Based on the Berktay's farfield solution, various preprocessing methods were proposed to reduce the distortion of the highly directional audible signal in the parametric loudspeaker. However, the Berktay's farfield solution is an approximated model of nonlinear acoustic propagation. To determine the effectiveness of these methods, we analyze various preprocessing methods theoretically for directional speech reproduction using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, which provides a more accurate model of nonlinear acoustic propagation. In order to reduce the distortion effectively in the parametric loudspeaker with these preprocessing methods, the initial sound pressure level of the carrier frequency is found to be less than 132 dB according to the KZK equation. Unlike the Berktay' farfield solution that results in a +12 dB/octave gain slope, different gain slopes are derived using the KZK equation and appropriate equalizers are proposed to improve the frequency response of the parametric loudspeaker. The optimal preprocessing method for directional speech reproduction is established based on the KZK equation, which has a relatively flat frequency response of the desired speech signal and the best total harmonic distortion performance.