International Journal of ISSN 0974-2107 Systems and Technologies Vol.3, No.1, pp 127-137 IJST KLEF 2010 Use of Two-Way CDMA Ranging for Precise Orbit Determination of IRNSS Satellites T.Subramanya Ganesh * C K Sharma S.Venkateswarlu * G Jagannath Das ** B S Chandrasekhar S.K.Shivakumar ISRO Telemetry Tracking and Command Network, Bangalore-560058, India ABSTRACT Indian Regional Navigation Satellite System (IRNSS) is ISRO s initiative to build an independent satellite navigation system based on a constellation of GEO and GSO satellites. The IRNSS is regional navigational system providing position accuracy better than 20m in and around the Indian region. IRNSS will have three main segments, namely the space segment, the ground segment and the user segment. The ground segment consists of a network of one-way ranging stations and a network of two-way CDMA ranging stations a precise timing facility along with control centers for navigation and satellite control. It is planned to carry out 2-way CDMA ranging of IRNSS satellites for calibration. In view of this a suitable network of CDMA ranging stations has to be set up for IRNSS satellites. This paper addresses the design considerations, link margin analysis that was carried out and the strategy that is planned for CDMA ranging to achieve the mission goals. I.INTRODUCTION Indian Regional Navigation Satellite System (IRNSS) is ISRO s initiative to build an independent satellite navigation system based on a constellation of 3 GEO and 4 GSO satellites. The objectives of IRNSS are to Provide accurate Position, Navigation and Time (PNT) to the User Better than 20 m in Horizontal and Vertical Position in the service volume Better than 20 nano seconds in Time IRNSS space segment is formed by a constellation of 7 satellites, which will broadcast ranging signals along with time. The satellites will be placed in three different orbital planes; 3 satellites in the Geo-stationary orbit (GEO) and 4 satellites in two Geo-synchronous orbit (GSO) with an inclination of 29º. For providing very high position accuracy to the users, the orbit of the satellites has to be determined to very hih accuracy, say of the order of tens of centimeters. For enabling precise 127
T.Subramanya Ganesh orbit determination of the IRNSS satellites, one-way CDMA ranging data from IRIMS, twoway CDMA ranging data from IRCDR and laser ranging data from ILRS is planned to be used. Two-way CDMA ranging technique, using a C-Band transponder, measures the range between the satellites and the ground stations with an achievable accuracy of few centimeters. By fitting range measurements From multiple ranging stations simultaneously, the orbit of the satellite can be determined precisely with an accuracy of few tens of centimeters. CDMA ranging will be used periodically to calibrate the IRNSS orbit determined by the other techniques. Four CDMA ranging stations are planned to be established for IRNSS project. These CDMA ranging stations will perform ranging simultaneously to the IRNSS satellites. The ranging data will be used post facto for orbit determination. This paper brings out the system engineering that was carried out for establishing the CDMA ranging stations and the method of trilateration for orbit determination using least squares for achieving high accuracy in orbit determination. This work is supported by mathematical rigor through modeling and analysis. 2. PRINCIPLE OF CDMA RANGING Direct sequence PN code is generated such that its length on time scale is more than the two-way distance between the ground station and satellite. The chipping rate is selected according to the accuracy that is required in the ranging exercise. The PN code is modulated on uplink carrier F1 and is transmitted to the satellite and at the satellite it is translated to frequency F2 (preserving the code modulation) and is re-transmitted. The re-transmitted signal reaches the transmitted site with a time delay corresponding to the two-way signal propagation delay. A receiver then synchronizes to the return signal and measures the number of chips code delay between the signal (code) that is transmitted and received and determines the two-way range from the ground station to satellite. For unambiguous range measurement the length of the code should be long enough and for achieving high accuracy in the range measurements the code chi p rate should be high enough. In practice measurements are commonly made as a fraction of the chip period. The generated direct sequence spectrum must therefore meet two criter 128
