Advances in Data Reduction Techniques to Solve Power Spectrum Estimation Problems for Emerging Wireless Networks

New trends in the development of wireless networks are due to the rapid growth of the speed and computing power of software and hardware digital signal processing. The increase in the rate of information transfer leads to a decrease in the duration of processing signals, which means that finding faster and more efficient methods of spectrum signal processing for future 5G/6G networks becomes relevant. The generally accepted methods of spectral analysis based on harmonic basis functions (Fourier transform) become inefficient since their implementation increases either the cumbersomeness of the spectral representation or the reproduction error due to the use of weight windows. Moreover, the application of non-harmonic basis functions when implementing the discrete wavelet transform is even less effective than the discrete Fourier transform because of the complexity of eliminating temporal redundancy. The chapter proposes state-of-the-art techniques to reduce redundancy in signal spectrum estimation tasks in order to improve the efficiency of computing resources for these new 5G/6G wireless systems. Namely, a new technique for estimating the autocorrelation function (and power spectrum) of a stationary random signal for finite sampling at different variants of nonuniform data sampling is proposed. The peculiarity of the technique is the orientation to minimize the number of sampled data by reducing the redundancy. In the long term, it allows to offload significantly the wireless communication channels and digital signal processing systems with high noise immunity. The concepts of reduction ruler are introduced to estimate the autocorrelation function and power spectrum. The ways of its construction according to the known Golomb's ruler are described and analyzed, as well as the convenient ways of application in practice based on irregular sampling with the switching of the sampling frequency with two close frequencies. The results of numerical modeling of estimation accuracy based on the calculation of the standard deviation, which, as a rule, increases when the number of data decreases, are given and illustrate the efficiency of estimation of different data selection options. The proposed solution will reduce the amount of computation in the implementation of digital signal processing for emerging wireless networks.