Code Tracking Accuracy Research Articles

Chaff Cloud Integrated Communication and TT&C: An Integrated Solution for Single-Station Emergency Communications and TT&C in a Denied Environment

In response to potential denial environments such as canyons, gullies, islands, and cities where users are located, traditional Telemetry, Tracking, and Command (TT&C) systems can still maintain core requirements such as availability, reliability, and sustainability in the face of complex electromagnetic environments and non-line-of-sight environments that may cause service degradation or even failure. This paper presents a single-station emergency solution that integrates communication and TT&C (IC&T) functions based on radar chaff cloud technology. Firstly, a suitable selection of frequency bands and modulation methods is provided for the emergency IC&T system to ensure compatibility with existing communication and TT&C systems while catering to the future needs of IC&T. Subsequently, theoretical analyses are conducted on the communication link transmission loss, data transmission, code tracking accuracy, and anti-multipath model of the emergency IC&T system based on the chosen frequency band and modulation mode. This paper proposes a dual-way asynchronous precision ranging and time synchronization (DWAPR&TS) system employing dual one-way ranging (DOWR) measurement, a dual-way asynchronous incoherent Doppler velocity measurement (DWAIDVM) system, and a single baseline angle measurement system. Next, we analyze the physical characteristics of the radar chaff and establish a dynamic model of spherical chaff cloud clusters based on free diffusion. Additionally, we provide the optimal strategy for deploying chaff cloud. Finally, the emergency IC&T application based on the radar chaff cloud relay is simulated, and the results show that for severe interference, taking drones as an example, under a measurement baseline of 100 km, the emergency IC&T solution proposed in this paper can achieve an accuracy range of approximately 100 m, a velocity accuracy of 0.1 m/s, and an angle accuracy of 0.1°. In comparison with existing TT&C system solutions, the proposed system possesses unique and potential advantages that the others do not have. It can serve as an emergency IC&T reference solution in denial environments, offering significant value for both civilian and military applications.

Partial response continuous phase modulation with a prolate spheroidal wave function for compass system in the S-band

Continuous phase modulation (CPM) has the characteristics of high power efficiency, spectral efficiency, and less out-of-band radiation, which is very suitable for the Compass S-band (2483.5–2500 MHz) with limited power and bandwidth. However, as more and more navigation systems share the S-band, the mutual interference between different systems is gradually increasing, and the compatibility of CPM signals with rectangular or raised cosine pulses needs to be further improved. To enhance the navigation performance and compatibility of current CPM candidate signals, we propose to apply continuous phase modulation with prolate spheroidal wave function (CPM-PSWF) to S-band navigation. The proposed modulation scheme selects PSWF with excellent time-frequency energy aggregation and flexible time-bandwidth product as the frequency pulse function of CPM. Then, the influence of key modulation parameters such as M, L, h, and C on CPM-PSWF power spectral density is analyzed, and a specific partial-response CPM-PSWF signal is proposed as the S-band candidate navigation signal. Finally, the navigation performance evaluation criteria are derived, and the proposed signal scheme and existing candidate schemes are comprehensively evaluated. Theoretical analysis and simulation results indicate that compared with CPM with BM2RC(8), cos-phase binary offset carrier (BOCc(4,4)), sin-phase binary offset carrier (BOCs(4,4)), minimum shift keying-BOCs (MSK-BOCs(4,4)) and binary offset carrier (BPSK(8)), the proposed signal scheme not only delivers exceptional spectral performance but also exhibits superior performance in code tracking accuracy and multipath suppression. In addition, in the acquisition and tracking phase, compared with other candidate signals except for BOCc(4,4), the mutual interference between the proposed signal scheme and most S-band signals is the lowest, which is easier to realize the compatibility of the Compass system with IRNSS, Galileo, and Globalstar systems.

A Novel Signal Design and Performance Analysis in NavCom Based on LEO Constellation.

