Eigen-basis analysis of expected modulus perturbation for constrained signal design

Radar waveforms typically require a constant modulus (constant amplitude) transmit signal to efficiently exploit the available transmit power. However, recent hardware advances and the capability for arbitrary (phase and amplitude) designed waveforms have forced a re-examination of this assumption to quantify the impact of modulus perturbation from phase only signals. In this paper, we express the signal modulus in terms of an eigen-basis obtained from a well-known eigenvalue distribution that is equivalent, in the limit of large data, to the eigen-spectrum of an interference and noise covariance matrix for certain radar data. We also derive a generalized predictive model for the signal-to-interference-and-noise ratio (SINR) as a function of the modulus and basis dimension to aid in the decision making process of an adaptive radar. Monte Carlo computer simulations are used to validate the analytical findings.