Widely linear processing (WLP) can provide attractive performance improvement in wireless communication systems. However, performance improvement brought by WLP is mainly achieved by exploiting signal's non-circularity, which leads to the fact that existing works on WLP are mainly confined to the cases related to non circular signals or improper signals with imbalanced I/Q components. In this paper, WLP for circular signals, such as PSK signals, is investigated by exploiting the hidden properties of PSK signals. The hidden properties of PSK signals are firstly studied, and a unified mathematical model is derived to describe the hidden properties of PSK signals. Furthermore, a widely linear sphere decoding (WLSD) algorithm exploiting PSK signals' hidden properties is proposed for MIMO systems. Compared to traditional sphere decoding (SD), WLSD has little performance loss, and it transforms the traditional SD searching for the true transmitted vector into the shrunk searching for the corresponding rotation vector, the candidate rotation vectors of WLSD are only (1/2)^NT of SD candidate vectors. Simulation results show that the proposed algorithm can achieve quasi-optimal BER performance, while the computational complexity is significantly reduced by more than a half compared with Schnorr-Euchner sphere decoder.