Beacon receiver and method for receiving a beacon signal.

Description

1 / 28 Beacon receiver and method for receiving a beacon signal. TECHNICAL FIELD OF THE INVENTION

[0001] A pilot beacon receiver is disclosed using a common digital Fourier transform (DFT) module for pilot / beacon acquisition and tracking. The receiver provides finer estimation using a generalized complex interpolator and operates at a very low signal-to-noise ratio (SNR), for example, a negative SNR. The receiver also handles interrupts with and without redundancy. The receiver provides reliable frequency in the presence of faults. The receiver can handle multiple beacons to improve system availability. BACKGROUND OF THE INVENTION

[0002] Ground equipment can be frequency synchronized with a satellite using beacon signals. The satellite transmits beacon signals to assist group synchronization of equipment between groups, satellites, and terminals. The channel between the satellite and ground equipment can be compromised by atmospheric loss at high frequencies, for example, in the Ka band. Severe attenuation of a beacon signal can lead to an interruption. Attenuation or compromise of the channel can also be caused by phase noise. SUMMARY OF THE INVENTION

[0003] This Summary is provided to introduce a selection of concepts in a simplified form which is further described below in the Detailed Description section. This Summary is not intended to identify the main or essential features of the subject matter claimed, nor is it intended to be used for Petition 870250060834, dated 07 / 16 / 2025, page 5 / 37 2 / 28 limit the scope of the matter.

[0004] The present receiver provides a wide reception frequency range for a continuous wave (CW) signal. Robust performance is provided in the presence of phase noise and a low SNR, for example, a negative SNR. The receiver embodiments can handle a beacon reception interruption with redundancy.

[0005] In some respects, the techniques described herein refer to a beacon receiver that includes: a digital Fourier transform (DFT) module including compartments for acquiring and tracking a beacon signal; an acquisition processor to find beacon signal acquisition frequency estimates, to improve the acquisition frequency estimates with a generalized complex interpolator and to linearize the acquisition frequency estimates; and a tracking filter to track the acquired beacon signal and to calculate tracking frequency estimates;and a synchronization manager to apply frequency correction to an oscillator based on acquisition frequency estimates or tracking frequency estimates, where the DFT module uses a first bin size for bins to acquire and a second bin size for bins to track, and the first bin size is larger than the second bin size.

[0006] In some respects, the techniques described here refer to a beacon receiver, where the first compartment size is greater than 6 Hz.

[0007] In some respects, the techniques here Petition 870250060834, dated 07 / 16 / 2025, p. 6 / 37 3 / 28 described refer to a beacon receiver, where a frequency correction error of the first compartment size is greater than 0.1 Hz when the beacon signal has a frequency range of + / - 1.5 kHz.

[0008] In some respects, the techniques described herein refer to a beacon receiver, including a raised square root cosine (SRRC) filter that operates on a beacon symbol in the beacon signal at a symbol rate that is an integer multiple of a beacon symbol rate.

[0009] In some respects, the techniques described herein refer to a beacon receiver, which also includes a generalized complex Lagrange (GCL) interpolator to improve tracking frequency estimates.

[0010] In some respects, the techniques described here refer to a beacon receiver, where the acquisition processor improves acquisition frequency estimates with a generalized complex Lagrange interpolator (GCL).

[0011] In some respects, the techniques described herein refer to a beacon receiver, also including a signal-to-noise ratio (SNR) estimator to provide an SNR estimate for the acquisition processor.

[0012] In some respects, the techniques described herein refer to a beacon receiver, also including a control to detect loss of the beacon signal and an SNR estimator to provide an SNR estimate for the control.

[0013] In some respects, the techniques described here refer to a beacon receiver, also including a control to restore a last known good state to the acquisition processor during the transition of an interrupt. Petition 870250060834, dated 07 / 16 / 2025, p. 7 / 37 4 / 28

[0014] In some respects, the techniques described herein refer to a beacon receiver, including a beacon redundancy module, in which the beacon signal includes redundant beacon signals, and a control for switching from a first beacon signal of redundant beacon signals to a second beacon signal of redundant beacon signals when an interruption of the first beacon signal is detected.

[0015] In some respects, the techniques described here refer to a beacon receiver, where the DFT module for acquiring the beacon signal and the DFT module for tracking the beacon signal are the same.

[0016] In some respects, the techniques described here refer to a beacon receiver, where the tracking filter is a first-order filter with a feedback control α set to 0.1.

[0017] In some respects, the techniques described herein refer to a beacon receiver, wherein the beacon signal includes a beacon symbol rate of 23.4 kilo symbol signals per second (ksps), wherein the beacon signal includes a structure with a duration less than or equal to 100 ms.

[0018] In some respects, the techniques described herein refer to a beacon receiver, wherein the first compartment size is 30 Hz, and wherein the second compartment size is 1 Hz.

[0019] In some respects, the techniques described herein refer to a beacon receiver, where the beacon signal includes the satellite beacon signal.

[0020] In some respects, the techniques described herein refer to a beacon receiver, including a received signal strength indicator (RSSI) estimator. Petition 870250060834, dated 07 / 16 / 2025, p. 8 / 37 5 / 28 to provide a linearized estimate of RSSI, where the RSSI estimator operates at a signal rate of the beacon signal.

