Design of Peak-finding Algorithm on Acquisition of Weak GPS Signals

Transcription

1 006 IEEE Conference on Systems, Man, and Cybernetics October 8-11, 006, Taipei, Taiwan Design of Peak-finding Algorithm on Acquisition of Weak GPS Signals W. L. Mao, A. B. Chen, Y. F. Tseng, F. R. Chang, H. W. Tsao, W. S. Huang Abstract GPS is the system combined CDMA technique and trilateration to obtain precision position information. The main goal of this paper is design of high-sensitivity receiver on acquisition of weak GPS signals. A new peak-finding algorithm is developed to search the C/A code phase in the -based correlation domain. This method can estimate the peak location accurately and provides a faster performance in the software-based signal acquisition. The integration time deciding algorithm is also utilized to enhance the capability of waveform search under indoor environments. Simulation results demonstrate that our proposed scheme can acquire the GPS signal efficiently under the power level of -155dBm in frequency domain processing. G I. INTRODUCTION lobal positioning system (GPS) that provides accurate positioning and timing information has become a commonly used navigation instrument for aircraft precision approaches, missile systems, automated vehicle guidance, and other civil applications. Each GPS satellite simultaneously transmits on two L-band frequencies denoted by L1 and L, which are and MHz, respectively. The carrier of L1 signal consists of an in-phase and a quadrature-phase component. The in-phase component is biphase modulated by a 50-bps data stream and a pseudorandom code where chipping rate is 1.03 MHz. It is the basis for the vast majority of civil applications and will be the object of most of our attention in this paper. We call it as the civilian signal even through the military also uses this signal. The quadrature-phase component is also biphase modulated by the same 50-bps data stream but with a different psedudorandom code called the P-code, which has a 10.3 MHz chipping rate and a one-week period. The conventional GPS used outdoor can meet all the signal and measurement requirements for commercial applications. The biggest challenge of indoor GPS receiver is that the indoor signal is at power levels 30dB (one thousand times) below those found outside. The high sensitivity GPS [1, ] which make use of real-time convolution processor instead of an early-late correlator is proposed. The convolution processor contains over 000 correlators per satellite, and become the most computation consuming operation. The DSP-based approach is a store-and-process method that performs the convolution in frequency domain. The code averaging correlation [3] use the -based correlator for implementation the acquisition process in outdoor environments. They are converted to frequency domain using 104-point complex and multiplied by the conjugate of the of the averaged-local-code. For indoor GPS operation, the extra millisecond of data can be integrated and then yielded the SNR gains that approach N for each extra N millisecond. It takes more time for acquisition in indoor GPS receiver. The most important contribution of this paper is the weak signal can be acquired even the signal power is -155dBmW. The circular convolution in frequency domain is performed and average correlation method is then implemented. A peak-finding algorithm is developed to detect the C/A code delayed phase accurately in the autocorrelation domain. The integration time deciding algorithm is also presented to determine the suitable dwell time in each search bin. Simulation results show that our proposed peak-finding algorithm can be utilized in indoor applications even through the signal level is of -155 dbm. The remainder of this paper is organized as follows. Section describes the GPS received signal and acquisition process. In Section 3, the acquisition in frequency domain using scheme is introduced. The proper size for averaging correlation is proposed. The peak-find and integration time deciding algorithms are developed for indoor GPS receiver. Simulation results are demonstrated in Section 5. Some conclusions are stated in the last section. M. L. Mao is with the Graduate Institute of Electrical Engineering and Department of Electrical Engineering, Mingchi University of Technology, Taipei county, Taiwan ( wlmao@ccsun.mit.edu.tw ) A. B. Chen is with MediaTek Inc, Hsinchu City, Taiwan ( theman0930@yahoo.com.tw ) Y. F. Tseng is with Department of Electrical Engineering, University of California, Los Angeles, USA. ( yifen14@yahoo.com.tw ) F. R. Chang and H. W. Tsao are with the Graduate Institute of Electrical Engineering and Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan. ( frchang@cc.ee.ntu.edu.tw, tsaohw@cc.ee.ntu.edu.tw ) W. H. Huang is with Evermore Inc, Hsinchu City, Taiwan ( maped@emt.com.tw ). II. GPS SIGNAL AND ACQUISITION PROCESS The transmitted spread spectrum signal is represented as S ( t ) [ D ( t ) CA ( t )]cos( f 1 t ) (1) where D(t) is the binary data with duration T ( T= 0ms ). CA(t) represents the binary Gold Code with chip duration T c L /06/$ IEEE

