with the accompanying drawings, in which:

[0014] Figure 1 A top-down view of a satellite with two integrated linear antenna arrays.

[0015] Figure 2 This is a top-down view of a satellite with four integrated linear antenna arrays.

[0016] Figure 3A A bottom-up view of a satellite with two integrated linear antenna arrays.

[0017] Figure 3B This is a bottom-up view of a satellite with two integrated rectangular antenna arrays.

[0018] Figure 4 This is a bottom-up view of a satellite with four integrated linear antenna arrays.

[0019] Figure 5 is a side view of a partially folded linear antenna array.

[0020] Figure 6 is a side view of the fully folded linear antenna array.

[0021] Figure 7 A plurality of antenna modules are shown interconnected with each other.

[0022] Figure 8 These are the top and bottom views of the antenna module.

[0023] Figure 9 is a side view of a satellite with two linear antenna arrays.

[0024] Figure 10 is a side view of a satellite with four linear antenna arrays.

[0025] Figure 11 is a side view of a satellite with its linear antenna array folded inside.

[0026] Figure 12 is a top-down view of a satellite with two linear antenna arrays folded inside.

[0027] Figure 13A is a block diagram of the antenna module receiver electronics.

[0028] Figure 13B is a block diagram of the antenna module transmitter electronics.

[0029] Figure 14 Depicted are multiple receive radio beams generated by a linear antenna array having N antenna elements.

[0030] Figure 15 The orbital reference frame is shown.

[0031] Figure 16 A contour plot showing the radio beam energy of a two-spoke linear antenna array.

[0032] Figure 17 The column beams generated by the x-antenna spokes are shown.

[0033] Figure 18 The traveling beams generated by the y-antenna spokes are shown.

[0034] Figure 19 A matrix of row and column beams generated by a two-spoke linear antenna configuration is shown.

[0035] Figure 20 The Fourier transform of M-ARY FSK symbols is depicted, where M=256.

[0036] Figure 21 Depicted is the spectrum of two M-ARY FSK symbols that overlap in time but not in frequency.

[0037] Figure 22 Depicted are symbols from two endpoints being transmitted simultaneously and received by the same column antenna beam but different row antenna beams.

[0038] Figure 23 Depicts decoding ambiguity.

[0039] Figure 24 A flow chart for decoding M-ARY orthogonal signals using multiple rectangular antenna arrays is shown.

[0040] Figure 25 Shown is a block diagram of the M-ARY FSK multi-spoke signal decoder.

[0041] Figure 26 A block diagram of a chirped spread spectrum multi-spoke signal decoder is shown.

[0042] Figure 27A A set of direct sequence spread spectrum signals that are orthogonal in the code domain is shown.

[0043] Figure 27B The time shift of a self-orthogonal direct sequence spread spectrum signal is shown.

[0044] Figure 28 A block diagram of a direct sequence spread spectrum multi-spoke signal decoder is shown, where the incoming signal is a self-orthogonal signal.

[0045] Figure 29 A block diagram of a direct sequence spread spectrum multi-spoke signal decoder is shown, where the signal sets are orthogonal in the code dimension.

[0046] Figure 30A The symbols of the quadrature modulation in the frequency dimension are shown.

[0047] Figure 30B The symbols of the quadrature modulation in the frequency and time dimensions are shown.

[0048] Figure 30C The symbols modulated orthogonally in frequency, time and code dimensions are shown.

[0049] Figure 31 is a graph of the Doppler shift of the radio carrier of a received endpoint packet as observed by a low earth orbit satellite.

[0050] Figure 32 is a graph of the variation of the Doppler shift of the carrier of the received endpoint packet as observed by a low earth orbit satellite over a 50 mS preamble duration.

[0051] Figure 33 Depicted is the block diagram of the M-ARY quadrature signal decoder with Doppler frequency correction function.

[0052] Figure 34 Describes the architecture for satellite attitude estimation using ground-based transmitters with known positions.

[0053] Figure 35 Depicts a terrestrial wireless network deploying two spatially separated linear antenna arrays.

[0054] Figure 36 Depicts a radio beam formed by a terrestrial wireless network deploying two spatially separated linear antenna arrays.

[0055] Figure 37 Depicts an endpoint that automatically switches between Bluetooth Low Energy or WiFi networks and terrestrial and satellite LPWANs using the same radio.

[0056] Figure 38 Depicted is a satellite with two antenna arrays that transmit column and row beams that scan along the ground and are received by an endpoint, which uses these signals to estimate its position.

[0057] Figure 39A Depicted is a satellite flying over the United States, with two urban areas contained within the beam formed by the x-antenna spokes.

[0058] Figure 39B Depicted is a satellite flying over the United States, with an urban area contained within the beam formed by the x-antenna spokes. DETAILED DESCRIPTION

[0059] The present disclosure relates to a wireless communication method for enhancing the performance of a radio system utilizing multiple rectangular antenna arrays. In the present disclosure, the rectangular antenna arrays are also referred to as antenna spokes. Figure 1 A top view of a satellite comprising two linear antenna spokes 1 is shown. Figure 1 The embodiment in includes solar cells 2 mounted on top of the antenna array, which are used to power the satellite electronics. Each antenna spoke has two branches, which can optionally be spatially offset as shown to allow greater flexibility when installed in the satellite housing. Figure 2 A satellite with four antenna spokes is shown. Alternative embodiments may include any number of antenna spokes. The antennas of each spoke are mounted so that the antenna array faces nadir (pointing toward the Earth). Figure 3A A bottom view of a two-spoke linear antenna array mounted on a satellite is shown, with antennas 3 mounted along the spokes. Figure 3B A bottom view of a two-spoke rectangular antenna array is shown, where each spoke is two antennas wide. In one embodiment, the antenna elements are spaced approximately 1 / 2 the wavelength of the radio carrier; antennas in alternative embodiments can have smaller or larger spacings. Greater antenna spacing provides increased spatial resolution but increases the size of the antenna array. Figure 3A and Figure 3B An antenna array using helical antenna elements is shown, but other types of antenna elements may be used including, but not limited to, monopole antennas, dipole antennas, or aperture-fed or probe-fed patch antennas. Figure 4 A bottom view of a 4-spoke linear antenna array is shown. The antenna spokes are composed of one or more foldable modules, each containing one or more antennas. Before satellite deployment, each antenna spoke is stored in a folded configuration inside the satellite housing. Figure 5 An embodiment of an antenna spoke is shown in a partially folded configuration, each module of which contains two antennas 6, Figure 6The spokes are shown in a fully folded configuration. The antenna modules are mechanically and electrically interconnected 5 along the edges of the circuit board 4. One of the wires distributes a common radio frequency (RF) local oscillator signal from a separate module within the satellite housing to all antenna modules. In an alternative embodiment, the RF local oscillator is distributed from one module to the remaining modules. One or more of the wires carry raw or processed complex baseband data from each antenna module and distributes this data to other modules or a processor mounted inside the satellite housing for use in the packet decoding process. In an alternative embodiment, communication between modules is accomplished via wireless communication rather than wired communication. In one embodiment, the antennas are arranged on alternating modules so that when the modules are folded, the antennas fold more compactly by not overlapping with the antennas 6 of adjacent modules. Figure 7 More details are shown for the electrical and mechanical connections between the antenna module circuit boards. One or more ribbon springs 7, made of steel or composite material, are attached along the edges of the antenna module circuit boards and apply torque to adjacent antenna modules to deploy them from the folded configuration when not held within the satellite housing. One or more flexible PCBs 8 are used to electrically connect adjacent antenna module circuit boards. Because the antenna array operates in a zero-gravity environment, only a small torque is required to deploy the folded antenna modules into a straight array.

