ANALYSIS OF THE IONOSPHERIC INFLUENCE ON SIGNAL PROPAGATION AND TRACKING OF BINARY OFFSET CARRIER (BOC) SIGNALS FOR GALILEO AND GPS

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1 ANALYSIS OF THE IONOSPHERIC INFLUENCE ON SIGNAL PROPAGATION AND TRACKING OF BINARY OFFSET CARRIER (BOC) SIGNALS FOR GALILEO AND GPS Thomas Pany (1), Bernd Eissfeller (2), Jón Winkel (3) (1) University FAF Munih, Institute of Geodesy and Navigation, Neubiberg, Germany. (2) As (1) above, but (3) IfEN GmbH, Alte Gruber Str. 6, 85588, Poing, Germany. INTRODUCTION The next generation European satellite based navigation system Galileo will make use of binary offset arrier (BOC) signals for preise pseudo range determination in addition to binary phase shift keying signals urrently used by the GPS [3]. The main harateristi of this innovative BOC signal struture for satellite navigation systems is that the signal power is not onentrated around the arrier frequeny. The main power is loated in two main lobes to the left and right of the arrier frequeny, whose separation is given by twie the subarrier frequeny. While this feature has many advantages, the dispersive harater of the ionosphere may distort the signal signifiantly if the main lobes separation beomes large. We investigate the influene of a homogenous ionosphere, haraterized only by the total eletron ontent (TEC) value, on the deformation of the navigation signal autoorrelation funtion and on its delay (resp. advane). We will show that the influene is almost insignifiant (despite the delay) if realisti values for the TEC are hosen. Only the standard formula for the ionospheri arrier phase advane shall be modified if the arrier phase of a BOC signal is traked. THE BOC SIGNAL BOC modulations are haraterised by two parameters: subarrier frequeny and spreading ode rate, denoted by BOC(f s, f ), where f s is the subarrier frequeny and the ode rate is f. Both values are in MHz. Aording to the Galileo Signal Task Fore, the European system might use a BOC(14,2) signal at E2-L1-E1 ( MHz) whih has its main lobes of the power spetral density at E2 and E1 to have a spetral separation from the GPS signals at L1 ( MHz) [3]. We investigate only the BOC(14,2) signal, beause this signal has the highest subarrier frequeny and onsequently the deformation of the autoorrelation funtion and the orretion to the standard ionospheri delay formula are highest. Our results an be easily generalized to all other BOC signals. The E2-L1-E1 BOC(14,2) signal s(t) whih might be emitted from the Galileo satellites is part of the Publi Regulated Servie and is desribed as s( t) = k p( tf k) with p( φ) = ret( φ)sign(sin(2πφf s / f ))os(2πφf / f ) k =. (1) For the arrier frequeny f we use MHz, for the ode rate f we use MHz and for the subarrier frequeny f s MHz [3]. The time is denoted as t. The ode sequene is k and it should be noted that its atual values are of no importane for this investigation as well as a possible Doppler shift due to the motion of the satellite and/or the reeiver. Also the amplitude of the signal, resp. its signal to noise ratio has no influene on the results. The funtion ret represents a retangular pulse of unit amplitude and duration. Bandpass filtering of the signal within the satellite to keep the power spetral density within the alloated frequeny band is not inluded in (1). However, it will be inluded in the navigation reeiver frontend (f. Fig. 1). The signal s(t) is a onvolution of the ode sequene k with the waveform of a single hip p(φ). Therefore it is suffiient to onsider the ionospheri influene on p(φ) only. This simplifies the alulations sine p(φ) is different from 0 only if 0<φ<1. IONOSPHERIC ADVANCE/DELAY AND DISPERSION The influene of the ionosphere on the signal will be analyzed via a disrete Fourier transform. Therefore we write

