Integrating Compression and Multi-Rate Algorithms for Robust Acquisition: Analysis using GPS L2C Signal

S.R. Babu, A. Kumar, V. Gambhir

Abstract:	The acquisition of GPS signals using FFT based circular correlation is the preferred approach for implementation on the SDR platform. The main challenge in such an implementation using the circular correlation method is the size of the data block used for processing. As the size of the data block is directly related to the size of the FFT, any reduction in the data size directly reduces the complexity of the processing. The size of the L2C signal assumes more significance compared to L1 C/A signal due to the longer length of the L2C code. This paper proposes a combination of compression and multi-rate algorithms to reduce the data size and thereby reducing the FFT complexity. Compressed sensing is an important technique to acquire signals at sub-Nyquist frequency. One of the key requirements of the compressed sensing in the acquisition of the signal is the preservation of the autocorrelation properties. The correlation properties are preserved either by projecting the signal vector using a symmetric Toeplitz matrix or by using a deterministic compression matrix. In this paper, the latter approach is used. Deterministic compression matrices are generated using perfect ternary sequences, -1,0,1, such as Ipatov. One of the advantages of these ternary sequences is that the multiplication operations are completely eliminated. The GPS L2C signal of length M is mapped into length N by the linear compression matrix M x N. As the L2C code is longer in length, ternary sequences of higher length are obtained by periodically multiplying two ternary sequences of relatively prime length. Also, the longer lengths of the L2C code, 10230 chips, provide unbiased estimates when the spectrum estimation is done using such compressive matrices. To implement the compressed sensing algorithm, firstly the Ipatov sequence was generated from the m-sequence. The m sequence is constructed using the Galois Field (3^13) with 3^13 elements using a polynomial of the order 13. The m sequence with 3^13 elements is converted into Ipotav sequence of M elements. From the Ipatov sequence of M elements the linear compression matrix is constructed for the size M×N. Here, N is the desired compression value. The linear projection of this matrix on the input raw data (M samples for one digitized GPS L2C signal block) and the locally generated signal data (also of M samples) results in the compressed signal of N samples per data block for both the input and the local signals. To further reduce the sampling frequency and reduce the burden of FFT, a multi-rating algorithm was implemented on the compressed input spectrum and the local signal. An interpolator was designed to convert the samples into power of 2 before giving to the FFT algorithm. The interpolator was divided into multiple stages to reduce the complexity of the processing. An anti-aliasing filter with lesser number of taps was also carefully designed to reduce the latency and remove the frequency folding effects. Then, the circular correlation is performed using the input and the local signals resulting in the acquisition of the code delay and Doppler frequency of the GPS L2C signal. For validating the algorithms, the GPS L2C signal with the following specifications was used: IF frequency – 4.134MHz, Sampling frequency – 16.3676MHz, Data size – 327352 samples / 20msecs. By processing this data set using the proposed algorithms, compression and multi-rating, it is observed that a sampling frequency reduction of a factor of about 16 is achieved, i.e., 20460 samples. The Doppler frequency and code phase estimates of the acquisition loop using the proposed algorithms were found to be the same as that of the uncompressed spectrum, thereby validating the analysis. A detailed analysis of the algorithms design was also discussed in the paper.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	114 - 120
Cite this article:	Babu, S.R., Kumar, A., Gambhir, V., "Integrating Compression and Multi-Rate Algorithms for Robust Acquisition: Analysis using GPS L2C Signal," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 114-120.
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