Use of Two-Way CDMA 1. The chipping rate must be much higher than the bandwidth of the modulating information being sent. 2. Some function other than the information being sent is employed to determine the resulting modulated RF bandwidth. A typical CDMA ranging station is shown in Fig-1. For a direct sequence signal that is modulated using BPSK, the bandwidth (NULL to NULL) of the main lobe is twice that of the rate at which the code is clocked. This means that the 3-dB bandwidth would be approximately, 0.88 times that of the rate at which the code is clocked. The first side lobe is about 13 db lower than the main lobethe unambiguous range is determined as R = [(2 n -1) / f c ] * c Where, R is the unambiguous range, n is the number of shift registers used in code generation and f c is the bit rate of PN sequence. Unambiguous range depends upon the length of the code while the range accuracy depends upon the period of a digit that is used in generation of code. The PRN code selected for ranging should have four basic characteristics. a) To avoid the range ambiguity in the range measurement, the length of one complete code cycle should be greater than the maximum anticipated round trip transmit time. b) The code symbol repetition rate must be sufficiently high to meet the required specification on accuracy of the range measurements. 129
T.Subramanya Ganesh c) The auto correlation function of the code should be such that the sequence should have the maximum correlation when it is compared to itself and a uniform degree of mismatch when compared with its K digit shift. d) To improve the efficiency of transmission, it is desirable to provide balance use of power in the carrier side band by requiring the ranging code to have nearly the same number of ones and zeros within one complete period of sequence pattern. At the receiver, code synchronization and tracking are the crucial factors in completing the CDMA ranging activity. The search for correlation is done in parallel, in three correlation detectors, each of which compares an incoming product code modulated signal with one of the component codes. Fig-2 explains the auto-correlation process that happens in a CDMA receiver. Fig-2: Auto-correlation of Codes for Range Measurement The time delay involved in correlating the signal multiplied with the velocity of light will thus provide the two-way range between the transmitter and the satellite. 3. SYSTEM ENGINEERING AND DESIGN DRIVERS OF A CDMA RANGING STATION The following are the broad system engineering aspects that drive the overall design of a CDMA ranging station. a) The choice of modulation and code rate is highly dependent on the system in which they are to be used. One must consider band width availability, process gain required, and the basic data rate. RF band width restriction is of more than usual importance in direct sequence ranging systems, for degradation of correlation function, could result in a loss of ability to measure timing precisely. Bandwidth restriction therefore can reduce the range resolution. b) When a number of users using different codes, are to share a frequency band, the code sequences must be carefully chosen to avoid interference between users. In other word, the codes should be orthogonal. 130
Use of Two-Way CDMA c) In a ranging system a range measurement is ensured of being d) accurate within one chip by using the correlation peak as the marker for measurement. This may be accomplished by setting the correlation detector in such a way that it recognizes the level associated within ±1 chip synchronizations and does not recognizes the lower level. The following are the major design drivers of a CDMA ranging station. Chip Rate and Code Length Code chip rate in spread spectrum system affect the system in many ways. The most obvious is the fact that in a BPSK direct sequence system, the transmission band width is a direct function of code chip rate (i.e. main lobe null-null RF band width is twice the code chip rate). Code repetition rate is also a function of the chip rate. The repetition rate determines the line spacing in RF output spectrum and is an important consideration in system design. It is advisable that a direct sequence system s code repetition rate be adjusted by choosing a satisfactory code length so that it will not lie in the information band, otherwise, unnecessary noise will be passed in to the information demodulators, especially under jammed condition. For the IRNSS CDMA Ranging station (IRCDR), it is planned to have a chip rate of 20 MChips/second. This high chipping rate will provide the necessary accuracy required for precise ranging. Overall Transmitter Design Selection of the intermediate frequency (IF) generally depends upon chip rate and the fact that is a direct sequence system or frequency hopping system. The transmitter must take a modulated fixed frequency (IF frequency) input signal and move it to the intended operational (Transmitted) frequency, amplify it to the desired level, and output to the antenna. The operation of moving the modulation from an intermediate to a transmitted frequency may be performed two ways: translation and multiplication. The IF chosen for the IRCDR is 70 MHz. Power Amplification At the transmission frequency the spread spectrum modulated signal is amplified to the required power level and applied to the antenna. The