Near-Optimal Self-Iterative VAMP Equalization Enabled by Hadamard-Haar Random Precoding

A self-iterative vector approximate message passing (VAMP) soft frequency-domain equalizer (SFDE) is a preferred choice for turbo equalization due to its excellent complexity-performance tradeoff. To maximize its performance, the equivalent channel matrix is required to be right-rotationally invariant (RRI) which generally does not hold though. As a result, existing VAMP-SFDEs cannot reach the performance bound. To solve such a dilemma, we propose in this letter to introduce a precoding operation on the transmitter side such that a RRI equivalent channel matrix can be obtained. The designed precoding scheme is named the Hadamard-Haar random precoding (HHRP), which is the concatenation of an inverse fast Fourier transform matrix, a random interleaving matrix, and a Hadamard-Haar transform (HHT) matrix. Attributed to the HHRP, the VAMP-SFDE applied in turbo equalization achieves extra performance gain and enjoys faster convergence over existing VAMP-SFDEs.