Constructing Equiangular Tight Frames Based on Singular Values Energy Homogenization Under Normalization Constraint

The construction of equiangular tight frames (ETFs) has been proven very difficult. As ETFs do not exist for all dimension scenarios, some scholars call those approximate ETFs incoherent unit norm tight frames that are also the objects we consider here. As the name implies, these frames contain two properties-incoherence and tightness. In this paper, employing alternating projection method, a procedure based on singular values energy homogenization is proposed to obtain these properties of the designed frames. As the columns of the desired frame should be with unit norm, a new model that embeds the column normalization within the construction procedure is developed. The new construction model is then addressed by a gradient-based approach with low computational complexity. Simulations demonstrate the superiority of the proposed ETFs construction method.