[0021] In some respects, the techniques described herein refer to a method for receiving a beacon signal that includes: transformation, for acquisition and tracking, of the beacon signal using a binned Digital Fourier Transform (DFT) module; acquisition of the beacon signal by finding beacon signal acquisition frequency estimates, improving the acquisition frequency estimates using a generalized complex interpolator and linearizing the acquisition frequency estimates; tracking the acquired beacon signal and calculating tracking frequency estimates;and synchronization of an oscillator by applying a frequency correction based on acquisition frequency estimates or tracking frequency estimates, wherein the DFT module uses a first bin size for the bins for acquisition and a second bin size for the bins for tracking, and the first bin size is larger than the second bin size.

[0022] In some respects, the techniques described here refer to a method in which the generalized complex interpolator includes a generalized complex Lagrange interpolator (GCL).

[0023] In some respects, the techniques described here refer to a method, including further improvement of tracking frequency estimates using a generalized complex Lagrange interpolator (GCL).

[0024] In some respects, the techniques described here refer to a method, in which a DFT module for Petition 870250060834, dated 07 / 16 / 2025, page 9 / 37 6 / 28 acquiring the beacon signal and a DFT module for tracking the beacon signal are the same.

[0025] In some respects, the techniques described herein refer to a method in which the beacon signal includes redundant beacon signals, and the method further includes switching from a first beacon signal of redundant beacon signals to a second beacon signal of redundant beacon signals when an interruption of the first beacon signal is detected.

[0026] Additional resources will be set out in the following description and will, in part, become apparent from the description or can be learned by practicing what is described. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] To describe the manner in which the aforementioned and other advantages and resources can be obtained, a more particular description is provided below and will be made by reference to the specific embodiments thereof, which are illustrated in the attached drawings. It being understood that these drawings represent only typical embodiments and, therefore, should not be limited in scope, implementations will be described and explained with additional specificity and detail with the attached drawings.

[0028] FIG. 1A illustrates a beacon receiver, according to the various embodiments.

[0029] FIG. 1B illustrates the acquisition processor, according to the various embodiments.

[0030] FIG. 2A illustrates a frequency error comparison of various interpolation techniques for a 30 Hz compartment, according to the various realizations.

[0031] FIG. 2B illustrates an error comparison. Petition 870250060834, dated 07 / 16 / 2025, page 10 / 37 7 / 28 frequency for GCL interpellation and linearized GCL interpellation for a 30 Hz compartment, according to the various embodiments.

[0032] FIG. 2C illustrates the frequency estimation performance for various techniques, according to different realizations.

[0033] FIG. 3A illustrates a frequency response of a signal received using a beacon receiver of the present teachings under an uncompromised condition, according to the various realizations.

[0034] FIG. 3B illustrates an enlarged version of the frequency response of FIG. 3A, according to the various embodiments.

[0035] FIG. 4A illustrates a maximum 3-point Lagrange interpolation error and GCL RMS interpolation for a 30 Hz compartment, according to various embodiments.

[0036] FIG. 4B illustrates a correction of the GCL interpolator, according to the various embodiments.

[0037] FIG. 5A illustrates a rough estimate of SNR calculated for an SNR sweep from -10 dB to 20 dB in 1 dB steps, with 1000 frames per SNR, according to various realizations.

[0038] FIG. 5B illustrates a linearization of the SNR estimate from FIG. 5A.

[0039] FIG. 5C illustrates a rough SNR estimation performance of the SNR estimator, according to the various realizations.

[0040] FIG. 6 illustrates the probability of error detection when the acquisition detection threshold is Petition 870250060834, dated 07 / 16 / 2025, p. 11 / 37 8 / 28 set at -1 dB for the selected threshold level for 20,000 tests.

[0041] FIG. 7 illustrates a method for a receiver to supervise the tracking of frequency estimation over time, according to various realizations.

[0042] FIG. 7A illustrates the tracking filter of FIG. 7, according to the various embodiments.

[0043] FIG. 7B illustrates the interrupt detection state transitions, according to the various embodiments.

[0044] FIG. 8A illustrates a method for tracking and acquiring redundant beacon signals, according to various embodiments.

[0045] FIG. 8B illustrates a method for tracking and acquiring redundant beacon signals, according to various embodiments.

[0046] FIG. 9 illustrates a flowchart of a method for receiving a beacon signal, according to the various embodiments.

[0047] Throughout the drawings and detailed description, unless otherwise stated, identical reference numerals in the drawing will be understood to refer to the same elements, features, and structures. The relative size and representation of these elements may be exaggerated for purposes of clarity, illustration, and convenience. DETAILED DESCRIPTION OF THE INVENTION

[0048] The realizations are discussed below in detail. While specific implementations are discussed, this is done for illustrative purposes only. Those skilled in the art will recognize that other components and Petition 870250060834, dated 07 / 16 / 2025, page 12 / 37 9 / 28 settings can be used without deviating from the spirit and scope of the subject matter of this revelation.

