In this paper, we propose an efficient acquisition scheme for GPS receivers. It is shown that GPS signals can be effectively sampled and detected using a bank of randomized correlators with much fewer chip-matched filters than those used in existing GPS signal acquisition algorithms. The latter use correlations with all possible shifted replicas of the satellite-specific C/A code and an exhaustive search for peaking signals over the delay-Doppler space. Our scheme is based on the recently proposed analog compressed sensing framework, and consists of a multichannel sampling structure with far fewer correlators.The compressive multichannel sampler outputs are linear combinations of a vector whose support tends to be sparse; by detecting its support one can identify the strongest satellite signals in the field of view and pinpoint the correct code-phase and Doppler shifts for finer resolution during tracking. The analysis in this paper demonstrates that GPS signals can be detected and acquired via the proposed structure at a lower cost in terms of number of correlations that need to be computed in the coarse acquisition phase, which in current GPS technology scales like the product of the number of all possible delays and Doppler shifts. In contrast, the required number of correlators in our compressive multichannel scheme scales as the number of satellites in the field of view of the device times the logarithm of number of delay-Doppler bins explored, as is typical for compressed sensing methods.

Abstract-An important receiver operation is to detect the presence specific preamble signals with unknown delays in the presence of scattering, Doppler effects and carrier offsets. This task, referred to as "link acquisition", is typically a sequential search over the transmitted signal space. Recently, many authors have suggested applying sparse recovery algorithms in the context of similar estimation or detection problems. These works typically focus on the benefits of sparse recovery, but not generally on the cost brought by compressive sensing. Thus, our goal is to examine the trade-off in complexity and performance that is possible when using sparse recovery. To do so, we propose a sequential sparsityaware compressive sampling (C-SA) acquisition scheme, where a compressive multi-channel sampling (CMS) front-end is followed by a sparsity regularized likelihood ratio test (SR-LRT) module.The proposed C-SA acquisition scheme borrows insights from the models studied in the context of sub-Nyquist sampling, where a minimal amount of samples is captured to reconstruct signals with Finite Rate of Innovation (FRI). In particular, we propose an A/D conversion front-end that maximizes a well-known probability divergence measure, the average Kullback-Leibler distance, of all the hypotheses of the SR-LRT performed on the samples. We compare the proposed acquisition scheme vis-à-vis conventional alternatives with relatively low computational cost, such as the Matched Filter (MF), in terms of performance and complexity. Our experiments suggest that one can use the proposed C-SA acquisition scheme to scale down the implementation cost with greater flexibility than MF architectures. However, we find that they both have overall complexities that scale linearly with the search space despite of the compressed samples. Furthermore, it is shown that compressive measurements used in the SR-LRT at low SNR lead to a performance loss as one could expect given that they use less observations, while at high SNR on the other hand, the SR-LRT has better performance in spite of the compression.

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Most scheduled communication systems rely on either central coordination, or on the presence of an external reference clock that is accessible to all nodes in the network. Such requirements often limit the scalability and applicability of time division multiple access (TDMA) solutions to ad-hoc networks, which largely rely on conflict resolution based on random access mechanism. We show that, by borrowing mechanisms of coordination found in nature, we can self-organize nodes in a network in time division without a central clock, nor a common reference signal. We show that a common clock reference and a conflict free schedule can emerge from our signaling control scheme, using simple local computations that are based on the so called Pulse Coupled Oscillator (PCO) dynamics. Compared to the prior art on PCO, our work provides an integrated solution for network synchronization and collision free TDMA that is completely decentralized and can lead to efficient transmission of data at a regular and reliable pace. We discuss how this scheme can be used to provide an alternative to the popular Zigbee interface, and produce collision free clustered synchronous networks.

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