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In this paper, we carry out a simulation study of the sensitivity of handover performance to standard deviation of lognormal shadow fading in a mobile radio environment. The handover algorithm is based on received signal strength measurements. Handover rate and initiation delay are used as performance metrics. It is shown that the performance metrics depend on standard deviation of shadow fading. In a nonuniform environment, the standard deviation may be different at different places and a given handover scheme with fixed design parameters cannot give optimum results consistently in the entire cellular service area. Through numerical results, it is further shown that the effect of hysteresis margin on handover performance depends on its relative value as referred to standard deviation of lognormal shadow fading in the prevailing cellular propagation environment. To achieve optimum handover performance, hysteresis margin as a handover design parameter is determined in terms of standard deviation of shadow fading in varied radio propagation environments.