The statistical characteristics of navigation cosine binary offset carrier modulated signals (CosBOC signals)

The features and statistical characteristics of cosine binary offset carrier modulated signals (BOC signals) of new-generation satellite radio navigation systems, in particular the Galileo system, are considered. Analytical expressions for the correlation functions (CFs) of the cosine meander symbols (MSs) of the pseudorandom sequence of a ranging code are found for various values of the multiplicity coefficient of meander pulses. The energy spectra of cosine MSs are obtained with the help of the Fourier transform of the CFs. Plots are depicted, and the CFs and energy spectra of cosine MSs are analyzed for the following types of meander modulation: CosBOC (1,1), CosBOC (15,10), CosBOC (10,5), and CosBOC (5,2).     

The correlation functions of single elements of the modulating functions of double complex meander noise-like navigation signals (alternative binary offset carrier modulated signals)

The correlation characteristics of elements of complex meander pseudo-random sequences (PRSs) are analyzed. These sequences are the basis for forming double complex meander (DCM) noise-like signals (alternative binary offset carrier modulated signals—AltBOC signals) applied in new-generation satellite radio navigation systems (in particular, the European Galileo and Chinese Bei-Dou/Compass systems). Analytical expressions are obtained for the correlation functions (CFs) of single complex meander symbols (MSs) and for the cross CFs (CCFs) of the sine and cosine components of complex MSs. Formulas for the CFs of single elements of the modulating functions (MFs) of an elementary (two-component) AltBOC signal and a four-component AltBOC signal are derived for typical values of multiplicity coefficient N _m (N _m = 2 and 3). Plots of CFs and CCFs are depicted, and the properties of these functions are discussed. The Fourier transform is applied to obtain the energy spectra of single MSs of an elementary AltBOC signal and a complete four-component AltBOC signal. In the examples, the attention is focused on AltBOC signals with the AltBOC (15, 10) modulation and the repetition rate of PRS elements f _s = 10 f _ref = 10.23 MHz, where the reference frequency is f _ref = 1.023 MHz.     

Correlation functions of complete CBOC signals derived as the inverse Fourier transform of energy spectra

For the complete composite binary offset carrier (CBOC) signals of new-generation global satellite radio-navigation satellite systems (SRNSs), analytical expressions for correlating functions (CFs) characterizing the single components of the modulating function are derived in terms of the inverse Fourier transform (IFT) of energy spectra at different fractional coefficients. The CF calculation technique is based on the energy spectra of complete CBOC signals represented as a partial sum of the series of cosines of the angles that are multiples of the angle γ_CBOC = ωτ_M2, where τ_M2 is the meander-pulse duration of the subcarrier oscillation of binary offset carrier (BOC) signals with BOC(6,1) modulation. In a number of cases, the IFT of energy spectra applied to calculating the CFs of complete CBOC signals is preferable (in particular, from the viewpoint of labor intensiveness) to the procedures by which CFs are obtained using the general definition. The CFs graphs constructed with the help of complete CBOC signals employed in the E1 band of the Galileo SRNS are presented.     

The spectral characteristics of navigation alternative binary offset carrier modulated signals (AltBOC signals)

Analytical expressions are obtained for spectral densities and energy spectra of single elements and single periods of modulating functions of alternative binary offset carrier modulated signals (AltBOC signals) for new-generation satellite radio navigation systems (SRNSs) (in particular, the Galileo system). The spectral characteristics are presented and analyzed for an elementary (two-component) AltBOC signal, a complete AltBOC with a time-variable envelope (a four-component complete AltBOC signal), and a complete AltBOC with a constant envelope (an eight-component complete AltBOC signal) in the case when the multiplicity coefficient of meander pulses has an arbitrary value. Plots are depicted, and the properties of energy spectra of single elements of modulating functions of all groups of AltBOC signals are discussed in the cases of the following modulation types: AltBOC(10, 10), AltBOC(15, 10), AltBOC(20, 10), and AltBOC(25, 10).     

