Abstract
This paper investigates the impact of nonlinear transformation on signal detection from a minimum error probability perspective. Firstly, we derive the probability density distributions of three transformed received signal over binary input additive white Gaussian noise (BIAWGN) channel, including square transformation, abs (absolute value) transformation and changing the sampling times. Then, we derive the three optimal decision thresholds respectively for the three transformations under the criteria of minimum error probability. Furthermore, we make simulations to compare the minimum error probability of the three transformed ones with the original signal, trying to find the nonlinear transformation with smaller minimum error probability.
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