Linear Turbo Equalization Analysis via BER Transfer and EXIT Charts

In this paper, two analytical methods are presented to investigate the soft information evolution characteristics of a soft-input soft-output (SISO) linear equalizer and its application to the design of turbo equalization systems without the reliance on extensive simulation. Given the channel and a SISO equalization algorithm, one method explored is to analytically compute the bit-error rate (BER) of the SISO equalizer in two extreme cases (no and perfect a priori information) from which a BER transfer characteristic is estimated. The second approach is to compute the mutual information [a key parameter of the extrinsic information transfer (EXIT) chart] at the two end points of the EXIT function. Then, by modeling the SISO equalizer BER transfer and EXIT functions as linear, some of the behavior of linear turbo equalization, such as how the BER performance can be improved as iterations proceed, can be predicted. Further, soft information evolution characteristics of different linear SISO equalizers can be compared and the usefulness of iterative methods such as linear turbo equalization for a given channel can be determined. Compared with existing methods for generating EXIT functions, these predictive methods provide insight into the iterative behavior of linear turbo equalizers with substantial reduction in numerical complexity.