# Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)
## 1 Introduction
However, due to the larger amount of data required to store the data received from the IF, this approach to store and process data requires a large amount of hardware or enough central processing unit (CPU) capacity. [PERSON] and [PERSON] developed a basic correlator using MATLAB and Simulink to validate the results and performance techniques when actual GPS satellite signal records are used, and formulated and implemented alternative parallel architectures to perform a circular correlation by decomposing the initial circular correlation into several smaller ones, which are independent and can be processed in parallel. When applied to GNSS signals, using FFT-based, parallel-code-phase search (PCS) has advantages for hardware-based implementations using field programmable gate arrays. The parallel architectures implemented are radix, FFTs, multipliers, adders, and NCOs. Additionally, the coded QuickSync algorithm, which exploits the sparse nature of the synchronization problem, and relays in an important property of aliasing a signal in the time domain, is equivalent to subsampling the signal spectrum [10]. The authors are in favor of software-defined radio (SDR) and the work presented provides a set of functional tools that allow to pretest initial prototypes of the GNSS-SVD-C algorithm. The development of software-based GNSS receivers is rapidly revolutionized in satellite-based navigation applications, and the receiver technology needs to be updated efficiently for high positional accuracy requirements under noisy environments. As discussed before, the acquisition based on spread spectrum technology is an essential process for identifying satellites, with the development of GNSS and the emergence of multisystem joint positioning, the receiver design is moving towards more data processing and, therefore, hardware scale needs to be improved. The fundamental cause is that most of the sampled data is obtained by using the Nyquist-Shannon sampling theorem [14]. The theorem states that a signal can be exactly reproduced if it is sampled at a frequency F, where F is greater than twice the maximum frequency in the signal [15]. However, even though this is a sufficient condition for accurate recovery, it is not a necessary condition. This condition increases the system computation time and cost of modern wideband receivers. In a real application, sampling at the Nyquist rate usually produces a high number of samples. Additionally, the front-end design of future GNSS receivers must meet the needs of multi-navigation signal reception. Thus, the instantaneous bandwidth of RF front end is increased and increases the complexity of baseband signal processing [16]. The bandwidth of the receiver should be large enough to avoid signal to noise ratio (SNR) loss. This generally requires higher sampling rates with an attendant increase in power consumption and processing loads, a factor that is detrimental to low-cost and low-power consumer applications [6]. [PERSON] proposed a faster acquisition algorithm via subsample FFT. The algorithm first downsamples by a factor '\(d\)' and then multiplies the FFT of the received signal with the FFT of the locally-generated PRN code, and takes the IFFT of the resulting signal, which produces a single spike at the correct time shift [17]. The problem with this algorithm is that the downsampling factor '\(d\)' increases the noise contamination linearly, even though the computation time decreases exponentially, \(d\)\(log\)\((d)\). The truncation of PRN sequences leads to a reduction in the correlation of the GPS signals and may not be an appropriate solution.