[0049] The terminology used herein serves to describe realizations only and is not intended to be limiting of the present disclosure. As used herein, the singular forms a, an, and the are intended to include the plural forms as well, except where the context clearly indicates otherwise. Furthermore, the use of the terms a, an, etc. does not indicate a limitation of quantity, but rather the presence of at least one of the items mentioned. The use of the terms first, second, and similar does not imply any order, but are included to identify individual elements or to distinguish one element from another.It will also be understood that the terms *compris* and / or *comprising*, or *includes* and / or *including*, when used in this descriptive report, specify the presence of declared resources, regions, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other resources, regions, integers, steps, operations, elements, components, and / or groups thereof. Although the same resources may be described in relation to individual exemplary achievements, the aspects need not be limited to these, so that the resources of one or more exemplary achievements may be combinable with other resources of one or more exemplary achievements.

[0050] The present receiver provides a wide reception frequency range for a continuous wave (CW) signal. The receiver offers a simpler implementation by using the same DFT with a small number of compartments for acquisition and tracking, and using Petition 870250060834, dated 07 / 16 / 2025, p. 13 / 37 10 / 28 complex interpolation to improve frequency accuracy. Robust performance is provided under phase noise and low SNR, for example, a negative SNR. Receiver embodiments can handle beacon reception interruption with redundancy, for example. In some embodiments, the beacon source can provide separate primary and redundancy beacon signals, for example, by 60 MHz in the Ka band. The beacon signals can be frequency-locked to a payload MRO (master reference oscillator) on a beacon source, such as a satellite port. In this way, any deviation in the MRO frequency will be reflected in the beacon carrier frequency. The beacon source can be a satellite or a satellite port.

[0051] The receiver provides accurate frequency estimation using a DFT-based module. The receiver's acquisition range can be + / - 1.5 kHz. The receiver's frequency tracking range can be + / - 50 Hz. The beacon receiver can provide frequency, SNR and RSSI. The beacon signal can be a 23.4 symbol kilo-per-second (ksps) signal. The input to the beacon receiver can be the output of a square root raised cosine filter (SRRC) operating on beacon samples, for example, at 4x the symbol rate (4 x 23.4 ksps). The beacon receiver processes the configurable data rate, for example, a 40 ms frame. This duration can be configured for a shorter or longer period depending on a target operating SNR and frequency deviation rate.

[0052] FIG. 1A illustrates a beacon receiver, according to the various embodiments.

[0053] A beacon receiver 100 can provide a beacon signal 134 to an SRRC filter 102 to generate a signal Petition 870250060834, dated 07 / 16 / 2025, p. 14 / 37 11 / 28 received 130 at a symbol rate of 4x. In some embodiments, the beacon signal 134 is a CW waveform transmitted by a satellite in the Ka band to help a gate achieve frequency synchronization. The beacon receiver 100 acquires the beacon signal 134 within a defined frequency range with sufficient precision to allow the beacon receiver 100 to track variations in the beacon signal 134 over time. The beacon receiver 100 tracks the beacon signal 134 after signal acquisition. After acquisition, a frequency of the beacon signal 134 can be refined and continuously tracked for variations over time to provide a stable gate reference.

[0054] The beacon receiver 100 includes a synchronization manager 126 which includes an acquisition processor 118 for acquiring a beacon signal, a tracking filter 120 for tracking an acquired beacon signal, and a control 122. The synchronization manager 126 can provide statistical reports 132. The statistical reports 132 can include one or more of an RX state, a frequency estimate, a signal-to-noise ratio (SNR) estimate, an RSSI estimate, or similar. The control 122 provides acquisition, tracking, and interrupt state control. The control 122 can selectively enable the acquisition processor 118 to output an acquisition frequency facq to initially acquire or reacquire the facq. After acquisition, the control 122 can selectively enable the tracking filter 120 to initially track or retrack the ftrk.Control 122 can determine whether a primary or redundancy signal should be acquired and tracked based on its respective SNR. Petition 870250060834, dated 07 / 16 / 2025, page 15 / 37 12 / 28

[0055] During tracking, the SNR can be provided by an SNR estimator 116. The SNR estimator 116 can be selectively enabled by control 122 during signal tracking. The beacon receiver 100 can provide SNR and RSSI estimates for each processed frame. The synchronization manager 126 can receive an estimate of the received signal strength indicator (RSSI) from an RSSI estimator 104 which can be made available by the statistical reports 132.

[0056] Acquisition Mode

[0057] The beacon receiver 100 searches for the beacon signal 134 in a frequency range of + / - 1.5 kHz. The goal is to provide a frequency estimate and / or a frequency correction of the received beacon signal 134 with an accuracy of + / - 10 Hz. The received signal 130, at the output of the SRRC filter 102, is sampled at 4x the symbol rate. During this time, the frequency correction value (fcorrection), which controls the NCO 110 (numerically controlled oscillator), is set to 0 Hz.

[0058] A DFT 112 frequency estimator provides a frequency estimate (facq) and a confidence indication of the frequency estimate accuracy. The frequency estimate and confidence indication can be provided for each processed frame.

[0059] Acquisition processor 118 collects M frequency acquisition estimates and their corresponding acquisition flags to determine if a successful acquisition has occurred and provides an initial frequency correction value (fcorrection). During acquisition, the SNR can be provided by acquisition processor 118. Control 122 can Petition 870250060834, dated 07 / 16 / 2025, page 16 / 37 13 / 28 provide a frequency correction fcorrection to control an output of an (NCO) 110 during tracking.