[0060] Top and bottom views of an embodiment of a module for building a linear antenna array are shown in Figure 8 , where each module is fabricated from circuit board material and mounted with solar cells 9, one or more antenna elements 10, and RF, analog, and digital beamforming circuitry 11. In one embodiment, to increase the compactness of the folded antenna module, openings in the circuit board consisting of slots or holes 12 are integrated into the module circuit board material, allowing beamforming and other electronic components from adjacent modules to fit into the slots or holes when the module is folded. In alternative embodiments, the solar cells can be mounted separately on the satellite housing, however, mounting on the antenna module itself can provide additional volume efficiency. The module circuitry and solar cells are assembled on a glass-reinforced epoxy laminate, or it can be assembled on Teflon or other material that allows for mounting of electronic components.

[0061] For better visualization, Figure 9A side view of a satellite with an integrated linear antenna array is shown in FIG. The figure shows one of the spokes. In the illustrated embodiment, the second spoke is perpendicular to the first and is not shown. The spoke antenna elements are pointed toward Earth as the satellite orbits. The satellite uses a GPS receiver 13 to estimate its position. Magnetic sensors and a star tracker 14 are used to estimate the satellite's attitude (roll, pitch, and yaw). A magnetorectron 15 and a reaction wheel 16 are mounted within the satellite housing and are used to control the satellite's attitude. A battery 17, contained within the satellite housing, provides power to the satellite electronics as the satellite orbits in overlapping portions of its orbit. A separate two-way radio link 18 is used to communicate with one or more ground stations on Earth. This radio link is used to transmit collected endpoint packet data back to Earth and to receive commands or firmware updates from the ground stations. The antenna spokes can be designed to be unidirectional (Earth-to-satellite) or bidirectional. In the bidirectional case, the antenna spokes can serve a dual purpose, transmitting data to the endpoints or back to the ground stations using the same frequency band as the endpoint-to-satellite frequency band. When the spoke antenna is a single-band antenna, this is accomplished by time-division multiplexing the communication channels (this is called time division duplexing). In an alternative embodiment, the antenna spoke is designed to be dual-band, in which case the antenna spoke can simultaneously transmit on one frequency band and receive on a second frequency band (this is called frequency division duplexing). Figure 10 A side view of a satellite with four antenna spokes is shown. Two antenna spokes perpendicular to spokes 1 and 3 are not shown. Spokes 1 and 3 are shown at a 90-degree relative yaw angle, although this is not depicted. To increase the compactness of the retracted antenna spokes in the case of four antenna spokes, in this embodiment, the antenna spokes are positioned at different z positions as shown.

[0062] Figure 11 A side view of the satellite is shown, with antenna spokes 19 stowed inside. For clarity, only one spoke with two branches is shown. When the antenna modules are stowed inside the satellite, they are held in place by a burn wire 20 or a mechanical door with a solenoid for releasing the door. Alternative embodiments may have other release mechanisms, such as a magnetic latch. Once the burn wire is burned or the mechanical door is opened, the antenna modules unfold and form two or more antenna spokes.

[0063] Figure 12A top view of a stowed antenna array for a two-spoke configuration with two branches per spoke is shown. Arrows indicate the direction of spoke expansion. The figure shows spoke branches 21, 22, each with half the antenna elements of a full spoke. This facilitates compact stowage. All antenna spokes and branches are electrically connected to each other or to a central processor to perform the necessary signal processing on the downconverted received signal, decode the received packets, and transmit the packets down to an Earth-based ground station.

[0064] A block diagram of an embodiment of the antenna module receiving electronics is provided in Figure 13A . This circuit is used to downconvert the RF signal to baseband and process the downconverted received signal. Each antenna on the module is fed into a bandpass filter 23, followed by a low-noise amplifier (LNA) 24. An additional bandpass filter 25 can optionally follow the LNA to further reduce out-of-band noise. An RF mixer 26 downconverts the incoming signal to a lower intermediate frequency (IF). The mixer is followed by an amplifier 27 and an anti-aliasing filter 28. The downconverted signal is then fed into an analog-to-digital converter (ADC) 29. The digitized signal is fed into a digital processor 30. The processor can be a microprocessor, a field-programmable gate array, or a custom digital ASIC. The processor receives baseband signals from the antenna modules in the array and performs calculations on these signals, as described below. In an alternative embodiment, signal processing can be performed on a processor within the satellite's main housing, not on the antenna array module, but on a separate PCB. In one embodiment, packet decoding is performed locally on the satellite. In an alternative embodiment, the raw or partially processed downconverted and digitized complex baseband signal from each antenna can be sent directly downlink to a ground station. When the satellite transmits the complex baseband signal directly to the ground station, the packet decoding process will be performed at the computer or server located on Earth. However, sending the received complex baseband signal directly down to the ground station will require a higher satellite-to-ground station communication bandwidth.

