Compute-and-Forward on a Multi-User Multi-Relay Channel

In this paper, we consider a system in which multiple users communicate with a destination with the help of multiple half-duplex relays. Based on the compute-and-forward scheme, each relay, instead of decoding the users' messages, decodes an integer-valued linear combination that relates the transmitted messages. Then, it forwards the linear combination towards the destination. Given these linear combinations, the destination may or may not recover the transmitted messages since the linear combinations are not always full rank. Therefore, we propose an algorithm where we optimize the precoding factor at the users such that the probability that the equations are full rank is increased and that the transmission rate is maximized. We show, through some numerical examples, the effectiveness of our algorithm and the advantage of performing precoding allocation at the users. Also, we show that this scheme can outperform standard relaying techniques in certain regimes

Robust MMSE Precoding Strategy for Multiuser MIMO Relay Systems with Switched Relaying and Side Information

In this work, we propose a minimum mean squared error (MMSE) robust base station (BS) precoding strategy based on switched relaying (SR) processing and limited transmission of side information for interference suppression in the downlink of multiuser multiple-input multiple-output (MIMO) relay systems. The BS and the MIMO relay station (RS) are both equipped with a codebook of interleaving matrices. For a given channel state information (CSI) the selection function at the BS chooses the optimum interleaving matrix from the codebook based on two optimization criteria to design the robust precoder. Prior to the payload transmission the BS sends the index corresponding to the selected interleaving matrix to the RS, where the best interleaving matrix is selected to build the optimum relay processing matrix. The entries of the codebook are randomly generated unitary matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in the case of imperfect CSI.

Signal-Aligned Network Coding in K-User MIMO Interference Channels with Limited Receiver Cooperation

In this paper, we propose a signal-aligned network coding (SNC) scheme for K-user time-varying multiple-input multiple-output (MIMO) interference channels with limited receiver cooperation. We assume that the receivers are connected to a central processor via wired cooperation links with individual limited capacities. Our SNC scheme determines the precoding matrices of the transmitters so that the transmitted signals are aligned at each receiver. The aligned signals are then decoded into noiseless integer combinations of messages, also known as network-coded messages, by physical-layer network coding. The key idea of our scheme is to ensure that independent integer combinations of messages can be decoded at the receivers. Hence the central processor can recover the original messages of the transmitters by solving the linearly independent equations. We prove that our SNC scheme achieves full degrees of freedom (DoF) by utilizing signal alignment and physical-layer network coding. Simulation results show that our SNC scheme outperforms the compute-and-forward scheme in the finite SNR regime of the two-user and the three-user cases. The performance improvement of our SNC scheme mainly comes from efficient utilization of the signal subspaces for conveying independent linear equations of messages to the central processor.Comment: 12 pages, 4 figures, submitted to the IEEE Transactions on Vehicular Technolog

Phase Precoded Compute-and-Forward with Partial Feedback

In this work, we propose phase precoding for the compute-and-forward (CoF) protocol. We derive the phase precoded computation rate and show that it is greater than the original computation rate of CoF protocol without precoder. To maximize the phase precoded computation rate, we need to 'jointly' find the optimum phase precoding matrix and the corresponding network equation coefficients. This is a mixed integer programming problem where the optimum precoders should be obtained at the transmitters and the network equation coefficients have to be computed at the relays. To solve this problem, we introduce phase precoded CoF with partial feedback. It is a quantized precoding system where the relay jointly computes both a quasi-optimal precoder from a finite codebook and the corresponding network equations. The index of the obtained phase precoder within the codebook will then be fedback to the transmitters. A "deep hole phase precoder" is presented as an example of such a scheme. We further simulate our scheme with a lattice code carved out of the Gosset lattice and show that significant coding gains can be obtained in terms of equation error performance.Comment: 5 Pages, 4 figures, submitted to ISIT 201