Binary Offset Carrier Modulated Signals Research Articles

Enhanced Synchronization Algorithms for BOC Signals Based on Reconstructed Sub-Correlation Functions

Aiming at the ambiguous synchronization of binary offset carrier (BOC) and composite binary offset carrier (CBOC) modulation signals due to secondary peaks for Global Navigation Satellite System (GNSS), a reconstructed sub-correlation function synchronization algorithm (RSSA) for BOC and CBOC is proposed. The general autocorrelation subfunctions of BOC and CBOC are obtained by deriving the subfunctions of the cross-correlation function between BOC signals with different modulation orders. According to the characteristics of the subfunctions, the corresponding reconstruction rules are set to obtain the unambiguous correlation functions. To further reduce the complexity of the local auxiliary signal, a local auxiliary signal optimization algorithm (LASOA) is proposed based on RSSA, which only needs to generate a local two-level signal compared to the conventional CBOC local four-level signal. The simulations show that the two algorithms proposed in this paper reduce the amplitude of the side peaks of the normalized correlation peaks of BOC by at least 0.09 compared with the autocorrelation side-peak cancellation technique (ASPeCT), maintain a high detection probability, and the multipath error is smaller than that of the autocorrelation side-peak cancellation technique (ASPeCT) and other traditional algorithms. The phase discrimination curves show that the linear region slope gains of the two algorithms in this paper are above 2 dB compared with the ASPeCT and other conventional algorithms.

차세대 GNSS를 위한 GIG 부호 기반 시간다중 이진부호심볼 변조기법

In this paper, we propose a time multiplexed binary coded symbol (TMBCS) modulation scheme based on Gray and inverse Gray (GIG) codes for the next generation global navigation satellite system (GNSS). A representative binary coded symbol (BCS) is a binary offset carrier (BOC). Compared to the existing binary phase shift keying (BPSK) modulation, which is a representative GNSS modulation scheme, BOC modulation has a high degree of freedom in terms of frequency band shape design and is less affected by multipaths because the correlation function is sharper at the correct code phase. However, since several sub-peaks occur in the correlation function of the BOC-modulated pseudo-noise signal, false locks can easily occur during code tracking. This disadvantage is called the ambiguity of the BOC modulated signal. Time multiplexed binary Walsh spreading (TMBWS) modulation, which is a TMBCS scheme that uses a Walsh code, is one method for reducing ambiguity and is a perfectly orthogonal code with a very good correlation among BCSs. However, Walsh codes can only be generated with a power of two length. In this paper, we propose a novel TMBCS modulation scheme using quasi-orthogonal GIG codes that can be generated with lengths that are multiples of 2. The proposed scheme maintains the same bandwidth and spectral separation coefficient compared to TMBWS when a symbol of length 8 is used. In addition, the proposed scheme has a higher degree of freedom in terms of band shape design compared to TMBWS modulation, because the length can be designed in multiples of 2 (such as 6, 10, or 12) and has high multipath immunity with unambiguity.

An Unambiguous Synchronization Scheme for GNSS BOC Signals Based on Reconstructed Correlation Function.

Binary offset carrier (BOC) modulation is a new modulation method that has been gradually applied to the Global Satellite Navigation System (GNSS) in recent years. However, due to the multi-peaks in its auto-correlation function (ACF), it will incur a false lock and generate synchronization ambiguous potentially. In this paper, an unambiguous synchronization method based on a reconstructed correlation function is proposed to solve the ambiguity problem. First, through the shape code vector constructed in this paper, the general cross-correlation function (CCF) expression of the BOC modulated signal will be obtained. Based on the features of the signal correlation function, it is decomposed into a matrix form of trigonometric functions. Then, it generates two local signal waves using a specific method, then the proposed method is implemented to obtain a no-side-peak correlation function by reconstructing the cross-correlation between the received signal and the two local signals. Simulations showed that it fully eliminates the side-peak threat and significantly removes the ambiguity during the synchronization of the BOC signals. This paper also gives the improved structure of acquisition and tracking. The detailed theoretical deduction of detection probability and code tracking error is demonstrated, and the corresponding phase discrimination function is given. In terms of de-blurring ability and detection probability performance, the proposed method outperformed other conventional approaches. The tracking performance was superior to the comparison methods and the phase discrimination curve only had a zero-crossing, which successfully removed the false lock points. In addition, in multipath mitigation, it outperformed the ACF of the BOC signal, and performs as well as the autocorrelation side-peak cancellation technique (ASPeCT) for BOC(kn,n) signals.

