  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.
