L/C双频段联合导航信号中通用调制方案研究
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (4): 778-784  DOI: 10.11990/jheu.201610022 0

### 引用本文

SUN Yanbo, XUE Rui, WANG Dun, et al. General modulation scheme for L/C dual-frequency combined navigation signal[J]. Journal of Harbin Engineering University, 2018, 39(4), 778-784. DOI: 10.11990/jheu.201610022.

### 文章历史

L/C双频段联合导航信号中通用调制方案研究

1. 哈尔滨工程大学 信息与通信工程学院, 黑龙江 哈尔滨 150001;
2. 天地一体化信息技术国家重点实验室, 北京 100086

General modulation scheme for L/C dual-frequency combined navigation signal
SUN Yanbo1, XUE Rui1, WANG Dun2, ZHAO Danfeng1
1. College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China;
2. Beijing Institute of Satellite Information Engineering, Beijing 100086, China
Abstract: To ease the already overcrowded radio spectrum in the L band, the C band (5 010~5 030 MHz) was allocated by the international telecommunication union (ITU) to the navigation service, which makes it possible to combine navigation of the L and C frequency bands.The modulation scheme is the core part of the design of signal structure, and it is necessary to design a general modulation scheme that meets the requirements of all bands, reduces complexity of the multi-frequency terminal, and accelerates the practical course of multi-band combined navigation.Aimed at the distribution of frequency points of (BDS) B3 signal, this paper designs a double-frequency combination model of the L and C bands, and proposes to take continuous phase modulation (CPM) as the general modulation scheme for the above bands.In comparison with the prevailing scheme, simulation results indicate that CPM has high spectral efficiency.In addition, it has advantages in terms of tracking accuracy, multipath mitigation, and compatibility.Furthermore, it also satisfies stringent constraints required for the C band and makes general signal design possible.This paper therefore provides a new concept and provides a feasible demonstration of the future BDS signal modulation scheme.
Key words: L/C dual-frequency band    combined navigation    signal structure    modulation scheme    continuous phase modulation    signal design    tracking accuracy    multipath mitigation    compatibility

C频段导航信号的设计必须首先满足与射电天文(radio astronomy, RA)和微波着陆(microwave landing system, MLS)系统的兼容性约束要求。文献[6]的研究结果表明:基于二进制相移键控(binary phase shift keying, BPSK)和二进制偏移载波(binary offset carrier, BOC)的导航信号在占用C频段20 MHz的全部可利用带宽时, 如果没有带外抑制较强的输出滤波器限制, 均不能满足C频段信号设计的兼容性约束要求。这就需要C频段的调制具有更高的旁瓣衰落特性, 以减小带外频谱泄漏, 相位连续的调制方式成为C频段调制方案的首选[7]。在L频段, 大多数GNSS信号采用BOC调制, 文献[8-9]提出一类可代替BOC的连续相位调制子集信号, 该类CPM信号在定位精度、多径消除、抗干扰、兼容性等方面具有和BOC调制相比拟的性能。

1 CPM信号模型 1.1 时域模型

CPM调制信号的时域表达式为

 $s\left( t \right) = \sqrt {\frac{{2E}}{T}} {\rm{cos}}(2{\rm{ \mathsf{ π} }}{f_0}t + \varphi \left( {t, \mathit{\boldsymbol{\alpha }}} \right) + {\phi _0})$ (1)

 $\begin{array}{l} \varphi \left( {t, \mathit{\boldsymbol{\alpha }}} \right) = 2{\rm{ \mathsf{ π} }}h\sum\limits_{i = 0}^n {{\alpha _i}\int_{-\infty }^{t-iT} {g\left( \tau \right){\rm{d}}\tau, } } \\ nT \le t \le \left( {n + 1} \right)T \end{array}$ (2)