[0060] Tracking Mode

[0061] In tracking mode, the beacon receiver 100 refines an acquisition frequency estimate and tracks frequency variations over time. The frequency estimate can have a range of + / -50 Hz with a resolution of 1 Hz. As discussed above, the acquisition mode can provide an initial value for f-correction. The residual frequency error in the beacon signal can be + / -10 Hz after the initial f-correction. A DFT processor 114 improves the accuracy of this estimate with the finer resolution of a DFT processor 114. A frequency estimate (fest) from the DFT frequency estimator 112 passes through a DFT processor 114 to a first-order tracking filter 120 to produce a filtered frequency estimate ftrk and a filter state 136. SNR estimates can be computed from the received signal 130.After a transition period, during which the tracking filter 120 adapts to the received signal 130, the control 122 can enable interruption detection to monitor the received signal 130. Interruption detection can be based on the state of the filter 136.

[0062] The filtered frequency estimate (such as facq or ftrk), the state of filter 136, and the interrupt flag are inputs to control 122 for frequency synchronization management. Control 122 oversees the selection of the appropriate frequency correction value (fcorrection), determined given the current conditions as:

[0063] a.fcorrection fcorrectioni + fcorrection^ acqJCUI1 tracking Petition 870250060834, dated 07 / 16 / 2025, page 17 / 37 14 / 28

[0064] Acquisition frequency estimate

[0065] FIG. 1B illustrates the acquisition processor, according to the various embodiments.

[0066] During acquisition, acquisition processor 118 finds beacon signal 134 within a frequency range of + / - 1.5 kHz using the frequency estimator of DFT 112 to DFT 134 beacon signal between bins in a DFT 140 computation, for example, 103 bins of 30 Hz (step size) each for + / -1.5 kHz beacon for 20,000 tests. The bins in the DFT 140 computation can be searched using a peak locator 142 by the DFT 114 processor. The frequency shift found within one of the bins in the DFT 140 computation is found to include the peak by the DFT 114 processor. In some embodiments, a 3-point interpolator 144 is used to improve the accuracy of the frequency shift (facqi) based on the peak. The output of the DFT 114 processor and a peak location can be used to compute a rough estimate of SNR with the rough SNR estimator. 146. The coarse SNR estimator 146 can be used by the DFT processor 114 to decide on signal acquisition 148 to indicate that the signal was detected and report it.

[0067] Acquisition DFT Processing

[0068] When using DFT for frequency estimation, there is a trade-off between the number of bins, the frequency range (aperture), and processing complexity. Processing complexity is directly proportional to the number of bins used. The bin size is the ratio between the beacon frequency range and the number of bins; therefore, a Petition 870250060834, dated 07 / 16 / 2025, page 18 / 37 A larger 15 / 28 compartment size covers the beacon frequency range when a small number of compartments is used. On the other hand, using a larger compartment size increases a frequency estimation error that can be up to 1½ times the compartment size even at high SNR, due at least in part to compartment quantization.

[0069] Interpolation techniques can minimize compartment quantization error. Three-point Lagrange interpolation is a common interpolation choice that can minimize compartment quantization error in a small range. For three-point Lagrange interpolation, the table below shows the number of compartments needed to cover a frequency range of + / -1.5kHz for different compartment sizes. TABLE 1 Compartment size Approximate frequency estimate error Number of compartments Hz Hz 1 4.11E-04 3003 6 ~ 0.1 503 30 ~ 11.0 103

[0070] FIG. 2A illustrates a frequency error comparison for various interpolation techniques for a 30 Hz compartment, according to the various embodiments.

[0071] FIG. 2A illustrates a graph of frequency errors for various interpolation techniques for a 30 Hz bin. For the same bin size, the reduction of generalized complex Lagrange interpolation (GCL) 204 for a frequency error is greatly reduced compared to the reduction of Lagrange interpolation 202 for the frequency error. Petition 870250060834, dated 07 / 16 / 2025, page 19 / 37 16 / 28

[0072] Frequency error linearization can further minimize the number of bins. GCL frequency error linearization removes the bias of frequency estimation (accurate estimation). GCL frequency error linearization allows the use of a smaller number of bins, thus minimizing processing complexity without sacrificing performance. In some embodiments, a lookup table can be used for linearization. For Lagrange interpolation, error compensation can only be achieved for the frequency offset range of 12 d fo d 18Hz due to the Lagrange interpolation error response. In contrast, for GCL interpolation, error compensation can be achieved for the entire bin size range (0 d fo d 30Hz) due to the GCL interpolation error response.

[0073] FIG. 2B illustrates a frequency error comparison for GCL interpolation and linearized GCL interpolation for a 30 Hz bin, according to the various embodiments.

[0074] FIG. 2B illustrates a graph 210 of frequency errors for GCL interpolation and linearized GCL interpolation for a 30 Hz bin. For the same bin size, frequency error 214 after linearized GCL interpolation.

[0075] FIG. 2C illustrates the frequency estimation performance for various techniques, according to different realizations.

[0076] FIG. 2C illustrates a 220 frequency mean plot for various techniques. For the same compartment size, a Lagrange interpolation mean of 222, a Petition 870250060834, dated 07 / 16 / 2025, page 20 / 37 17 / 28 linearized Lagrange interpellation mean 228, a GCL mean 224, and a linearized GCL mean 226 are illustrated. The linearized GCL mean 226 outperforms the other means while maintaining low processing complexity (small number of compartments).

