Limits on classifying pulsed signals

Fundamental bounds are presented for classifying pulsed signals observed in additive Gaussian noise. The bounds specify the maximum number of signals that can be reliably classified as a function of the signal to noise ratio (SNR) and the dimension of the subspace containing the signals. The bounds are based on a “sphere packing” arrangement for the signals that maximizes the probability of correct classification. The bounds are easy to compute and provide a reference to facilitate comparisons between classification algorithms. An example is presented in which the signals consist of RF pulses with different center frequencies, and the sphere packing bounds are compared with the performance of the maximum likelihood classifier