[0065] In one embodiment, the antenna module is designed to provide two-way communication with endpoints on the ground by integrating transmit radio electronics into the module. Figure 13BThe transmit electronics are shown, including a digital-to-analog converter (DAC) 31, which receives the digitized, discrete-time complex baseband information to be modulated onto a carrier and converts it into an analog continuous-time signal. The complex baseband signal is optionally fed into a low-pass filter 32 to remove any unwanted out-of-band signals. The signal is then amplified 33 and quadrature mixed 34 with a local oscillator signal. The signal is then further amplified 35 and optionally filtered 36 to reduce any out-of-band harmonics before being sent to an antenna. The receive and transmit electronics can share the same antenna via a time-division duplex channel or by using a dual-band antenna that allows frequency-division duplexing. In an alternative embodiment, separate transmit and receive antennas are mounted on each antenna module to avoid the need to share antennas between transmit and receive circuitry. In the transmit direction, the gain and phase of the complex baseband signal are selected to allow one or more transmit beams to be pointed in the direction of one or more endpoints. Multiple beams, each containing a different packet transmission, can be created simultaneously by properly selecting the gain and phase in both the transmit and receive directions. The signal processing performed on the received signal is described in the next section.

[0066] Each antenna array spoke is programmed to receive radio energy from several focal regions, which can have varying degrees of beam overlap. For an N-antenna linear array, approximately N / 2 beams have a small spatial overlap in their radio receive beams over an elevation span from -45 degrees to 45 degrees. Although any number of M beams can be formed, they can have varying degrees of spatial overlap between beams. Higher beam overlap allows for better positioning accuracy of endpoint radio transmissions. In addition, since satellites travel at approximately 7.8 km / s in low-Earth orbit, beam overlap also provides redundancy if endpoint transmissions are long enough to cross from one beam region into an adjacent beam region. Figure 14 The calculations necessary to create M focused receive beams 37 for a linear antenna array are shown. The baseband signal received at each of the N antennas is given by x1 to x2. Ndenoted by . These signals are multiplied by the matrix denoted by H. To create a beam, the beamformer matrix shifts the received signal at antenna k relative to antenna k-1 by a constant phase shift that depends on the spacing between the antennas and the elevation angle of the beam being formed. The phase-shifted signals from each antenna are then accumulated. The phase shift is chosen to add the radio energy at each antenna in phase to maximize the signal strength in a specific beam direction. For a specific beam elevation angle along the antenna array, the phase shift is calculated by calculating the phase difference in the radio arrival signal at each antenna. The beamformer matrix then uses these phase shift values ​​in signal processing to align all received signal phases by multiplying the incoming baseband signal by the complex conjugate of a complex exponential representing the predicted arrival radio wave phase shift for each beam elevation angle. When the antenna spoke is split into two spatially offset branches, the phase shift calculation is adjusted to account for the offset between the branches. Each incoming baseband signal can also be multiplied by a gain factor, trading a wider mainlobe width for smaller sidelobes. To create M beams using an N-antenna linear array, a matrix H of size MxN is required that multiplies the incoming baseband signal by a complex exponential (and possibly a gain for tapering) to create the necessary phase shifts to align the received signal and create the beam. The phase shift used in the receive direction to form a beam at a specific elevation angle can also be used in the transmit direction to form a transmit beam along the same elevation angle. In an alternative embodiment, the beamformer matrix H is selected so that the generated beams sweep across the ground to counteract the motion of the satellite and are also adjusted to counteract any changes in the satellite's attitude. In this case, each beam will be focused on a specific area on the earth, and the beam coverage area will not move with satellite motion. In this case, the beamformer matrix H will be composed of time-varying complex exponentials.

[0067] For clarity, we use the orbital reference frame to discuss Figure 15 The geometric concepts shown. The azimuth angle is defined as the propagation angle of the radio wave relative to the direction of the orbital plane. The elevation angle is defined as the propagation angle of the radio wave relative to the -Z axis of the orbital reference frame. When observing the beam pattern from the Earth, the beam profile of maximum beam energy is parabolic in shape because the phase difference of the radio waves arriving at consecutive antennas is a function of both the azimuth and elevation angles of the radio waves received in the spoke reference frame. The phase difference of the radio wave carrier for consecutive antennas spaced half a wavelength along a linear antenna array is calculated as:

[0068] Phase difference = π cos (azimuth_s) sin (elevation) Equation 1 where azimuth_s is the azimuth angle in the spoke reference frame (azimuth_s = 0° is the radio wave arriving along the length of the spoke). Figure 16Several beam profiles are shown for the nine beams formed by each linear antenna spoke for a two-spoke system with vertical spokes. These profiles would be observed on flat ground and were created assuming a satellite altitude of 600 km. θx and θy represent the phase differences of the arriving radio waves between consecutive antennas for the x and y spokes, respectively. The horizontal profiles in the figure are formed by the spokes pointing in the Y direction, while the vertical profiles are formed by the spokes pointing in the X direction. In the orbital reference frame, azimuth_x is defined as the azimuth of the x spoke and azimuth_y is defined as the azimuth of the y spoke. When the spokes are vertical, azimuth_x = azimuth_y + 90°. For each formed receive beam, the phase difference between the consecutive antennas of the two spokes is pre-calculated. For the two-spoke configuration, we obtain two equations and two unknowns when receiving the endpoint symbol transmission via the beam from each spoke. The equations are:

[0069] Phase difference (y spoke) = πcos(azimuth_sy)sin(elevation angle) Equation 2 Phase difference (x spoke) = πcos(azimuth_sx)sin(elevation angle) Equation 3 Where azimuth_sy is the azimuth of the radio wave in the y-spoke reference frame, and azimuth_sx is the azimuth of the radio wave in the x-spoke reference frame. Assuming the satellite's pitch and roll angles are zero and converting them back to the orbital reference frame, the following equations are obtained:

[0070] azimuth_sy + satellite yaw angle = azimuth equation 4

[0071] azimuth_sx = azimuth_sy + φ Equation 5

[0072] Where φ is the orientation of the x-spoke relative to the y-spoke and is 90 degrees when the spokes are vertical. The satellite yaw angle is defined as the azimuth of the Y-spoke relative to the orbital plane. The known variable is the phase difference in the beam generated from the two spokes. The unknown quantities are the azimuth and elevation of the radio waves corresponding to the symbol transmission from the corresponding endpoint. From the above equations, the azimuth and elevation of the radio waves in the orbital reference frame can be calculated. These angles define the endpoint position on the ground because the position and attitude of the satellite relative to the earth are known using an onboard GPS radio, magnetic sensors, and sun sensors, as well as attitude estimation methods described later in this disclosure. Non-zero pitch and roll angles can be integrated into the above equations using appropriate rotation matrices. For each symbol received, the azimuth and elevation of the corresponding radio wave are calculated as described above, and a position coordinate is assigned to that symbol.

