Faster Acquisition Technique for Software-defined GPS Receivers

Acquisition is a most important process and a challenge task for identifying visible satellites, coarse values of carrier frequency, and code phase of the satellite signals in designing software defined Global positioning system (GPS) receiver. This paper presents a new, simple, efficient and faster GPS acquisition via sub-sampled fast Fourier transform (ssFFT). The proposed algorithm exploits the recently developed sparse FFT (or sparse IFFT) that computes in sub-linear time. Further it uses the property of fourier transforms (FT): Aliasing a signal in the time domain corresponds to sub-sampling it in the frequency domain, and vice versa. The ssFFT is an FFT algorithm that computes sub-sampled version of the data by an integer factor ‘d’, and hence, the computational complexity is proportionately reduced by a factor of ‘d log d’ compared to conventional FFT-based algorithms for any length of the input GPS signal. The simulation results show that the proposed ssFFT based GPS acquisition computation is 8.5571 times faster than the conventional FFT-based acquisition computation time. The implementation of this method in an FPGA provides very fast processing of incoming GPS samples that satisfies real-time positioning requirements.Defence Science Journal, Vol. 65, No. 1, January 2015, pp.5-11, DOI:http://dx.doi.org/10.14429/dsj.65.557

FPS-SFT: A Multi-dimensional Sparse Fourier Transform Based on the Fourier Projection-slice Theorem

We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of M-D DFT of the M-D data onto those lines. The M-D sinusoids that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving practical problems

Simultaneously Sparse Solutions to Linear Inverse Problems with Multiple System Matrices and a Single Observation Vector

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that solves the system. We will refer to this as the multiple-system single-output (MSSO) simultaneous sparsity problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts a thorough initial exploration of algorithms with which to solve it. Seven algorithms are formulated that approximately solve this NP-Hard problem. Three greedy techniques are developed (matching pursuit, orthogonal matching pursuit, and least squares matching pursuit) along with four methods based on a convex relaxation (iteratively reweighted least squares, two forms of iterative shrinkage, and formulation as a second-order cone program). The algorithms are evaluated across three experiments: the first and second involve sparsity profile recovery in noiseless and noisy scenarios, respectively, while the third deals with magnetic resonance imaging radio-frequency excitation pulse design.Comment: 36 pages; manuscript unchanged from July 21, 2008, except for updated references; content appears in September 2008 PhD thesi