Symmetry detection algorithm to detect forwarded spoofing interference signals of BOC modulation receivers

In this paper, the symmetry detection algorithm based on the symmetry of binary offset carrier (BOC) modulation signals is proposed to solve the problem of the global navigation satellite system (GNSS) spoofing interference in BOC modulation and acquisition phase which set on the base of the characters of correlation peaks, and achieve the detection of the forwarded spoofing interference signals. The theoretical value and the simulation value of the receiver operating characteristic (ROC) curve of the symmetry detection algorithm can be obtained by the numerical calculation and the experimental simulation. It can be seen from the simulation that with the increase of the accumulation times after the correlation, the signal to noise ratio (SNR) of the spoofing signal compared to the real signal, and the SNR of the real signal, the detection probability of the spoofing signal increases as well. When the power of the spoofing signal is 3 dB greater than that of the real signal, the detection probability can be more than 99% under the condition that the false alarm probability is 0.1%. Given that it only needs to add the module to the software receiver to detect spoofing signals, the algorithm proposed in this paper is of practical significance.

Unambiguous Acquisition/Tracking Technique Based on Sub-Correlation Functions for GNSS Sine-BOC Signals.

The autocorrelation function (ACF) of the Binary Offset Carrier modulation (BOC) signal for Global Navigation Satellite System (GNSS) has multiple peaks, ambiguity is easily generated during the synchronization of the baseband signal. Some methods have been proposed to remove the ambiguity, but the performance is not suitable for high-order BOC signals or does not maintain narrow correlation characteristics. This paper proposes a sub-function reconstruction synchronization algorithm to solve this problem, of which the key is to design a new local auxiliary code: the local Pseudo-Random Noise (PRN) code is divided into several new codes with different delays. The auxiliary code performs a coherent integration operation with the received signal. Then, a correlation function without any positive side peaks is obtained by multiplying the two correlation results to make the acquisition/tracking completely unambiguous. The paper gives a design scheme of navigation signal acquisition/tracking and deduces the theoretical analysis of detection performance. The phase discrimination function is provided. The performance of the method is analyzed from both theoretical and simulation aspects. Compared with the Binary phase shift keying-like (BPSK-LIKE) method, Subcarrier Phase Cancellation (SCPC) method and the Autocorrelation Side-Peak Cancellation Technique (ASPeCT) method, the proposed method has the best detection probability for the acquisition, which is 0.5 dB-Hz better than ASPeCT. For tracking, the proposed method performs best in terms of phase-detection curve, anti-multipath performance, and anti-noise performance. For high-order BOC signals, the SRSA technique successfully removes the false lock points, and there is only one multipath error envelope, and the code tracking error is almost the same as the ASPeCT method.

Detection and Classification of GNSS Signal Distortions Based on Quadratic Discriminant Analysis

Satellite signal distortions, or so called “evil waveforms” (EWFs), may cause severe distortions of the cross-correlation function in receivers. Undetected EWFs could result in large range errors and threaten the integrity of Global Navigation Satellite System (GNSS). Analog distortion and digital distortion are two classical types of signal distortions. With the advent of modernized GNSS signals, more failure types are considered to cover potential EWFs of Binary offset carrier (BOC) modulated signals, such as code-only distortion and subcarrier-only distortion. Different failure types affect the correlation functions and the tracking precision in different ways. Therefore, it is useful to identify the failure type of a detected distortion. Conventional multi-correlator method can detect signal distortions; however, it is infeasible to identify the failure types. We developed a novel multi-correlator method based on Quadratic Discriminant Analysis (QDA). The QDA-based method also uses correlation-domain detection metrics but performs distortion type classification by supervised learning algorithm. Experimentally measured results on Beidou B1C data signals are presented, which show the effectiveness and robustness of proposed method. Compared with conventional multi-correlator method, the QDA-based signal quality monitoring (SQM) method shows better performance on detecting EWFs and provides an extra capability to identify the failure types accurately.