[0073] For illustration purposes, it is assumed that the beam profile is straight along the x-axis and y-axis. Figure 17 The beam profile generated by the X-spokes and the Figure 18 This simplification is shown for illustrative purposes in Figure 1 for a beam profile generated by a Y spoke. When the antenna spoke is rectangular and has more than one antenna along the narrow dimension, the beam profile will look similar, except that the beam width can be controlled in both the x and y dimensions. For simplicity, this disclosure will focus on the case of using a vertical linear antenna array. When a nonlinear rectangular antenna array is used, the resulting beam is two-dimensional rather than one-dimensional. In this case, the same principles apply to solving for the location of the endpoint transmission.

[0074] In the simplified case where the beam profile is approximated as a straight line, Figure 19 The figure shows the superimposed beam profile of two linear antenna arrays that are perpendicular to each other, creating an array of x-column beams and y-column beams. When the signal reaches the satellite at the spokes of the x and y linear antenna arrays, the location of the radio wave source can be estimated by converting the phase difference observed along the antenna spokes into the angle and elevation of the propagating radio wave and then into a location on Earth. This can be visualized using the 2D matrix shown in the figure, where the endpoint transmits symbol 38 from position row 4 and column 2. As mentioned earlier, after adjusting for non-rectilinear beam profiles, the row and column positions will be converted into locations on Earth.

[0075] In radio communications, quadrature modulation is used to increase the radio sensitivity for a target communication rate by spreading the available energy over as much bandwidth as possible. A disadvantage of quadrature modulation is that it has low spectral efficiency. The combination of multi-antenna hub-and-spoke beamforming and quadrature modulation provides significant performance improvements over single-antenna radios using quadrature modulation by improving the spectral efficiency of the system. An example of quadrature modulation is M-ARY frequency shift keying (FSK) modulation. The FFT of a M-ARY FSK symbol is Figure 20 The Log2(M) bits are mapped to one of M orthogonal frequency tones, and one of the possible tones is sent out over the communication channel to encode the bits. Figure 20 The diagram illustrates the case when M = 256, where 8 bits are encoded into a specific tone frequency. In this example, the bits '01001110' = 78 are encoded into the tone frequency. At the receiver, each received tone is then demodulated and converted back into the correct bit. In a shared wireless network, if two orthogonal modulation symbols sent from two different endpoints overlap in time, the receiver may be confused about which symbol corresponds to which transmitter. Figure 21Depicts the spectra of two symbols from two different endpoints that overlap in time but not in frequency. Symbols that overlap in time with one or more other orthogonal modulation symbols can only be correctly decoded if the symbol to be decoded does not overlap with other symbols in the orthogonal dimension range (for M-ARY FSK, the orthogonal dimension range is 2 M frequencies). The spectral efficiency of M-ARY orthogonal modulation using a single antenna receiver is approximately Log2(M) / M bits / second / Hz. In the case of multi-spoke beamforming, in order to improve spectral efficiency, symbols from different endpoints that overlap in time are assigned positions, and these symbols can be distinguished based on each symbol position. This is Figure 22 , which shows a first symbol 39 from a first endpoint picked up by row beam 4 and column beam 3, and a second symbol 40 from a second endpoint picked up by row beam 12 and column beam 3. If the two symbols overlap in time but not in frequency, then the symbols can be distinguished and decoded separately because they are detected by unique row and column beam pairs. In order to successfully decode two symbols with a single antenna receiver, the symbols would need to be non-overlapping in time or non-overlapping in orthogonal frequency ranges.

[0076] Figure 23The following example shows a case where the first endpoint transmits symbol 41, which is picked up by row beam 4 and column beam 3. The second endpoint transmits symbol 42, which is picked up by row beam 12 and column beam 3. The third endpoint transmits symbol 43, which is picked up by row beam 4 and column beam 13. If the second and third endpoints transmit their symbols at the same time as the first endpoint, and furthermore, if the second and third endpoints also transmit their symbols on the same frequency as each other (but different from the first endpoint to avoid symbol collisions), there may be ambiguity when decoding the first endpoint's symbols. The decoder cannot tell whether the overlapping symbols from the second and third endpoints are actually a single symbol picked up by the intersecting row and column beams. However, this scenario is unlikely because it requires the symbols to overlap in both time and frequency. Ignoring this scenario, the spectral efficiency of a two-spoke linear antenna receiver using M-ary FSK modulation and N non-overlapping beams per spoke has an upper limit of N*Log2(M) bits / second / Hz, where N*M represents an improvement over a single-antenna receiver using M-ary FSK modulation. In practice, satellite radiocommunication links operate reliably over limited elevation angles due to the increased endpoint-to-satellite range at higher elevation angles and the lower antenna gain at higher elevation angles. For this analysis, the elevation angle is assumed to be limited to a maximum of 45 degrees. In this case, a 128-element linear array can create approximately 64 non-overlapping beams on the ground, covering a 45-degree elevation range. Including the case where symbols overlap in time and frequency as described above, a two-spoke linear antenna array system with 128 antennas per spoke and 64 non-overlapping beams using 64-degree FSK modulation has been simulated to have approximately 700x better spectral efficiency compared to a single-antenna receiver using 64-degree FSK modulation. For the same amount of bandwidth, this translates to a 700x improvement in network capacity. The same two-antenna spoke system using 64-degree FSK modulation has been simulated to have approximately a 150x improvement in spectral efficiency compared to a single-antenna receiver using 2-degree FSK modulation. A standard square antenna array has the same volume as a 128-element-per-spoke antenna array. A two-spoke linear array would have an array size of approximately 16×16 antenna elements and generate 8×8=64 non-overlapping beams on the ground within a 45-degree elevation range. A two-spoke linear antenna array with 128 antenna elements per spoke receiving a 64-ary FSK signal has an improvement in network capacity of approximately 700 / 64=10.9x over a 16×16 square antenna array receiving a 64-ary FSK modulated signal, and an improvement in network capacity of approximately 150 / 64=2.3x over a 16×16 square antenna array receiving a 2-FSK modulated signal. Another advantage of using multiple spoke antenna arrays over square antenna arrays is that, for the same antenna volume, the location of endpoints on the ground can be estimated with greater accuracy.The accuracy of position along the x or y dimension is inversely proportional to the length of the antenna array along each dimension. Two linear antenna arrays with 128 elements along each of the x and y dimensions will be able to estimate the position of an endpoint with approximately 8x higher accuracy than a 16×16 element square antenna array (assuming the same spacing between antennas for the linear and square arrays).

