There’s isn’t a need to do a conversion in Matlab code . CVx itself is supposedly adaptable and strongly works well with Matlab. Their implementing of error messages is to guide where you had gone wrong .What is missing is your lack of understanding towards CVX programming and convex optimization. This example of your paper gives an added advantage of how CVX programming on SDP is well written but can futher improved with implicit comment enhancement with readabilty . I highly recommend that you spend time on courses and video availability of Dr Stephen Boyd and Dr Ahmad Bazzi to strengthen your core understanding and get the basic and fundamental right . Their videos are easily available on the net.