The modified autocorrelation technique for parameter estimation of random FH signals
Multiple-hop autocorrelation (MHAC) processing is used for estimating the parameter of frequency-hopping (FH) signals in the presence of broadband thermal noise. The dependence on hopping frequency carrier phase and hop timing is suppressed by power sampling in the MHAC domain, while maintaining signal power and hop-rate information. We propose and analyze a joint recursive signal power and hop-rate estimator, based on maximum likelihood arguments. The conditional mean and variance of the estimator are derived and compared to a similar method assuming a priori knowledge of signal power.
In this paper we study the multivariate ANOVA decomposition for $1$-periodic functions on the torus. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. Relationships between the Fourier coefficients of the function and its ANOVA terms lead to special frequency index sets and give an understanding of the decomposition working in the frequency domain. Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in $\mathrm{L}_\infty$ and $\mathrm{L}_2$. We present an approximation method based on the truncated decomposition with regard to a superposition dimension $d_s$.