Investigation of Error Probability for Grid and Random Uniform Topologies in a Variable Noise Environment

Abstract

Investigation of the effect of topology on the communication efficiency of WSN nodes is carried out through simulation of 9 nodes in a 12 by 12 meters area. The obtained data and plots indicate that the grid topology is a more efficient and stable topology to use in comparison to the random uniform topology. The deduction is supported by probability of error as a function of error distribution values. Five different noise levels are used in the simulation (0dBm, −20 dBm, −40 dBm, −60 dBm, −80 dBm, and −100 dBm) with an output power of −10 dBm. The work shows that at −60 dBm redistribution of probability of error as a function of error values started to occur with higher level error values associated with the random uniform topology compared with the grid topology occurring at −60 dBm noise. The work also shows the relationship between received signal strength indicator (RSSI) and probability of error which decreases as RSSI increase in a similar manner as signal to noise ratio (SNR). Both RSSI and SNR are related through the mathematical model presented in the paper which is based on the path loss model. Common features between the error probability model and Gaussian interpolation function are also presented. A simplified 1-D design model is also presented to enable initial topology considerations. Criteria are also established to enable relating SNR, RSSI, topology, and WSN incremental position.