Binary-Offset-Carrier modulation techniques with applications in satellite navigation systems

Transcription

1 WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2007; 7: Published online 7 July 2006 in Wiley InterScience ( DOI: /wcm.407 Binary-Offset-Carrier modulation techniques with applications in satellite navigation systems Elena Simona Lohan *,, Abdelmonaem Lakhzouri and Markku Renfors Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, FIN Finland Summary An important aspect in designing the modulation scheme for various satellite systems, such as the modernized GPS and Galileo, is to obtain good spectral properties and suitable spectral shaping. For example, in the future satellite navigation systems, some of the main goals are: low interference with the existing GPS signals, good rootmean-square (RMS) bandwidth, good time resolution (in order to allow the separation between channel paths and to decrease the synchronization errors) etc. Starting from the recently proposed cosine- and sine-boc modulation families for GPS and Galileo systems, we introduce a new, generalized family, denoted here by double-boc (DBOC) modulation. We derive and analyze the properties of the power spectral densities (PSD) and autocorrelation functions (ACF) of the DBOC modulation with various orders, we show its relationship with BPSK, sine- and cosine-boc modulations, and we illustrate via several examples how to choose optimally the parameters of this new modulation family, according to different optimization criteria. The examples are targeting at applications such as the design of suitable modulations for Galileo open service (OS) and public regulated service (PRS) signals, but the authors believe that the DBOC concept might be useful to other satellite-based applications, when the available bandwidth is large enough. Copyright 2006 John Wiley & Sons, Ltd. KEY WORDS: binary-offset-carrier modulation; Galileo; GPS; power spectral densities; root-mean-square bandwidth; satellite systems; spectral separation coefficient 1. Background and Motivation The global navigation satellite systems (GNSS) is experiencing an exponential growth of the consumer segment demand. Many applications emerged after the E- 911/E-112 regulations, such as location based services, search and rescue services, maritime, land or air transportation [1 3]. The two core satellite constellations existing on the sky nowadays are the Navstar global positioning system (GPS) and the global navigation satellite system (GLONASS), provided by the US and Russia, respectively [4]. A future core system (Galileo) is currently under standardization process [5]. Galileo positioning system is to be provided by the European Union and it is meant to be a civil-operated system (GPS and GLONASS systems are military-operated) *Correspondence to: Elena Simona Lohan, Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, FIN Finland. elena-simona.lohan@tut.fi The work was done when Abdelmonaem Lakhzouri was working at Tampere University of Technology. Contract/grant sponsors: National Technology Agency of Finland (Tekes); Academy of Finland. Copyright 2006 John Wiley & Sons, Ltd.

2 768 E. S. LOHAN, A. LAKHZOURI AND M. RENFORS and interoperable with the existing GNSS systems. GPS and GLONASS systems have 24 satellites in operation, each orbiting the earth in about 12 h. The Galileo satellites, 30 in number, will be placed on medium earth orbits at a greater inclination to the equatorial plane than GPS, with the target of achieving better coverage at high latitudes to meet the needs of Northern Europe. The Galileo system is planned to be operational by While the GLONASS systems uses a frequency division multiple access (FDMA) scheme and carrier frequencies different from GPS [4], the GPS and Galileo systems use code division multiple access (CDMA) scheme and some of the GPS and Galileo signals will share the same frequency bands [4 6]. Frequency bands represent the most important resource for GNSS systems, and, more generally, for any satellite-based communication system. For example, the GPS civil C/A-code, the military M-code and P/Y-code, and Galileo open service and public regulated service signals are all clustered around the 1575 MHz band of the L1 frequency. Thus, the spectral separation between various Galileo and GPS signals is an important issue when designing new modulation types for Galileo and modernized GPS systems. The details on Galileo frequency plan and signal structure can be found in References [5 7]. The Galileo system will provide five different services: an open service (OS), providing positioning, navigation and timing services, free of charge, for mass market navigation applications, a safety-of-life service (SoL), compliant to standards in the aeronautical, maritime, and rail domain, with service guarantee included, a commercial service (CS), generating commercial revenue, a public regulated service (PRS) for