In this letter, a novel linear transmission strategy to design the linear precoding matrix (PM) at base station (BS) and the beamforming matrix (BM) at relay station (RS) for multipleinput multiple-output (MIMO) relaying broadcast channels with direct channel (DC) is proposed, in which a linear PM is designed at BS based on DC, and the RS utilizes the PM, the backward channel and the forward channel to design the linear BM. We then give a quite tight lower bound of the achievable sumrate of the network with the proposed strategy to measure the performance. The sum-rates achieved by the proposed strategy is compared with other schemes without considering the DC in design in simulations, which shows that the proposed strategy outperforms the existing methods when RS is close to BS.Index Terms-Precoding; Relay beamforming; Sum rate; MIMO relay broadcast channels.

Abstract-Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer non-linear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.Index Terms-discrete shunt control, security constrained optimal reactive power flow, large-scale transmission networks, optimization methods, integer programming, optimal control, loss minimization, power system modelling, reactive power control

In this paper, we investigate joint source precoding matrices and relay processing matrix design for multi-user multiple-input multiple-output (MU-MIMO) non-regenerative relay networks in the presence of the direct source-destination (S-D) links. We consider both capacity and mean-squared error (MSE) criterions subject to the distributed power constraints, which are nonconvex and apparently have no simple solutions. Therefore, we propose an optimal source precoding matrix structure based on the point-to-point MIMO channel technique, and a new relay processing matrix structure under the modified power constraint at relay node, based on which, a nested iterative algorithm of jointly optimizing sources precoding and relay processing is established. We show that the capacity based optimal source precoding matrices share the same structure with the MSE based ones. So does the optimal relay processing matrix. Simulation results demonstrate that the proposed algorithm outperforms the existing results.Index Terms-MU-MIMO, non-regenerative relay, precoding matrix, direct link. I. INTRODUCTIONR ECENTLY, MIMO relay network has attracted considerable interest from both academic and industrial communities. It has been verified that wireless relay can increase coverage and capacity of the wireless networks [1]. Meanwhile, MIMO techniques can provide significant improvement for the spectral efficiency and link reliability in scattered environments because of its multiplexing and diversity gains [2]. A MIMO relay network, combining the relaying and MIMO techniques, can make use of both advantages to increase the data rate in the network edge and extend the network coverage. It is a promising technique for the next generation's wireless communications.The capacity of MIMO relay network has been extensively investigated in the literature [3]- [7]. Recent works on MIMO non-regenerative relay are focusing on how to design the

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