2 N /2 k 1 pt ( f) = exp(2 π it f) p ( f) with f = and t = ( j 1) t. (2) j j k k k j k= N/2+ 1 N t We hoose N = and t = ns to ahieve a proper resolution of the Fourier transform of the single hip funtion p ( f k ). The emitted signal propagates through the ionosphere whih is onsidered to be homogeneous. Thus the total effet of the ionosphere on the signal is determined by the TEC along the signal propagation path. Sintillation effets, diffration or ray bending are not onsidered here. It is well known that the ionosphere advanes the sinusoidal waves by 40.3 TEC/f 2 m [4]. We neglet higher order effets f -n, n>2 whih ause an advane below a few m [4]. Thus the Fourier transform of the single hip funtion after propagation through the ionosphere p has the form 2π 40.3TEC p ( fk) = p ( fk)exp( ii( fk)) with I( fk) = (3) f and the signal as a funtion of ode phase (resp. time) an be obtained via the inverse disrete Fourier transform. The onstant is the speed of light. The ionospheri advane funtion I(f) has to fulfil ertain symmetry properties whih, however, shall not be disussed here. To analyze the ionospheri dispersion we rewrite the advane funtion as 2π 40.3TEC 1 fk f 1 1 fk f I( fk ) = (4) f f fk f f The three terms in the main parenthesis of (4) will be disussed in the following. The first term is onstant and is a simple multipliation of the whole signal. The seond term is linear in the frequeny f k and auses a onstant group delay of the signal, independent of the frequeny. This is the delay whih is usually referred to as the ionospheri delay. For a high TEC value of m -2 the group delay is about 16 m. The third term (the parenthesis within the main parenthesis) is nearly quadrati in (f k -f ) and distorts the shape of the single hip funtion. Its influene beomes larger the wider the signal spetrum is. SIMULATION OF THE NAVIGATION RECEIVER FRONTEND The single hip funtion p is fed into a Matlab/Simulink simulation of a reeiver frontend. The frontend onverts the real-valued signal from f to the intermediate frequeny (IF) and is shown in Fig. 1. Note that we use an IF of 0 MHz. The inoming signal is bandpass filtered by a finite impulse response filter of order 1024 and multiplied by the omplex nominal arrier with the frequeny of f. The output of the multiplier is lowpass filtered and the resulting omplex signal p IF is stored for further proessing. For two exemplary TEC values the output is shown in Fig. 2. It should be noted that from the single hip funtion output of the frontend the entire reeived navigation signal at the IF level an be reonstruted by onvoluting it with the ode sequene. CODE TRACKING, THE S-FUNCTION We determine the ionospheri delay (plus the reeiver hardware delay) by evaluating the orrelation funtion R( φ) = pif ( φ + φ)ret( φ )sign(sin(2 πφ fs / f )) dφ (5) φ = between the single hip funtion p IF at IF level and the internally generated referene hip funtion. k Fig. 1 Matlab/Simulink simulation of the navigation reeiver frontend.

3 Fig. 2 Real part (solid line) and imaginary part (dotted line) of the single hip funtion at IF level p IF. The green line refers to a vanishing TEC value, the blue line to a TEC value of m -2. The reeiver hardware ode delay of this simulation is m or hips. The position of the maximum of the (omplex) orrelation funtion R(φ) determines the estimated ionospheri plus reeiver hardware delay. Sine diret determination of the maximum is impratial within a real navigation reeiver, the so-alled S-funtion is formed by orrelating the inoming signal with a slightly delayed and a slightly advaned replia of the ode. The distane (in units of hips) of the early and late ode replia is alled orrelator spaing d. If the output of both orrelation proesses is equal the maximum of the orrelation funtion is found. For this analysis we onsider an early-power minus late-power ode disriminator [1] and the orresponding S-funtion is given by 2 2 ( ) S( φ) = γ R( φ d/ 2) R( φ + d/ 2). (6) The value of the onstant γ must be hosen suh that S(φ)=φ for small values of φ. The position of the zero-rossing of the S-funtion determines the estimated delay. In Fig. 3 we show the S-funtion for various TEC values and a orrelator spaing d=0.071, hosen to trak the main peak of the BOC(14,2) orrelation funtion [5]. For a better omparison we shift all S-funtions to the same origin. Thus the delay due to the different TEC values is not visible in Fig. 3. From Fig. 3 one learly sees that the S-funtion does not hange its shape for realisti TEC values. Only for the extreme value of m -2 it deforms signifiantly. In Fig. 4 we show the deformation of the orrelation funtion if the TEC assumes unrealisti high values. For realisti values no hanges in the orrelation funtion are visible. Fig. 3 Early-power minus late-power S-funtion. All funtions are shifted to the same origin. The green line refers to a vanishing TEC value, the blue line to a TEC value of m -2 but nearly no differene is visible to the green line. The red line refers to an unrealisti high TEC value of m -2. Fig. 4 Correlation funtion. All funtions are shifted to the same origin. The green line refers to a vanishing TEC value, the red lines to unrealisti TEC values of m -2, m -2, m -2, m -2 and m -2.