Unambiguous and precise correlation receiver for binary offset carrier modulated signal

SummaryThe binary offset carrier (BOC) modulated signal can improve the positioning accuracy and increase the multipath resistance in global navigation satellite system (GNSS), and it may cause potential ambiguity in the process of signal acquisition and code tracking. In this paper, a simple but efficient unambiguous receiver is firstly proposed for multiple side‐peaks mitigation by implementing correlation of the received BOC signal with local sine wave instead of square wave used at the transmitter. Moreover, the potential degradation of sharpness of the nonlinear correlation induced by the sine wave is well compensated by optimizing the early‐to‐late spacing. The other reason leading to ambiguity is the multipath propagation, so we further propose a maximum likelihood (ML) estimator with Newton iteration method, where the received GNSS signal is modeled via the line‐of‐sight (LOS) component and the first‐arrived non‐line‐of‐sight (NLOS) component. Finally, the analytical expression of multipath propagation Cramer‐Rao bound is derived for the designed ML estimator. Simulation results indicate that compared with the conventional BOC modulation, the proposed sine wave receiver can achieve unambiguous and more precise code tracking performance and thus turns out to be more robust to multipath propagation.

FFT based unambiguous acquisition method for BOC modulation signal

This paper presents an unambiguous acquisition algorithm for Binary Offset Carrier (BOC) modulation signals, which is adopted by modernized Global Navigation Satellite System (GNSS). By utilizing FFT, the spectrum of BOC signals is derived. This paper proposes an unambiguous acquisition method based on FFT to get rid of the BOC modulation drawback. By utilizing FFT, the spectrum of BOC signal is derived. The up and down sideband are separated in frequency domain by rectangular function, which means sideband filtering. Due to sparsity of filtered BOC spectrum, frequency compression method is proposed to reduce the number of IFFT points. Theoretical and simulation results show that this technique completely removes the ambiguity threat in acquisition process.

Cross‐correlation codeless processing of BOC modulated signals

Encrypted global navigation satellite system signals (GNSS) can be tracked using codeless techniques that do not require the knowledge of the spreading code used for signal generation. These techniques can also be applied to binary offset carrier (BOC) modulated signals whose unknown code sequence can be removed through squaring. In this study, an alternative codeless approach based on the cross-correlation principle is considered. Cross-correlation codeless processing is commonly used for tracking signal components on different frequencies, such as the global positioning system (GPS) L1 and L2 P(Y) signals, and it is adapted here to BOC modulations broadcast on a single frequency. A cross-correlation codeless framework is proposed where the BOC signal is split into two data streams that are cross-multiplied to remove the unknown code sequence. Two architectures, open-loop and closed-loop processing, are proposed and analysed. The codeless cross-correlation function is introduced and open-loop processing is used to reconstruct it from the received samples. Closed-loop processing based on cross-correlation phase lock loop (PLL) and delay lock loop (DLL) are used to estimate the signal parameters. The proposed cross-correlation framework is thoroughly analysed theoretically, through simulations and using real data. The analysis shows the effectiveness of the cross-correlation framework.

A novel acquisition algorithm based on two-dimensional delay estimation for BOC signals

Binary offset carrier (BOC) modulated signals are widely utilized in the new generation global navigation satellite system (GNSS), but the multiple peaks of the correlation function result in the ambiguity of acquisition. In this paper, a novel unambiguous acquisition algorithm is proposed, in which spreading code delay and subcarrier delay are estimated separately in a two-dimensional (2-D) space. Exact explicit expressions of the acquisition detection function based on 2-D estimation is obtained by derivation and simplification. The properties of acquisition function and the performance analysis considering noise are studied. Theoretical analysis and experimental results indicate that the proposed acquisition function completely eliminates ambiguity and it demonstrates a good performance in the terms of detection probability, main peak ratio and complexity.

