An adaptive equalizer updates its tap coefficients with the aid of an error signal e(k)=sign[z(k)]*(R.sub.S-|z(k)|.sup.2) where sign[ ] is the sign function, z(k) is the equalizer output at symbol time k, | | is the magnitude function and R.sub.S is a positive real constant, which is optimally defined as R.sub.S=E{|a.sub.n|.sup.3}/E{|a.sub.n|}, where E{ } is the mathematical expectation function and a.sub.n is the information symbol at symbol time n. A generalized equalizer error signal satisfies e(k)=sign[z(k)]*(R.sub.Sp-|z(k)|.sup.p) where R.sub.Sp is a positive real constant, which is optimally defined as R.sub.Sp=E{|a.sub.n|.sup.p+1}/E {|a.sub.n|} and p is a positive integer. The equalizer conducts blind equalization of an Advanced Television Systems Committee-High Definition Television signal and any other one-dimensional modulation system.