applications devoted to European and Member States national security, and a search and Rescue support service (SAR) in charge with emergency situations. Since the publication of Betz article [8], the sine- BOC modulation (SinBOC) has gained a particular attention in the context of modernized GPS and Galileo signals, due to its good spectral isolation with the existing GPS signals and to its potentially better time-resolution capabilities compared to traditional binary-phase-shift-keying (BPSK) modulation Historically, the offset-carrier modulation had been proposed earlier: in 1997, by an engineer at Hughes Network Systems for Direct TV (the idea was not published) and at ION-GPS 1997, under the form of Tricode Hexaphase Modulation [8]. [7,10 15]. In June 2004, US and European negotiators have reached an agreement regarding the common baseline structure for OS, namely the SinBOC(1, 1), which uses a MHz square-wave sub-carrier modulated by spreading code bits (or chips) at a chip rate of MHz [5]. The proposals for PRS services included SinBOC(15, 2.5) [7], SinBOC(14, 2) [16], SinBOC(10, 5) [11,16], and, more recently, it includes also an improved variant of BOC modulation, namely cosine-boc modulation (CosBOC). For PRS, CosBOC(15, 2.5) was proposed in References [5,7] and seems to remain the most likely candidate. Nevertheless, the spectral and time-resolution properties of SinBOC and CosBOC modulations are still not fully understood and there is place for further optimization of BOC parameters. Currently, to the authors knowledge, there is no unified analysis of various BOC-modulation classes (e.g., SinBOC and CosBOC) and the theoretical formulas available for the ACF and PSD of these families are typically given for particular cases. For example, theoretical formulas for the PSD are given in References [9,15] for SinBOC signals and in Reference [7] for CosBOC of even modulation orders only. Furthermore, the ACF for SinBOC and CosBOC signals is typically derived based on simulations [9,17,18]. Therefore, the existence of a unitary framework for the analysis of BPSK, SinBOC and CosBOC modulations can bring a significant analytical tool for the study of BOC-modulation properties and for designing future navigation systems. The main goal of our paper is to introduce this unitary framework, under the form of double-boc (DBOC) modulation family, which covers not only the BPSK, SinBOC and CosBOC modulations types, but, also, a wider and more flexible range of split-spectrum modulations, as it will be described in what follows. We also show how the parameters of DBOC-modulation family can be optimized according to different spectral criteria, in order to get better spectral separation between existing GPS signals and potential Galileo signals. The analytical expressions presented here for ACF and PSD of DBOC-modulated signals may be useful not only in the context of analyzing the spectral properties of GNSS signals as shown in this paper and in Reference [19], but also for acquisition studies [13,17,20 22], for The BOC modulation order is defined here as twice the ratio between the sub-carrier frequency and chip rate (see Section 2).

3 BINARY-OFFSET-CARRIER MODULATION TECHNIQUES 769 tracking studies [14,23 25], for capacity studies [15] etc. We remark that, another generalization of BOC modulation classes was proposed in Reference [26], but the approach there is completely different from our approach, it covers only SinBOC and CosBOC modulations, and it provides non-unitary, separate PSD formulas for odd and even modulation orders, as well as for SinBOC and CosBOC cases. In the next section, we first introduce an equivalent form of SinBOC and CosBOC modulation and we extend the concept to a new modulation family, namely the DBOC modulation. We then show how the power spectral density (PSD) and the autocorrelation function (ACF) of this new modulation class can be easily derived in a generic form. These theoretical results are shown for the first time, to the authors knowledge, in an unified form. In Section 3 we define several criteria for analyzing the modulated waveforms in frequency and time domains. Section 4 shows the steps of the design process for choosing properly the parameters of DBOC modulation, according to various optimization criteria. The examples are taken from the signals proposed for future Galileo OS and PRS services. Conclusions are given in Section Double-BOC (DBOC) Modulation and its Relationship with SinBOC and CosBOC Modulation BOC modulation is a square sub-carrier modulation, where a signal is multiplied by a rectangular subcarrier of frequency f sc, which splits the spectrum of the signal into two parts [9,10,15]. Typically, the sine and cosine BOC modulations are defined via two parameters BOC(m, n) [9], related to the reference MHz frequency as follows: m = f sc /1.023 and n = f c /1.023, where f c is the chip rate (both f sc and f c are expressed