REALIZATION OF FAST ACQUISITION FOR SPREAD SPECTRUM SIGNAL BASED ON FFT

Transcription

1 REALIZATION OF FAST ACQUISITION FOR SPREAD SPECTRUM SIGNAL BASED ON FFT QI Jian-zhong, Gong Yang, Song Peng College of Information Engineering, North China University of Technology, China ABSTRACT Acquisition based on Fast Fourier Transform (FFT) can acquire Pseudo-random code phase quickly and improve the performance of the satellite navigation receivers. In the paper Realtime receiver adopts the FPGA to realize the function of FFT and uses DSP processor to control the implementation process of Acquisition. For increasing the sensitivity of Acquisition incoherent accumulation were used in the process. Also, in the paper we have discussed the process method for decreasing the negative influence of signal power changes and carrier s Doppler frequency. KEYWORDS FFT; Acquisition; Real-time receiver; Incoherent Accumulate; Doppler Residual INTRODUCTION The traditional serial search method of spread-spectrum signal cannot adapt to the development of receiver technology, researchers have proposed a variety of parallel acquisition algorithm in order to improve receiver performance. Circular correlation acquisition algorithm based on FFT obtained widespread attention because of its superiority in civil code, but most studies stop at the basic theory of the algorithm, without considering the realization of the algorithm. In fact, the circular correlation acquisition algorithm will encounter problems that affect performance of the algorithm in the implementation process. We need to analyze the actual situation and explore solutions. THE BASIC PRINCIPLES OF CIRCULAR CORRELATION Circular correlation algorithm used the cyclical of pseudo-code and used the principle of circular convolution, converted time domain convolution into frequency domain multiplication in order to reduce computation burden. The algorithm parallel search pseudo-code phase and achieve carrier Doppler frequency rapid by FFT and IFFT. The basic block diagram of the algorithm [1] is shown in Figure 1. 1

2 Figure 1 Basic block diagram of circular correlation The basic idea of the algorithm is: calculate the phase delay in each Doppler search range, then find the maximum correlation value and record its location. If the maximum value exceeds a predetermined threshold, detected signal is considered. The time interval is the roughly carrier Doppler, the location is the pseudo-code phase. Thus the serial search is converted into a parallel. The method improves the parallelism, can significantly speed up the capture. The algorithm processing is shown: (1) Carrier strip. Digital IF signal multiplied the cosine and sine signals from local carrier NCO, and then get IQ baseband signal. The output signal contains residual carrier Doppler. (2) Decimation filtering. Decimation is used to reduce the sampled data and the logic resource and storage space usage. Resample the data after a low pass filter in order to meet a power of 2 between 1ms interval. While resample the local pseudo-code at the same sampling rate and then stored in memory. (3) IQ baseband signal will be combined into complex signal used to execution FFT. Then stored into memory sequentially, waiting for conjugate. (4) Use the local pseudo-code to do the FFT, conjugate the results, while reading the temporary sequence of FFT of the baseband signal results. Multiply them and save to memory. (5) When the FFT transform is completed, read the temporary data sequentially and transform the result by modulo, then add last 1ms results of the transformation. The algorithm processing will find the maximum, the second largest value and the position of maximum. At the same time save the transform result, used to next non-coherent accumulation. Set the status flag after transform and return to repeat (1) to (5) steps. (6) DSP polls the status flag and then reads the maximum, the second largest value, the position and then clears the flag. If the ratio of maximum and the second largest value exceeds a predetermined threshold is considered to capture, the position is the code phase. If the ratio is lower, then continue (1) to (5) steps. If times of non-coherent accumulation exceed the intended number, Doppler frequency search forward a step, then continue (1) to (5) steps. PERFORMANCE ANALYSIS OF CIRCULAR CORRELATION Theoretical analysis shows that the level of signal to noise ratio, the level of the sampling rate, the position of data transition, the size of the residual carrier Doppler, non-coherent integration and so on have an impact on algorithm performance. Detailed analysis of these factors needs in the project. 2

