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In this article, we introduce a frequency-based waveform design to maximize binary target classification. The optimization problems can be solved via optimal solvers available in the literature. The presented formulation is applicable to the classification scenarios where the extended target frequency responses (TFRs) are complex, random, and normally distributed with unequal mean vectors. However, their covariance matrices are either identical or different. For the former, i.e., identical covariance matrices, the optimization problem consists of a cost function that has been obtained by deriving a closed-form expression of the probability of misclassification. For the latter, i.e., different covariance matrices, we present an optimization problem where the cost function has been obtained via the Fisher separation function. For this, we also present a closed-form expression for an approximate solution to the optimization problem. We show that the proposed solution achieves performance levels comparable to the exact solution of the optimization problem obtained via state-of-the-art optimization solvers while incurring low computational complexity. We expand on the two main scenarios by introducing clutter (i.e., signal-dependent interference) in the signal model and studying possible closed-form designs in extreme waveform energy levels. Simulations are conducted using synthetically generated data in addition to the civilian vehicle data from the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset, in order to validate the proposed method.

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