2 ( RC 1/ TC1. 03MHz ). f L1 is the L1 carrier frequency (1575.4MHz). The integer PG T / T 43 db is the c processing gain of the GPS system. A GPS receiver must conduct a two-dimensional search in order to find each satellite signal, where the dimensions are C/A code delay and carrier frequency. Fig. 1 shows the block diagram of the serial search. It must be conducted across the full delay range of the C/A code for each frequency searched. A generic method for conducting the search is that the received waveform is multiplied by delayed replicas of C/A code, translated by various frequencies, and then passed through a baseband correlator containing a low-pass filter which has a relatively small bandwidth (perhaps Hz)[10]. The output energy of the detection filter serves as a signal detection statistic and will be significant only if both selected code delay and frequency translation match that of the signal. When the energy exceeds a predetermined threshold, a tentative decision is made that a signal is being received, subject to later confirmation. The value chosen for the threshold is a compromise between the conflicting goals of maximizing the probability P D of detecting the signal when it is actually present at a given Doppler and code delay and minimizing the probability P FA of false alarm when it is not. Fig. 1 shows the block diagram of serial acquisition process. Sequence in 0.5 chip increments through full span of 103 chips Received signal r(t) Code generator Sequence frequency in 500 Hz increments through span of 10 KHz Carrier NCO Digital IF 4.09MHz I Q Fig. 1 Signal search method 0 90 T dt 0 T dt 0 I Q T 0. 5chip Detection threshold Declare signal if and no signal if 0.5 chip increments. Each code phase search increment is a code bin. The combination of one code and one Doppler bin is a cell. Fig. illustrates the two-dimensional search process. The center of the frequency interval is located at f f, where fc is the L1 carrier frequency and f d is the estimated carrier Doppler shift. A typical range for frequency search interval is f 5 KHz. The frequency search is conducted in c N discrete frequency steps that cover the entire search interval. For coherent processing used in many GPS receivers, the frequency bin width is approximately the reciprocal of the search dwell time. Typical values of frequency bin ( f ) are Hz. Assuming a5 KHz frequency search range, the number N of frequency steps to cover the entire search interval would typically be By the above discussion, if f =500 Hz, acquisition in time domain needs = 4090 bins to search. If signal is strong (above -10dBmW), the dwell time (integration time) is 1 ms, the total search time is needed 40.9 second. The acquisition process has a very large space to search and it takes a lot of time. So, acquisition process is the most time consumption in GPS receiver. III. ACQUISITION IN FREQUENCY DOMAIN Acquisition in time domain needs more signal bins to search because the process has two-dimension search pattern. If the data are transformed to frequency domain, the search pattern can be reduced from two dimensions to one dimension. A multiple numbers of period data are transformed on frequency domain once. Fig. 3 shows this search pattern. The only one dimension searched is Doppler shift in frequency domain. The total searching steps are about 0 bins (from -5 KHz to +5 KHz). Besides algorithm in DSP chip is easily to be implemented. 6 4 T 0. 5chip c d f 50 ~1000Hz 6 4 f 50 ~1000Hz Start of Search 1 Search Direction 3 Start of Search 1 Search Direction Doppler search sequence 046 code positions Doppler search sequence 046 code positions Fig. Two-dimensional C/A code search pattern The following example assumes that a C/A code search is being performed and that all 046 C/A code phase positions are being examined. The code phase is typically searched in Fig. 3 One-dimensional C/A code search pattern A. Search Algorithm The conventional time-domain acquisition can compute autocorrelation function in a simplest way, but it takes a lot of number of operations. The convolution process in time domain equals to multiplication in frequency domain. If x[n]

