Signature scheme using RSA and SHA512

What do you think about this signature scheme using RSA with 4096 bit keys?

Being R pseudorandom padding, fixed length (4096 - 512 bits):

RSApriv(R || SHA512(M))

I know that it's not as secure as RSASSA-PSS, but it looks better than RSASSA-PKCS1 to me (because of the random padding).

Am I missing anything important?

Thanks in advance.