How to create random matrices for compressive sampling?

Hi all, I'd like to reconstruct a time domain signal from an undersampled signal which is sparse in the frequency domain. In order to do regression (iterated ridge), I need first my compressive sensing matrix as my regressor. Let's say: I have y=A*x, where y is the undersampled data in the time domain of size n and A is the measurement matrix and x the original signal of size N. n<<N. Then x=ifftmatrix*z, where z is the sparse signal in the frequency domain. The formula for iterated ridge is made for non complex values. See that my regressor is going to be A*ifftmatrix, and hence I am dealing with complex numbers. Some people said that to avoid working with complex values I should split ifftmatrix into real() and imag() and then the estimated value reshape it. I thought it was sufficient to set A as a random matrix that takes the undersample data randomly and not uniformly, but this is not working...does somebody know what is wrongly stablished here? My power drops significantly though some higher power is seen at the excited frequencies. Thanks in advance