characteristics of the power amplifier are more important because many antennas are broadband enough to pass the spread spectrum signal satisfactorily. It is necessary, of course, to design the power amplifier with sufficient band width to pass the spread spectrum signal. The EIRP of the IRCDR station will be about 80dBW. VSWR An area of particular sensitivity for spread spectrum signals, when some care must be taken to ensure proper impedance match, is that VSWR (voltage standing wave ration). The broad band nature of spread spectrum signals and the acute frequency dependency of VSWR when a termination is improper combine to work against the spread spectrum system. Transmit Phase Noise The total phase noise induced on an un-modulated C-band test carrier transmitted by the transmit chain will have a single sided power spectral density spectrum in which each side band, above and below the carrier, will not exceed the following values of frequency offset from carrier versus signal level in dbc/hz. Transmit Harmonics The total EIRP of any harmonic signal below 40 GHz generated by the navigation carrier 131
T.Subramanya Ganesh will not exceed 20 dbw. The EIRP difference between the fundamental and harmonic signals will be deterministic. Transmit Frequency The transmit frequency of the navigation carrier transmitted in C -band will be with in ±100 Hz of the required frequency. The uplink frequency bandwidth of the IRCDR station is between 5.725 GHz to 6.725 GHz while the receive frequency bandwidth lies between 3.4 GHz to 4.2 GHz. Receiver RF Considerations Design of the RF section in a spread spectrum receiver is more critical than the transmitter design, mainly because of the presence of interfering signals before the processing stages. The receiver should accept the desired signal, amplify it, translate it to the operating intermediate frequency, and deliver it undistorted to the correlator. Direct sequence systems can suffer a 6 db or larger loss in jamming to signal ratio when passed through a limiter concurrently with a larger jamming signal. The LNA and the antenna of the IRCDR have been sized to have a G/T of better than 29 db/ ºK. Timing and Frequency Reference One of the most important requirements of a CDMA ranging station is that of precise timing and frequency reference. This requirement is met by using Cesium atomic frequency standards. The cesium standards have stability better than 1E-14.Having designed the four CDMA ranging stations, one of the most important features for performing simultaneous ranging is to synchronize the clocks that are resident at the four CDMA ranging stations. The clock synchronization will help in performing orbit determination by trilateration. To perform the clock synchronization, the most efficient method is Two-Way Satellite Time and Frequency Transfer (TWSTFT). 4. TWO WAY SATELLITE TIME AND FREQUENCY TRANSFER Two-way Satellite Time and Frequency Transfer technique is used to measure the offset between two clocks situated in two different locations. Time of a clock at one location is transmitted to clock at a second location, where time difference measurement (M1) is made. In order to eliminate the propagation delay the reverse process of time measurement (M2) is performed simultaneously. Measurement data is exchanged in order to compute the instantaneous clock difference. The equipments required are a time transfer modem, VSAT transmitter, receiver, up converter, Solid-state power amplifier, down converter, Low noise amplifier, antenna, Geo stationary satellite transponder link, connecting cables and other accessories. In the TWSTFT technique the basic time interval measurements are made with Time Interval Counters (TIC s) at each site. The TICs are started by a pulse from the local clock and stopped by the received pulse from the remote clock. At the same time as the local clock pulse is starting the TIC it is also being transmitted to the other station. The same process goes on at both stations. Typically a one pulse per second (PPS) signal is used. This time interval data is recorded at both sites and then the data files are exchanged and differenced. Generally there is sufficient bandwidth in the communications link that the data can be transferred at the same time that the timing pulses are being transmitted. Thus the two-way technique can be used in 132
