Performance analysis of random angle based quantization modulation

The random angle based quantization modulation (RAQM) is a new watermarking method invariant to valumetric scaling attack. In this paper, the performance of RAQM is theoretically evaluated in two aspects: the embedding distortion and the decoding performance against additive noise attack. The analyses are developed under the assumptions that the host and noise vectors are mutually independent and both of them have independently and identically distributed components. We establish the stochastic models for several concerned signals. Based on them, the expressions of the embedding distortion and the decoding bit-error probability are derived in closed form. We also present the simplified but effective approximations to these analytical results. The analyses allow us to get more insight into the impact of various factors on the performance of RAQM. Numerical simulations confirm the validity of our analyses and exhibit the performance advantage of RAQM over similar modulation techniques.