Advantages of application of the tanh-pulse shaping in the base-band

In this paper, we apply the tanh-shaped pulses to transmit binary random data in the base-band. The theoretical formula of the Fourier transform of the tanh-pulse is derived. The power spectral density of the tanh-pulse calculated numerically is presented. The advantages of applying the tanh-model are shown. In comparison to commonly used rectangular or raised-cosine pulse shaping, here we change the slope of the pulse and form the bandwidth. We propose two methods of application of the tanh-pulse shaping to transmit additional information. In the first method, the change of the slope of the pulse in successive M frames is introduced. The second method applies the change of the position of the pulse in successive M frames. The paper is illustrated with numerous examples.