Complete alternative binary offset carrier modulated signals (AltBOC signals) with variable and constant envelopes for new-generation satellite radio navigation systems

The formation and structure of four- and eight-component complete alternative binary offset carrier modulated signals (AltBOC signals) for new-generation satellite radio navigation systems (SRNSs) (in particular, the Galileo and BeiDou-2 SRNSs) are considered. A four-component complete AltBOC signal has a time-variable envelope, while the envelope of an eight-component complete AltBOC signal is constant. The envelopes and phases of such AltBOC signals are analyzed for various values of the multiplicity coefficients of meander pulses. The combination components of an eight-component complete AltBOC signal are plotted, and the features of these components that ensure the time constancy of the envelope are revealed. A classification of AltBOC signals is proposed. Practical characteristics are analyzed on the basis of the AltBOC (15, 10) modulation, which is typical of the Galileo and Compass SRNSs.     

Complex meander pseudorandom code sequences and alternative binary offset carrier modulation (AltBOC modulation) in new-generation satellite navigation systems

Complex meander pseudorandom sequences (MPRSs) that are the basis for formation of alternative binary offset carrier modulated signals (AltBOC signals) for new-generation satellite radio navigation systems (in particular, the Galileo and Compass systems) are considered. The properties and characteristics of MPRSs are analyzed. Analytical expressions for the spectral densities and power spectrum densities of complex and complex conjugate meander symbols (MSs) of the MPRS of a ranging code are found for various values of the multiplicity coefficient of meander pulses. The modulating function of an elementary AltBOC signal is considered. The power spectrum densities of complex and complex conjugate MSs are plotted and analyzed for typical values of the multiplicity coefficient.     

Correlation functions of BOC and AltBOC signals as the inverse Fourier transforms of energy spectra

The navigation signals with sine binary offset carrier (sinBOC), cosine BOC (cosBOC), and alternative BOC (AltBOC) modulations are discussed. A technique for calculating the correlation functions (CFs) of the single components of modulating functions (MFs) inherent to the given signals, which is based on the inverse Fourier transform (IFT) of energy spectra, is proposed. This technique makes it possible to derive analytical expressions for the CFs characterizing the single components of the MFs of sinBOC and cosBOC signals and complete AltBOC waveforms with a constant envelope at the multiplicity coefficients N_m = 2?4. The graphs of CFs are constructed. Several illustrating examples, in which most attention is paid to sinBOC, cosBOC, and AltBOC signals employed in the Galileo satellite radio-navigation system and the global positioning system, are presented.     

Correlation functions of complete AltBOC signals with a constant envelope

The structure of the modulating function (MF) of a complete alternative binary offset carrier modulated signal (AltBOC signal) with a constant envelope (eight-component complete AltBOC signal) is considered. Analytical expressions for the correlation functions (CFs) of single elements of the MFs of complete AltBOC signals with a constant envelope are derived at typical values of multiplicity coefficient N _m of meander pulses (N _m = 2 and 3). Plots of the CFs of single elements of the MFs of complete AltBOC signals with a constant envelope are obtained for N _m = 2 and 3. The properties of these CFs are discussed. With the help of the Fourier transform applied to the CFs, the energy spectra (spectral power densities) of single elements of the MFs of complete AltBOC signals with a constant envelope are calculated at N _m = 2 and 3. In illustrating examples, most attention is focused on complete AltBOC signals with a constant envelope at the carrier frequency f _car = 1191.795 MHz for the AltBOC (15, 10) modulation and the repetition rate of the elements of ranging-code pseudorandom sequences f _s = 10f _ref = 10.23 MHz, where the reference (base) frequency is f _ref = 1.023 MHz. These signals are applied in the Galileo European satellite radio navigation system (SRNS) and, as is supposed, in the Chinese BeiDou-2/Compass SRNS.     

Correlation Functions of Navigational cosGBOC Signals as the Inverse Fourier Transform of the Energy Spectra

Journal of Communications Technology and Electronics - Abstract—The modulating functions (MFs) of cosGBOC signals (cosine generalized BOC signals) for new-generation satellite radio...     

