On The Capacity Of The State-dependent Relay Channel With Channel State Information

In many communication scenarios, the channel is time-varying or is state-dependent. The communicating nodes may acquire some state information to improve the channel capacity. State-dependent channels with state information can be used to model many communication systems, e.g. in the communication systems with cognitive radio, the channel state can be viewed as the signals of the primary communication and the informed nodes with channel state information can be viewed as the cognitive secondary users. In order to improve the achievable rates of the secondary communication system and the frequency spectrum efficiency, it is important for the cognitive secondary users to adapt their coding schemes to mitigate the interferences caused by the primary communication. Moreover, the broadcast nature of the wireless channels facilitates the cooperation among the communicating nodes. The design of cooperation strategies with high-performance and low complexity is one of the most important research points. In this thesis, the capacity of the state-dependent relay channel is studied. The main results are summarized as follows:For the multiple-hop relay channel with linear relaying by which the relay nodes transmit linear combination of their past received signals, the exact capacity is derived. It is proved that the capacity of the multiple-hop relay channel with linear relaying can be equivalent to a “single-letter” optimization problem when some certain conditions are satisfied. It is further shown that the solution to this “single-letter” optimization problem has the same form as the expression of the achievable rate of the multiple-hop relay channel with time-sharing amplify-and-forward(TSAF) relaying. An iterative algorithm is given to solve this “single-letter” optimization problem to derive the achievable rate for the TSAF relaying. Numerical results show that the achievable rate with TSAF relaying is close to the capacity when the channel gain of each hop varies significantly. For the multiple-hop relay channel, though the decode-and-forward(DF) relaying achieves the capacity, the complexity of the TSAF relaying is almost as low as that of the amplify-and-forward(AF) relaying since the TSAF relaying doesn’t require any encoding and decoding at the relay nodes. Therefore, for the networks such as wireless sensor networks, of which the processing ability is poor, the transmission power is limited, nodes usually communicate through multiple-hop routes and channel gain of each hop varies significantly among different paths, the TSAF scheme can achieve a good trade-off between processing complexity and achievable rates.For the discrete memoryless state-dependent relay channel with orthogonal channels from the source to the relay and from the source and the relay to the destination, it is assumed that the two orthogonal channels are corrupted by two independent channel states. When the source node and the relay node know the channel state information(CSI) non-causally, the lower bound on the capacity is derived combining partial-decode-and-forward(PDF) relaying and cooperative GP(Gel’fand-Pinsker) coding. It is further shown that the lower bound is tight for a class of semi-deterministic orthogonal relay channel for which the exact capacity is characterized. When the CSI is known causally at the source node and the relay node, the lower bound is derived combining Shannon’s strategy and PDF relaying.The capacity results derived for the above discrete memoryless relay channel are then extended to the Gaussian orthogonal relay channel with additive interferences, where the channel states model the additive interferences. When the source node and the relay node know the CSI non-causally, the capacity is characterized exactly based on cooperative dirty-paper coding and PDF relaying. And the capacity is the same as that of the orthogonal relay channel without interferences, which means that the interferences are cleaned totally. However, when the CSI is known causally to the source node and the relay node, the capacity cannot be characterized in general. In this case, only the lower bound on the capacity is established based on generalized dirty-paper coding. Further, the capacity is characterized when the power of the relay is sufficiently large to meet some certain conditions. Some numerical examples of the causal state information case are provided to illustrate the impact of the channel state and the role of the relay in information transmission and in cleaning the channel state.The capacity region of the state-dependent two-way relay channel with two independent additive Gaussian interferences is studied assuming part of the nodes know partial CSI. Three conditions are considered:(1) each of the two users knows one of the two interferences respectively;(2) one user knows one of the interferences while the relay node knows the other;(3) the relay node knows both the interferences. For the above three cases, the nodes with CSI can exploit the knowledge of the channel states to pre-cancel part of the interferences. Combing nested lattice coding and compute-and-forward relaying, the inner bounds of the capacity regions under the above three conditions are derived respectively and the inner bounds derived in this thesis are within constant gaps from the corresponding cut-set outer bounds regardless of the interferences:(1) when each of the two users knows one of the two interferences, the inner bound is within 1 bit from the cut-set outer bound;(2) when one user knows one of the interferences while the relay node knows the other, the achievable rate R1 of the message from user 1 is within 1 bit from the upper bound while the achievable rate R2 of the message from user 2 is within 1/2 bit from the upper bound;(3) when the relay knows both the interferences, the inner bound is within 1/2 bit from the cut-set outer bound.