3 is the input signal, then R[ m] x[ n] CA[( nm ) L] x [ n] CA[ n ] n 1 () 1 F ( x[ n]) F ( CA[ n]) F L CA[n] is C/A code generator generates code, means convolution, F is Fourier Transform and F -1 means Inverse Fourier Transform. Acquisition in frequency domain can reduce a large of number of operations and then increase the speed of computation. For example, in time domain, one period has points (16 103), there are multiplications and additions need be done. In frequency domain, with 16K size will be used first log complex multiplications (3.1) log complex adders (3.) The block diagram of GPS frequency-domain acquisition is shown in Fig. 4. Digital IF X[n] cos[wn] sin[wn] I Q CA [n] I I Q Intergration Fig. 4 Block diagram of GPS acquisition in frequency domain Data Collection System NCO Decimate 16K to 4K Decimate C/A code Peak Search and NCO Controller I Fig. 5 Block diagram of averaging correlation algorithm B. Size If the size of the is not a power of two, a mixed-radix algorithm can be used to manipulate the non power of two s. The sampling rate is set as MHz in our simulation, and almost points are calculated in one period. The 16K and I must be used to accomplish the transformation. It is difficult to implement the 16K and become the circuit burden. If the incoming sampled GPS signal is down sampled from to 4 103, the size can be reduced to 4K. So the correctness and efficiency between 16K and 4K must be considered. In Fig. 5, the averaging correlation algorithm [3] is utilized and the R[m] size can be reduced to 4K. IV. PROPOSED PEAK FINDING ALGORITHM Once the autocorrelation function is computed, the code delay phase needs to be determined from the time of peak value occurrence. Especially if signal power is weak, it is hard to get an optimal method to decide the correct peak time. For the strong signal, the peak value is always evident. The distance between maximum number (peak value) and second maximum number is not very far. Increasing the integration time is a simple way to become a higher peak value. It also increases the search time and then degrades the receiver efficiency. The determination of time of peak vale and integration time are essential to be considered in weak signal acquisition. Here, the Monte-Carlo method and statistical properties are combined to decide the suitable integration time. A. Peak finding algorithm In order to reduce the computation burden on receiver and obtain a better code phase effectively, a peak finding algorithm is proposed: Step1: Compute the autocorrelation function using the method. Step : Find the maximum value, second maximum value and mean in correlation domain. Step 3: Normalize the autocorrelation function (i.e., maximum value =1). Step 4: If (maximum value-mean) > V TH1, AND (maximum value- second maximum value) > V TH, then the time with peak value is code delay. The meaning of peak value is the maximum value of all. In order to avoid miscarriage, it is necessary to detect the difference between maximum value and second maximum value simultaneously. If the difference between maximum value and second maximum value is large enough, the probability of false alarm will be decreased. One vital index to evaluate the signal strength is SNR. The SNR in the autocorrelation function can be obtained as: max d n meand n SNR( db) 10 log (4) s. t. dd n where d n is the data sample in autocorrelation function. And combine the third step of the algorithm, it can be rewritten as (maximum value-mean) = SNR (standard deviation) > V TH1 (5) Using the rule of thumb, a good performance signal has SNR more than 10dB and standard deviation is about 0.03 (after normalization). So SNR (standard deviation) > 0.3, and V TH1 = 0.3 (6) Then, the maximum value is assumed as two times bigger than second maximum value. The relationship can be represented as:

4 SNR db SNR nd _ max_ valuedb db (6.1) max_ value 3 d n meand n.. s t d d n maxd n meand n s. t. dd n max log (6.) nd log 0.3 The equation becomes max d n meand n max d n nd max d n (6.4) From the Eq. (6), max d n mean d n 0. n 3 d n max d nd max (6.5) The variable V TH is set as These two parameters are decided and utilized in the acquisition process. B. Integration time deciding algorithm GPS receiver does not know the signal power level in the indoor situation. It is necessary to provide an efficient method to decide the integration time instead of increasing the integration time straight forward. The integration time deciding algorithm is follows: Step 1: The starting of integration time is 1ms. Step : The input signal is processed by peak finding algorithm, and then its code delay is found. Step 3: If the code delay cannot be found obviously, the integration time is increased to the next longer duration. The integration time step is as:1ms 10ms 50ms 100ms 00 ms 500ms 1000 ms. Using the algorithm above, the receiver can reduce the probability of false alarm and acquire an unknown power signal efficiently. (a) (b) V. SIMULATION RESULTS The simulation results of the peak-finding method are conducted to verify the acquisition performances. The received signal is bandpass filtered, amplified and down-converted to IF and then digitized. The IF is fixed at 4.09 MHz, and a sampling frequency of MHz is selected. The averaging correlation algorithm is verified and then chose the most feasible number of size. In the first experiments, the signal power is set as -10dBmW, noise power is set as -109 dbmw, integration time is 1 ms, and zero Doppler frequency shift. The size of is varied as 104(1K), 4096(4K) and 16368(16K) points. The output signal-to-noise ratio (SNR) and processing gain are compared for different sizes. Fig. 6 shows the outputs of autocorrelation function with different sizes using frequency domain method. (c) Fig. 6 Autocorrelation function for different sizes, (a) 1K size, (b) 4K size, and (c) 16K size under the input SNR = -11dB. In the second experiment, the real data are recorded from the receiver with one-bit resolution. The signal power level is -15dBmW, noise power is -109 dbmw, integration time is 10 ms, Doppler frequency is 00 Hz, and the Clock offset is Hz. Fig. 7 shows the autocorrelation function with different size under the input SNR of -16dB. (a)

