Watermarking provides an additional way to authenticate users in a stealthy way. This thesis investigates the possibility of hiding constellation dithered watermarks within oscillator phase noise of BPSK modulated signals. Message bit error rates and watermark bit error rates are compared for different phase noise standard deviations and watermark positions. Goodness of fit tests utilizing the Lilliefor's test, are conducted to determine if the investigated watermarking method can be considered stealthy.