Mathematical Problems in Engineering

Volume 2015, Article ID 165097, 8 pages

http://dx.doi.org/10.1155/2015/165097

## A Flexible Modulation Scheme Design for C-Band GNSS Signals

College of Information & Communication Engineering, Harbin Engineering University, Harbin 150001, China

Received 9 February 2015; Revised 10 June 2015; Accepted 10 June 2015

Academic Editor: Emiliano Mucchi

Copyright © 2015 Rui Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Due to the spectrum congestion of current navigation signals in L-band, C-band has been taken into consideration as a candidate frequency band for global navigation satellite system (GNSS). As is known, modulation scheme is the core part of signal structure, and how to design a modulation waveform that could make full use of narrow bandwidth 20 MHz and satisfy the constraint condition of frequency compatibility in C-band is the main research content of this paper. In view of transmission characteristics and constraint condition of compatibility in C-band, multi-*h* continuous phase modulation (CPM) is proposed as a candidate modulation scheme. Then the classical channel capacity estimation and a comprehensive evaluation criterion for GNSS modulation signals are employed to assess the proposed scheme in the aspects of the capacity over additive white Gaussian noise (AWGN), tracking accuracy, multipath mitigation, antijamming, and so on. Simulation results reveal that, through optimizing the number and size of modulation indexes, the flexible scheme could offer better performance in terms of code tracking, multipath mitigation, and antijamming compared with other candidates such as MSK and GMSK while maintaining high band efficiency and moderate implementation complexity of receiver. Moreover, this paper also provides a reference for next generation modulation signals in C-band.

#### 1. Introduction

With the rapid development of global navigation satellite systems (GNSS), namely, GPS, GLONASS, Galileo, and Compass, together with various regional navigation satellite systems and space-based augmentation systems, the number of navigation signals in space is anticipated to be over 400 by 2030 [1], which will further aggravate an already crowded radio spectrum in L-band (11641610 MHz). Consequently, improving the signal spectral efficiency [2] and providing new bands for radio navigation satellite service (RNSS) are the main means to solve the above problem, and the frequency band between 5010 MHz and 5030 MHz offering a bandwidth of 20 MHz has been already allocated as C-band portion by International Telecommunication Union (ITU) for RNSS applications. Unfortunately, the use of C-band navigation signals offers both advantages and drawbacks [3]. However, technological progress in electronics and spacecraft might balance some of the disadvantages, and C-band has caused great interests as a candidate for the future GNSS services [4].

Although the performance of signals in C-band is difficult to surpass L-band [5], signal combination of L- and C-band could improve positioning accuracy and timing performance and promote the comprehensive performance of RNSS [6, 7]. Predictably, the multiband combined navigation and compatibility among different navigation systems will become research hotspots in the future. As is known to all, modulation scheme whose quality completely determines the upper bound of GNSS performance is the core part of signal structure, and power spectrum envelopes decided by modulation waveforms could play a dominant role in tracking accuracy, multipath mitigation, antijamming, and so forth. At present, how to design a modulation scheme that can make full use of bandwidth 20 MHz and satisfy the constraint condition of frequency compatibility is the main challenge subject of C-band signal system.

The compatibility between newly introduced signals in C-band and the existing signals in adjacent frequency bands such as radio astronomy (RA) band and microwave landing system (MLS) must be carefully analyzed before any new band for satellite navigation is put into use [8]. Therefore, band-limited signals or signals with continuous phase should be the first choice for C-band signal system. In addition, the signals are easily distorted due to the nonlinear effect of the high power amplifier (HPA) [9], and a constant envelope modulation reveals the excellent characteristic that HPA can run in saturation or close to saturation, which could increase the total efficiency of amplification. By the above analysis, a modulation scheme with constant envelope and continuous phase will be a top priority for C-band signal.