Improved synchronisation algorithm based on reconstructed correlation function for BOC modulation in satellite navigation and positioning system

With the development of the new generation satellite navigation and positioning systems utilise binary offset carrier (BOC) modulation to improve inter-operability. The main shortcoming of BOC modulation is its ambiguity of searching for a multi-peaked auto-correlation function (ACF). In this study, an improved unambiguous synchronisation algorithm based on compensated correlation reconstructed technique (CCRT) is proposed for the arbitrary-order BOC, which is a new modulation technique for navigation modernisation. The key technique used in this study is to generate local reference signals with different shape vectors. By recombining the piecewise correlation functions of the step-shape coded symbol, a reconstructed correlation function which has only one peak is obtained, and the energy loss is compensated by the ACF. In the proposed algorithm, different shape vectors are employed in different BOC modulation signals. The simulation results demonstrate that the ambiguity problem is completely eliminated. Compared with traditional synchronisation methods, the proposed algorithm shows outstanding detection and multipath mitigation performance. Moreover, the CCRT can be utilised for arbitrary stage BOC modulation signals.

A new evil waveforms evaluating method for new BDS navigation signals

With the advent of new global navigation satellite systems (GNSSs) and new signals, GNSS users will rely more on them to obtain higher-accuracy positioning. Evil waveform monitoring and assessment are of great importance for GNSS to achieve its positioning, velocity, and timing service with high accuracy. However, the advent of new navigation signals introduces the necessity to extend the traditional analyzing techniques already accepted for binary phase-shift keying modulation to new techniques. First, the well-known second-order step thread model adopted by the International Civil Aviation Organization is introduced. Then the extended new general thread models are developed for the new binary offset carrier modulated signals. However, no research has been done on navigation signal waveform symmetry yet. Simulation results showed that, waveform asymmetry may also cause tracking errors, range biases, and position errors in GNSS receivers. It is thus imperative that the asymmetry be quantified to enable the design of appropriate error budgets and mitigation strategies for various application fields. A novel evil waveform analysis method, called waveform rising and falling edge symmetry (WRaFES) method, is proposed. Based on this WRaFES method, the correlation metrics are provided to detect asymmetric correlation peaks distorted by received signal asymmetry. Then the statistical properties of the proposed methods are analyzed, and a proper deformation detection threshold is calculated. Finally, both simulation results and experimentally measured results of Beidou navigation satellite system (BDS) M1-S B1Cd signal are given, which show the effectiveness and robustness of the proposed thread models.

Theoretical analysis of unambiguous 2-D tracking loop performance for band-limited BOC signals

Code-tracking accuracy, an important attribute of receiver performance assessment, depends both on characteristics of the ranging signal being tracked and on the structure of the tracking channel. The implementation of binary offset carrier (BOC) modulated signals and the development of new tracking channel structures with a two-dimensional (2-D) loop architecture, in which both the code and subcarrier delays are estimated independently by two separate tracking loops, have resulted in the theories of 2-D loop tracking performance being of increased interest. However, the theories of tracking performance in white noise for band-limited BOC signals using the most representative and most mature 2-D tracking method are still not mature. Therefore, we present the exact expression for tracking performance prediction for limited front-end bandwidths to show how well double estimator technique (DET) could perform for given conditions. While evaluation of the exact expression requires numerical integration, a simple yet accurate closed-form analytical approximation is also provided for a more intuitive description of tracking performance. Moreover, we present a bandwidth-dependent, quasi-optimal, discriminator parameter selection rule to simplify the work of receiver designers while improving tracking performance. These results can provide further guidance for the design, parameters selection, and optimization of the receiver.