[0077] Another advantage of using quadrature modulation is improved energy efficiency. Compared to a 2-ary FSK radio over an additive white Gaussian noise (AWGN) channel, a 64-ary FSK radio requires approximately 2x (3dB on a decibel scale) less energy to transmit the same-sized packet (with a 10% probability of symbol error). In summary, multi-spoke beamforming receivers offer significant improvements in network capacity and energy efficiency compared to single-antenna receivers. The multi-spoke architecture allows for the use of compact antenna arrays that can be easily accommodated in small satellites while still providing good network capacity and spectral efficiency.

[0078] The multi-spoke symbol decoding method is applicable not only to M-ARY FSK modulation, but also to any other orthogonal modulation schemes. Figure 24 A flow chart is shown for decoding any packet using orthogonal modulation. First, M spatial beams are created for each antenna spoke 44. Then, for each beam created by each spoke, a preamble detection circuit 45 searches for a preamble symbol sequence along both the spoke and all beams. If a preamble sequence is detected simultaneously by both spokes, a position is assigned to that preamble sequence 46. The system then looks for a subsequent data symbol transmission assigned the same position as the preamble transmission 47. Finally, consecutive symbols with similar positions to the preamble symbol sequence are grouped together, and the packet containing these symbols is decoded 48.

[0079] The quadrature signal decoders for different quadrature modulations are described in more detail in the following paragraphs. Figure 25The figure shows the reception of an M-ary FSK signal 49, where one of M orthogonal frequency tones is selected at the transmitter to encode a bit sequence. At the receiver, the signal is fed into an FFT 50 for each beam of each antenna spoke. In one embodiment, the sampling rate of the incoming signal entering the FFT is set to the bandwidth of the communication channel, and the number of samples calculated for each FFT is set to the symbol duration multiplied by the sampling rate. For each antenna spoke beam, a preamble detector 51 searches for a preamble symbol sequence in time and frequency. When the preamble detector detects a valid preamble, the circuit has achieved frequency and time synchronization with the incoming data packet. The preamble detection circuit outputs from all antenna spokes and beams are fed into a processor 52, which checks whether a valid preamble sequence appears at the same time and frequency on the receive beams of two different spokes. Once the processor detects a valid preamble sequence arriving simultaneously on two different spokes, the decoder is now synchronized in time, frequency, and space. The figure shows an example where both spoke 1, beam m, and spoke 2, beam n, detect preambles simultaneously. The decoder 53 then decodes the data symbols that arrive at the appropriate time, frequency and space (the intersection of the two beam profiles on Earth where the preamble was detected). Figure 25 The case where the data symbols associated with the preamble sequence arrive from the same row and column beams as the preamble symbol sequence is shown. However, it is important to note that the row and column beams that receive the preamble symbol sequence are not necessarily the same row and column beams that received the associated data symbols. This is only true if the changes in satellite motion and satellite attitude over the duration of the packet transmission are small enough not to change the beam that receives the data symbols (compared to the beam that received the preamble symbol sequence). In an embodiment where the beam weights vary over time and are selected to counteract the motion of the Earth and adjust the satellite attitude, the beams will track a fixed contour on the Earth, and the same set of row and column beams that received the preamble sequence will also receive the corresponding data symbols of the packet. During the decoding process, if a data symbol frequency does not match between the two spokes, or if more than one frequency matches between the two spokes, the data symbol is declared an erasure. The packet can still be decoded by using an appropriate error correction code that can correct for a certain number of symbol errors and / or erasures.

[0080] Another orthogonal signal that can be used with a multi-spoke antenna array receiver is a chirped spread spectrum signal. Figure 26A chirped spread spectrum modulated signal 54 is shown that modulates bits based on cyclic time shifts of a base chirp signal (a chirp with zero time delay). At the receiver, the chirp signal is convolved with the base chirp signal for each beam of each spoke. After convolution, when the received symbols are time-aligned with the base chirp, the resulting signal is simply the M-ARY FSK modulated signal. The convolved signal is then fed into the FFT block 55, and the remainder of the decoding process is the same as the M-ARY FSK decoding process.

[0081] The above examples illustrate orthogonal signaling in the frequency dimension (M-ARY FSK, chirped spread spectrum). Orthogonal signaling can also be implemented in the time dimension, the code dimension, or a combination of the frequency, time, and code dimensions. To achieve orthogonality in the time and / or code dimensions, direct sequence spread spectrum (DSSS) signals are typically used. As a brief background, to achieve orthogonality in the code dimension, M DSSS signals are generated. Each symbol is orthogonal to the others, and each symbol encodes Log2(M) bits, as Figure 27A In order to achieve orthogonality in the time dimension, a DSSS signal with good self-orthogonality is selected so that the time shift of the same code sequence is orthogonal to other time shifts of multiples of the chip period T, as shown in Figure 27B As shown. A DSSS signal group that achieves orthogonality in both the time dimension and the code dimension can also be selected. In order to achieve orthogonality in the frequency and time dimensions, a DSSS signal with good self-orthogonality properties can modulate an M-ARY FSK signal. In order to achieve orthogonality in the frequency domain, time domain and code domain, a group of K orthogonal DSSS signals are selected, each of which also has good self-orthogonality. Each DSSS signal modulates an M-ARY FSK signal. In order to encode Log2(M*K*T) bits per symbol, one of the M FSK tones is selected, modulated with one of the K orthogonal DSSS signals, and then time-shifted with one of the T time shifts. As more orthogonal dimensions are added, the decoder computational complexity increases.

