Maximum-likelihood (ML) detection in a multi-antenna system can be cast as a problem of closest point search in a finite lattice, which can then be efficiently solved by a sphere decoder. Although the state-of-art sphere decoding algorithms proposed by M.G. Damen et al. (see IEEE Trans. Inf. Theory, vol.49, no.10, 2003) have considered the finiteness of the lattice, many points outside the finite lattice are still tested, resulting in much unnecessary computation. We address this problem by incorporating true lattice-boundary-awareness, such that testing on any point outside the finite lattice is completely avoided. This new lattice-boundary-aware sphere decoder offers two important advantages: (i) compared to the sphere decoder proposed by Damen et al., it achieves up to 32% reduction in the number of multiplications and up to 39% in the number of additions; (ii) the complexity reduction tends to increase as SNR decreases. The proposed approach can thus significantly relax the requirements on hardware implementation of the sphere decoder.

Based on the data statistics and field investigation of domestic sewage treatment in 1414 township-level units and 17664 administrative villages in Guizhou Province, this paper summarizes and analyzes the coverage of administrative villages of sewage treatment facilities in Guizhou Province and the current treatment technology model. About 13.24% of the domestic sewage in administrative villages in the whole province has been centralized or partially centralized, and the degree of sewage treatment is relatively low. Among them, Zunyi and Guiyang are relatively high, with the coverage rates of 30.7% and 27.4% respectively. However, Bijie is the lowest with the largest rural population, which is 7.4%. In addition, through the investigation of rural sewage treatment technology mode in Guizhou Province, it can be concluded that in areas with relatively concentrated villages, centralized treatment technologies for rural domestic sewage are commonly adopted, including constructed wetlands and integrated sewage treatment equipment, and a decentralized sewage treatment system is often adopted for single households. In the selection of rural domestic sewage treatment technology scheme, the principles of simple process, low infrastructure cost, easy maintenance, and pollution-free and good removal effect of rural domestic sewage are taken as far as possible.

The study of the ecological footprints of urban water resources is of great significance for sustainable urban development and water resource management. To study the scientific utilization of urban water resources, the water resources of the nine cities and states in Guizhou Province were analyzed from 2013 to 2022 based on the water resources ecological footprint model, the water resources ecological carrying capacity model, and the water resources sustainable utilization evaluation indices. This allowed for a comparison of the regional water resource use status and prediction of the water resources ecological footprints of Guizhou Province from 2023 to 2027 using the long short-term memory (LSTM) model. The results showed that: (1) the ecological footprint of production water use in the nine cities and states of Guizhou Province had fluctuated slightly in the past decade, while both the ecological water use and domestic water use had rapidly risen after 2017. (2) The ecological carrying capacities of the nine cities and states in Guizhou Province were divided into three levels. The three cities at the highest level and with the relatively highest ecological carrying capacities fluctuated the most, and several other cities and states fluctuated less. (3) The nine cities and states in Guizhou Province were in ecological surplus, the pressure indices were all in a safe state, and the fluctuations were relatively smooth, except for in Guiyang City, where the pressure index was relatively high, and the other pressure indices were very small. (4) With economic development, the ecological footprint of water resources per capita of 10,000-yuan gross domestic product (GDP) in Guizhou Province showed a decreasing trend, indicating an improvement in the efficiency of water resource utilization. This study of the ecological footprint of urban water resources helps to realize urban development sustainability, promote effective water resource management, and protect aquatic environments. This study has important implications for the long-term prosperity of cities and the quality of life of residents.