Correlation Functions of Navigational GBOC Signals

The structure of generalized binary offset carrier (GBOC) signals of satellite radio navigation systems, such as global positioning system (GPS) (USA), global navigation satellite system (GLONASS) (Russia), Galileo (European Union), and BeiDou/Compass (China), is examined. Analytical expressions for the correlation functions (CFs) characterizing the single components of the GBOC-signal modulation function (MF) are derived at the typical pulse multiplicity coefficients N_R (N_R = 2 and 4) and different duty cycles. The CFs properties of the components of GBOC-signal MFs are discussed and their graphs are constructed at ρ = 0 (or ρ = 1) corresponding to binary phase-shift keying signals, ρ = 0.1 (or ρ = 0.9), ρ = 0.25 (or ρ = 0.75), ρ = 0.3 (or ρ = 0.7), ρ = 0.45 (or ρ = 0.55), and ρ = 0.5 corresponding to binary offset carrier signals. The energy spectra (power spectral densities) of the single components of GBOC-signal MFs are calculated via the Fourier transform of CFs at the pulse multiplicity coefficients N_R= 2 and 4.     

Test signals with multilevel subcarriers as applied to satellite radio-navigation systems

Noise-like meander signals are proposed to generate on the basis of multilevel pseudorandom sequences making it possible to include multilevel subcarriers. It is demonstrated that such signals are characterized by the pronounced central region of the principal peak of the real part of their complex autocorrelation function and its other values remain almost identical in the time interval corresponding to the principal correlation peak. They are several times less than those of binary offset carrier modulated signals. It is established that the selection of a subcarrier phase structure makes it possible to more flexibly control the shape of the power spectral density of signals and its arrangement on the frequency in comparison with BOC signals.     

同源多码流直接序列扩频信号性能分析

新一代GPS系统加入了二相偏移载波(BOC)调制信号。相对GPS传统PSK-R信号,BOC信号具有更多的高频分量,在抗干扰性能、码跟踪精度、频谱利用和给定带宽条件下的多信号复用诸方面获得改善和提高。该文分析提出,GPS传统C/A码和P(Y)码信号做为整体时具有与BOC信号相似的特性。该文将其推广到一般化同源多码流信号,分析表明,可以将同源多码流信号作为新信号形式联合处理,以在白噪声和人为干扰具主导作用环境提高码跟踪性能。该文得出两种经典信号谱型条件下,以信号参数表示的码跟踪误差改善的表达式并给出了实现3 dB码跟踪性能改善的参数数值。     

BPSK-LIKE算法信号级仿真验证与分析

针对BOC信号的频谱分裂和副峰模糊特性,在分析BPSK-LIKE跟踪算法的理论基础上,通过对上、下边带分别进行BPSK解调验证该算法的正确性。通过比较BPSK盲解调得到的伪码极性和时延的一致性达到验证的目的。从而证明了在实际解调中,可以通过处理任意1个边带的信号或者分别处理2个边带信号来完成BOC信号的跟踪解调。在此基础上,通过信号级仿真实现了该算法对BOC信号的跟踪。     

Unambiguous sine-phased binary offset carrier modulated signal acquisition technique

In this letter, a side-peak cancelation unambiguous acquisition technique is proposed for sine-phased binary offset carrier (BOC) modulated signals. The test criterion used in this technique is based on a synthesized correlation function which has no major positive side peak. This synthesized correlation function is obtained by subtracting the cross-correlation between the received sin-BOC signal and an auxiliary signal from the autocorrelation of sin-BOC signal. For different types of BOC signal, the proposed technique employs corresponding modulated symbols of the auxiliary signal. The common solution of the symbol shape vector is derived, and the theoretical false alarm and detection performance formulas are given. Theoretical and simulation results show that at the expense of some performance degradation this technique completely removes the ambiguity threat in acquisition process.     