The mega-launch of low Earth orbit satellites (LEOs) represents a critical opportunity to integrate navigation and communication (NavCom), but first, challenges related to signal design must be overcome. This article proposes a novel signal scheme named CE-OFDM-PM. Via research on the in-band or adjacent band, it was found that the proposed signal scheme was suitable for S-band and had a wide normalized power spectrum density (PSD), high peak-to-side lobe ratio (PSR), and multiple peaks in autocorrelation. In an analysis of the simulation performance evaluation in navigation and communication, it is found that the proposed signal scheme has the potential for high accuracy, a code tracking accuracy of up to 0.85 m, a small mutual influence between the proposed signal scheme and other schemes, excellent anti-interference properties, and a better performance at both short and long distances in terms of its anti-multipath capability. Furthermore, the proposed signal scheme shows the ability to communicate between satellites and the ground and is outstanding in terms of its bit error rate (BER), CNR, and energy per bit to noise power spectral density ratio (Eb/N0). From the technical, theoretical, and application perspectives, our proposed signal scheme has potential as an alternative scheme in future BDS, PNTs, and even 5G/B5G.

Unambiguous Tracking Technique Based on Shape Code for BOC Signals

The multiple peaks characteristic of binary offset carrier (BOC) autocorrelation function (ACF) makes ambiguity easy to be generated. There are some methods to eliminate ambiguity, but for higher-order BOC Signal, it will sacrifice signal energy or cannot maintain narrow correlation. This paper studies these problems. According to the idea of GRASS algorithm shape code, this paper proposes an unambiguous tracking algorithm, Sub Cross-correlation Shift Technique (SCST), which is suitable for BOC(m,n) signals. The key to this algorithm is to generate a new cross-correlation function between the BOC signal and the PRN code based on the shape code. The new cross-correlation function is linearly combined with the autocorrelation function of the BOC signal to remove sub-peak interference and achieve high-accuracy tracking. The phase discrimination function is given, and the effectiveness of the tracking algorithm is analyzed theoretically. The disadvantage of this method is that it needs multilevel storage, which will bring extra resource consumption to the receiver. For comparison, Unit Correlation, ASPeCT, GRASS, and the algorithm proposed by Yan are proposed. Experiments show that SCST can completely remove the side peak, and the phase discriminator output has only two main peaks, which successfully eliminates the false lock point. The multipath error envelope has only one and the smallest area. In terms of code tracking accuracy, for a BOC(10,5) signal with a received signal-to-noise ratio (SNR) of −28 dB, SCST is less than 45.8%, 67.5%, and 12.2% of the Unit Correlation, GRASS, and Yan proposed algorithms.

A new unambiguous tracking algorithm for sine-BOC(m, n) signals

Binary offset carrier (BOC) modulation technology is widely used in newly developed and modernized global navigation satellite systems. BOC signal offers superior performance over conventional binary phase-shift keying signal due to its sharp auto-correlation function. However, the main drawback of BOC signal tracking is the ambiguity problem caused by the presence of multiple side-peaks in the auto-correlation function. We derive a new analytical model to solve the ambiguity issue. Based on the derived analytical model, a code tracking algorithm that completely removes all ambiguities is introduced. Theoretical analysis and simulation show that the proposed technique significantly improves the multipath mitigation performance and code tracking accuracy in thermal noise over those of existing side-peaks-cancellation techniques.

Weighted Discriminator Function Based Unambiguous Tracking Method for Dual-Frequency Constant Envelope Modulated Signals

The dual-frequency constant envelope modulated (DCEM) signals, represented by alternative binary offset carrier signal, have obvious advantages in code tracking accuracy and anti-multipath performance compared with traditional binary phase shift keying signal, and are attracting more and more attention in the field of global navigation satellite system signal design. However, DCEM signal has a multiple-peaked auto-correlation function, which would lead to the tracking ambiguity problem. To deal with this problem, this paper proposes an unambiguous tracking method based on weighted discriminator function (WDF). This method uses the discriminator functions of noncoherent early minus late power (NELP) and sub carrier phase cancellation (SCPC) to generate a linear WDF without no false-lock points. In addition, a simplified version of the proposed WDF method is also provided for interoperable application. The theoretical code tracking error in thermal noise is derived out and verified. The performance of the proposed WDF is evaluated and compared with SCPC and pseudo correlation function methods with the help of simulation. Results show that our method has a significant improvement in code tracking accuracy. Not only the ambiguity threat is efficiently removed, but also the outstanding performance of DCEM signal is maintained.

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.

