# Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)
## 6 Conclusions and Future Scope  
A novel GNSS signal acquisition algorithm based on CS and SVD is proposed aiming to reduce the computational complexity of GPS and BOC satellite signals. A methodology is presented to choose the effective compression ratio by using a scree plot in combination with the probability of detection.  
The algorithm enhances the input for the baseband and provides a simple dimensionality reduction mechanism to condense the dataset. The SVD-based sensing of GNSS signals approach is dependent on finding the economy SVD of the autocorrelation trajectory matrix of noisy input samples (Toeplitz) and maintaining the structure of the matrix by applying suitable convex relaxation methods. The main idea was to use a Toeplitz matrix with the time-shifted reference signal as the dictionary that leads to a sparser representation.  
When testing with recorded real GNSS signals, this method achieves the same results of the conventional regular detection method for SNR's above 20 dB, with implicit signal filtering and within  
Figure 26: Distribution of the detection probability and compression ratio for several SNRs, Dataset 2.  
Figure 25: Distribution of the detection probability for several SNRs, Dataset 1 and Dataset 2.  
an acceptable mean acquisition time. The detection of the number of visible satellites is maintained, and the re-acquisition of GPS data is avoided. At the same time, the use of SVD to sample the GNSS signals where random matrices (Gaussian) may not be the best choice, the combined GNNS-SVD-C algorithm offers a good approach to signal energy-oriented low-rank approximation to GNSS signal reconstruction. The theoretical foundation of this work is based on non-traditional compressive sensing as we do not adhere to the strict RIP condition. As explained in Section 1, RIP is only a sufficient, but not a necessary condition, for reconstruction accuracy; therefore, a stable solution is still recoverable by \(\ell_{1}\) minimization.  
The methodology also allows to sense the signal at the front end and store it in the time domain and/or transmit it for processing where more computational resources are available. For delay-tolerant applications, offloading GPS signals for processing to the cloud or to base stations is possible. GNNS-SVD-C is a CS approach that will limit the associated costs in transfer operations, and the sparse representation based GPS acquisition technique can efficiently capture and embed information in a lower-dimensional space and, subsequently, recover it from an underdetermined system where the criteria to design the measurement basis may take advantage of a priori knowledge of the signals to acquire.  
Our work in this paper is guided by the current hardware limitations of low-cost and low-power sensor platforms. We believe that the key observations and principles derived here will find their way to applications in acquisition systems that have constrained hardware resources to handle the bulk of data processing. Further, we believe that the algorithm we introduce has other applications in signal processing. We plan to explore those applications in future work.  
[PERSON] designed the mathematical model of the proposed algorithm and wrote the paper; [PERSON] performed the experiments; [PERSON] analyzed the data. This research received no external funding. This research was partially supported by Technical University of Madrid. We thank our reviewers who provided insight and expertise that greatly assisted the research. The authors declare no conflicts of interest.