Power Series Characterization of the Discrete Nonlinear Satellite Channel

In most digital satellite communications links the message is determined on the basis of periodically sampled voltages of the received signal. Assuming that in the absence of noise each sample voltage depends significantly only on a finite number of message bits, one can define a discrete channel in the form of a power series in these bits. From a complete set of sample voltages computed by simulation the coefficients of the series are readily obtained by means of the fast Hadamard transform. Examples computed for rudimentary nonlinear channels that include limiters, amplitude-to-phase converting elements, or traveling wave tubes show that the series contains only a small number of significant terms, and that each specific type of nonlinearity is associated with specific nonlinear terms. The degradation in performance in the presence of noise that results from the largest nonlinear terms in the expansion is of an inherent nature, and can only be corrected in small part by receiver equalization. On the other hand, a simple minded predistortion scheme appears to remove most of this degradation.