We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two di#erent design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maximize the worst case SINR subject to a power constraint. We show that both problems can be solved using standard conic optimization packages. In addition, we develop conditions for the optimal precoder for both of these problems, and propose two simple fixed point iterations to find the solutions which satisfy these conditions. The relation to the well known downlink uplink duality in the context of joint downlink beamforming and power control is also explored. Our precoder design is general, and as a special case it solves the beamforming problem. In contrast to most of the existing precoders, it is not limited to full rank systems. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders. 1

In this two-parts paper we propose a decentralized strategy, based on a game-theoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipoint-to-multipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and bandwidth. We assume, as optimality criterion, the achievement of a Nash equilibrium and consider two alternative optimization problems: 1) the competitive maximization of mutual information on each link, given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies; and 2) the competitive maximization of the transmission rate, using finite order constellations, under the same constraints as above, plus a constraint on the average error probability. In Part I of the paper, we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies. Then, we prove that the optimal precoding/multiplexing scheme for both games leads to a channel diagonalizing structure, so that both matrix-valued problems can be recast in a simpler unified vector power control game, with no performance penalty. Thus, we study this simpler game and derive sufficient conditions ensuring the uniqueness of the Nash equilibrium. Interestingly, although derived under stronger constraints,

Abstract—We consider jointly designing transceivers for multiple-input multiple-output (MIMO) communications. Assuming the availability of the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR), we propose a scheme that can decompose a MIMO channel, in a capacity lossless manner, into multiple subchannels with prescribed capacities, or equivalently, signal-to-interference-and-noise ratios (SINRs). We refer to this scheme as the tunable channel decomposition (TCD), which is based on the recently developed generalized triangular decomposition (GTD) algorithm and the closed-form representation of minimum mean-squared-error VBLAST (MMSE-VBLAST) equalizer. The TCD scheme is particularly relevant to the applications where independent data streams with different qualities-of-service (QoS) share the same MIMO channel. The TCD scheme has two implementation forms. One is the combination of a linear precoder and a minimum mean-squared-error VBLAST (MMSE-VBLAST) equalizer, which is referred to as TCD-VBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as TCD-DP. We also include the optimal code-division multiple-access (CDMA) sequence design as a special case in the framework of MIMO transceiver designs. Hence, our scheme can be directly applied to optimal CDMA sequence design, both in the uplink and downlink scenarios. Index Terms—Channel capacity, channel decomposition, dirty paper (DP) precoding, generalized triangular decomposition, joint transceiver design, multiple-input multiple-output (MIMO), optimal CDMA sequences, quality-of-service, VBLAST. I.

We consider the design of linear precoders (beamformers) for broadcast channels with Quality of Service (QoS) constraints for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. We consider a deterministically-bounded model for the channel uncertainty of each user, and our goal is to design a robust precoder that minimizes the total transmission power required to satisfy the users ’ QoS constraints for all channels within a specified uncertainty region around the transmitter’s estimate of each user’s channel. Since this problem is not known to be computationally tractable, we will derive three conservative design approaches that yield convex and computationally-efficient restrictions of the original design problem. The three approaches yield semidefinite program (SDP) formulations that offer different trade-offs between the degree of conservatism and the size of the SDP. We will also show how these conservative approaches can be used to derive efficiently-solvable quasi-convex restrictions of some related design problems, including the robust counterpart to the problem of maximizing the minimum signal-to-interference-plus-noise-ratio (SINR) subject to a given power constraint. Our simulation results indicate that in the presence of uncertain CSI the proposed approaches can satisfy the users ’ QoS requirements for a significantly larger set of uncertainties than existing methods, and require less transmission power to do so.

This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zero-forcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities for the symbol streams. The precoder and DFE matrices are optimized jointly with bit allocation. It is shown that the generalized triangular decomposition (GTD) introduced by Jiang, Li, and Hager offers an optimal family of solutions. The optimal linear transceiver (which has a linear equalizer rather than a DFE) with optimal bit allocation is a member of this family. This shows formally that, under optimal bit allocation, linear and DFE transceivers achieve the same minimum power. The DFE transceiver using the geometric mean decomposition (GMD) is another member of this optimal family, and is such that optimal bit allocation yields identical bits for all symbol streams—no bit allocation is necessary—when the specified error probabilities are identical for all streams. The QR-based system used in VBLAST is yet another member of the optimal family and is particularly well-suited when limited feedback is allowed from receiver to transmitter. Two other optimization problems are then considered: a) minimization of power for specified set of bit rates and error probabilities (the QoS problem), and b) maximization of bit rate for fixed set of error probabilities and power. It is shown in both cases that the GTD yields an optimal family of solutions.

This paper considers the robust design of a linear transceiver with imperfect channel state information (CSI) at the transmitter of a MIMO link. The framework embraces the design problem when CSI at the transmitter consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix. The design of the linear MIMO transceiver is based on a general cost function covering several well known performance criteria. In particular, two families are considered in detail: Schur-convex and Schur-concave functions. Approximations are used in the low SNR and high SNR regimes separately to obtain simple optimization problems that can be readily solved. Numerical examples show gains compared to other suboptimal methods. 1.

This paper considers a DSL system in which a subset of the twisted-pair copper wires within a bundle can perform a joint processing at both sides of the communication system (e.g., links between central offices and remote terminals or between central offices and private networks). The DSL channel is treated as a multiinput multi-output (MIMO) system over which many substreams are established. It is assumed that the signal constellation to be used at each substream is given (possibly after some kind of bit distribution optimization) with a corresponding Quality of Service (QoS) constraint, e.g., to guarantee a certain error probability.

Multiantenna MIMO channels have recently become a popular means to increase the spectral efficiency and quality of wireless communications by the use of spatial diversity at both sides of the link [1–4]. In fact, the MIMO concept is much more general and embraces many other scenarios such as wireline digital subscriber line (DSL) systems [5] and singleantenna

In the downlink of a Multi-user MIMO (Multiple Input Multiple Output) communication system, intelligent algorithms are needed to choose transmit vectors for spatial multiplexing.

Several algorithms have recently been proposed for multiplexing multiple users in multiple-input, multiple-output (MIMO) downlinks. The ability of a transmitter to accomplish this using spatial methods is generally dependent on whether the users' channels are linearly independent. Up to this point most of the multiplexing algorithms have been tested on uncorrelated Gaussian channels, a best-case scenario. In this paper we examine the performance of multiplexing multiple users using actual channel measurements. We impose the constraint that all inter-user interference must be zero, and optimize the transmit vectors to maximize total throughput under this constraint. The maximum throughput was calculated for different user separation distances, and the results show that for this particular set of measurement data, a separation of five wavelengths is enough to achieve close to the maximum available performance for two users.