Predictive power estimation of complex-valued signals

Prediction of the instantaneous power of complex-valued narrowband lowpass signals corrupted by wideband noise is investigated. We evaluate two different strategies: prediction of the squared input signal vs. prediction of the real and imaginary components separately before squaring. A constant level signal in additive complex-valued Gaussian noise is employed, which is a simplified model for slowly-varying signals, e.g., in mobile radio channels. Analytical expressions of output signal-to-noise ratios (SNRs) in terms of filter-dependent parameters and input SNR are derived and verified by simulations. The condition under which one scheme is superior over the other is obtained. These are helpful in practical design and evaluation of power prediction systems, allowing any two filters to be easily compared for this application. The obtained formulas can be employed in the design of optimal predictors