Fixed-Point Implementation of Cascaded Forward–Backward Adaptive Predictors

Adaptive least mean square (LMS) predictors with independently low-order cascaded structures, such as the cascaded forward LMS (CFLMS) and cascaded forward-backward LMS (CFBLMS), have proven effective in combating the misadjustment and eigenvalue spread effects of linear predictors. Further developing this cascade structure, we study the fixed-point implementation of CFBLMS with applications to speech signals. Moreover, two groups of predictors with a total of six cases are compared. Group 1 employs the transversal structure for LMS, CFLMS, and CFBLMS algorithms. Group 2 employs the lattice structure for LMS, CFLMS, and CFBLMS algorithms. Experimental results show that, in group 1, the performance degradation of CFBLMS and CFLMS predictors becomes significant when the number of bits is reduced to 8, while that of the LMS predictor becomes significant when the number of bits is reduced to 9. On the other hand, in group 2, the performance degradation of CFBLMS and CFLMS predictors becomes significant when the number of bits is reduced to 5, while that of the LMS predictor becomes significant when the number of bits is reduced to 6. In both groups, the performances of CFBLMS and CFLMS are significantly superior to that of LMS, and CFBLMS is superior to CFLMS, in terms of the rate of convergence, misadjustment, and mean-square error (MSE).