[0082] Figure 28 A decoder capable of decoding across orthogonal frequency and time dimensions is shown in FIG. In the figure, a DSSS signal with good self-orthogonality properties modulates a multi-band FSK signal. At the receiver, the received signal 57 is convolved with the DSSS signal matched filter for each beam of each spoke. When the received symbols are aligned in time with the matched filter, we are left with the multi-band FSK signal. This signal is injected into FFT block 58, and the remainder of the decoding process is identical to that of a multi-band FSK decoder, except that bits can also be encoded in the time shift of the symbols.

[0083] The above examples illustrate orthogonal signaling in the frequency domain (M-ary FSK, chirp spread spectrum) and orthogonal signaling in the time and frequency dimensions (DSSS modulated M-ary FSK signal with T possible time shifts of the data symbols). Orthogonal signals can also be generated in the code dimension, in the code and time dimensions, and in the code, time, and frequency dimensions. Figure 29 A computationally more complex decoder that can decode symbols in all three dimensions is shown in . In this figure, a DSSS signal is picked from an alphabet of K orthogonal codes, each with good self-orthogonality, and modulates a multi-dimensional FSK signal. A time shift T is also added to each transmission to encode bits along the time dimension. At the receiver, for each beam and each spoke, the received signal 59 is convolved with a bank of matched filters 60, where each matched filter is one of the K DSSS signals. When the received symbol is time-aligned with one of the matched filters, we are left with a multi-dimensional FSK signal. Each matched filter output is injected into an FFT block 61, and the remainder of the decoding process is identical to that of a multi-dimensional FSK decoder, except that additional bits can also be encoded in the symbol's time shift and in the code selected for each symbol. The preamble detector now searches in the time, frequency, and code dimensions during the preamble search process.

[0084] Figures 30A to 30C It shows that the two endpoints transmit symbols along different orthogonal dimensions. Figure 30A Orthogonal signaling in the frequency dimension as shown in , multi-spoke array processing allows resolving ambiguities that occur when symbols are not transmitted using the same frequency but rather over the same symbol frequency range used to encode the bits. Figure 30B Orthogonal signaling in the frequency and time dimensions as shown in , multi-spoke array processing allows resolving ambiguities that occur when symbols from different endpoints do not collide in time and frequency but are transmitted on the same time and frequency range used to encode bits. Figure 30C With orthogonal signaling in the time, frequency, and code dimensions as shown in [1], multi-spoke array processing allows for resolving ambiguities that occur when symbols from different endpoints do not collide in time, frequency, and code space, but are transmitted over the same time, frequency, and code ranges used to encode the bits. In general, the improved spectral efficiency / capacity improvement is independent of the type of orthogonal modulation used and depends only on the number of symbols used in the alphabet used to encode the bits and the number of antennas used in the antenna array spokes.

[0085] As the satellite moves toward the endpoint from which the packet is being transmitted, the transmitter's observed carrier frequency will increase. As the satellite moves away from the endpoint, the observed carrier frequency will decrease. This change in observed frequency is due to a Doppler shift equal to v*f / c, where v is the relative velocity of the satellite to the endpoint, f is the carrier frequency, and c is the speed of light. Figure 31 This Doppler shift is shown in for a satellite whose position varies from -600 km to 600 km along the direction of travel relative to the endpoint position. For a 2.4 GHz carrier frequency, for a satellite altitude of 600 km and a speed of 7.6 km / s, the Doppler shift varies from approximately -35 KHz to 35 KHz. If the shift were constant, this would not be a problem as the receiver would be able to lock onto the carrier frequency when searching for the preamble. The challenge becomes dealing with variations in the Doppler shift over multiple data symbols, which can cause the receiver to lose frequency synchronization and incorrectly decode symbols. This can be clearly seen in the example case of M-ARY FSK, where, assuming 125 Hz spacing per symbol, small variations in Doppler shift of approximately 125 Hz can cause bits to be decoded incorrectly. In . Figure 32 The variation of Doppler frequency for a carrier frequency of 2.4 GHz and a typical preamble duration of 50 mS is shown in FIG. As shown, the worst case frequency variation over the preamble duration is about 30 Hz. Even with this offset, the preamble detection circuit is still able to lock onto the preamble and will only suffer a small performance degradation (about 0.5 dB reduction in preamble detection sensitivity for an 8 mS long symbol). The process of Doppler correction for orthogonal or non-orthogonal signal decoders is described in Figure 33, which works for all orthogonal and non-orthogonal modulated signals, including but not limited to M-ARY FSK, chirp spread spectrum, direct sequence spread spectrum, BPSK, and QPSK signals. Multiple signal demodulators 62 process incoming signals from all beams and each spoke. A preamble detector 63 operates along each beam and searches for the preamble symbol sequence. When preamble detection occurs simultaneously on both the row and column beams, the position of the preamble transmission is estimated 64. The figure shows an example where both spoke 1, beam m, and spoke 2, beam n, detect the preamble simultaneously. Using the preamble position estimate, the change in Doppler frequency shift for the remainder of the packet data symbol is estimated 65 by looking up a deterministic Doppler frequency vs. time curve 66 for the estimated endpoint position. As an alternative to a lookup table, the change in Doppler frequency vs. time can be calculated analytically as a function of the endpoint position relative to the satellite position and the known satellite velocity. Each data symbol received from the correct spatial location after the preamble sequence is then frequency adjusted 67 based on an estimated Doppler correction factor calculated from the Doppler frequency versus time curve. The frequency adjusted symbols are then sent to a block decoder 68, which converts the data symbols into bits and optionally applies bit deinterleaving and error correction to the bits.