in MHz here). It should be mentioned that SinBOC modulation generalizes the Manchester scheme [15,27] to more than one zero crossing per spreading symbol or chip (i.e., Manchester coding is equivalent to SinBOC(n, n)). From the point of view of the equivalent baseband signal, the BOC modulation can be defined via a single parameter, denoted in what follows by BOC modulation order N BOC1 : N BOC1 2 m n = 2f sc (1) f c We remark that N BOC1 should be an integer number (therefore m and n should be chosen in such a way that 2m/n is an integer). If N BOC1 and the chip and carrier frequencies are known, we can easily reconstruct the passband signal. The SinBOC-modulated signal x(t) can be seen as the convolution between a SinBOC waveform s SinBOC (t) and a modulating waveform d(t), as follows: x(t) = + n= c k,n s SinBOC (t nt sym kt c ) b n S F k=1 = s SinBOC (t) + S F n= k=1 b n c k,n δ(t nt sym kt c ) s SinBOC (t) d(t) (2) where is the convolution operator, d(t) is the spread data sequence, b n is the nth complex data symbol (in case of a pilot channel, it is equal to 1), T sym is the symbol period, c k,n is the kth chip corresponding to the nth symbol, T c = 1/f c is the chip period, S F is the spreading factor (S F = T sym /T c ), and δ(t) is the Dirac pulse. In order to derive the expression of Equation (2), we used the Dirac property: s(t) = s(t) δ(t), signal s(t). In Equation (2), we assumed to have wideband data, that is, spread via a pseudorandom (PRN) sequence, because the signals used in GPS and Galileo are wideband signals. However, the model holds also for narrowband data. According to its original definition in Reference [9], the SinBOC waveform s SinBOC (t) is defined as s SinBOC (t) = sign ( sin ( NBOC1 πt T c )), 0 t T c (3) where sign( ) is the signum operator and T c = 1/f c is the chip period. Since the above waveform is a sequence of +1 and 1, the authors noticed, via reasoning and graphical representations that Equation (3) can be also re-written as: s SinBOC (t) = p TB1 (t) N BOC1 1 i=0 ( 1) i δ(t it B1 ) (4) where p TB1 ( ) is the rectangular pulse of amplitude 1 and support T B1 = T c /N BOC1. Similarly, the CosBOC-modulated signal is the convolution between the modulating signal and the following waveform [7]: s CosBOC (t) = sign ( cos ( NBOC1 πt T c )), 0 t T c (5)

4 770 E. S. LOHAN, A. LAKHZOURI AND M. RENFORS Fig. 1. Examples of time-domain waveforms for SinBOC, CosBOC and higher-order DBOC-modulated, N BOC1 = 2 (i.e., f sc = f c ). which can be re-written, after careful observation of the s CosBOC ( ) waveforms, as: s CosBOC (t) = p TB1 (t) 1 k=0 N BOC1 1 i=0 ( δ t it B1 kt B 1 2 ( 1) i+k ) (6) By looking at the expression of Equation (6), we see that CosBOC modulation acts as two-stage BOC modulation, in which the signal is first SinBOC modulated, and then, the sub-chip is further split into two parts. The following generalization can be straightforwardly inferred: s DBOC (t) p TB (t) N BOC2 1 k=0 ( 1) i+k δ ( t it B1 kt B ) N BOC1 1 i=0 (7) and a DBOC-modulated wideband signal x(t) can be written as x(t) = s DBOC (t) d(t) (8) where p TB ( ) is a rectangular pulse of amplitude 1 and support T B = T c /(N BOC1 N BOC2 ) and N BOC2 can be seen as the BOC-modulation order of the second stage (N BOC2 should also be integer). Above, d(t) is the spread data sequence, shown in Equation (2). The DBOC modulation is therefore completely defined via Equation (7) according to three parameters (N BOC1,N BOC2,f c ). For various factors N BOC2,we also cover the BPSK, the SinBOC and the CosBOC cases (i.e., all the modulations existing nowadays in GPS and Galileo systems): N BOC1 = 1 and N BOC2 = 1 DBOC BPSK N BOC1 > 1 and N BOC2 = 1 DBOC SinBOC N BOC1 > 1 and N BOC2 = 2 DBOC CosBOC N BOC1 > 1 and N BOC2 > 2 Higher order DBOC (new concept) (9) Examples of the time-domain waveforms for SinBOC (N BOC2 = 1), CosBOC (N BOC2 = 2) and higher-order DBOC (N BOC2 = 4) are shown in Figure 1. By further analyzing the properties of DBOC modulation, we also noticed that for N BOC2 odd, the DBOC modulation is equivalent with SinBOC modulation of order N BOC1 N BOC2. Equation (7) allows an unified analysis of all BOC-modulation families Power Spectral Densities of DBOC Modulation Waveforms The expression of Equation (7) allows us to compute the PSD P DBOC (f ) of DBOC-modulation family in an easy and generic way: P DBOC (f ) S DBOC (f ) 2 (10) where S DBOC (f ) is the Fourier transform of s DBOC (t), and therefore, from Equation (7) it is equal to S DBOC (f ) = P TB (f ) N BOC2 1 k=0 N BOC1 1 i=0 ( 1) i+k e j2πfit B 1 e j2πfkt B (11)

