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In this paper we study the effect of phase noise (PHN) in a single carrier cyclic prefix (SCCP) system operating with a known cyclic prefix. The PHN process is a limiting factor in high throughput communication systems as higher-order constellations are extremely sensitive to it. In this paper we propose a robust and non-iterative scheme to enhance both the estimation of, and compensation for, the PHN process and this also includes channel estimation. In contrast to existing approaches for PHN compensation, in this paper we use a known cyclic prefix, pilot bins and interpolation over the PHN estimates. Simulation results show that the performance of SCCP with a known cyclic prefix is superior to SCCP systems with conventional compensation schemes in the moderate and higher SNR region for all values of PHN.