Generalized Theory of BOC Signal Unambiguous Tracking With Two-Dimensional Loops

The multipeaked correlation functions of binary offset carrier (BOC) modulated signals introduce an ambiguity threat into the code tracking. Several techniques have been proposed to solve this problem, such as a class of two-dimensional (2-D) tracking techniques, in which the spreading code and the subcarrier are tracked separately. In this paper, the key properties of correlation functions and the theoretical tracking performance analysis considering noise and multipath environments of the general 2-D tracking loop are studied. Exact explicit expressions, taking into account the effects of local subcarrier waveform mismatching and the front-end bandlimiting, are provided for the correlation function employed in 2-D tracking. From these expressions, the key characteristics of 2-D correlation functions such as the shape, coupling relation between dimensions, and the effects of bandlimiting can be clearly seen. Moreover, general theoretical methods to predict the performance of the 2-D tracking techniques under the multipath and noise environments are provided. The results obtained in this paper can facilitate investigations in the area of 2-D tracking technique parameter optimization and performance assessment.

Coherent side‐band BOC processing

Binary offset carrier (BOC) modulated signals are characterised by multi-peaked correlation functions which may lead to false peak locks that occur when a secondary correlation lobe is tracked instead of the main peak. To solve this problem, side-band processing (SBP) operates on the two main lobes of the BOC spectrum separately, in a binary phase shift keying like fashion. Although an unambiguous correlation function is obtained, the information provided by the BOC subcarrier is lost. This information is preserved by the double estimator and by the double phase estimator (DPE) which adopt an additional tracking loop to process the subcarrier component. In this study, the connection between SBP and independent subcarrier processing is shown and a novel SBP scheme, the coherent side-band (CSB) approach, is proposed. As in standard SBP, the two main lobes of the BOC spectrum are processed separately and upper and lower correlators are computed. These correlators are then combined to recover the subcarrier information. CSB provides subcarrier measurements and achieves the performance of the DPE. CSB tracking is thoroughly characterised and simulations and real-data processing are used to support theoretical findings. The CSB approach is an effective alternative to independent subcarrier processing.

A Main Peak Extraction Method for High-Order BOC Signals

Binary Offset Carrier (BOC) modulation signals have been applied in Global Navigation Satellite Systems (GNSS) because they offer a higher positioning accuracy and higher multipath rejection. However, there is a drawback in that the autocorrelation functions have multiple side peaks, meaning that this technique also leads to the large main peak estimation error problem and a low correlation decision efficiency problem. In this paper, we propose a new Main Peak Extraction (MPE) method for high-order BOC signals to solve these problems. In the new method, the synthesis cross-correlation function is established, and the geometry graph is formatted to calculate the estimation main peak. We eliminate all side peaks and improve the main peak phase estimation precision under the condition that the sub-carrier phase is offset. The results of the simulation demonstrate that the new method can achieve better main peak decision efficiency, side peak cancellation ability and phase estimation performance than traditional methods.

Unambiguous Tracking Method for Cosine-BOC Signals Based on an Optimizing Combined Correlation Functions

This paper proposes an unambiguous tracking method based on the optimized combined autocorrelation function (ACF) for the cosine-phased binary offset carrier (cosine-BOC) modulated signals, which are applied in global navigation satellite system (GNSS). The main idea is to generate a specially constructed local reference waveform for cosine-BOC modulated signals, which is equivalent to get a group of samples of the ACF, then the unambiguous combined correlation function is obtained by weighting and adding these samples. Simulations show that the proposed method not only eliminate the ambiguity completely, but also maintains a narrow main-peak to obtain outstanding tracking accuracy performance of the cosine-BOC modulation. Additionally, the proposed method is proven to be with good performance in moderate and long multipath interferences mitigation.

Generalized unambiguous tracking method based on pseudo correlation function for multi-level coded symbol modulated signals

