We consider the beamformer design for multipleinput multiple-output (MISO) broadcast channels (MISO BCs) using zero-forcing dirty paper coding (ZF-DPC). Assuming a sum power constraint (SPC), most previously proposed beamformer designs are based on the QR decomposition (QRD), which is a natural choice to satisfy the ZF constraints. However, the optimality of the QRD-based design for ZF-DPC has remained unknown. In this paper, first, we analytically establish that the QRD-based design is indeed optimal for any performance measure under a SPC. Then, we propose an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework. The beamformer design is first formulated as a rank-1-constrained optimization problem. Exploiting the special structure of the ZF-DPC scheme, we prove that the rank constraint can be relaxed and still provide the same solution. In addition, we propose a fast converging algorithm to the beamformer design problem, under the duality framework between the BCs and multiple access channels (MACs). More specifically, we show that a BC with ZF-DPC has the dual MAC with ZF-based successive interference cancellation (ZF-SIC). In this way, the beamformer design for ZF-DPC is transformed into a power allocation problem for ZF-SIC, which can be solved more efficiently.

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.

Successive zero-forcing (SZF) is a precoding technique for broadcast channels that partially precancels the multiuser interference. Due to the residual interference, the optimal precoder design for SZF is difficult to find, and currently unknown. This letter proposes a suboptimal iterative precoder design for the sum rate maximization problem for SZF, using a local optimization method. In each iteration, the precoders are updated to maximize a first-order approximation of the sum rate, which can be easily solved since the approximation is concave with the precoders. By initializing the precoders with zero matrices, we analytically prove that the iterative design can achieve a larger sum rate than the block diagonalization (BD) approach. Moreover, numerical results demonstrate the superior sum-rate performance of the proposed design over the existing scheme, which is based on a heuristic method.

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser MIMO downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity.When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective cha- nel matrices.

This paper considers the precoder designs for successive zero-forcing dirty paper coding (SZF-DPC), a suboptimal transmission technique for MIMO broadcast channels (MIMO BCs). Existing precoder designs for SZF-DPC often consider a sum power constraint. In this paper, we address the precoder design for SZF-DPC with per-antenna power constraints (PAPCs), which has not been well studied. First, we formulate the precoder design as a rank-constrained optimization problem, which is generally difficult to handle. To solve this problem, we follow a relaxation approach, and prove that the optimal solution of the relaxed problem is also optimal for the original problem. Considering the relaxed problem, we propose a numerically efficient algorithm to find the optimal solution, which exhibits a fast convergence rate. Suboptimal precoder designs, with lower computational complexity, are also presented, and compared with the optimal ones in terms of achievable sum rate and computational complexity.

Successive zero-forcing dirty paper coding (SZF-DPC) is a simplified alternative to DPC for MIMO broadcast channels (MIMO BCs). In the SZF-DPC scheme, the noncausally-known interference is canceled by DPC, while the residual interference is suppressed by the ZF technique. Due to the ZF constraints, the precoders are constrained to lie in the null space of a matrix. For the sum rate maximization problem under a sum power constraint, the existing precoder designs naturally rely on the singular value decomposition (SVD). The SVD-based design is optimal but needs high computational complexity. Herein, we propose two low-complexity optimal precoder designs for SZF-DPC, all based on the QR decomposition (QRD), which requires lower complexity than SVD. The first design method is an iterative algorithm to find an orthonormal basis of the null space of a matrix that has a recursive structure. The second proposed method, which will be shown to require the lowest complexity, results from applying a single QRD to the matrix comprising all users' channel matrices. We analytically and numerically show that the two proposed precoder designs are optimal.

Distributed space-time block codes (DSTBCs) have been developed to exploit diversity gains in cooperative communications systems. In this paper, we propose a new DSTBC based on unique word (UW) extension, referred to as the D-UW-STBC. The D-UW-STBC is devised for wireless relay networks with the amplify-and-forwarcl protocol and frequency selective fading channels. The data is transmitted from the source to the destination by a block-wise manner, resembling the block level of the Alamouti scheme. At the source, a UW is padded to the tail of each data block, which plays as a cyclic prefix, and thus allows for low-complexity implementation in the frequency domain. The additional purpose of using UW in this paper is to estimate the channels. However, the introduction of UWs makes it difficult to decouple the detection of data blocks. To achieve the orthogonality of the equivalent space-time channel, we carefully cancel the interference induced by the UWs. Also, a least square (LS) channel estimation approach is proposed, in which, the relay is transparent to the source and destination. The optimal UWs arc designed to minimise the effect of additive noise. Bit-crror-ratc (BER) performance comparison of various receiver schemes is carried out by computer simulations.

We consider the beamformer design for zero-forcing dirty paper coding (ZF-DPC), a suboptimal transmission technique for MISO broadcast channels (MISO BCs). For the sum rate maximization problem under a total power constraint, the existing beamformer designs in the literature are based on the QR decomposition (QRD), which is used to satisfy the ZF constraints. However, the optimality of the QRD-based design has been unknown previously. In this paper, we prove that the QRD-based design is optimal for ZF-DPC for any performance measure under a sum power constraint. For the per-antenna power constraints, the QRD-based designs become suboptimal, and we propose an optimal design, using a convex optimization framework. Low-complexity suboptimal designs are also presented, and numerically shown to achieve a significant fraction of the sum rate provided by the optimal design.

In this paper1, we investigate different practical automatic repeat request (ARQ) retransmission protocols for twoway wireless relay networks based on network coding (NC). The idea of NC is applied to increase the achievable throughput for the exchange of information between two terminals through one relay. Using NC, throughput efficiency is significantly improved due to the reduction of the number of retransmissions. Particularly, two improved NC-based ARQ schemes are designed based on go-back-N and selective-repeat (SR) protocols. The analysis of throughput efficiency is then carried out to find the best retransmission strategy for different scenarios. It is shown that the combination of improved NC-based SR ARQ scheme in the broadcast phase and the traditional SR ARQ scheme in the multiple access phase achieves the highest throughput efficiency compared to the other combinations of ARQ schemes. Finally, simulation results are provided to verify the theoretical analysis.

This paper considers the reliable transmission for wireless multicast networks where multiple sources want to distribute information to a set of destinations with assistance of a relay. Basically, the reliability of a communication link is assured via automatic repeat request (ARQ) protocols. In the context of multisource multicast networks, the challenge is how to retransmit the lost or erroneous packets efficiently. In traditional approaches, the retransmission of lost packets from a single source is treated separately, and thus it may cause a considerable delay. To solve this problem, we propose the relay detects, combines, and forwards the packets which are lost at destinations using network coding. In the proposed ARQ protocol, the relay detects packets from different sources and combines the lost packets using NC. In particular, two packet-combination algorithms are developed to guarantee that all lost packets are retransmitted with the smallest number of retransmissions. Furthermore, we analyze the transmission bandwidth and provide the numerical results to demonstrate the superior performance of the proposed ARQ protocol over some existing schemes.