Use of Two-Way CDMA essentially real time. The time interval information that is recorded at each station contains the clock differences as well as various delays as shown in the equations below. TIC(A) = A - B + dtb + dbs + dsba + dsa + dra + SB (1) TIC(B) = B - A + dta + das + dsab + dsb + drb + SA (2) where TIC(A) and TIC(B) are the time interval counter readings, A and B are the respective clock times, the dxx s are the respective propagation delays illustrated in the Fig-3 and SA and SB are Sagnac corrections. Here SB = -SA and SA is positive if B is east of A. The value of SA is 2Ar/c2 for stations on the Earth s surface, where is the angular velocity of the earth, c is the speed of light, and Ar is the area defined by the projections onto the equatorial plane by the line segments connecting the satellite and the earth s center to the two earth stations. The TIC values are always positive for reasonably well-synchronized clocks since the time up to and back from the satellite is on the order of a quarter of a second. The time difference between clocks A and B can be determined from equations 1 and 2 by differencing the individual simultaneous TIC readings with the result shown below. Fig-3: Two-Way Satellite Time and Frequency Transfer As can be seen most of the path delays tend to cancel. However, there is no reason for the transmit and receive delays of the earth station equipment to cancel perfectly since they are caused by physically different pieces of equipment. This area is one of the major sources of instability and inaccuracy in the two-way technique The satellite delays, dsab and dsba, may perfectly cancel since in some cases the same satellite transponder is used for both directions. In other cases different transponders are used and then the cancellation is not perfect. The up and down link paths are physically the same, but the propagation delay is not exactly the same if the up and down link frequencies are different. This way, all the clocks at the four CDMA ranging stations will be synchronized with the IRNSS Precise Timing facility. This ensures that all the range measurements from each of the CDMA ranging station can be co-related to a common time reference. This is fundamental for orbit determination using trilateration by least squares as explained in the next section. 5.ORBIT DETERMINATION BY TRILATERATION The satellite position is computed by trilateration, which is basically to compute the intersection of three or more spheres. The IRCDR ground station positions are considered as P stn1, P stn2, P stn3 133
T.Subramanya Ganesh and P stn4 respectively. The satellite position is taken as P sat. P sat =(X sat Y sat Z sat ) represents the position of the satellite at a given time in the Earth Centered Inertial (ECI) frame and P stn =(X stn Y stn Z stn ) represents the position of the IRCDR station at the same time also in the same frame of reference. Range=P sat - P stn The satellite position is initially fixed and the station-satellite ranges are computed. The trilateration model which uses an over determined least squares algorithm estimates the satellite position using the station coordinates and the station-satellite ranges. The concept of trilateration is explained in Fig-4 and Fig-5. Each satellite that the receiver locks onto allows the receiver to calculate range (distance) that it must be from satellite. That puts the satellite somewhere on the surface of a circle (sphere in case of 3D) that surrounds the station. A - B = [TIC(A) - TIC(B)] / 2 + (dta - dra) / 2 - (dtb - drb) / 2 + (das - dsa) / 2 - (dbs - dsb) / 2 + (dsab - dsba) / 2 TIC readings Earth station equipment Propagation delay Delay in satellite - 2 Ar/c2 Sagnac effect Fig- 4 Satellite position from two stations 134
Use of Two-Way CDMA This is the region where all the three station ranges should coincide but they usually don't. That's because of station clock errors. A fourth station is required to achieve the level of accuracy required by IRNSS satellite system and for redundancy. The method of Least Squares is used to approximately solve over determined systems i.e. systems of equations in which there are more equations than unknowns. Least Squares is often applied in statistical contexts, particularly regression analysis. Least Squares can be interpreted as a method of fitting data. Given four station positions and their ranges with respect to a satellite, the satellite position can be computed using Trilateration by using the method of least squares. Let (X stn1,y stn1,z stn1 ), (X stn2,y stn2,z stn2 ), (X stn3,y stn3,z stn3 ), (X stn4,y stn4,z stn4 ) be the station coordinates and (X sat,y sat,z sat ) be the satellite coordinates respectively. Then the ranges are given by distance formula as, 135
T.Subramanya Ganesh 6. CONCLUSION IRNSS system requires accurate ranging techniques for precise orbit determination. Use of twoway CDMA ranging has been proposed. Since the orbit determination is proposed to be solved by trailateration, all the four CDMA ranging stations are time synchronized by TWSTFT methods. It is estimated that the ranging accuracies of the the CDMA ranging stations will be better than a few centimeters leading to an orbit determination accuracy of better than a meter. This when implemented successfully will be a critical technology mastered by ISTRAC. 7. REFERENCES [1] Global Positioning System: Theory and Applications Parkinson and Spilker Volume-I and II Fundamentals of Astrodynamics and Applications- Vallado [2] Digital Communications and Spread Spectrum Systems- Roger Peterson et al 136