Disclosed are methods and a device for Multi-resolution PMI Feedback. In one implementation, a user equipment finds a rank 1 or rank 2 Precoding Matrix Indicator based on the signal channel matrix and interference covariance matrix, defines an error vector, obtains an orthonormal basis for the projection matrix, finds the (M−1)-dimensional vector from a codebook (e.g., oversampled Discrete Fourier Transform) with the minimum Euclidean distance, and sends a feedback representing to the base station regarding the vector that it found in the codebook.