[0077] FIG. 3A illustrates a frequency response of a signal received using a beacon receiver of the present teachings under an uncompromised condition, according to the various realizations.

[0078] FIG. 3A illustrates an uncompromised acquisition frequency estimate from 300 to 0 Hz using a beacon receiver from the present teachings. The vertical axis of FIG. 3A illustrates a dB signal at a DFT, while the horizontal axis illustrates the frequency in Hz.

[0079] FIG. 3B illustrates an enlarged version of the frequency response of FIG. 3A, according to the various embodiments.

[0080] Interpolation

[0081] FIG. 4A illustrates a maximum 3-point Lagrange interpolation error and GCL RMS interpolation for a 30 Hz compartment, according to various embodiments.

[0082] To improve the accuracy of the frequency shift determined from the DFT peak, interpolation techniques are commonly used. Three-point Lagrange interpolation is a common choice. Using simulation, the 3-point Lagrange interpolation 402 has a maximum error of + / - 10.26 Hz when applied to a 30 Hz bin. A generalized complex 3-point Lagrange interpolation (GCL) 404 is also represented in FIG. 4A. A comparison of the error Petition 870250060834, dated 07 / 16 / 2025, page 21 / 37 The 18 / 28 residual between the 3-point Lagrange interpellation 402 and the GCL interpolation 404 illustrates that the 2-point GCL interpellation 404 has a maximum error of + / - 4 Hz with an RMS error of 2.95 Hz. The vertical axis of FIG. 4A illustrates frequency error in Hz, while the horizontal axis illustrates reference frequency (fo) in Hz.

[0083] Let X[i] be the complex output of the DFT for compartment i, and let ko be the representation index where the DFT peak is found. Then, the GCL interpolation method is defined as:

[0084] „ ,, (Re{X[k-1]}-Re{X[k+1]})*(2Re{X[k]}-Re{X[k-1]}-Re{X[k+1]} o=l*--------------------------- s

[0085] 1 ( / m{X[fc-1]}- / m{X[fc+1]})*(2 / m{X[fc]}- / m{X[fc-1]}- / m{X[fc + 1]} s

[0086] where 0 < Γ < 1, and

[0087] 5 = (2fle{X[fc]} - fle{X[fc - 1]} - fle{X[fc + 1]})2 +

[0088] (2 / m{X[fc]} — / m{X[fc — 1]} — / m{X[fc + 1]})2

[0089] In some embodiments, the error function of the GCL interpolator can be compensated for by using a lookup table with linear interpolation between the entries. from the table.

[0090] FIG. 4B illustrates a correction of the GCL 414 interpolator (dotted line) and a compensation value 412 (dashed line). The vertical axis of FIG. 4B illustrates the reference frequency (f0) in Hz, while the horizontal axis illustrates a frequency estimate (fest).

[0091] Rough SNR estimate

[0092] Let X[i] be the complex output for bin i of the DFT. Let k be the index where the DFT peak is located. Then, the signal power is computed as:

[0093] 5 = |X[fc — 1]|2+ |X[fc]|2+ |X[fc + 1]|2 Petition 870250060834, dated 07 / 16 / 2025, page 22 / 37 19 / 28

[0094] Noise power is computed as the power in all DFT bins except those used to compute signal power, for example,

[0095] N = Z for all i except i = fc-1, fc, fc+1 |^[i]|

[0096] Then

[0097] SNR = 10 * log10(£)

[0098] FIG. 5A illustrates a rough estimate of SNR calculated for an SNR sweep from -10 dB to 20 dB in 1 dB steps, with 1000 frames per SNR, according to various realizations.

[0099] FIG. 5B illustrates a linearization of the SNR estimate from FIG. 5A.

[0100] In some realizations, the estimate of SNR can be linearized. The SNR estimate response can be divided into multiple segments for linearization. All segments can use linear approximations. In FIG. 5A, the vertical axis illustrates the SNRest in dB and the horizontal axis illustrates the SNR in dB. In FIG. 5B, the vertical axis illustrates the SNR in dB and the horizontal axis illustrates the SNRest in dB.

[0101] FIG. 5C illustrates a rough SNR estimation performance of the SNR estimator, according to the various realizations.

[0102] The vertical axis of FIG. 5C illustrates the trend of the coarse estimator of SNR, standard deviation, and RMS in dB, and the horizontal axis is the SNR in dB. Line 502 represents the trend, while line 504 represents the standard deviation; the RMS generally overlaps line 504.

[0103] Probability of successful acquisition

[0104] In some realizations, the estimate Petition 870250060834, dated 07 / 16 / 2025, page 23 / 37 A coarse linearized 20 / 28 SNR can be used to declare a successful acquisition. A successful acquisition occurs when the frequency error is within 10 Hz of the expected value.

[0105] FIG. 6 illustrates the probability of error detection when the acquisition detection threshold is set to -1 dB for the selected threshold level for 20,000 tests.

[0106] In FIG. 6, the vertical axis represents the probability of error detection, and the horizontal axis represents the SNR in dB. As observed from FIG. 6, even with a mere 1 dB signal, the probability of error detection is less than 10-4.

