Capacity and coding/modulation study for partially coherent additive white Gaussian noise channels

Due to the synchronization problem, perfect phase detection is almost impossible for a practical signal transmission system. The phase-lock-loop circuit is widely used in wireless communication and digital communication to detect the phase of a transmitted signal. In the sense of either theory or practice, it is interesting to examine coding problems when channel phase cannot be obtained accurately. Since channel capacity is the limit of reliable communication, looking for channel capacity for a particular channel is a good starting point for channel coding.; This dissertation considers Shannon capacity of a partially coherent additive white Gaussian noise (PCAWGN) channel where partial coherence is due to phase-lock-loop circuits. Using various techniques such as calculus of variation, functional analysis with probability measure, real analysis, constrained optimization and complex analysis, conditions of capacity-achieving signals for PCAWGN channels are studied and hence the Kuhn Tucker condition for capacity-achieving input to the channel is obtained. Using this condition, it is easy to show that Gaussian signals cannot be optimal in the sense of capacity, which, however, is true for AWGN channels.; Diversity techniques are extensively used in wireless communication applications; which can decrease bit error probability effectively and substantially. In this dissertation, we apply diversity technique to PCAWGN channels in order to investigate if this technique can mitigate phase uncertainty without much sacrifice of capacity. It is shown in this dissertation that temporal diversity introduced by a long orthogonal (all-pass) filter can transform a PCAWGN channel to a quasi-AWGN channel where quasi-AWGN means the channel is not a truly joint Gaussian but only marginally Gaussian. The capacity (for this quasi-AWGN channel), however, is significantly reduced a lot, which is caused by intersymbol interference. This shows that such an application of diversity technique is not appropriate for PCAWGN channels.; One of the merits that digital communication has is that the performance achieved by digital communication can be as good as that by analog communication but has the lower implementation cost. To use digital communication over PCAWGN channels more efficiently, signal-constrained capacity is investigated and compared with a tight lower bound to channel capacity we have obtained. For a typical PCAWGN channel, it is shown that non-equiprobable signaling with signal set expansion factor 4 is needed, in contrast with an AWGN channel which has expansion factor 2 and does not need non-equiprobable signaling except at high rates. Several constellations are suggested and their capacity performances are evaluated, which can be used for future coding design.; Finally, coding and modulation approaches are studied. Several signal constellations found earlier are used for code design in order to achieve coding and shaping gain. Because of complexity and nonlinearity of PCAWGN channels, high-dimensional modulation with shaping encoder is considered as well.