5 BINARY-OFFSET-CARRIER MODULATION TECHNIQUES 771 where P TB (f ) is the Fourier transform of a rectangular pulse, that is, P TB (f ) = T B sinc (πft B ) e jπft B, with sinc(x) sin(x)/x. The right-hand expression of Equation (11) contains two separable sums of geometric series, hence, after several computations we get: ( 1 ( 1) N BOC2 e j2πft ) B 1 S DBOC (f ) = T B sinc (πft B ) 1 + e j2πft B ( 1 ( 1) N BOC1 e j2πft ) c 1 + e j2πft e jπft B (12) B 1 It follows from Equations (10) and (12) that ( P DBOC (f ) = 1 ( 1) N T BOC2 e j2πft ) B 1 Bsinc (πft B ) 1 + e j2πft B ( 1 ( 1) N BOC1 e j2πft ) c e j2πft (13) B 1 Therefore, developing Equation (13), we get: 1. If N BOC1 = odd and N BOC2 = odd : ( ( ) ( )) 2 sin πftb cos πftc P DBOC (f ) = πf cos ( ) (14) πft B 2. If N BOC1 = odd and N BOC2 = even : ( ( ) ( ) ( )) 2 sin πftb sin πftb1 cos πftc P DBOC (f ) = πf cos ( ) ( ) (15) πft B cos πftb1 3. If N BOC1 = even and N BOC2 = odd : An alternative way of defining PSD (instead of P DBOC (f )) is to normalize it with the chip period (or, equivalently, the signal power over infinite bandwidth) similar with [7,9,10]: P DBOC,norm (f ) = P DBOC(f ) (18) T c Using the normalized expression of Equation (18), we remark that, for N BOC2 = 1, we get exactly the expressions reported in References [7,9] for SinBOC modulation. The normalized PSDs P DBOC,norm (f ) for several DBOC modulated signals are shown in Figure 2 for a chip frequency f c = MHz. The SinBOC in this figure corresponds to the classical case BOC(1, 1) [7]. The BPSK case can be also seen as an extreme case of DBOC family (i.e., N BOC1 = 1 and N BOC2 = 1). The PSDs in Figure 2 are shown in db. An alternative way, typically found in GNSS papers [9,10] is to define the PSDs in dbw/hz, that is, P DBOC,norm [dbw/hz] 10 log 10 P DBOC,norm 60 db. We remark that, when N BOC2 order increases, the signal main lobes move further towards the outer sides of the spectrum. This is also in accordance with the observations in Reference [7], where it was noticed that the CosBOC modulation had the advantage that it concentrated more power on outer sides of spectrum compared to SinBOC modulation of the same order, and therefore, the interference with GPS signals could be reduced. Based on Figure 2, we also see that by increasing N BOC2 order, we may further reduce the interference with GPS signals (at the expense of a higher bandwidth). Based on the PSD of DBOC family (shown in Equation (13) and detailed in Equations (14 17)), we can also derive the PSD of any DBOC-modulated signal ( ( ) ( )) 2 sin πftb sin πftc P DBOC (f ) = πf cos ( ) (16) πft B 4. If N BOC1 = even and N BOC2 = even : ( ( ) ( ) ( )) 2 sin πftb sin πftb1 sin πftc P DBOC (f ) = πf cos ( ) ( ) (17) πft B cos πftb1 where T B = T c N BOC1 N BOC2 and T B1 = T c N BOC1. N 1 The following relationship was used: x i = 1 xn 1 x, with i=0 x = e j2πft B and, respectively, x = e j2πft B 1. Fig. 2. Examples of normalized PSDs of DBOC-modulated waveforms (BPSK, SinBOC, and CosBOC are particular cases of the generic DBOC-modulation family).

6 772 E. S. LOHAN, A. LAKHZOURI AND M. RENFORS x(t) (x(t) is shown in Equation (8)): S x (f ) = D(f )S DBOC (f ) (19) where S x (f ) is the PSD of x(t) and D(f ) is the PSD of d(t). Furthermore, under the assumption of independent code and data symbols and ideal code sequences (i.e., E(c k,n c i,m ) = δ(n m)δ(k i), where E( )isthe expectation operator), we obtain that D(f ) = 1 and the DBOC-modulated PRN signal has the same PSD as the DBOC waveform Autocorrelation Functions of DBOC-Modulation Waveforms Based on Equation (7), the ACF R DBOC ( ) of DBOC modulation waveforms can be obtained as R DBOC (t) s DBOC (t) s DBOC (t) = TB (t) N BOC2 1 k=0 N BOC2 1 j=0 N BOC1 1 i=0 N BOC1 1 l=0 ( 1) k+j+i+l δ(t it B1 + lt B1 kt B + jt B ) (20) where TB (t) = p TB p TB is the triangular pulse of support 2T B, shown in Figure 3. Furthermore, the ACF of any DBOC-modulated signal x(t) is ( ) ( ) R x (t) E x(t) x(t) =E d(t) d(t) R DBOC (t) (21) Under the assumption of ideal PRN code properties, T B Λ (t) T B 1 T B Fig. 3. Illustration of a triangular pulse TB (t) of support 2T B. E(d(t) d(t)) = δ(t), and the ACF of the DBOCmodulated code takes the shape of the ACF of the DBOC waveform. Equations (13) and (20) present for the first time (to the authors knowledge) a unified formula for the PSD and the ACF of BOC-modulation waveforms. They have the advantage of a simple and straightforward implementation (e.g., in Matlab), which allows a fast analysis of DBOC-modulated signal. We note that ACF has been derived so far only for particular cases (e.g., SinBOC(1,1) and CosBOC(15,2.5) as the inverse Fourier transform of PSD [7], and the expressions given in Reference [7]. The ACFs of several DBOC modulated signals are shown in Figure 4 for OS signal candidates (left plot) and for PRS signal candidates (right plot). The ACF of a BPSK signal is also shown for reference purpose. We notice that, typically, the higher the N BOC2 is, the smaller width of the main lobe we have (and hence, better resolution during delay tracking). However, for N BOC2 high enough (as in the right plot of Figure 4), t Fig. 4. Examples of normalized ACFs of DBOC-modulated waveforms. Left: OS candidate signals; Right: PRS candidate signals.