[0107] Transition from acquisition to tracking

[0108] The acquisition algorithm collects the M frequency acquisition estimates and their corresponding acquisition flags to determine if a successful acquisition occurred and provides f_acq_correction. Let f_acqi and acq_flagi be the frequency acquisition estimate and acquisition flag for frame i. Then,

[0109] acq_flagi = individual acquisition success failure { 0

[0110] beacon_detection_flagi = nlk=í-M+iacq_flagk

[0111] In some embodiments, the default value of M is 5. When beacon_detection_flag=0 [beacon detection flag], acquisition failed; and the beacon receiver continues to attempt acquisition. When beacon_detection_flag =1, then there was successful acquisition and the receiver moves to tracking mode using acquisition frequency correction as Petition 870250060834, dated 07 / 16 / 2025, page 24 / 37 21 / 28 initial frequency correction:

[0112]

[0113] fcorrection_acq =MΣί=0 / L^CQi Tracking -- Frequency estimation

[0114] During tracking mode, the receiver can refine the frequency shift calculated by the acquisition stage. Additionally, the receiver monitors tracking frequency variations over time, for example, in the + / -50 Hz range. The receiver can use the same DFT algorithm used during acquisition, except the step size can be changed to 1 Hz. The DFT can be followed by an interpolation routine to refine the frequency estimate.

[0115] FIG. 7 illustrates a method for a receiver to supervise the tracking of frequency estimation over time, according to various realizations.

[0116] A method 700 for a receiver to supervise frequency estimation tracking over time can be used for an RX 714 signal. In some embodiments, the RX 714 signal may include a 4x23.4 ksps signal. The RX 714 signal can be provided to a DFT 702. For tracking frequency variations, method 700 can use finer granularity for a frequency range between the same number of bins as for acquisition, for example, 103 bins with a step size of 1 Hz. An output of the DFT 702 can be interpolated with a peak location operation 704 to provide the F_esti 716 signals between the bins. The F_esti 716 signals can be provided to a trace filter 705. The trace filter 705 produces F_trki 720 signals and the estado_Filtroi ​​722 signals for handling interrupt 706. The RX 714 signal can be provided Petition 870250060834, dated 07 / 16 / 2025, page 25 / 37 22 / 28 to an estimated SNR of 710 which provides an SNR of 718 to interrupt detection 712. Interrupt detection 712 can provide interrupt signals 724 to interrupt handling 706. The selected compartments 103 of 1 Hz each can cover a range of + / -50 Hz to meet the tracking objectives.

[0117] DFT 702 can be the frequency estimator of DFT 112, peak location operation 704 and interpolation can be the processor of DFT 114, tracking filter 705 can be tracking filter 120, SNR estimation 710 can be SNR estimator 116 and interrupt detection 712 can be control 122.

[0118] The compartments are consulted to find the peak, and the frequency shift is found in the compartment. A 3-point interpolation technique can be used to further refine the frequency shift (f_esti). The frequency shift is the input to the tracking filter. In a parallel path, the received signal is processed directly to estimate the SNR. Finally, an interrupt detection algorithm monitors the received signal to control the filter state and frequency correction (f_correctioni) in case of an interrupt.

[0119] To improve the accuracy of the frequency estimate determined from the DFT peak, interpolation techniques are used. A 3-point Lagrange interpolation error is small due to the bin size (1 Hz), so no additional processing is needed. Using simulation, it was determined that 3-point Lagrange interpolation has a maximum error of + / - 0.00041 Hz when applied to a 1 Hz bin. In some embodiments, the same Petition 870250060834, dated 07 / 16 / 2025, page 26 / 37 23 / 28 implementation of the generalized complex Lagrange interpolator can be used for Lagrange interpolation by setting the imaginary part to zero and scaling the output by a constant.

[0120] FIG. 7A illustrates the tracking filter of FIG. 7, according to the various embodiments.

[0121] The 705 tracking filter in FIG. 7 can be a first-order tracking filter for processing frequency estimates. The structures of the 705 tracking filter are illustrated in FIG. 7A, according to the various embodiments. Different values ​​of a can be used. Based on the results observed for constant frequency and for tracking a variable frequency, the value of a = 0.1 can be used in some embodiments.

[0122] SNR Estimate

[0123] SNR estimation during tracking mode can operate at a known symbol rate. This reduces the amount of processing and provides the SNR per symbol for a received frame. Linearization techniques can be used to improve SNR estimation. Let r4i, r4i+1, r4i+2, r4i+34 samples be received at a symbol rate of 4 x 23.4 ksps, for example. They are combined to form the i° complex symbol Xt, as follows

[0124] a. fle{Xj = flefaj + flefaí+J + flefa^ + flefo^

[0125] b. Imag{Xi}= Imagfai} + Imagfai+i} + Imag{r4i+2} + Zmag{r4f+3}

[0126] When the receiver operates in 40 ms frames, the number of symbols to be processed is K=936. Let

[0127] a. 2 = ^=-0^½} K

[0128] b. y =1^=-01Zmag^J K Petition 870250060834, dated 07 / 16 / 2025, p. 27 / 37 24 / 28

[0129] c. Nreal= IZ^oWK}- %)2 K

[0130] d. N,mag = ^1,=0(Imag{X,] - y^)2

[0131] Then, the signal power S, the noise power N, and the SNR are computed as:

[0132] a. S = (x)2+ (jz)2

[0133] bN= Nreal+ Nimag

[0134] c. SNR = 10 * log10(^)

[0135] Interruption detection and handling

[0136] FIG. 7B illustrates interrupt detection state transitions, according to the various embodiments.

