Cooperative secrecy transmission in multi-hop relay networks with interference alignment

In this study, the authors consider the secrecy communication of one source-destination pair in a wireless multi-hop relay network, where each node is equipped with multiple antennas. They use the method of interference alignment for secrecy transmission in the presence of an eavesdropper. Firstly, they propose a decode-and-forward (DF) relaying protocol and give a new result on the joint probability density function of the first, second, horizontal ellipsis , kth ($k=1, 2,\ldots $k=1,2, horizontal ellipsis ) largest eigenvalues of the complex Wishart matrices $\boldsymbol{H} \boldsymbol{H}<^>H$HHH, where $\boldsymbol{H}$H is an matrix whose elements are independent identically distributed complex Gaussian variables with zero mean and unit variance. They then utilise this result to characterise the legitimate outage probability and the diversity order of the proposed DF protocol. The case where the relay works in the amplify-and-forward (AF) mode is considered at last, and the diversity order of the proposed AF protocol is given.