Variable rate data transmission by size of constellation and symbol duration adaptation

In variable rate modulation, maximisation of data rate can be achieved either by fixing the symbol rate with an adaptive control of the constellation size, or by fixing the constellation size and changing the symbol duration. It is proved that for joint optimal control of both types, they should be used separately: the constellation size changes under a constant maximal symbol rate, and when these opportunities have been exhausted the symbol rate adaptation should be used.