[0137] Interrupt detection is based on the SINR estimate computed while in trace mode. The following table lists the example parameters for interrupt handling. TABLE 2 SINR threshold for interrupt input Th0 -9 dB SINR threshold for interrupt output Th1 -7.5 dB Number of observations Mo 5

[0138] Interrupt detection can enter an interrupt state for a signal-to-interference-to-noise ratio SINRí, and an observation is made when comparing SINRí with a threshold,

[0139] i _ C1 single interruption event if SINRí < Th0bi = 1 „ . , . t 0 otherwise

[0140] Multiple consecutive observations can contribute to the detection of an interruption, such as

[0141] Dl = Σ& = ί-Μο + 1^: Petition 870250060834, dated 07 / 16 / 2025, pp. 28 / 37 25 / 28

[0142] In some embodiments, an interruption is declared when: Di=M0.

[0143] Once interrupted, the determination of when to exit the interrupted state can compare SINR[ with a threshold,

[0144] Li = single event outside of interrupt if SINR[ > Th1t 0 otherwise

[0145] Several consecutive determinations can contribute to a detection, such as [014 6] Hi= ^k=i-Mü+iLk

[0147] and exiting an interrupt can be declared when H = M0.

[0148] Interrupt handling can be varied. For example, while not in the interrupt state,

[0149] O0 0 _ 0 Save the filter state Fs

[0150] While in the interrupt state, the trace filter state can be frozen to the last known good condition. So when,

[0151] Set the filter to saved state Fs Do nothing

[0152] This ensures that upon exiting the interrupt, the trace filter resumes operation from a known good state. For example, after single interrupt detection of Mo, the interrupt flag is created by interrupt detection 712. Initially, when the interrupt occurs, random values ​​may be reported at the filter output, but as soon as the interrupt flag is created, the filter output is established at a last known good state. It remains until the interrupt ends. Petition 870250060834, dated 07 / 16 / 2025, pp. 29 / 37 26 / 28 Subsequently, tracking resumes with the last known good status.

[0153] One thousand simulations of a 10 s interruption scenario, for example, 10 s normal reception, 10 s interruption, 10 s normal reception resulted in the interruption detection probability shown in the table below. TABLE 3 INTERRUPTION WITHOUT INTERRUPTION SINR (dB) Error detection (%) False detection (%) Error detection (%) False detection (%) 16 0.0 0.0 0.0 0.0 6 0.0 0.0 0.0 0.0 1 0.0 0.0 0.0 0.0 0.0

[0154] RSSI Estimate

[0155] An RSSI estimate can be performed in the same way in both acquisition and tracking modes. In some embodiments, the estimator operates at the symbol rate. Let r4i,r4i+1,r4i+2,r4i+34 samples be received at a symbol rate of 4 x 23.4 ksps. The 4 received samples can be combined to form the 10th complex symbol Xt as follows

[0156] fle{Xi} = Refai] + flefoi+J + Refa^] + Re{r4i+3}

[0157] Imag{Xi} = Imag{r4i} + Imag{r4i+1} + Imag{r4i+2} + Imagfa^}

[0158] Since the receiver operates on 40 ms frames, the total number of symbols to be processed in a frame is K=936. Then

[0159] RSSI = 10*log10(1'Zi=o((Re{Xi}')2+ (Imag{Xi}')2)).

[0160] In some embodiments, the RSI estimate response can be linearized. The response of Petition 870250060834, dated 07 / 16 / 2025, pp. 30 / 37 27 / 28 RSSI is linearized to break down the response into 4 segments.

[0161] FIG. 8A illustrates a method for tracking and acquiring redundant beacon signals, according to various embodiments.

[0162] FIG. 8B illustrates a method for tracking and acquiring redundant beacon signals, according to various embodiments.

[0163] FIG. 9 illustrates a flowchart of a method for receiving a beacon signal, according to the various embodiments.

[0164] FIG. 9 illustrates a flowchart of a method 900 for receiving a beacon signal. The method 900 may include, in step 902, the operation of an SRRC filter on a beacon symbol on the beacon signal at a symbol rate that is an integer multiple of a beacon symbol rate. The method 900 may include, in step 904, transformation to acquire and track the beacon signal using a binned Digital Fourier Transform (DFT) module. The method 900 may include, in step 906, acquisition of the beacon signal by finding acquisition frequency estimates of the beacon signal, improving the acquisition frequency estimates using a generalized complex interpolator, and linearization of the acquisition frequency estimates. The method 900 may include, in step 908, tracking the acquired beacon signal and calculating the tracking frequency estimates.Method 900 may include, in step 910, linearization of one or more of the acquisition frequency estimates and tracking frequency correction. Method 900 may include, in step 912, estimation of a signal-to-noise ratio (SNR) to provide an SNR estimate for the... Petition 870250060834, dated 07 / 16 / 2025, pp. 31 / 37 28 / 28 acquisition. Method 900 may include, in step 914, beacon signal loss detection based on an SNR estimate. Method 900 may include, in step 916, switching a first beacon signal from redundant beacon signals to a second beacon signal from redundant beacon signals when an interruption of the first beacon signal is detected. Method 900 may include, in step 916, synchronizing an oscillator by applying a frequency correction based on acquisition frequency estimates or tracking frequency estimates.

