A communication signal receiver includes a feed-forward filter and a coefficient adjusting circuit. The feed-forward filter generates an estimated imaginary-part component signal according to a real-part component of a complex data signal by using tap coefficients of the feed-forward filter. The coefficient adjusting circuit adjusts the tap coefficients of the feed-forward filter according to a control information, wherein the control information comprises a phase error information. The phase error information changes as a phase of the complex data signal changes, wherein the phase is adjusted or not adjusted by the coefficient adjusting circuit.