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Input-distribution optimization for channels with estimation errors

Gaussian signals are widely assumed in various design and analysis since the classical work of Shannon. However, the optimality of Gaussian signals is valid only when perfect channel information is available at the receiver. In many practical applications, only a channel estimate is available with certain estimation errors. It is therefore of practical importance to ask what is the optimal input distribution for such a system. The optimization can theoretically be formulated in the framework of variational calculus which, however, is in general mathematically intractable. This letter therefore takes a compromise between the optimality and tractability by confining our optimal search within the popular Pearson's distribution system. The result is Pearson's type-VII (PT-7) distribution and its superiority over the Gaussian distribution is confirmed by both theoretical analysis and computer simulations.