[0086] Typically, a satellite will use star trackers and magnetic sensors to estimate the satellite attitude (pitch, roll, and yaw). A satellite can use a radio navigation system such as the Global Positioning System (GPS) to calculate its three-dimensional position coordinates. However, position and attitude estimates are not always very accurate, and it is beneficial to be able to use additional means to estimate satellite position and attitude. To this end, the proposed system relies on multiple radio transmitters on the ground with known positions. The ground-based transmitter positions can be static or dynamic, such as Figure 34As shown. These ground-based transmitter positions can be estimated in real time using a vehicle-mounted GPS receiver, or estimated during transmitter installation (assuming it is a static transmitter). The transmitter is a static transmitter 69 or a mobile transmitter. The mobile transmitter may include a standard smartphone 70 that has GPS and the ability to communicate with satellites for estimating its position. The transmitter may also be an endpoint on the ground that has an integrated GPS receiver and can send its GPS position to satellites 71. Any combination of radio transmitters with known positions can be used for satellite position and attitude estimation. These transmitters send periodic messages to the satellites, where the messages contain the transmitter's position. In order to estimate the satellite position and attitude, six or more transmitters spread out far enough apart on the ground transmit their known positions to the satellites at approximately the same time. If the satellite positions are already known using a radio navigation system such as GPS 72, only three or more transmitters on the ground are needed to estimate the three attitude variables. GPS time synchronization or other means such as the Network Time Protocol can be used to synchronize the ground-based transmitters. To allow for more accurate satellite position or attitude estimates, ground-based transmitters should be spread out in both latitude and longitude by approximately the antenna array beamwidth spacing or more. The satellite antenna array receives position information from the ground-based transmitters. The satellite combines the position information received from the ground-based transmitters with an estimate of the angle of arrival of each transmitter's transmission. These equations can be solved for unknown position and attitude variables (elevation, azimuth, range, pitch, roll, and yaw). When six or more transmitters on the ground are spaced far enough apart so that each transmitter is at least one beamwidth apart from the others, the system of equations is overdetermined, and a least-squares estimate can be calculated to improve the accuracy of the satellite attitude estimate. If the transmissions from the ground-based transmitters do not occur simultaneously, a Kalman filter on the satellite integrates the position data from the ground transmitters with the satellite inertial measurements to calculate an estimate of the satellite's position and attitude. The position and attitude estimates can also be continuously updated by the Kalman filter between transmissions, as transmissions may not occur continuously to reduce the required uplink bandwidth. The position and attitude estimate calculations can be performed locally on the satellite or remotely on a server.

[0087] Satellite-based IoT networks work well for rural and suburban environments but face challenges in urban environments where tall buildings create radio wave obstruction and experience higher levels of radio interference. For urban environments, it can be beneficial to supplement satellite networks with terrestrial networks to offload the satellite networks and provide more reliable coverage. The multi-spoke beamforming techniques discussed for satellite can also be applied to terrestrial networks with minor architectural changes. Instead of co-locating multiple rectangular antenna arrays as in the satellite case, in the terrestrial case, two or more antenna arrays are installed at geographically separated locations, with each array mounted parallel to the ground and oriented to create radio waves parallel to the Earth. Figure 35 and Figure 36 A top view of this architecture is shown in FIG. Each antenna spoke 73 generates N receive radio beams. For illustration purposes, each spoke in the figure includes four antennas 74. When a preamble symbol sequence is transmitted from endpoint 75, it is received by spoke 1, beam m, and spoke 2, beam n, as shown in FIG. Figure 36 As shown. For each subsequent data symbol sent by an endpoint belonging to the same packet, the same beam from each spoke should pick up these symbols (assuming minimal endpoint motion during packet transmission). Other endpoints with different locations will send symbols picked up by different beams, and even when the symbols overlap in time, they can be spatially distinguished, similar to the satellite case. In the satellite case, when multiple data symbols arrive at the antenna array, they can be decoded locally. In the terrestrial case, since the antenna arrays are spatially separated, the symbols need to be sent by wire or wireless means and processed at a processor node 76 co-located with one of the antenna spokes or at a geographically separated location. Antenna spoke data can also be routed to the processing nodes via the Internet. Similar to the satellite case, the terrestrial antenna spoke position and orientation can be estimated using multiple transmitter nodes on the ground with known locations that are spatially separated so that each transmitter's radio transmission is picked up by a different receive beam. If the yaw angle of the antenna array is known but the array's position is unknown, two transmitters with known positions will be required to estimate the unknown antenna array position. If the yaw angle of the antenna array is also unknown, four transmitters will be required for a two-antenna array system. Unlike the satellite case, in the terrestrial case, this calibration only needs to be done once because the ground antenna array is static. In the ground antenna array calibration case, a single transmitter can also be used in multiple locations, and the transmissions can be completed sequentially by the ground antenna array and combined for position and attitude estimation.

[0088] The multi-spoke decoding process can also be applied to rectangular antenna arrays mounted on other platforms, such as aircraft. Furthermore, the decoding process can utilize multiple antenna beams, each generated from a different platform. For example, one beam can be generated from an antenna array mounted on a base station on the ground, and a second antenna array can be mounted on a satellite. Preamble symbol sequence and data symbol detection can occur at the various antenna arrays, and these detections can be sent to a server or other location to aggregate these detections and apply the decoding methods described in this disclosure.

[0089] It is advantageous to have a single radio that can communicate on a wide range of networks, including personal area networks (PANs) such as Bluetooth Low Energy (BLE), longer range local area networks (LANs) such as WiFi, longer range terrestrial low power wireless networks (LPWANs), and satellite networks. To enable seamless transitions between networks, the endpoint radio first attempts to establish communication with the lowest power network, which is typically a PAN or LAN network. If communication cannot be established, the radio then attempts to communicate with the terrestrial LPWAN network. Finally, if no other network is available, the endpoint radio sends its message to the satellite network. This is done in Figure 37 Shown in.

