Performance Analysis and Improvement for VAMP Soft Frequency-Domain Equalizers

The vector approximate message passing (VAMP) soft frequency-domain equalizer (SFDE) has been proposed for turbo equalization. It consists of an inner soft equalizer (ISE) and an inner soft slicer (ISS), which iteratively exchange block-wise extrinsic information to improve the equalization performance, analogous to the outer turbo iteration between a soft equalizer and a soft decoder. However, a comparison of the VAMP-SFDE with other types of self-iterative SFDEs, including the self-iterative block-wise soft interference cancellation (SI-BSIC) SFDE and the generalized approximate message passing (GAMP) SFDE, is lacking. Moreover, comprehensive performance analysis for the VAMP-SFDE is yet to be performed. In this paper, relations among the VAMP-SFDE, the SI-BSIC-SFDE, and the GAMP-SFDE are first revealed. After that, the performance analysis is provided for the VAMP-SFDE and it leads to an improved semi-adaptive damping (SAD) scheme for maintaining the independence between the ISS and ISE. The resulting SAD-VAMP-SFDE shows improved mean square error (MSE) evolution curves compared with the original VAMP-SFDE. The SAD-VAMP-SFDE-based turbo equalization outperforms those using the SI-BSIC-SFDE or GAMP-SFDE and approaches the matched filter bound (MFB) over low signal-to-noise ratio region. To further demonstrate its superiority, the SAD-VAMP-SFDE is employed to enable a near-capacity transceiver design, which adopts the serial concatenation of an irregular convolutional code and a unity-rate code on the transmitter side.