4 The ionospheri ode delay is obtained by alulating the (entral) zero-rossing of the S-funtion. Its value for a vanishing TEC determines the delay aused by the bandpass and lowpass filter (i.e. the reeiver hardware delay). This value has to be subtrated from all other delays to obtain only the ionospheri delay. RECEIVER TRACKING CHANNEL SIMULATION To determine the ionospheri ode delay and the arrier phase advane in another way we simulate a BOC(14,2) traking hannel via Matlab/Simulink. The simulation runs at a rate of 32 MHz. It uses the signal p IF to reonstrut the full navigation signal at IF level. The GPS C/A ode sequene PRN 5 is used. The arrier phase is traked using an artan phase disriminator [1] and the phase-lok-loop bandwidth is 18 Hz. The ode is traked using an early-power minus late-power disriminator and the delay-lok-loop bandwidth is also 18 Hz [1]. No thermal noise is inluded in the simulation sine it has no influene on the ionospheri delay (resp. advane). For more details see [5]. The simulation runs for 3 s, suffiient to determine the estimated arrier phase and ode values. The ode hip funtion at IF level p IF orresponding to a vanishing TEC value is used to determine the reeiver hardware delays for ode and phase separately. After that alibration run we use p IF funtions orresponding to various TEC values and subtrat the hardware delays from the estimated arrier phase and ode values to obtain the ionospheri delay (resp. advane). RESULTS The standard formula predits for the ionospheri ode delay and for the phase advane in m the values (f. [4]) I CODE = 40.3TEC 40.3TEC and I f =. (7) 2 PHASE 2 f A more aurate formula an be obtained if the BOC signal is approximated by the addition of two sinusoidal waves with a frequeny of f ±f s. From this assumption we derive (without explaining it here) I BOC CODE 40.3TEC TEC 1 1 BOC = and IPHASE = +. (8) 2fs f fs f + fs 2f f fs f + fs In the limit f s 0 (8) equals (7). For Tab. 1 the ionospheri ode delay is alulated by all four different methods disussed above. One sees that all values agree within a few mm. The ionospheri phase advane is shown in Tab. 2. No S-funtion analysis has been performed. The simulation agrees at the sub mm-level with (8) and it should be noted that the standard formula (7) for the ionospheri advane differs from the other two olumns by a few mm. Sine the phase measurement noise is usually less than 1 mm, this differene is signifiant. Tab. 1 Ionospheri ode delay in mm for a BOC(14,2) signal at the Galileo E2-L1-E1 band. The values of the last three olumns are differenes with respet to (8). Add the value of the seond olumn to obtain the full delay. TEC [10 16 m -2 ] Equation (8) Equation (7) S-Funtion Analysis Simulation / / / / /- 0.04

5 Tab. 2 Ionospheri phase advane in mm for a BOC(14,2) signal at the Galileo E2-L1-E1 band. All values are modulo /(2 f ) = 95.1 mm beause the Costas phase-lok-loop used in the simulation gives the advane modulo half the arrier wavelength. The values of the last two olumns are differenes with respet to (8). Add the value of the seond olumn to obtain the full advane. CONCLUSIONS TEC [10 16 m -2 ] Equation (8) Equation (7) Simulation / / / / / We investigated the ionospheri ode delay, the phase advane and the deformation of the ode traking S-funtion for a BOC(14,2) signal at the Galileo E2-L1-E1 band. For ode traking we find that the S-funtion does not hange its shape signifiantly even for high TEC values suh that ode traking is possible. Furthermore, the standard formula (7) for the ionospheri ode delay gives the delay with mm-auray. Sine ode measurement errors due to thermal noise or multipath are muh higher no modifiation to (7) is neessary. We also investigated the ase of an unrealisti high TEC. Although suh high a TEC value does not our in nature it beame lear that the frontend of the reeiver must have a reasonable onstant group delay over the whole frequeny band, otherwise ode traking might beome diffiult [2]. The onlusions are different for the ionospheri phase advane sine the phase measurement error due to thermal noise is below 1 mm. Therefore we suggest to replae the standard ionospheri advane formula (7) by (8) to aount for the separation of the two main peaks of the BOC(14,2) signal spetrum. The proess of arrier phase traking itself (yleslips, signal-to-noise ratio) is not negatively influened by the ionospheri advane. ACKNOWLEDGMENTS The investigations and developments of a future GNSS RTK reeiver are supported within the sope of the researh projet FKZ: 50NA0003 in ontrat with DLR. REFERENCES [1] Van Dierendonk, A. (1996): GPS Reeivers, In: W. Parkinson and J. Spilker: GPS Positioning System Theory and Appliations Vol., Progress in Astronautis and Aeronautis Vol Amerian Institute of Aeoronautis and Astronautis., pp [2] Felhauer T. (1997): On the Impat of Front-End Group Delay Variations on GLONASS Pseudorange Auray, Pro. ION GPS 1997, pp [3] Hein G. et al., (2001): The Galileo Frequeny Struture and Signal Design, Pro. ION GPS 2001, pp , Salt Lake City, September [4] Klobuhar, J. (1996): Ionospheri Effets on GPS, In: W. Parkinson and J. Spilker: GPS Positioning System Theory and Appliations Vol., Progress in Astronautis and Aeronautis Vol Amerian Institute of Aeoronautis and Astronautis., pp [5] Pany T., M. Irsigler, B. Eissfeller and J. Winkel (2002): Code and Carrier Phase Traking Performane of a Future Galileo RTK Reeiver, Pro. GNSS2002, Kopenhagen, May