Binary offset carrier (BOC) modulation and BOC-derived modulations such as multiplexed BOC (MBOC) and alternative BOC (AltBOC) have been already widely accepted by next generation GNSS. Nevertheless, the BOC modulated signals have larger spectral side lobes and are more prone to produce larger interferences with signals of other coexisting navigation systems [10]. Reference [11] has pointed out that minimum shift keying (MSK) can offer better ranging precision within a certain bandwidth and introduce less interference to other signals. Subsequently, MSK, MSK-BOC, and Gaussian-filtered MSK (GMSK) have been proposed as potential candidates for C-band signals by Galileo system. However, the tracking bias of MSK-BOC modulated signals has not been solved effectively so far [12], and hardware implementation of GMSK is complicated and its tracking performance is hard to optimize. Moreover, MSK and GMSK are the special cases in continuous phase modulation (CPM), but they do not possess the optimal performance in CPM family.

Based on the above problems, a special subclass of CPM, that is, multi- CPM, is presented as a modulation waveform for C-band signal due to its many excellent characteristics, such as flexible parameter adjusting, high power and spectrum efficiency, a large number of alternative waveforms, and being easily compatible with existing signals. The rest of this paper is organized as follows. Section 2 describes mathematical model and an improved calculation of power spectra for multi- CPM signals. The capacity of multi- CPM signals is derived in Section 3. Section 4 provides performance evaluation criterion for GNSS modulation. Simulation results are discussed in Section 5. Finally, we conclude the paper in Section 6.

#### 2. Multi- CPM Signal

##### 2.1. Mathematical Model

The complex-baseband multi- CPM signal is given by where is the information-carrying phase, denoted as where is the symbol duration, are the information symbols in the -ary alphabet , is the phase pulse, and is a set of modulation index where is constant in symbol duration . In this paper, the underlined subscript notation in (2) is defined as modulo-; that is, . We always assume because power spectra of CPM will behave like BOC signals with spectrum splitting when modulation index is more than one, which goes against compatibility with other signals in relatively narrow bandwidth.

The phase pulse and the frequency pulse are related by The frequency pulse is supported over the time interval and is subject to the constraints When the signal is called full-response formats and when the signal is called partial-response formats. Some general pulse shapes are length- rectangular (REC), length- raised-cosine (RC), and Gaussian.

In light of the constraints on and , (2) can be rewritten as where the term is a function of the symbols being modulated by the phase pulse. For ( integers), the phase state takes on distinct values. The signal is described by a trellis containing states, with branches at each state. Each branch is defined by the ( + 1)-tuple .

##### 2.2. Easy Calculation of Power Spectra

Reference [13] provides an easy method which allows a fast calculation of the spectra of -ary multi- CPM signals under the general hypothesis of (1) -ary symbols ( a power of 2); arbitrary pulse shaping; partial response signaling; an arbitrary set of modulation indexes. The procedure of the easy method is as follows.

Let be the complex envelope of the transmitted signal . To find the baseband equivalent of the power spectrum of the signal , we use the so-called “autocorrelation-based” approach.

The autocorrelation function of is defined as As we know, and = superbaud period and the independence of the data symbols; we are able to put in the form; that is, where

The process is cyclostationary in the wide sense with period and average autocorrelation is expressed as

It is seen that when or . The number of factors in (7) can be reduced and (9) is rewritten as where , , maximum integer ≤, and minimum integer ≥.

The power spectral density (PSD) can be derived from by Fourier transform (FT); that is,where , , and denotes real part of complex.

In this paper, we always assume the spread spectrum code rate and in all schemes are equal to 5 1.023 MHz and 2, respectively. The PSD of CPM signals with different parameters are shown in Figure 1. As seen in Figure 1, the CPM signals using RC pulse can effectively decrease PSD amplitude of side lobes and concentrate more energy into main lobe compared to REC pulse when the modulation indexes are the same. Moreover, it is noteworthy that energy in main lobe tends to be more centralized and decay rate of side lobes is almost the same when the average of all elements in set is getting larger. In terms of main lobe energy, the CPM signals with RC or REC are more concentrated than GMSK. Also, power fluctuation of side lobes in GMSK decays faster than CPM signals with REC, inferior to CPM adopting RC pulse.