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In the cold start of a Global Navigation Satellite Systems (GNSS) receiver, fast acquisition of the GNSS signal requires either an extensive usage of hardware resources for massive parallel correlators or a high computational complexity for fast Fourier transform (FFT) and inverse FFT operations. Because GNSS uses direct-sequence spread spectrum (DSSS) signaling with binary phase-shift keying (BPSK) or with BPSK and binary offset carrier, any GNSS signal can have a sparse representation so that the concept of compressed sensing can be applied to detect GNSS signals. To achieve a fast acquisition of the GNSS signal with a reduced number of correlators and low computational complexity, we propose a two-stage deterministic compressed GNSS acquisition technique using the Walsh-Hadamard matrix. The proposed technique makes fast acquisition possible for a receiver using a much smaller number of correlators than the conventional parallel-correlator-based technique, which requires much less computational complexity than the FFT-based technique. We provide complexity analysis of the proposed technique and compare the statistical performance of the proposed technique with other techniques applicable to the fast GNSS acquisition. The proposed technique is easy to implement and is the first compressed-sensing-based GNSS acquisition technique.