What are the practical constraints on designing Sensing matrix in compressed Sensing? In a typical compressed sensing scenario,  $y=Ax$, where $x$ is a sparse signal and $A$ is the sensing matrix.
To reconstruct the sparse signal $x$ from $y$,  $A$ should posses the Restricted Isometry Property (RIP). Therefore, if a matrix does not possess RIP the reconstruction of $x$ will not be possible. How can we check a matrix for RIP ?
Secondly what are the practical constraints on designing the sensing matrix $A$ ? Like should the matrix consists of real values or complex? What distribution to use for generating the matrix $A$ ? etc,.
Checking for RIP of a matrix is an NP-Hard problem which means it is not computationally feasible to accomplish. RIP is used in matrix design mostly in theoretical aspects. Stealing @David 's comments, RIP is a tight condition.
To design sensing matrices, another weaker condition named Coherence is used, which its computational complexity is tractable ($O(n^2)$ where $n$ is length of matrix). No matter what type of elements form the matrix, you can always check for its coherence.
A similar question has been asked here:
Compressive sensing: numerical generation of RIP matrices . Check it out for more details.