A Compressed Sensing Technique for GPS Signal Acquisition

Abstract

In a cold start, a GNSS receiver performs a signal search by testing all likely hypotheses to acquire the code phase (code delay) and the Doppler frequency of the incoming GNSS signal [1]. In order to complete the signal acquisition process quickly, a conventional receiver is generally equipped with a large number of parallel correlators. In practice, a receiver still can complete the process with a smaller number of correlators, but it takes longer acquisition time. Therefore, reducing both the number of correlators and the acquisition time in the cold start is not an easy task for a conventional GPS receiver. An alternative, FFT based GNSS signal acquisition scheme [2], has gained lots of attention, since it can speed up the hypothesis testing process without requiring a large amount of hardware resources for correlators, but it needs high computing power of the digital signal processor (DSP). In general, the FFT based scheme requires FFT of the received signal, complex multiplications in the frequency domain, and IFFT of the frequency domain signal. Therefore, an ideal GNSS signal acquisition technique may be one that can complete the acquisition process fast while using lower number of correlators and lower computational power in the receiver than other conventional or FFT based schemes. In this paper, we propose a GPS signal acquisition technique using a novel compressed sensing (CS) technique that requires low computation and low hardware cost but completes the acquisition process quickly. CS techniques make sensing the information with a smaller amount of measurement than what Nyquist-Shannon sampling theorem requires is possible [3], [4]. While most of studies in CS focus on utilizing a random sensing matrix as a general incoherent matrix with most of sparsifying matrices, we pay attention to the deterministic sensing matrix for GPS signal acquisition, since the deterministic sensing matrix allows an algebraically straight-forward and much simpler decoding process (therefore, low computation) than the decoding process required for the random sensing matrix [5], [6]. The proposed GPS CS technique shows that GPS signal acquisition can be completed with 10 or more times less number of correlators performing correlation of compressed signals and receiver generated signals and that the overall computation is much lower than the computation required by the FFT based scheme.