The global navigation satellite system (GNSS) signal modulation type plays a crucial role in determining the performances of positioning, navigation and timing (PNT) services. Currently, the binary offset carrier (BOC) modulation signal and binary coded symbol (BCS) modulation signal are both bipolar signals, which greatly restrict the room of improving the GNSS signal performance. Therefore, multi-level coded symbol (MCS) modulation has received great attention in the field of GNSS signal design. The MCS modulation is the most extensive step-coded symbol modulation mode, where BOC modulation and BCS modulation are its special cases. Since the waveform symbol of the MCS modulation signal can be arbitrarily valued, the optimal GNSS signal can be designed. However, like the BOC modulation signal, the MCS modulation signal also has the problem of ambiguous tracking, and then results in a large pseudo range measurement error, which is unacceptable for the new generation GNSS with high accuracy. In recent years, the unambiguous tracking of GNSS signals has become a hot research subject in the navigation signal processing domain and many methods are presented, and those methods can be divided into three categories:BPSK-like method, bump jump (BJ) method, and side-peak cancellation (SC) method. However, these methods are designed for BOC signal, and they are not suitable for MCS signal. Therefore, in this paper we propose a general unambiguous tracking algorithm based on the pseudo correlation function (PCF), which is suitable for MCS modulated signals. Firstly, the unitary expression of MCS modulated signal based on waveform value vector is given, then the unitary formula of cross-correlation function for MCS signal is derived and the definition of PCF is given. Then the constraint condition which should be satisfied to realize unambiguous tracking is analyzed in depth, and the universal constructing method of two reference signals and the relationship between each other are derived according to this constraint condition, which brings great convenience for solving the specific MCS signal. The code tracking loop model of GNSS receiver based on the proposed method is illustrated. It is observed that the proposed method can receive different MCS signals under the same receiver loop framework, and can simplify the design of the receiver while eliminating the tracking ambiguous problem. Finally, as a special case of MCS signal, the applications of the proposed method in four kinds of BOC signals are discussed respectively, and then the waveform value vector of the reference signal and the unitary expression of code discriminator are derived. Simulation results show that the proposed method can effectively solve the ambiguous tracking problem of MCS signal, which has good performance and broad application prospect.

Unambiguous sine-phased binary offset carrier modulated signal tracking technique

In this paper, an unambiguous tracking technique is proposed for arbitrary order sine-phased binary offset carrier (BOC) modulated signals, which are used in the modernized global navigation satellite systems (GNSS). Firstly, two local auxiliary signals are designed, which correlate with the received BOC signal respectively to form two cross-functions. Then, the two cross-functions are used to obtain a composed correlation function (CCF). The side-peaks are removed completely in the CCF, thus there is only one lock point on the discriminator output. The performances of the proposed technique on noise resistance and multipath mitigation are analyzed and verified. The numerical results show that the proposed technique can remove tracking ambiguity completely and has better noise and short-delay multipath mitigation performance than the conventional techniques.

Synthesis of Optimal Incoherent Subcarrier Tracking of BOC(1,1) Navigation Signals

Navigation receivers of global positioning systems that are operated in complex electromagnetic environment must have an increased noise immunity characteristic. One way of such noise immunity rising is to use incoherent operating mode of navigation receiver. There are known processing algorithms for navigation signals with Binary Phase Shift Keying (BPSK) modulation. But in the near-term outlook Global Navigation Satellite Systems (GLONASS), Global Positioning Systems (GPS) and Galileo known navigation signals with Binary Offset Carrier (BOC) modulation will be radiated. Processing algorithms for such signals are not described in scientific literature. So it is interesting to work out processing algorithms for BOC modulated signals in incoherent operating mode of navigation receiver. The article is devoted to synthesis and analysis of incoherent subcarrier tracking system under receiving BOC (1,1) navigation signals. To synthesize an optimal tracking system, optimal estimation theory and dual estimation method are used that allow taking into account multi-peak a posteriori distribution of delay that caused by the periodic process (digital sinusoid) in the radio signal modulation function. When analyzing the synthesized estimation algorithm, the procedure for describing delay discriminators and dual variable discriminators were used in the form of a statistical equivalent, including discrimination and fluctuation characteristics. New equations have been obtained that describe optimal tracking system for incoherent mode of a navigation receiver. New expressions for delay and dual variable discriminators are derived. The article gives a scheme for these discriminators and formulas for their statistical characteristics. Simulated results are provided that illustrate accuracy characteristics enhancement. The obtained tracking algorithms may be used in the navigation consumer equipment of GLONASS, GPS, Galileo and other radio-navigation satellite systems operating with BOC(1.1) modulated signals.