7 BINARY-OFFSET-CARRIER MODULATION TECHNIQUES 773 the ACFs of SinBOC and CosBOC waveforms tend to become quite similar (result which was also reported in Reference [7]). 3. Time and Frequency Properties of DBOC Family When dealing with navigation systems, the most illustrative measure of performance is the distance error or, equivalently, the delay error in the estimation of the line of sight (LOS) path [15]. This is different from the case of communication systems, where bit error rates (BER) are the most comprehensive measures of performance. BER has no significant meaning from the point of view of the navigation systems, since it cannot be related straightforwardly to the LOS acquisition and tracking capabilities of the navigation system. Another aspect of interest in navigation systems is the interference with other systems in the same band. This is particularly useful for studies of interference between GPS and Galileo signals transmitted in L1 band [7]. Therefore, several performance measures related to the acquisition, tracking, and interference properties of the signals (and, therefore, to their spectral properties and time-resolution properties) have been derived in the context of navigation systems. These performance measures are comprehensively described by the following factors [9,10,28 30]: 1. Time- and distance-resolution factors: It defines the tracking resolution of a signal (i.e., the ability of separation between multiple paths). We define the time-resolution factor ( t) res as half of the width of the main lobe of the absolute value of ACF. For example, BPSK modulation has a resolution of ( t) res = 1 chip, SinBOC(1, 1) modulation has ( t) res = 0.34 chips, CosBOC(1, 1) modulation has ( t) res = 0.20 chips, and DBOC modulation with N BOC1 = 2, N BOC2 = 4 has ( t) res = 0.08 chips. We remark that, for a constant (N BOC1,N BOC2 ) pair we get a constant resolution in chips, independent of the chip rate. However, the distance error in meters (distance-resolution factor) ( d) res = c( t) res /f c will depend on the chip rate (e.g., 0.34 chips delay error for f c = MHz translates to about 99.7 m distance error, while for f c = MHz, it translates to about 49.8m distance error). Above, c = m/s is the speed of light. Typically, paths spaced at more than the time-resolution factor can be separated by the receiver, therefore, a small time-resolution factor is associated with good resolution properties. 2. Spectral Separation Coefficient (SSC) κ SSC :Itisa measure of the amount of interference between two signals (the lower the SSC is, the better spectral separation between signals we have). SSC between two signals within a complex finite bandwidth B T is defined similar to [9], as κ SSC = BT /2 B T /2 ( BT /2 where P υ (f )=P υ (f )/ P 1 (f ) P 2 (f )df (22) ) B T /2 P υ(f )df, υ =1, 2 is the PSD of the υth signal, normalized to the unit power over the bandwidth of interest. Typically, B T is the receiver input bandwidth [9] and P υ ( ), υ= 1, 2 is given by Equation (13) or (18), because all Galileo and GPS signals are particular cases of DBOC-modulated signals. Here, we are mostly interested in the SSC between DBOC-modulated signals and the existing GPS signals, such as C/A code (i.e., BPSKmodulated signal with f c = MHz [28]), military M-code (i.e., SinBOC(10,5) with chip frequency f c = MHz [10]) and P(Y) code (i.e., BPSK-modulated signal with f c = MHz [28]). Moreover, the self-ssc factor κ SSC,itself of a DBOC-modulated waveform may be also of interest in choosing the proper DBOC parameters, since a low self-ssc would ensure a low interference with the other Galileo satellites in the same frequency band. An example of the SSC coefficients between DBOC-modulated signals and the existing GPS signals is shown in Figure 5. The self interference SSC Fig. 5. Spectral Separation Coefficient as a function of N BOC2 for Galileo OS, f c = MHz, N BOC1 = 2.

