Given a multiple-antenna source and a multiple-antenna destination, a multiple-antenna relay between the source and the destination is desirable under useful circumstances. A non-regenerative multiple-antenna relay, also called non-regenerative MIMO (multi-input multi-output) relay, is designed to optimize the capacity between the source and the destination. Without a direct link between the source and the destination, the optimal canonical coordinates of the relay matrix are first established, and the optimal power allocations along these coordinates are then found. The system capacity with the optimal relay matrix is shown to be significantly higher than those with heuristic relay matrices. When a direct link is present, upper and lower bounds of the optimal system capacity are discussed.

In this paper, we develop a unified framework for linear nonregenerative multicarrier multiple-input multiple-output (MIMO) relay communications in the absence of the direct source-destination link. This unified framework classifies most commonly used design objectives such as the minimal mean-square error and the maximal mutual information into two categories: Schur-concave and Schur-convex functions. We prove that for Schur-concave objective functions, the optimal source precoding matrix and relay amplifying matrix jointly diagonalize the source-relay-destination channel matrix and convert the multicarrier MIMO relay channel into parallel single-input single-output (SISO) relay channels. While for Schur-convex objectives, such joint diagonalization occurs after a specific rotation of the source precoding matrix. After the optimal structure of the source and relay matrices is determined, the linear nonregenerative relay design problem boils down to the issue of power loading among the resulting SISO relay channels. We show that this power loading problem can be efficiently solved by an alternating technique. Numerical examples demonstrate the effectiveness of the proposed framework.

Background

This article describes a pilot study evaluating a novel liquid biopsy system for non-small cell lung cancer (NSCLC) patients. The electric field-induced release and measurement (EFIRM) method utilizes an electrochemical biosensor for detecting oncogenic mutations in biofluids.

Methods

Saliva and plasma of 17 patients were collected from three cancer centers prior to and after surgical resection. The EFIRM method was then applied to the collected samples to assay for exon 19 deletion and p.L858 mutations. EFIRM results were compared with cobas results of exon 19 deletion and p.L858 mutation detection in cancer tissues.

Results

The EFIRM method was found to detect exon 19 deletion with an area under the curve (AUC) of 1.0 in both saliva and plasma samples in lung cancer patients. For L858R mutation detection, the AUC of saliva was 1.0, while the AUC of plasma was 0.98. Strong correlations were also found between presurgery and post-surgery samples for both saliva (0.86 for exon 19 and 0.98 for L858R) and plasma (0.73 for exon 19 and 0.94 for L858R).

Conclusion

Our study demonstrates the feasibility of utilizing EFIRM to rapidly, non-invasively, and conveniently detect epidermal growth factor receptor mutations in the saliva of patients with NSCLC, with results corresponding perfectly with the results of cobas tissue genotyping.