[0165] Although the subject matter has been described in language specific to structural features and / or methodological actions, it should be understood that the subject matter in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are disclosed as exemplary embodiments of the claims. Other configurations of the described embodiments are part of the scope of this disclosure. Furthermore, implementations consistent with the subject matter of this disclosure may have more or fewer actions than those described or may implement actions in a different order than shown. Consequently, the appended claims and their legal equivalents should only define the invention, rather than any specific examples provided. Petition 870250060834, dated 07 / 16 / 2025, pp. 32 / 37

Claims

1 / 4 CLAIMS 1. BEACON RECEIVER, characterized by comprising: a digital Fourier transform (DFT) module comprising compartments for acquiring and tracking a beacon signal; an acquisition processor for finding beacon signal acquisition frequency estimates, for improving acquisition frequency estimates with a generalized complex interpolator, and for linearizing acquisition frequency estimates; and a tracking filter for tracking the acquired beacon signal and for calculating a tracking frequency estimate;and a synchronization manager to apply a frequency correction to an oscillator, based on acquisition frequency estimates or tracking frequency estimates, where the DFT module uses a first bin size for bins to acquire, a second bin size for bins to track, and the first bin size is larger than the second bin size.

2. BEACON RECEIVER, according to claim 1, characterized in that the first compartment size is greater than 6 Hz.

3. BEACON RECEIVER, according to claim 1, characterized in that the frequency correction error of the first compartment size is greater than 0.1 Hz when the beacon signal has a frequency range of + / - 1.5 kHz.

4. BEACON RECEIVER, according to claim 1, Petition 870250088911, dated 10 / 01 / 2025, p. 39 / 47 2 / 4 characterized by further comprising a square root raised cosine filter (SRRC) that operates on a symbol beacon in the beacon signal at a symbol rate that is an integer multiple of a symbol beacon rate.

5. BEACON RECEIVER, according to claim 1, characterized by comprising a generalized complex Lagrange interpolator (GCL) to improve the tracking of frequency estimates.

6. BEACON RECEIVER, according to claim 1, characterized by the acquisition processor improving acquisition frequency estimates with a generalized complex Lagrange interpolator (GCL).

7. BEACON RECEIVER, according to claim 1, characterized by further comprising a signal-to-noise ratio (SNR) estimator to provide an SNR estimate to the acquisition processor.

8. BEACON RECEIVER, according to claim 1, characterized by further comprising a control for detecting loss of the beacon signal and an SNR estimator for providing an SNR estimate to the control.

9. A BEACON RECEIVER, according to claim 6, characterized by further comprising a control for restoring a known good state to the acquisition processor during the transition from an interrupt.

10. BEACON RECEIVER, according to claim 9, characterized by further comprising a beacon redundancy module, wherein the beacon signal comprises redundant beacon signals, and a control for changing from a first beacon signal of redundant beacon signals to a second beacon signal of redundant beacon signals, when an interruption of the first beacon signal is detected.

11. BEACON RECEIVER, according to claim 1, characterized in that the DFT module acquiring the beacon signal and the DFT module tracking the beacon signal are the same.

12. BEACON RECEIVER, according to claim 1, characterized in that the tracking filter is a first-order filter having a feedback control α set to 0.

1.

13. BEACON RECEIVER, according to claim 1, characterized by the beacon signal comprising a beacon symbol rate of 23.4 kilo symbol signals per second (ksps), wherein the beacon signal comprises a structure with a duration less than or equal to 100 ms.

14. BEACON RECEIVER, according to claim 1, characterized in that the first compartment size is 30 Hz, and the second compartment size is 1 Hz.

15. BEACON RECEIVER, according to claim 1, characterized by the beacon signal comprising a satellite beacon signal.

16. BEACON RECEIVER, according to claim 1, characterized by further comprising a received signal strength indicator (RSSI) estimator to provide a linearized estimate of RSSI, wherein the RSSI estimator operates at a signal rate of the beacon signal.

17. METHOD FOR RECEIVING A BEACON SIGNAL, characterized by comprising: transformation, for acquisition and tracking, of the beacon signal using a digital Fourier transform (DFT) module comprising compartments; acquisition of the beacon signal by finding estimates Petition 870250088911, dated 10 / 01 / 2025, p.41 / 47 4 / 4 of beacon signal acquisition frequency, improving acquisition frequency estimates using a generalized complex interpolator and linearizing acquisition frequency estimates; tracking the acquired beacon signal and calculating tracking frequency estimates; and synchronization of an oscillator by applying a frequency correction based on acquisition frequency estimates or tracking frequency estimates, wherein the DFT module uses a first bin size for the bins for acquisition, a second bin size for the bins for tracking, and the first bin size being larger than the second bin size.

18. METHOD, according to claim 17, characterized by further comprising improved tracking frequency estimates using a generalized complex Lagrange interpolator (GCL).

19. METHOD, according to claim 17, characterized in that a DFT module for acquiring the beacon signal and a DFT module for tracking the beacon signal are identical.

20. METHOD, according to claim 17, characterized in that the beacon signal comprises redundant beacon signals, and the method further comprises alternating from a first beacon signal of redundant beacon signals to a second beacon signal of redundant beacon signals when an interruption of the first beacon signal is detected. Petition 870250088911, dated 10 / 01 / 2025, pp. 42 / 47

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