8 774 E. S. LOHAN, A. LAKHZOURI AND M. RENFORS factor is also shown in the plot. We used some of the parameters proposed for Galileo OS [7], namely f c = MHz and N BOC1 = 2. The curves are shown as a function of N BOC2. For a fair comparison, we considered the bandwidth B T = 60 MHz, such that at least 80% of the modulated-signal power is contained within this bandwidth for modulation orders up to N BOC2 = 12 (when N BOC2 increases, the modulated-signal bandwidth increases). We remark from Figure 5 that the lowest interference with M-code in the B T = 60 MHz bandwidth is achieved for N BOC2 = 5 (when N BOC1 = 2 and f c = MHz). We also remark that neither SinBOC, nor CosBOC (i.e., first two points of the curves in Figure 5) are optimal choices from the point of view of SSC coefficients (if the available BW is 60 MHz) and that there is no N BOC2 factor which gives simultaneously the minimum of all the four curves. In Section 4, we will search for (N BOC1,N BOC2 ) pairs which minimize the sum of all these 4 spectral separation coefficients. One of the optimization criteria will therefore be the global SSC κ SSC,global : κ SSC,global [dbw/hz] = κ SSC,C/A code [dbw/hz] + κ SSC,M code [dbw/hz] + κ SSC,P(Y) code [dbw/hz] + κ SSC,itself [dbw/hz] (23) 3. Root mean square (RMS) bandwidth: β RMS is defined within a bandwidth B T by Reference [9]: BT /2 β RMS = f 2 P υ (f )df (24) B T /2 The higher the RMS BW is, the smaller the variance of the delay tracking process is [31]. On the other hand, if the RMS bandwidth increases, it becomes more difficult to resolve the ambiguities between sub-carrier cycles [9]. From the simulation results which will be shown in detail in Section 4, we notice that maximizing the RMS BW is equivalent with minimizing the time-resolution factor ( t) res. We also notice that BPSK modulation has the minimum RMS BW among all DBOC signals. Fig. 6. Power containment for representative DBOC modulated signals. 4. Maximum value of the spectrum (MVS): m MVS is defined as m MVS = max f B T P υ (f ) (25) The smaller the MVS is, the better the corresponding modulation is, because it enables the modulated signals to be transmitted at a higher power with less disturbance of the noise floor [9]. 5. Power containment factor: ε is the percentage of the signal power contained within a certain bandwidth and it is directly related to the demodulation and tracking properties of the signal (the smaller the bandwidth needed for a certain power containment, the better the bandwidth efficiency that can be achieved) [23]. For example, Figure 6 shows the power containment factor versus the bandwidth for several DBOC-modulated signals. Figure 7 shows the minimum required bandwidth as a function of the power containment ε for various DBOC signals. For example, we notice that all the considered DBOC signals at f c = MHz (left plot of Figure 7) have 90% of their power contained in less than MHz and 80% of their power contained in less than 10.2 MHz. On the other hand, DBOC signal at f c = MHz (PRS candidates) cannot achieve more than power containment with realistic bandwidths (i.e., up to 60 MHz).

9 BINARY-OFFSET-CARRIER MODULATION TECHNIQUES 775 Fig. 7. Minimum required bandwidth as a function of the power-containment percentage ɛ for representative DBOC modulated signals. Left: f c = MHz (OS candidates); right: f c = MHz (PRS candidates). 4. Designing the Optimal Parameters for DBOC Modulation This section addresses the problem of designing the DBOC-modulation orders (N BOC1,N BOC2 ) in an optimal way, under the constraint of having at least ε percents of signal power within the receiver bandwidth B T. The optimization criteria are those presented in Section 2. As it will be seen in this Section, it is usually not possible to optimize simultaneously all the considered time-spectral factors, and one has to make a tradeoff between different criteria. Here, the power containment factor ε, the bandwidth B T and the chip frequency f c are fixed design parameters. In what follows we present the results for the two chip frequencies selected as candidates for OS and PRS, respectively. Figure 1 shows the optimal DBOC-modulation parameters for a chip frequency of f c = MHz, which is in accordance with the main candidate chip frequency for OS [7]. The typical BW for OS is 4, 8, or 24 MHz [12,28]. However, higher bandwidths are also included in the Table I in order to cover also the hypothetical situation when PRS services would use a chip rate of f c = MHz. For the power containment factor there are no standardized values, but typically the higher ε is, the better the reception quality is. We considered here and. We note that the values shown in Tables I and II are the values for DBOC-modulation parameters (N BOC1, N BOC2 ) and not the (m, n) parameters of BOC(m, n)- modulation. The parameter N BOC1 is related to (m, n) parameters via the chip rate, according to Equation (1), while N BOC2 is a new parameter, characterizing the second stage of DBOC modulation (see Equation (9)). We notice from Table I that, if we have a low BW of B T = 4 MHz and we want that at least 90% of the signal power is contained within this BW, the only modulation which complies with this constraint is the BPSK modulation (N BOC1 = 1, N BOC2 = 1). This is the reason why BPSK appears as optimal modulation in certain cases. The modulation proposed so far for OS Galileo, namely SinBOC(1,1) modulation appears to be optimum from the point of view of all the three spectral criteria for B T = 8 MHz and. However, this combination is the optimum because it is the only DBOC modulation, besides BPSK, which satisfies the power containment criterion of 90% signal power within 8 MHz bandwidth. If we relax either the bandwidth constraint or the power containment factor, we get different optimal values than those currently used in the standard proposals. For example, Sin- BOC(3,1) modulation (i.e., N BOC1 = 6, N BOC2 = 1) satisfies 5 out of 7 considered optimization criteria for B T = 8 MHz and, while CosBOC(3.5,1) modulation (i.e., N BOC1 = 7, N BOC2 = 2) satisfies 5 out of 7 considered optimization criteria for B T = 24 MHz and (these results are valid only for f c = MHz; if we change the chip rate, the optimal parameters will change accordingly, as it will be seen, e.g., in Table II). Table II shows the optimal DBOC-modulation parameters for a chip frequency of f c = MHz, which is in accordance with the candidate chip frequency for PRS [7]. The typical BW for PRS is 40 MHz

10 776 E. S. LOHAN, A. LAKHZOURI AND M. RENFORS Table I. Optimal DBOC-modulation pairs (N BOC1, N BOC2 )atf c = MHz for various bandwidths B T, various power containment factors ε, and several optimization criteria. Optimization κ SSC,global κ SSC,C/A code κ SSC,M code κ SSC,P(Y) code κ SSC,itself m MVS β RMS / criterion ( d) res [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [MHz]/ [m] B T = 4 MHz (3.1) (3.1) (1.1) (3.1) (3.1) (3.1) (3.1) B T = 8 MHz (6.1) (6.1) (1.1) (6.1) (2.2) (6.1) (6.1) B T = 24 MHz (18.2) (18.2) (1.1) (18.2) (3.6) (2.10) (22.1) B T = 40 MHz (36.2) (36.2) (36.2) (20.2) (4.8) (3.10) (37.1) B T = 60 MHz (40.2) (56.2) (41.2) (40.2) (3.6) (3.18) (57.1) and (57.2) B T = 4 MHz (1.1) (1.1) (1.1) (1.1) (1.1) (1.1) (1.1) B T = 8 MHz (2.1) (2.1) (1.1) (2.1) (2.1) (2.1) (2.1) B T = 24 MHz (7.2) (7.2) (1.1) (7.2) (3.2) (7.2) (7.2) B T = 40 MHz (10.2) (12.2) (1.1) (12.2) (3.4) (2.6) (12.2) B T = 60 MHz (19.2) (19.2) (1.1) (19.2) (3.6) (3.6) (19.1) and (19.2) [28]. We remark from Table II that there exists no DBOC modulation (BPSK included) which has at least 90% of the signal power within B T = 4 MHz at a chip rate of f c = MHz (and there is only BPSK which has at least 80% of the signal power within B T = 4 MHz and at least 90% of the signal power within B T = 8 MHz for this chip rate). Therefore, high chip rates are not suitable for OS. Table II. Optimal DBOC-modulation pairs (N BOC1, N BOC2 )atf c = = MHz for various bandwidths B T, various power containment factors ε, and several optimization criteria. Optimization κ SSC,global κ SSC,C/A code κ SSC,M code κ SSC,P(Y) code κ SSC,itself m MVS β RMS / criterion ( d) res [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [MHz]/ [m] B T = 4 MHz (1.1) (1.1) (1.1) (1.1) (1.1) (1.1) (1.1) B T = 8 MHz (2.1) (2.1) (1.1) (2.1) (2.1) (2.1) (2.1) B T = 24 MHz (8.1) (8.1) (1.1) (8.1) (3.2) (8.1) (8.1) B T = 40 MHz (10.2) (10.2) (14.1) (8.2) (3.4) (2.6) (14.1) B T = 60 MHz (16.2) (20.2) (17.2) (16.2) (3.6) (2.10) (22.1) B T = 80 MHz (29.2) (29.2) (29.2) (24.2) (4.6) (3.8) (30.1) B T = 4 MHz B T = 8 MHz (1.1) (1.1) (1.1) (1.1) (1.1) (1.1) (1.1) B T = 24 MHz (3.1) (2.1) (1.1) (3.1) (3.1) (3.1) (3.1) B T = 40 MHz (3.2) (3.2) (1.1) (5.1) (2.2) (3.2) (5.1) B T = 60 MHz (7.2) (7.2) (1.1) (7.2) (3.2) (7.2) (7.2) B T = 80 MHz (10.2) (10.2) (1.1) (8.2) (2.4) (10.2) (10.2)

11 BINARY-OFFSET-CARRIER MODULATION TECHNIQUES 777 Table III. Comparison of the parameters for main current PRS proposal CosBOC(15, 2.5) (i.e., (12,2) pair at f c = MHz) with an alternative CosBOC(18, 1) signal (i.e., (36,2) pair at f c = MHz), at bandwidth B T = 40 MHz κ SSC,global κ SSC,C/A code κ SSC,M code κ SSC,P(Y) code κ SSC,itself m MVS β RMS ( d) res [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [dbw/hz] [MHz] [m] Current: (12,2) at MHz Possible: alternative (36,2) at MHz We also notice from Table II that the combination proposed so far for Galileo PRS (namely Cos- BOC(15,2.5) [7]), which corresponds to (N BOC1 = 12, N BOC2 = 2, f c = MHz), does not satisfy any optimality criteria for any of the considered bandwidth-power-containment constraints. If we selected a smaller chip rate, for example, MHz, we could find a DBOC modulation for PRS services which is better than the currently proposed modulation, as shown in the Table III. It follows from Table III that by decreasing the chip rate and by choosing some proper DBOC modulation parameters (according to B T and ε) we might increase the performance of the PRS Galileo signals in terms of better separation with current GPS signals and better time resolution. For example, the combination N BOC1 = 36, N BOC2 = 2, and f c = MHz (i.e., CosBOC(18, 1)) shown in the last row of Table III would provide, for a bandwidth B T = 40 MHz, around 11 dbw/hz better global spectral separation coefficient than CosBOC(15,2.5), 7.85 dbw/hz better separation with M signal, 2.9 MHz better RMS BW, and 0.81 m better time resolution, while the other factors are quite close to those of the current proposal. The bandwidth requirements are also slightly better for CosBOC(18, 1) than for CosBOC(15, 2.5) modulations when the available bandwidth is at least B T = 40 MHz, as seen in Figure 8 (and only slightly worse at B T = 24 MHz). Moreover, this combination with f c = MHz would also ensure a better compatibility with Galileo OS and GPS. 5. Conclusions This paper introduced a new BOC-modulation family, the DBOC-modulation class, which is a generalization of the modulation types currently proposed for Galileo and modernized GPS signals. This new modulation family provides a unified framework for analyzing the properties of GPS and Galileo signals, and might be a starting point for developing new modulation classes for other broadband satellite-based systems. We showed how this new concept may be used for designing the best modulation for Galileo OS and PRS signals, according to the available bandwidth, power containment factor, and chip rate. We also showed that, from the point of view of the separation with existing GPS signals and from the point of view of the delay estimation accuracy, better solutions may be found for OS and PRS Galileo signals than those currently proposed in the literature (e.g., SinBOC(3, 1) for OS signals and CosBOC(18, 1) for PRS signals. Acknowlegement Fig. 8. Power containment percentage versus bandwidth for the compared PRS signals. This work was carried out in the project Advanced Techniques for Mobile Positioning (MOT) funded by the National Technology Agency of Finland (Tekes). This work was also partly supported by the Academy of Finland, which is gratefully acknowledged.

12 778 E. S. LOHAN, A. LAKHZOURI AND M. RENFORS References 1. Reed JH, Krizman KJ, Woerner BD, Rappaport TS. An overview of the challenges and progress in meeting the E-911 requirement for location service. IEEE Communications Magazine 1998; 36: Heinrichs G, Bischoff R, Hesse T. Receiver architecture synergies between future GPS/Galileo and UMTS/IMT In Proceedings of IEEE 56th Vehicular Technology Conference (VTC) Fall. 2002; Quinlan M, Burden G, Rollet S, Gaudenzi RD, Harding S, Validation of novel navigation signal structures for future GNSS systems. In Proceedings of IEEE Position Location and Navigation Symposium (PLANS). April 2004; Daly P. Navstar GPS and GLONASS: global satellite navigation systems. IEEE Electronics and Communication Engineering Journal 1993; 5: GJU. Galileo standardisation document for 3GPP. Galileo Joint Undertaking (GJU) webpages, page.cfm?voce=s2&idvoce=64&plugin=1 (active Oct 2005), May Hein G, Godet J, Issler J, Martin J, Pratt T, Lucas R. 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Design and performance of code tracking for the GPSMcode signal. In CDROM Proceedings of ION Meeting, (Anaheim, CA), September Authors Biographies Elena Simona Lohan received her M.Sc. degree in electrical engineering from the Politehnica University of Bucharest, Romania, in 1997, the D.E.A. degree in Econometrics, at Ecole Polytechnique, Paris, France, in 1998, and the Doctor of Technology degree in telecommunications from Tampere University of Technology, Tampere, Finland, in She is currently a senior researcher in the Institute of Communications Engineering, Tampere University of Technology. Her research interests include GPS/Galileo positioning techniques, CDMA signal processing, and wireless channel modeling and estimation. Abdelmonaem Lakhzouri was born in Tunis, Tunisia, on January 01, He received his M.Sc degree in signal processing from the Ecole Supérieure des Communications de Tunis, Tunisia in 1999, the Diplôme d Etudes Approfondies (DEA) in telecommunications at Ecole Nationale d ingénieurs de Tunis, Tunisia in 2001, and his Doctor of Technology in Telecommunications from Tampere University of Technology, Tampere, Finland, in

13 BINARY-OFFSET-CARRIER MODULATION TECHNIQUES From 2000 till March 2006 he was a researcher at the Institute of Communication Engineering, Tampere University of Technology Finland. Now, he is with u-nav Microelectronics, as a Satellite Navigation specialist. Markku Renfors was born in Suoniemi, Finland, on January 21, He received his Diploma Engineer, Licentiate of Technology, and Doctor of Technology degrees from the Tampere University of Technology (TUT), Tampere, Finland, in 1978, 1981, and 1982, respectively. From 1976 to 1988, he held various research and teaching positions at TUT. From 1988 to 1991, he was a design manager at the Nokia Research Center and Nokia Consumer Electronics, Tampere, Finland, where he focused on video signal processing. Since 1992, he has been a professor of telecommunications at TUT. His main research area is signal processing algorithms for flexible radio receivers and transmitters.