Fast method for precoding and decoding of distributive multi-input multi-output channels in relay-based decode-and-forward cooperative wireless networks

It is well-known that the performance of the relay-based decode-and-forward (DF) cooperative networks outperforms the performance of the amplify-and-forward cooperative networks. However, this performance improvement is accomplished at the expense of adding more signal processing complexity (precoding/decoding) at each relay node. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be n??n matrices A=(a _jk) over a field F with the property AA ^??=nI _n, where A ^?? is the transpose matrix of the element-wise inverse of A, that is, A ^??=(a _kj ^-1), which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.