This paper analyzes the error performance of M-ary amplitude phase-shift keying (M-APSK) signals with annular-sector (AS) detection over the channel where both additive white Gaussian noise and oscillator phase noise exist. This AS detector performs ring detection and phase detection separately, and leads to the circular decision boundaries in the middle of rings. We derive a unified, closed-form expression for the symbol error probability (SEP) of M-APSK with phase reference error (PRE) due to imperfect phase estimation, based on our previously proposed additive observation phase noise model. The SEP result is analytically tractable and consists of products of Gaussian Q-functions. An accurate, unified approximation to the error floor is directly obtained as a sum of Gaussian Q- functions. Within a wide range of PRE variances, our approximations agree very well with the Monte Carlo simulation for all signal-to-noise ratio (SNR) values of interest. We show that as the PRE variance or the SNR or both increase, the AS detector outperforms the conventional minimum Euclidean distance detector. Moreover, our results provide explicit insight into how the parameters affect the error performance, and facilitate the optimization of M-APSK constellations in phase noise. Examples of ring radii optimization have been given.