This paper describes the general concept of the channel capacity, gives a detailed analysis of the channel capacity of the waveform channel, continuous channel and the discrete input continuous output memoryless channel, then derives their general formulae of the channel capacity respectively. Combined with several known m-ary multidimensional modulation techniques and their constellation analysis, Monte-Carlo simulation and the numerical integral simulation are given for their channel capacity. Finally the coding gain due to the signal sets expansion is analyzed.