Tailored spreading symbols in “Strobe Correlators” using “W2-pulses”

A “Strobe Correlator” is a correlation-based multipath mitigation technique that utilizes tailored reference waveform to shape the discriminator function for tracking Global Navigation Satellite System (e.g. Global Positioning System) signals. Multipath performance of these techniques for Binary Phase Shift Keying (BPSK) signals has been discussed for decades but for some, their noise performance may not be easily evaluated analytically. In this paper, a theoretical framework is provided for noise evaluation of “Strobe Correlators” using complex strobes for both BPSK and sine-phased Binary Offset Carrier (e.g. BOC(1,1)) signals. Mathematical expressions of the tailored spreading symbols as key factors are derived and used for theoretical code tracking variance analysis of various correlation techniques including the “Gating Function” using a complex strobe-pulse liked waveform (i.e. “W2-pulses”). Empirical results for the sine-phased BOC(1,1) signal are given as verification. Analytical results reveal that the techniques using a W2-pulse suffer from higher code tracking variance than others, due to increased sensitivity to noise. The sensitivity to pre-correlation bandwidth is found to relate to the relative placement of the strobe pulses.     

一种适用于BOC(m,n)的无模糊捕获算法

BOC信号的研究主要集中在BOC(n,n)族类,对于不限制m和n取值的无模糊捕获跟踪算法研究较少。该文提出一种适用于BOC(m,n)的基于相关函数的无模糊捕获算法,通过平移重构BOC信号自相关函数构造它的互补函数,再与原函数叠加以消除副相关峰。该算法在消除BOC调制带来的副峰的同时,保留了单一的窄主峰,保持主峰宽度不变,利用BOC调制方式高精度易跟踪的特点,解决了一般BOC信号捕获和跟踪过程中的模糊问题。仿真验证了新算法的特性,并与其他的算法进行了比较分析。     

电离层色散效应对宽带BOC信号的影响

电离层色散特性导致宽带二进制偏移载波(Binary Offset Carrier,BOC)信号的码片时域波形和相关函数曲线产生畸变,影响BOC信号完好性和跟踪性能。为了评估电离层对BOC信号传输的影响,构建了宽带BOC信号的电离层影响分析框架,分析了电离层色散效应对码片时域波形和相关特性的影响,并评估了三类典型BOC信号的带内电离层色散效应在码跟踪环路和载波跟踪环路引入的偏差。研究结果表明,电离层色散效应会导致宽带BOC信号时域码片实部和虚部边缘产生抖动现象,色散信号与标准信号间的互相关函数会产生明显的相关损耗;在电离层活跃期间,电离层色散效应在码跟踪与载波相位跟踪中均引入明显的鉴别误差。该结果对BOC信号的电离层误差的评估与校正有一定的参考意义。     

BOC调制导航信号关键技术研究

BOC调制作为一种导航信号体制,具有良好的抗多径和抗干扰性能,同时实现共用载波频率条件下的频谱分离。与BPSK调制信号相比,BOC调制信号具有多径误差小、码跟踪热噪声误差小的优点。通过对BOC调制技术和合路方式的深入分析,给出了各种BOC调制的自相关和功率谱函数,以及各种合路方式的分析比较。通过仿真验证了BOC信号的码跟踪性能和抗多径性能的优越性。     

导航信号的BOC调制方式

BOC调制方式适应导航发展的新需要,它实现了频谱分裂以充分利用现有频段资源,且具有比传统BPSK调制方式更好的相关性能,从而可以提高根据相关特性测距的精度。介绍了BOC调制信号的频谱、功率谱和相关函数的特点。针对BOC调制信号相关函数的多峰结构容易造成捕获模糊,提出了3种相应的接收处理方法:类似BPSK的单边带处理方法、峰跳法和一种无模糊跟踪鉴相器算法。     

同阶二元偏移载波调制信号跟踪技术

针对同阶二元偏移载波调制卫星导航信号,提出一种高效新算法解决信号跟踪中的模糊性。分析了同阶二元偏移载波调制原理、信号跟踪模糊性及解决方法,利用本地扩频码与接收信号的相关函数特点,构建了码跟踪环路鉴相曲线,选择了合适的相关间距作为符号判决,联合构成鉴相器,推导了算法设计的正确性,给出了实现架构。仿真结果表明,码相位捕获误差±0.9个码片内均可正确跟踪。该方法可进一步应用于全球卫星导航系统新体制信号的接收处理。