Limited feedback unitary precoding using improved Euclidean distance metrics for spatial multiplexing systems

This paper presents a new codeword selection criterion based on the Euclidean distance in the limited feedback unitary precoding systems. Because of the non-uniqueness of singular value decomposition (SVD), various precoding matrices may result in the same performance. We take the rotation and permutation invariance property into the definition of distortion function, then bring forward a new codeword selection criterion and distance metric derived from the improved Euclidean distance. A codebook design method based on the generalized Lloyd algorithm (GLA) is proposed thereafter. For the traditional subspace distance on the Grassmann manifold, the transmit data streams must be less than the transmit antennas, otherwise all the precoding matrices result in the same distortion results, however, our new distance metric can overcome this limitation. Simulation results show that our proposed distance metric can work properly with the unitary precoding codebook, apart from this, it can also acquire excellent performance under other spatial multiplexing environments.