Capacity scaling of multi-relay channels and cooperative scheme based on relay selection

The study on cooperative schemes has become an important component of future information technology research. A multi-relay channel is considered in this paper. Fixed relay stations are adopted here to help the transmission between the base and the users. The base-relay channel can be viewed as a broadcast channel (BC) and the relay-user channel can be viewed as a multiple-access channel (MAC). No direct link exists between the base and the user.
We investigate the capacity of this special multi-relay aided communication system. The relation between the capacity and the number of relays employed by the system is given. Then we generalize the study to two special cases: A. the noises at the relay stations are much greater than those at the user; B. the noises at the user are much greater than those at the relay stations. SVD decomposition is implemented at the base station and the user according to the equivalent channel response. The joint probability density of the eigenvalue of the equivalent signal-to-interference and noise ratio(SINR) is analyzed in this paper. The relation between the capacity and the number of relays employed by the system is detailed for that two cases mentioned above.
Some idiographic results are enumerated with mathematical analysis. For case A, we proposed to use a matrix which has an F-distribution to approximately describe the joint probability distribution of the equivalent channel matrix. We show that the corresponding capacity will decrease with the increase of the number of the relays. For case B, the joint probability distribution of the equivalent channel has a Wishart-distribution. The corresponding capacity will increase with the increase of the number of the relays. After mathematical analysis, numerical results are given. Simple and practical relay selection strategies are designed for different cases.