1.2 功率谱密度

 $\begin{array}{l} \mathit\Re \;\left( \tau \right) = \frac{1}{T}\int_0^T {\mathop {\mathit{\Pi }}\limits_{k = 1 - L}^{\left\lfloor {\tau /T} \right\rfloor } } \frac{1}{M} \cdot\\ \frac{{{\rm{sin}}\{ 2{\rm{\pi }}hM\left[ {q\left( {t + \tau - kT} \right) - q\left( {t - KT} \right)} \right]\} }}{{{\rm{sin}}\{ 2{\rm{\pi }}h\left[ {q\left( {t + \tau - kT} \right) - q\left( {t - KT} \right)} \right]\} }}{\rm{d}}t \end{array}$ (3)

 $\begin{array}{l} P\left( f \right) = 2\left\{ {\int_0^{LT} {\Re \left( \tau \right)} {\rm{cos}}2({\rm{ \mathsf{ π} }}f\tau ){\rm{d}}\tau + } \right.\\ \frac{{1-\psi ({\rm{j}}h){\rm{cos}}(2{\rm{ \mathsf{ π} }}fT)}}{{1 + {\psi ^2}({\rm{j}}h)-2\psi ({\rm{j}}h){\rm{cos}}(2{\rm{ \mathsf{ π} }}fT)}}\cdot\\ \int_{LT}^{\left( {L + 1} \right)T} {\Re \left( \tau \right){\rm{cos}}(2{\rm{ \mathsf{ π} }}f\tau ){\rm{d}}\tau-} \\ \frac{{\psi ({\rm{j}}h){\rm{sin}}(2{\rm{ \mathsf{ π} }}fT)}}{{1 + {\psi ^2}({\rm{j}}h) - 2\psi ({\rm{j}}h){\rm{cos}}(2{\rm{ \mathsf{ π} }}fT)}}\cdot\\ \left. {\int_{LT}^{\left( {L + 1} \right)T} {\Re \left( \tau \right)} {\rm{sin}}(2{\rm{ \mathsf{ π} }}f\tau ){\rm{d}}\tau } \right\} \end{array}$ (4)

 Download: 图 1 CPM信号在不同参数条件下的功率谱密度 Fig. 1 Power spectral density of CPM signals with various parameters
2 L和C波段组合信号 2.1 组合频点的设计

 ${f_2} = 4{f_1}$ (5)
 Download: 图 2 L和C波段信号的频点分布方案 Fig. 2 Frequency distribution schemes of combined signals for L and C bands

 $\begin{array}{l} {f_{2\_{\rm{up}}}} = 4{f_1}, {f_{2\_{\rm{up}}}} = 4{f_{1\_{\rm{up}}}}, {f_{2\_{\rm{up}}}} = 4{f_{{\rm{1\_down}}}}\\ {f_{2\_{\rm{down}}}} = 4{f_1}, {f_{{\rm{2\_down}}}} = 4{f_{1\_{\rm{up}}}}, {f_{2\_{\rm{down}}}} = 4{f_{1\_{\rm{down}}}}\\ {f_2} = 4{f_1}, {f_2} = 4{f_{1\_{\rm{up}}}}, {f_2} = 4{f_{1\_{\rm{down}}}} \end{array}$ (6)

2.2 L波段信号设计

 $\begin{array}{*{20}{l}} {{\sigma _{{\rm{NELP}},{\rm{s}}}} = c\sqrt {\frac{{{B_L}(1 - 0.5{B_L}{T_i})\int_{{B_\gamma }/2}^{{B_\gamma }/2} {{G_s}\left( f \right){\rm{d}}f} }}{{4{\rm{ }}{{\rm{\pi }}^2}\frac{{{G_s}}}{{{N_0}}}\left( {\int_{ - {B_\gamma }/2}^{ - {B_\gamma }/2} {f{G_s}\left( f \right)} {\rm{sin}}({\rm{ \pi }}f\Delta ){\rm{d}}f} \right)}}} \times }\\ {\sqrt {\left( {1 + \frac{{\int_{{B_\gamma }/2}^{{B_\gamma }/2} {{G_s}\left( f \right){\rm{co}}{{\rm{s}}^2}({\rm{ \pi }}f\Delta ){\rm{d}}f} }}{{{T_i}\frac{{{G_s}}}{{{N_0}}}{{\left( {\int_{ - {B_\gamma }/2}^{ - {B_\gamma }/2} {f{G_s}\left( f \right)} {\rm{cos}}({\rm{\pi }}f\Delta ){\rm{d}}f} \right)}^2}}}} \right)} } \end{array}$ (7)

