ION GNSS 2012
Session D3: GNSS Algorithms & Methods 1: Signal Processing

Title: A Low-complexity Acquisition Implementation for the Modernized GNSS Hardware Receivers
Author(s): R. Ding, L. Li, J. Zhong, M. Zhao, Zhejiang University, China
Room: 204 (NCC)

With the advent of the new GNSS (Global Navigation Satellite System) signal, such as Galileo and the modernized Global Positioning System (GPS), new signal structures and new modulations have been proposed with many enhanced signal properties to improve positioning accuracy and enhance multipath rejection. Unlike GPS L1 CA code, the new GPS signal and Galileo signal have the same data bit duration as the code period. As a result, a long coherent integration time is required in acquiring process. In the new structures, a bit sign transition occurring during the whole integration period usually represents a different correlation envelope by splitting the Cross Ambiguity Function (CAF) main peak into two smaller side lobes along the Doppler shift axis. As a result, the conventional acquisition method increases the probabilities of missing detection and incorrect Doppler shift. Meanwhile for modernized GNSS signal, the long coherent integration process usually requires huge operation counts, large usage of memory and high hardware cost for additions and multipliers. To overcome the bit sign transition problem, Bit transition cancellation (BTC) method has been proposed by Sanghoon in 2011 ION. The BTC method based on the fast Fourier transform (FFT) performs good detection probability, but needs the highest calculation time and hardware cost for multipliers and additions. Jin Zhao in 2009 IEEE has proposed a parallel differential matched filter (PDMF) method which synchronizes multiple satellite signals simultaneously to reduce the computational complexity of the acquiring process. In the PDMF, the number of operations reduces while memory consumption for coherent integration rises. Moreover it´s not flexible for Doppler frequency compensation since each satellite has its own Doppler frequency. To solve the bit transition problem and reduce the hardware consumption, the paper proposes a matched-filter-based low-complexity acquisition algorithm for bit transition cancellation.

The proposed acquisition algorithm modifies the BTC method and the PDMF method, and makes a corresponding improvement for their shortcomings. In the proposed algorithm, two code replicas are used. One is a code replica of the received signal, and the other is a modified one that has a bit transition at the middle of the code sequence. The correlation processes of the two code replicas are independently accomplished. After each I, Q branch is obtained, each CAF envelope is calculated and summed. The result of the summation is a new CAF envelope that indicates the correct Doppler shift value and code delay, eliminating the bit sign transition. The improved PDMF correlation algorithm is used in the coherent integration process instead of FFT method. It breaks local code replica of one satellite into shorter segments, and tackles different segments simultaneously. The rationale behind the improved PDMF is to fully share and reuse the partial and temporary correlation values, which are by-products during the coherent integration process of one section of a code replica. Taking the first segment as the referring code replica, other segments just have the same sign or inverse sign in the same position with that of the reference. So if different partial correlations have the same partial code, the result can be shared for reducing operation counts, the number of correlators and memory consumption. The proposed algorithm breaks the whole code replica into multiple segments corresponding to one millisecond. Then the coherent integration results of every millisecond are easily got with the improved PDMF method. By summing up all 1ms correlation results, the CAF envelope of the received signal replica is computed. And the CAF envelope of the other code replica with a bit transition in the middle is computed by summing up two correlation results: the former half code period is multiplied by positive one and the latter half is multiplied by negative one. In the final stage, each envelope is summed to get a new correlation power indicating a correct result of the acquisition process.

In order to evaluate the performance of the proposed algorithm, the acquisition of GPS L2C signal containing navigation data message with the symbol rate of 50 symbols/s and the sampling rate is 2.046M. The C/N0 of the signal is 45 dB-Hz, the Doppler shift is 1500Hz with a code delay of 2 ms and the coherent integration time is the whole code period of 20ms. The computational complexity of proposed algorithm is compared with the conventional MF and the FFT-based BTC method. The number of additions is counted to compare computational complexity. To be fair, we only compare the equivalent addition for each code-phase among three methods. The result shows that the addition number of the proposed algorithm is reduced by about 75% and 90% respectively in comparison with the conventional matched filter and the FFT-based method. Then the detection probability is compared among the three methods. The detection probability is the cumulative distribution function of the probability distribution function above the pre-determined signal acquisition threshold. In this paper, the binary hypothesis test which is the simplest detection hypothesis of signal-detection theory has been adopted. The result is shown under 1e-6 false alarm probability circumstances. Without a bit transition, the signal detection probability of the proposed algorithm is about 99.9%, the same as the other two methods. When the bit sign occurs, the average detection probability of this method is about 97%, comparing with 80% in the conventional method and 96% in BTC method. With a bit transition occurring in the middle of the code period, the signal detection probability of the proposed algorithm is about 99.9%, comparing with 75% in the conventional MF and 99% in BTC method. With a bit transition occurs in the 1/4 or 3/4 middle of the code period, which is the worst situation, the signal detection probability of the proposed algorithm is about 95%, comparing with 82% in the conventional MF and 94% in BTC method.

The proposed algorithm can be used to mitigate some disadvantages occurring in the acquisition process of the modernized GNSS receivers, such as huge hardware consumption, bit transition problem and long coherent integration time. Analytic and simulation results revealed that the computational complexity and consumption of additions are greatly reduced, the average signal detection probability is improved compared with the conventional acquisition method and the BTC method. The hardware implementation of this algorithm is also feasible.

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