The Large High Altitude Air Shower Observatory (LHAASO) is planned to be built at Daocheng, Sichuan Province, China. The water Cherenkov detector array (WCDA), with an area of 78,000 m2 and capacity of 350,000 tons of purified water, is one of the major components of the LHAASO project. A 9-cell detector prototype array has been built at the Yangbajing site, Tibet, China to comprehensively understand the water Cherenkov technique and investigate the engineering issues of WCDA. In this paper, the rate and charge distribution of single-channel signals are evaluated using a full detail Monte Carlo simulation. The results are discussed and compared with the prototype array.