This manuscript concerns the performance analysis in signal processing and consists into two parts : First, we study the lower bounds in characterizing and predicting the estimation performance in terms of mean square error (MSE). The lower bounds on the MSE give the minimum variance that an estimator can expect to achieve and it can be divided into two categories depending on the parameter assumption: the so-called deterministic bounds dealing with the deterministic unknown parameters, and the so-called Bayesian bounds dealing with the random unknown parameter. Particularly, we derive the closed-form expressions of the lower bounds for two applications in two different fields: (i) The first one is the target localization using the multiple-input multiple-output (MIMO) radar in which we derive the lower bounds in the contexts with and without modeling errors, respectively. (ii) The other one is the pulse phase estimation of X-ray pulsars which is a potential solution for autonomous deep space navigation. In this application, we show the potential universality of lower bounds to tackle problems with parameterized probability density function (pdf) different from classical Gaussian pdf since in X-ray pulse phase estimation, observations are modeled with a Poisson distribution. Second, we study the statistical resolution limit (SRL) which is the minimal distance in terms of the parameter of interest between two signals allowing to correctly separate/estimate the parameters of interest. More precisely, we derive the SRL in two contexts: array processing and MIMO radar by using two approaches based on the estimation theory and information theory. We also present in this thesis the usefulness of SRL in optimizing the array system.
