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This paper investigates the energy efficiency (EE) optimization for massive multiple-input multiple-output (MIMO) systems powered by wireless power transfer (WPT) with hardware impairments at sensor nodes (SNs). In the considered system, the SNs are first powered by the WPT from power beacon (PB). Then, the SNs use the harvested energy to transmit data to the base station (BS) with large scale of multiple antennas. Finally, the BS employs maximal-ratio combining (MRC) to detect the data symbols transmitted by the SNs. As the EE optimization problem is a non-convex problem which is difficult to solve directly. A lower bound approximation and variable substitution method are used to transform the EE maximization problem into a concave-linear fractional programming. Then, an energy efficient resource allocation algorithm that combines time and power allocation is proposed by fractional programming to maximize the EE of the system. Finally, simulation results are presented to show the effectiveness of the proposed algorithm and the impact of the hardware impairments on the system performance.INDEX TERMS Massive MIMO, wireless power transfer, energy efficiency, resource allocation, hardware impairments.

The deep integration of digital economy and green development has become an inevitable requirement and an important aid in achieving the goal of carbon peaking and carbon neutrality and promoting high-quality economic development. At the same time, the manufacturing industry is the main sector of energy consumption and carbon emissions in China and the main force for achieving the carbon peaking and carbon neutrality goals. This paper constructs a mathematical model to measure the scale of the digital economy development and the efficiency of the green, low-carbon transformation of the manufacturing industry. It builds a panel data model to study the effect of the development of the digital economy on the green, low-carbon transformation of the manufacturing industry based on data of 30 Chinese provinces from 2016 to 2020. The results find that (1) there is a significant positive effect of the digital economy on the green, low-carbon transformation of the manufacturing industry, with an impact coefficient of 0.477, and this finding remains significant in the robustness test. (2) A further test of the mediating effect finds that the digital economy can drive the green, low-carbon transformation of the manufacturing industry by enhancing technological innovation, and it shows a partial mediating effect that accounts for 28% of the total effect. (3) In the regional heterogeneity analysis, it is found that the effect of the digital economy in promoting manufacturing transformation is more prominent in the central region, and the impact coefficients are 0.684, 0.806, 0.340, and 0.392 for the east, central, west, and northeast regions, respectively. This study can provide a theoretical basis and policy support for governments and enterprises.