3 THE IMPACT OF THE INPUT SNR The level of the input SNR directly affects the capture efficiency of the algorithm. Sensitivity analysis and verify about the arithmetic will be executed by changing the input SNR. The study use the GPS L1 band C/A code signal as the object. The maximum power level [2] is about -128dBm when signal reaches the ground, corresponding to the maximum SNR is -17dB. The minimum power level is about -130dBm, corresponds to the minimum SNR is -19dB. It will encounter a certain loss because of transmission and processing. Assuming that the actual minimum SNR is -29dB, and obtained the simulation results by Matlab shown as Figure 2. Figure 2 performance of the input SNR Seen from Figure 2, when the input SNR is -19dB, the correlation peak relative to the noise floor is very obvious, the ratio is about 10dB. The correlation peak relative to the noise floor also decreased when the input SNR decreases. When reduced to -29dB, the ratio decreased to less than 3dB. If 3dB is the acquisition threshold, the circular correlation algorithm can work at 10dB below normal SNR. This verified the high sensitivity of the algorithm, and also verified the correctness of its functions. Baseband signal decimation filtering and down-sampling [3] are used because of the limitation of the hardware resources when realization in the FPGA. Down-sampling rate must satisfy the principle of sampling theorem. Generally, best choice is 2 or 4 times sampling than the code rate. In order to use FFT, it is required that the sampling points are a power of 2. Downsampling will reduce the sensitivity of algorithm in some extent. 3

4 THE IMPACT OF CARRIER DOPPLER RESIDUAL Circular correlation algorithm uses the cyclical of pseudo-code to capture. Only when the input signal is a continuous pseudo-code, the correlation peak is the largest. If there is data transition in the input signal, it will destroy the periodic, resulting internal in a cycle of code, thereby reducing the correlation peak [4]. Data transitions in different positions, peak reduction related to different degrees. In the capture phase, due to the unknown beginning of the navigation data, so the sampling data may contain navigation data transition. The closer the location of data transitions in the middle of pseudo-code period, the greater the attenuation peak is related. When the data transition occurs in the middle of pseudo-code period, even if the input SNR is high also can t detect correlation peak. Therefore, in order to prevent data leakage caused by transitions need to search each frequency step two or more times. Carrier Doppler residual is similar with the data transitions, and even has greater negative impact. Calculation of the signal power value [5] as shown: It shows that the signal power value is the function of Doppler f d. T is the pre-detection integration time in equation (1). P is normalized by dividing AR[τ(k)] to be sinc(f d T). This shows the power values associated with the trends of Doppler residuals. Assuming T = 1ms, when the Doppler residuals between 0 ~ 500Hz, correlation peak attenuation is less than 3bB. When the residuals larger than 500Hz, attenuation will exceed more than 3dB, correlation peak will be disappear. If the Doppler residuals in less than 250Hz, the signal can correctly capture, and capture after change tracking, tracking loop has the ability to reduce and eventually track the residual. If the Doppler residuals in to 500Hz or less, the strong signal is still able to capture, however, tracking loop will lose lock or judgments may be false arrest due to the frequency difference over locked loop range. So high threshold is needed to capture strong power satellites. Otherwise, there will frequently detect satellite and carrier to noise ratio is very high, but loss of lock frequently. This case, the decision threshold used to capture cannot be a single fixed threshold. Otherwise, if the threshold is too low, the weak satellite can be properly captured, strong satellite Doppler frequency of false arrest will occur. If the threshold is too high, you can properly capture the strong satellite, but not the weak satellite or more testing to find the correlation peak, the sensitivity to capture will be reduced. Therefore, reasonable capture strategies are needed to improve sensitivity and capture success rate. The zero-crossing of carrier Doppler will has the negative impact due to unknown the initial phase in practical applications. Assuming the carrier Doppler residuals is cos(2πf d t), initial phase is zero, residuals f d =200Hz, as shown in Figure 3. 4

5 Figure 3 the effects of Doppler residuals Shown in Figure 3, the first 1ms data does not cross the zero, its peak will be reduced due to the attenuation of the residual carrier Doppler. The second 1ms data close to zero, so there will be a substantial attenuation of the peak. The third 1ms data across the zero-crossing point, it will not detect the correlation peak. When the Doppler residual is large, the probability of sampling data across zero-crossing point is greater. In order to improve the detection probability, have to adjust the Doppler frequency search step properly. THE IMPACT OF NON-COHERENT INTEGRATION The probability of capture is low with 1ms data due to the aforementioned various factors. Coherent integration and non-coherent integration should be considered in order to improve acquisition sensitivity. Non-coherent integration will be used in the actual design which taking into account of hardware resource consumption. It uses 1ms data to capture and adds the results corresponding to the same location. It can avoid the growth of data length, reduce coherent integration time, thereby reducing the number of frequency search step, and finally reduce the capture time, save hardware resources consumption. In the algorithm, set the maximum number of non-coherent accumulation. If not detected correlation peak when the cumulative number of times does not exceed the limit, then continue to accumulate, otherwise, as captured. Stop the operation, adjust the frequency search step and continue to the next operation when the cumulative number of times meets or exceeds the maximum correlation peak but not detected. Compared 1ms and 5ms non-coherent accumulation results shown in Figure 4 by Matlab simulation. 5

