Optimizing the Data Rate in the MIMO Relay Channel using Partial Decode-and-Forward and Convex Programming
In a MIMO relay channel, a source node transmits information to a destination with the help of a relay, and all nodes are equipped with multiple antennas. For this scenario, the capacity-achieving coding scheme is still unknown, but the so-called partial decode-and-forward protocol has been shown to perform close to the (unknown) capacity  if the statistical properties of the transmit signals are chosen optimally. To choose these parameters, an algorithm based on convex programming techniques was derived in . However, this method requires that the so-called innovation covariance matrix, which is one of the optimization variables, has full rank. Unfortunately, this is not necessarily fulfilled in the optimal solution, and it is not even clear how well the approach can approximate the global optimum in cases where a rank-deficient innovation covariance is needed.
The aim of this thesis is to study how close the proposed algorithm can come to the optimal solution in these cases, and/or whether the algorithm can be generalized in a way that it allows for a singular innovation covariance matrix. The challenge is that the constraint qualifications of one of the arising subproblems are no longer fulfilled in case of such a singularity, i.e., it might be necessary to study other optimality criteria instead of the conventional Karush-Kuhn-Tucker (KKT) conditions.
 X. Jin and Y.-H. Kim, “The approximate capacity of the MIMO relay channel,” IEEE Trans. Inf. Theory, vol. 63, no. 2, pp. 1167–1176, Feb. 2017.
 T. Wiegart, C. Hellings, and W. Utschick, “Close-to-optimal partial decode-and-forward rate in the MIMO relay channel via convex programming,” in Proc. 20th Int. ITG Workshop on Smart Antennas (WSA), Mar. 2016, pp. 581–588.
- profound knowledge of convex optimization
- basic knowledge of stochastics and linear algebra
- knowledge of (multiuser) information theory and/or MIMO systems is helpful, but can also be acquired while working on the topic