 ${\varepsilon _{\tau, av}} = \frac{1}{{\Delta {\tau _{av}}}}\int_0^{\Delta {\tau _{av}}} {\frac{{|{\varepsilon _\tau }(\Delta {\tau _1}){|_0}| + |{\varepsilon _\tau }(\Delta {\tau _1}){|_\pi }|}}{2}} {\rm{d}}\Delta {\tau _1}$ (8)
 $\begin{array}{l} {\varepsilon _\tau }( \mathit\Delta {\tau _1}) = \\ \frac{{ \pm {{\bar a}_1}\int_{- B/2}^{B/2} {P\left( f \right){\rm{sin}}({\rm{ \mathsf{ π} }}fd){\rm{sin}}(2{\rm{ \mathsf{ π} }}f\Delta {\tau _1}){\rm{d}}f} }}{{2{\rm{ \mathsf{ π} }}\int_{- B/2}^{B/2} {fP\left( f \right){\rm{sin}}({\rm{ \mathsf{ π} }}fd)[1 \pm \overline {{a_1}} {\rm{cos}}(2{\rm{ \mathsf{ π} }}f\Delta {\tau _1})]{\rm{d}}f} }} \end{array}$ (9)

 Download: 图 4 L波段信号的码跟踪精度和平均多径误差包络 Fig. 4 Code tracking errors and running average multipath errors of L band signals

 $\Delta {({C_s}/{N_0})_{_{{\rm{eff}}}}}^{{\rm{max}}} = \frac{{{C_s}/{N_0}}}{{{C_s}/({N_0} + {I_{{\rm{Intra}}}}^{{\rm{max}}})}} = 1 + \frac{{{I_{{\rm{Intra}}}}^{{\rm{max}}}}}{{{N_0}}}$ (10)
 ${I_{{\rm{Intra}}}}^{{\rm{max}}} = {\rm{max}}\left( {\sum\limits_{i = 1}^{M\left( t \right)} {\sum\limits_{j = 1}^{{K_i}} {{P_i}A\frac{{\int_{-B/2}^{B/2} {{G_s}\left( f \right){G_{i, j}}\left( f \right){\rm{d}}f} }}{{\int_{-B/2}^{B/2} {{G_s}\left( f \right){\rm{d}}f} }}} } } \right)$ (11)

2.3 C波段信号设计

 Download: 图 6 C波段信号的功率谱密度 Fig. 6 Power spectral density of C band signals

 Download: 图 7 C波段信号的码跟踪误差和平均多径误差包络 Fig. 7 Code tracking errors and running average multipath errors of C band signals

 $\text{PFD}=\frac{{{10}^{0.1\times (\text{EIRP}-{{L}_{\text{atm}}})}}}{4\text{ }\!\!\pi\!\!\text{ }{{d}^{2}}}\underset{\begin{smallmatrix} f=\Delta f\_\text{RA} \\ f=\Delta f\_\text{MLS} \end{smallmatrix}}{\mathop{\int }}\,G\left( f \right)\text{d}f$ (12)

 $\begin{array}{l} {\rm{EIRP}} = [{\left( {{C_s}/{N_0}} \right)_{{\rm{eff}}}} + {L_{Im}} + {N_0}-A + \\ \;\;\;\;\;\;\;\;\;\;\;{L_{{\rm{free}}}} + {\rm{ }}{L_{{\rm{polar}}}} + {I_{{\rm{tro}}}}{]_{{\rm{dB}}}} \end{array}$ (13)

3 结论

1) 在L频段, BM1REC(2)较BOCs(11.5, 1)具有更好的码跟踪精度和抗多径能力, 同时表现出与B3信号更好的兼容性。2)在C频段, BM2RC(4)很好的兼顾C波段信号的带外约束性和导航性能的要求, 不仅呈现出与C波段候选信号相当或更好的性能, 而且具有更低的OOBE, 很大程度上降低了星上滤波处理的复杂度以满足RA波段严格的约束性条件。