6 Figure 4 the result of non-coherent accumulation Seen from Figure 4 that the correlation peak of 5ms non-coherent integration is much more obvious than of the 1ms correlation peak. In practice, due to the data transition and the presence of the carrier Doppler, each of 1ms correlation peak is not consistent. The correlation peak is very small or submerged in noise floor when data have transitions and carrier Doppler zerocrossing. If we accumulate the value at this time not only does not improve or even reduce the ratio of original correlation peak to noise floor. In this case, the results should be relevant to judge every 1ms. If the peak is too low, the results are not suitable for the accumulation, so as to reduce the impact and improve the detection probability of correlation peak. IMPLEMENTATION OF CIRCULAR CORRELATION This paper analysis the various factors affecting performance of the algorithm by simulation. In real-time receiver, require real-time calculation of the results, usually realizes the algorithm in the FPGA. It uses pipelining mode to control working. The current 1ms sampling data input to the calculation module, the next 1ms to calculate the correlation peak, and find the peak position. The algorithm processing will be described in following. Here the traditional quadrature downconversion way was adopted to achieve baseband signal that only need two multipliers. DSP set the frequency control word which used to generate the local carrier sine and cosine by writing register operation. Decimation filtering module is used to reduce input data rate. At the same time the down-sampling data through band-limited filter and then re-sampled to meet 1ms sampling points is a power of 2. FFT and IFFT transform is the core of the algorithm, according to the algorithm s processing, three FFT transforms need to get results. Two input FFT module allows two IQ inputs and local pseudo-code at the same time to transform. It can reduce the time and the complexity of logic design. But IFFT transformation must wait after the completion of the FFT transform to perform, in order to reduce resource consumption, so need a time-division multiplexing. Algorithm uses state machine to control logic module and FFT transform. Before the IFFT transform, the result of conjugate multiplying must be intercepted. Intercept location 6

7 correctly is the key factors related to algorithm. If the intercept position does not fit, will undermine the correctness of the algorithm, reduce the sensitivity or false arrest frequently or even not capture. Functional and timing simulation has to be executed after completing logic design of algorithm. Matlab generate a signal as input, assuming its SNR is -28dB and include 300Hz carrier residue, no data transition, continue 3ms time, the timing simulation results shown in Figure 5. Figure 5 Timing simulation of the algorithm The circular correlation algorithm was used in a GPS and GLONASS compatible GNSS receiver. The DSP program controls capture operation. The Doppler frequency search range is ±10KHz and the search step is 500Hz. The acquisition sensitivity of the algorithm verified by testing is better than -133dBm. It can complete capture all the visible stars in 4s, several times faster than traditional receivers. It meets the design requirements and enhances the speed of the first positioning and the dynamic performance of the receiver. CONCLUSION The paper carried out the processes of the algorithm based on the principle of circular correlation, analyzed various factors that affect the performance of the algorithm and simulated them. It proposed a simple solution for the realization of the algorithm and provided a theoretical basis to ensure the performance of the algorithm. Finally, according to design requirements, taking into account the characteristics of project implementation, through hardware and software design to realize the algorithm used in combo receiver verified by simulation and tested by experiments. It improved the overall performance of the receiver. REFERENCES [1] Gordon J.R.Povey, David G.M.Cruickshank; An FFT_Based Approach for Fast Acquisition in Spread Spectrum Communication Systems; Wireless Personal Communication 13:27-56, 2000 [2] Nesreen I. Ziedan; GNSS Receivers for Weak Signals, 2006 [3] Elliott D.Kaplan, Chriostopher J. Hegarty; Understanding GPS Principles and Applications (Second Edition) [4] D.Akopian; Fast FFT based GPS satellite acquisition methods; IEEE , 152(4): p277-p285 7