[0090] The multi-spoke beamforming architecture can also be applied in the transmit direction to send data to the endpoint and also provide the endpoint with the ability to calculate their position locally, as an alternative to using a separate GPS receiver. The benefit of this is that the endpoint can estimate its position locally using the same radio that the endpoint uses to transmit to the satellite. Although the endpoint position is also estimated at the satellite when the satellite receives the endpoint packet transmission, there are situations where it is beneficial for the endpoint to calculate its position locally without the need to send packets to the satellite. One example is a geo-fencing application where the endpoint only needs to transmit packets up to the satellite when it is outside of a certain geographic area. In this case, it is more energy efficient for the endpoint to transmit only when it is confident that it is outside the geo-fence boundaries. To achieve this functionality, the process is performed in Figure 38. A beam is generated from one of the antenna spokes and scans in the direction pointed by the spoke. In one embodiment, the scan angle is an angle from -45 degrees to 45 degrees in elevation. The number of beam positions along the scan should be sufficient so that every point on the ground will have strong coverage at some point along the scan. At each step of the beam, the antenna array transmits a beacon packet containing the time, satellite position, beam position, and an optional terrain correction factor. The terrain correction factor provides an estimate of the local terrain elevation profile so that this can be taken into account when estimating the endpoint's position. To estimate the endpoint's position, the endpoint needs to receive information from at least two antenna spokes. Each antenna spoke independently scans the generated beam in space. Collisions between beams are avoided by time-division multiplexing the packet transmissions from each beam. The endpoint combines this information from multiple antenna spokes to estimate its position. To save power, in one embodiment, the endpoint is provided with ephemeris data in the beacon, which allows the endpoint to know when a satellite will be overhead and when to expect the next beam to arrive at their location. This allows the endpoints to sleep as long as possible before waking up their radios to listen for the next arriving beacon.Ephemeris data can also be loaded into the endpoints by other means such as a nearby smartphone or cellular network.

[0091] When operating a radio in an unlicensed band, the radio needs to contend with external interference from multiple potential sources. For example, when operating in the 2.4 GHz unlicensed band, other sources of interference include WiFi radios, Bluetooth radios, and microwave ovens. Satellites orbiting above the Earth, integrated with a multi-spoke antenna array architecture, create beams of fairly narrow width on the Earth. The narrower the beamwidth, the more interference the antenna array can spatially filter out, thereby improving the performance of the satellite-based gateway receiver. There are certain situations where an antenna beam may still contain significant interference. For example, Figure 39A The example shows a satellite 77 flying over the United States and the beams generated by the x-spokes encompassing two urban areas 78. Urban areas typically contain significantly more interference sources than rural areas. Therefore, it would be beneficial to develop methods to reduce the interference picked up by each antenna array beam. One method to reduce received interference is to find the optimal yaw angle of the satellite so that the interference picked up by the antenna array beam is minimized. Figure 39BThe diagram shows a case where the satellite yaw angle is rotated 45 degrees so that the antenna array beam only picks up one urban area instead of two, thereby reducing the amount of interference picked up by the antenna array beam. To find the optimal yaw angle, the following approaches are taken. The first approach is to measure the interference level measured at each antenna array beam as the satellite orbits the Earth. When a second satellite orbits along approximately the same orbital plane, it can align itself to a different yaw angle relative to the first satellite. The second satellite then measures the interference level at approximately the same location as the first satellite measured the interference level. The interference measurements for each location along the orbital plane and each antenna spoke beam, as well as each yaw angle, are stored in memory and optionally transmitted down to a ground station and server, which aggregates all interference measurements from all satellites in the network. Assuming the interference level remains relatively constant over time, the system can learn over time what the optimal yaw angle is for each satellite as it orbits above a specific location above the Earth. In one embodiment, the optimal yaw angle is calculated on the server and transmitted back to the satellite using a ground station-to-satellite wireless communication link. Another approach is to average the interference by continuously rotating each satellite at a yaw angle as it orbits the Earth.In one embodiment, the rotation period is selected so that the rotation period is approximately equal to the packet duration.

[0092] While the foregoing description of certain preferred embodiments of the present invention has shown, described, and pointed out some of the essential novel features of the present invention, it should be understood that various omissions, substitutions, and changes may be made by those skilled in the art to the details of the described apparatus and the form of its use without departing from the spirit of the present invention. Therefore, the scope of the present invention should not be limited to the foregoing discussion.

Claims

1. A method for decoding orthogonal modulation symbols arriving at a plurality of rectangular antenna arrays, the method comprising: creating a plurality of first receive beams at a first antenna array among the antenna arrays; creating a plurality of second receive beams at a second antenna array in the antenna array; detecting a preamble symbol sequence of one of the plurality of first receive beams arriving at the first antenna array; detecting the preamble symbol sequence arriving at one of the plurality of second receive beams of the second antenna array; converting the first receive beam to a first contour on the earth from which the preamble symbol sequence was transmitted; converting the second receive beam to a second contour on the earth from which the preamble symbol sequence was transmitted; determining a range of orthogonal dimensions of data symbols associated with the preamble symbol sequence; detecting data symbols arriving within said orthogonal dimensions and originating from said first contour on the Earth; detecting said data symbols originating from said second contour on the earth; as well as The data symbols are decoded. The decoding method according to claim 1 , wherein the antenna array is installed on a satellite. The decoding method according to claim 1 , wherein the antenna array is installed on an aircraft.

4. The decoding method of claim 1, wherein each of the antenna arrays is mounted on a structure fixed to the earth.

5. The decoding method of claim 1, wherein the antenna array is mounted on a combination of a satellite, an aircraft, and a ground-based structure.

6. The decoding method according to claim 1, wherein the data symbols are modulated using M-ARY frequency shift keying modulation.

7. The decoding method according to claim 1, wherein the data symbols are modulated using chirp spread spectrum modulation.

8. The decoding method according to claim 1, wherein the data symbols are modulated using a direct sequence spread spectrum signal.

9. A method for correcting Doppler shift of incoming data symbol transmissions arriving at a plurality of rectangular antenna arrays mounted on a satellite, the method comprising: creating a plurality of first receive beams at a first antenna array among the antenna arrays; creating a plurality of second receive beams at a second antenna array in the antenna array; detecting a preamble symbol sequence of one of the plurality of first receive beams arriving at the first antenna array; detecting the preamble symbol sequence arriving at one of the plurality of second receive beams of the second antenna array; converting the first receive beam to a first contour on the earth from which the preamble symbol sequence was transmitted; converting the second receive beam to a second contour on the earth from which the preamble symbol sequence was transmitted; intersecting the first contour on the earth with the second contour on the earth to estimate a location of transmission of the preamble symbol sequence; using the preamble symbol sequence transmission position estimate to predict a Doppler shift of data symbols associated with the preamble symbol sequence; determining a range of orthogonal dimensions of the data symbols associated with the preamble symbol sequence; detecting data symbols arriving within said orthogonal dimensions and originating from said first contour on the Earth; detecting said data symbols originating from said second contour on the earth; as well as The Doppler shift prediction is utilized to adjust an incoming carrier frequency of the data symbols and the data symbols are decoded.

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