A note on the resolution of the entropy discrepancy

It was found by Hung, Myers and Smolkin that there is entropy discrepancy for the CFTs in 6-dimensional space-time, between the field theoretical and the holographic analysis. Recently, two different resolutions to this puzzle have been proposed. One of them suggests to utilize the anomaly-like entropy and the generalized Wald entropy to resolve the HMS puzzle, while the other one initiates to use the entanglement entropy which arises from total derivative terms in the Weyl anomaly to explain the HMS mismatch. We investigate these two proposals carefully in this note. By studying the CFTs dual to Einstein gravity, we find that the second proposal can not solve the HMS puzzle. Moreover, the Wald entropy formula is not well-defined on horizon with extrinsic curvatures, in the sense that, in general, it gives different results for equivalent actions.Comment: 12 pages, no figures, accepted by PL

Robust design for linear non-regenerative MIMO relays with imperfect channel state information

In this paper, we address statistically robust multiple-input multiple-output (MIMO) relay design problems under two imperfect channel state information (CSI) scenarios: (1) All nodes have imperfect CSI; (2) The destination node knows the exact CSI, while the other nodes have imperfect CSI. For each scenario, we develop robust source and relay matrices by considering a broad class of frequently used objective functions in MIMO system design and the averaged transmission power constraints. Simulation results demonstrate the improved robustness of the proposed algorithms against CSI errors

MMSE-DFE Based MIMO Relay System with Correlated Fading Channel

We consider a practical dual-hop nonregenerative multiple-input multiple-output (MIMO) relay system, where the relay node only knows the correlation matrix of the relaydestination channel. A nonlinear minimal mean-squared error (MMSE)-based decision feedback equalizer (DFE) is used at the destination node to retrieve the source signals. We derive the structure of statistically optimal source and relay precoding matrices to minimize a class of objective functions which are multiplicatively Schur-convex with respect to the diagonal elements of the MSE matrix. Simulation results demonstrate thatthe proposed algorithm has a very close performance compared to MIMO relay system with full channel knowledge at the relay node, and thus is very useful for practical relay systems

Superimposed channel training for MIMO relay systems

Based on the knowledge of instantaneous channel state information (CSI), the optimal source and relay pre-coding matrices have been developed recently for multiple-input multiple-output (MIMO) relay communication systems. However, in real communication systems, the instantaneous CSI is unknown and needs to be estimated at the destination node. In this paper, we propose a superimposed channel training method for MIMO relay communication systems. It is shown that to minimize the mean-squared error (MSE) of channel estimation, the optimal training sequence at each node matches the eigenvector matrix of the transmitter correlation matrix of the forward MIMO channel. Then we optimize the power allocation among different streams of the training sequence at the source node and the relay node. Simulation results show that the proposed algorithm leads to a smaller MSE of channel estimation compared with the conventional MIMO relay channel estimation algorithm

Multihop Nonregenerative MIMO Relays - QoS Considerations

For nonregenerative multihop multiple-input multiple-output (MIMO) relay communication systems, the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node. However, existing works do not consider any quality-of-service (QoS) constraints, which are important in practical communication systems. In this paper, we derive the optimal source and relay matrices of a multihop MIMO relay system that guarantee the predetermined QoS criteria be attained with the minimal total transmission power. In particular, we consider two types of receivers at the destination node: the linear minimal mean-squared error (MMSE) receiver and the nonlinear decision feedback equalizer (DFE) based on the MMSE criterion. We show that for both types of receivers, the solution to the original optimization problem can be upper-bounded by using a successive geometric programming (GP) approach and lower-bounded by utilizing a dual decomposition technique. Simulation results show that both bounds are tight, and to obtain the same QoS, the MIMO relay system using the nonlinear MMSE-DFE receiver requires substantially less total transmission power than the linear MMSE receiver-based system

Joint source and relay optimization for two-way linear non-regenerative MIMO relay communications

In this paper, we investigate the challenging problem of joint source and relay optimization for two-way linear non-regenerative multiple-input multiple-output (MIMO) relay communication systems. We derive the optimal structure of the source and relay precoding matrices when linear minimal mean-squared error (MMSE) receivers are used at both destinations in the relay system. We show that for a broad class of frequently used objective functions for MIMO communications such as the MMSE, the maximal mutual information (MMI), and the minimax MSE, the optimal relay and source matrices have a general beamforming structure. This result includes existing works as special cases. Based on this optimal structure, a new iterative algorithm is developed to jointly optimize the relay and source matrices. We also propose a novel suboptimal relay precoding matrix design which significantly reduces the computational complexity of the optimal design with only a marginal performance degradation. Interestingly, we show that this suboptimal relay matrix is indeed optimal for some special cases. The performance of the proposed algorithms are demonstrated by numerical simulations. It is shown that the novel minimax MSE-based two-way relay system has a better bit-error-rate (BER) performance compared with existing two-way relay systems using the MMSE and the MMI criteria

Optimal Joint Source and Relay Beamforming for MIMO Relays with Direct Link

In this letter, we investigate the optimal structure of the source precoding matrix and the relay amplifying matrix for non-regenerative multiple-input multiple-output (MIMO) relay communication systems with the direct source-destination link. We show that both the optimal source precoding matrix and the optimal relay amplifying matrix have a beamforming structure. Based on this structure, an iterative joint source and relay beamforming algorithm is developed to minimize the mean-squared error (MSE) of the signal waveform estimation. Numerical example demonstrates an improved performance of the proposed algorithm

Linear Non-Regenerative Multicarrier MIMO Relay Communications Based on MMSE Criterion

In this letter we propose linear non-regenerative multicarrier multiple-input multiple-output (MIMO) relay technique that aims to minimize the mean-squared error (MSE) of the signal waveform estimation at the destination. We generalize the existing result on the structure of the optimal relay amplifying matrix by considering the direct source-destination link. To minimize the MSE, a power loading algorithm is developed which has a significantly reduced computational complexity compared with existing techniques