Time domain raised cosine-binary coded symbol modulation for satellite navigation

The number of satellite navigation signals in space grows dramatically as the number of global and regional navigation satellites constant increases. This phenomenon further aggravates an already crowded radio spectrum in-band and increases out-of-band (OOB) emissions. One feasible solution to the issue of signal compatibility is to design a spectrum-efficient modulation signal that has better navigation performance and backward compatibility with adjacent signals and services in operation. In this study, a time domain raised cosine (TDRC) pulse is introduced as an alternative waveform. A binary coded symbol (BCS) modulation family based on TDRC pulse called TDRC-BCS is also proposed as a candidate for future global navigation satellite system (GNSS). An extensive study on the multipath model analysis approach is also provided. The proposed modulation and existing modulations are then comprehensively evaluated. Theoretical analysis and simulation results show that TDRC-BCS signals offer superior navigation performance compared with existing modulations in terms of code tracking accuracy, multipath mitigation capacity, while maintaining comparable or better anti-jamming performance. These signals can also attain higher spectral efficiency and better backward compatibility with the existing GNSS signals. The proposed modulation scheme provides additional degrees of freedom for GNSS signal design.

Unambiguous Acquisition/Tracking Technique for High-Order Sine-Phased Binary Offset Carrier Modulated Signal

The binary offset carrier (BOC) modulated signals have been widely employed in global navigation satellite systems due to its outstanding performance. The BOC signal can share frequency spectrum with traditional BPSK signal, meanwhile provide better code tracking accuracy. However, the multiple peaks auto-correlation function of BOC signal results in the acquisition and tracking ambiguity problem. Several methods have been proposed to remove the ambiguity, but they mainly focus on the low modulation order BOC signal, and not efficient enough for high-order BOC signal. In this paper, we propose an unambiguous acquisition/tracking technique for high-order sine-phased BOC signal. The key of this technique is to design a new local auxiliary signal. With the help of the cross-correlation function between the BOC signal and the local auxiliary signal, we obtain a combined correlation function without major positive side peaks. The proposed acquisition and tracking schemes are presented. The theoretical false alarm and detection performance are given, and the theoretical code tracking error in thermal noise is derived. The performance of the proposed method is analyzed by theory and simulation. Results show that for high-order sine-BOC signal, the proposed technique can remove the ambiguity threat. Compared with the existing methods, our method has a significant improvement in terms of acquisition sensitivity and code tracking performance.

Unambiguous combined correlation functions for sine-BOC signal tracking

Binary offset carrier (BOC) modulated signal has been widely employed in modern global navigation satellite system (GNSS). However, the multiple peaks auto-correlation function of BOC signal leads to tracking ambiguity problem. For high-order BOC signal, the above problem becomes more severe. We propose an unambiguous tracking method based on combined correlation functions for sine-BOC signal. The main feature of this technique is that two new local reference waveforms are used. Based on the cross-correlation functions between the BOC signal and these two local reference waveforms, unambiguous combined correlation functions without any main positive side-peaks are generated. To achieve unambiguous tracking for sine-BOC signal, we present two non-coherent discriminator functions, denoted as V1 and V2. The theoretical expressions of code tracking error in thermal noise are derived. Then, the impact of thermal noise and multipath is analyzed with the help of numerical simulations. Results show that V1 is easier to implement and has relatively better multipath mitigation performance at the expense of some performance degradation in code tracking error. V2 has better code tracking accuracy and provides the most robust code tracking process for high-order sine-BOC signal, but two additional complex correlators are required.

Generalized Theory of Code Tracking with an Early-Late Discriminator Part I: Lower Bound and Coherent Processing

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its sequel provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This first paper addresses coherent early-late processing (ELP) for given receiver precorrelation bandwidth and given early-late spacing, also providing a tight lower bound on code-tracking error independent of discriminator design. Theoretical expressions are derived, showing that code-tracking accuracy depends on more than merely signal-to-noise ratio and early-late spacing - the shape of signal and interference spectra are important, as is the receiver precorrelation bandwidth.

Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver

Code-tracking accuracy, an important attribute of GPS receivers, depends both on characteristics of the signal being tracked and on the design of the receiver. A simple expression has been available to predict code-tracking accuracy for early-late processing of signals with sinc-squared spectra in white noise for an infinite front-end bandwidth receiver. However, the literature has not indicated when this approximation holds. This paper provides a more exact analysis of code-tracking accuracy for early-late discriminators processing conven-tional binary phase shift keyed signals in white noise. New analytical expressions apply for various front-end bandwidths, discriminator spacings, and code-tracking loop bandwidths, while using linear models based on a small-error assumption. A theoretical lower bound is also supplied, indicating inherent limits on accuracy for given conditions. While evaluation of the exact expressions requires numerical integrations, new algebraic approximations are also provided. Numerical results compare the various expressions and approximations.