5 approximates to 100%. Table summarizes the integration time and the corresponding probability of peak location for indoor environments. (b) (c) Fig. 7 Autocorrelation function for different sizes, (a) 1K, (b) 4K, and (c) 4K under the input SNR=-15dB Table 1 shows the comparison between the 1K, 4K, and 16K sizes under different input SNR conditions. The choice of 4K size can have the better performance between processing gain and computation speed. The 16K has the highest processing gain, but it takes more than 4 times multiplication operations. (Accurately speaking, it takes log log times) Since the 67 processing gain of 1K is not high enough, the probability of false rate can be increased Table 1 The output SNR and processing gain for different lengths size 1K 4K 16K Experiment 1 output SNR(dB) processing gain Experiment output SNR processing gain The peak-finding algorithm is verified with difference input signal power. Each received data is simulated with 1000 runs, and noise power is -109 dbmw. The input SNR is varied from -10dBm to -155dBm. For the same signal power level, the dwell time is increased until the detect probability Table Integration time vs. detect probability of peak location Signal power (dbmw) Integration time (ms) Detect Probability (%) Signal power (dbmw) Integration time (ms) Detect Probability (%) Signal power (dbmw) Integration time (ms) Detect Probability (%) Based on the detective rate above, the adequate integration times are chosen and plotted on Fig 8. The proper dwell time are considered as the probability is near to 100%. Fig. 8 shows the very useful information to determine the integration time under variety of indoor circumstances. Fig. 8 Suitable integration time vs. different input SNR VI. CONCLUSION This paper presents a new peak-finding algorithm used in GPS C/A code acquisition under indoor environments. The average correlation method for signal search was simulated in frequency domain. Three types of power-of-two-based s,

6 i.e., 104-points, 4096-points, and points s are implemented to evaluate the performances of output SNR and processing gain. The 4K-points size can have the better performances between processing gain and computation speed. By including a longer integration time in each bin, the sensitivity can be increased to allow the indoor operation. The suitable dwell times for power level ranging from -10 dbm to -155 dbm have been simulated and summarized to the high-sensitivity acquisition process. ACKNOWLEDGMENT This research was supported by the Evermore INC., Hsinchu City, Taiwan, R. O. C. REFERENCES [1] F. van Diggelen and C.Abraham: Indoor GPS Technology, CTIA Wireless-Agenda, Dallas, May 001. [] F. van Diggelen: Indoor GPS theory & implementation : IEEE Position, Location & Navigation Symposium, vol.31, no.1, pp.40-47, 00. [3] J. Starzyk and Z. Zhu, Averaging correlation for C/A code acquisition and tracking in frequency domain, MWSCS, Fairborn, Ohio, August, 001. [4] E. D. Kaplan: Understanding GPS: principles and Application (Artech House, London, 1996.) [5] P. Misra and P. Enge, Global positioning system: signals, measurements and performances, Ganga-Jamuna Press. [6] J. B. Y. Tsui: Fundamentals of global positioning system receivers, a software approach (John Wiley & Sons, Canada, 000.) [7] M. S. Braasch, and A. J. Van Dierendonck, GPS receiver architecture and measurement, Proc. of the IEEE., vol.87, no.1, pp , Jan [8] Ralph Taylor and James Sennott, Navigation System and Method, United States Patent , NASA, Field May, [9] M. S. Grewal, L. R. Weil and A. P. Andrews, Global positioning systems, inertial navigation and integration, John Wiely & Sons Inc., 001. [10] Hary L. Van Trees, Detection, estimation, and modulation theory, Part 1, Wiley Inter Science, 001. [11] Mohamed Djebbouri and Djamel Djebbouri: Fast GPS Satelite Signal Acquisition, Electronics Leters.com, no.1/10/003 [1] A. J. Van Dierendonck, P. Fenton, and T. Ford, Theory and performance of narow corelator spacing in a GPS receiver, Navigation: J. Inst. Navigation, vol. 39, no. 3, pp , Fall 199. [13] A. J. Van Dierendonck, GPS receivers, in Global Positioning System: Theory and Application, vol. I, B. W. Parkinson and J. J. Spilker, Jr., Eds. Washington, DC: American Institute of Aeronautics and Astronautics, 1996, ch. 8, pp [14] P. Ward, Satelite signal acquisition and tracking, in Understanding GPS: Principles and Applications, E. Kaplan, Ed. Boston: Artech House, 1996, ch. 5, pp [15] B. W. Parkinson, and Jr. J. J. Spilker: Global positioning system: theory and applications (AAAI, USA, 1996.)