Capacity of One-dimensional and Two-dimensional Modulation Under AWGN Channels

Satellite and deep space communication channels are regarded approximately as white Gaussian noise channels approximately, so it's significant to study on channel capacities using usual modulation schemes under this channel. Starting from Shannon's information theory, this paper develops the channel capacities of one-dimensional and two-dimensional modulation schemes. Based on above, it explains that special modulation schemes ought to be adopted according to different signal to noise ratio. For example, BPSK modulation schemes is used in deep space communication because of very low signal to noise ratio. It also explains the essential of coding gain with the same spectral efficiency applying coded modulation. For instance, a rate R=2/3 convolutional code can be combined with 8-PSK modulation which can be compared with uncoded QPSK modulation, since they both have the same spectral efficiency of η=2 bit/symbol. The Shannon's limit of AM and PSK without bandwidth constraint and the asymptotic capacity of PSK with high signal to ratio are discussed at the end of this paper.