Generalized decision error probability for linear equalization using M-ary PAM transmission

A generalized formula for decision error probability is derived in terms of equalizer tap weight coefficients for linear equalization in bandlimited channels employing M-ary PAM transmission. The generalized decision error probability is valid for any equalizer tap weight assignment (non-optimum or optimum state) as well as for any equalization algorithm. From the generalized expression, we then deduce the formulas for zero-forcing, MSE, and other equalizers at optimum state, i.e., when the equalizer is optimized. Two examples are demonstrated. Decision error probabilities are obtained for these channels theoretically using the derived formulas as well as by Monte Carlo simulations. It is found that simulation results agree excellently with the theoretical formulas.