New constraints based on practical hardware are introduced in Compressive Sensing (CS) based rectangular antenna array thinning technique. In a standard CS array sparsity enforcement, antenna elements are considered as ideal point sources which does not comply with the practical hardware. It also does not consider the impact of mutual coupling of neighbouring antenna elements on the impedance mismatch. In this work, we propose a combination of constraints based on physical antenna array specifications, mutual coupling and practical antenna element radiation performance in the CS based array thinning enforcement. Analytical modelling along with a design example is presented and discussed. Array performance based on full--wave electromagnetic simulations show the reliability of the proposed approach.