Capture and imperfect power control in spread-ALOHA systems with lognormal shadowing

This paper investigates the performance of a spread slotted ALOHA system with power control errors that lead to the capture effect. This paper is motivated by the apparent uncertainties in the performance of a spread-ALOHA system with unequal received power at the base stations. The assumption made by Schwartz and Yeh (1982) that the sum of lognormal random variables is also lognormal, is used in determining an expression for the probability of capture. This paper shows that the analytical expression for capture gives the same throughput curves as lognormal power control errors. It is further shown that higher throughputs at heavy loads are obtained when there are imperfections in power control