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International audienceTransmit beamforming is a versatile technique for signal transmission from an array of N antennasto one or multiple users [1]. In wireless communications, the goal is to increase the signal power atthe intended user and reduce interference to non-intended users. A high signal power is achieved bytransmitting the same data signal from all antennas, but with different amplitudes and phases, suchthat the signal components add coherently at the user. Low interference is accomplished by making thesignal components add destructively at non-intended users. This corresponds mathematically to designingbeamforming vectors (that describe the amplitudes and phases) to have large inner products with thevectors describing the intended channels and small inner products with non-intended user channels.If there is line-of-sight (LoS) between the transmitter and receiver, beamforming can be seen as forminga signal beam toward the receiver; see Figure 1. Beamforming can also be applied in non-LoS scenarios,if the multipath channel is known, by making the multipath components add coherently or destructively.Since transmit beamforming focuses the signal energy at certain places, less energy arrives to otherplaces. This allows for so-called space-division multiple access (SDMA), where K spatially separatedusers are served simultaneously. One beamforming vector is assigned to each user and can be matchedto its channel. Unfortunately, the finite number of transmit antennas only provides a limited amount ofspatial directivity, which means that there are energy leakages between the users which act as interference.While it is fairly easy to design a beamforming vector that maximizes the signal power at the intendeduser, it is difficult to strike a perfect balance between maximizing the signal power and minimizingthe interference leakage. In fact, the optimization of multiuser transmit beamforming is generally anondeterministic polynomial-time (NP) hard problem [2]. Nevertheless, this lecture shows that the optimaltransmit beamforming has a simple structure with very intuitive properties and interpretations. Thisstructure provides a theoretical foundation for practical low-complexity beamforming schemes

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Multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication. Recently, efficient space-time codes have been developed that utilize a large portion of the available capacity. These codes are designed under the assumption that the transmitter has no knowledge about the channel. In this work, on the other hand, we consider the case when the transmitter has partial, but not perfect, knowledge about the channel and how to improve a predetermined code so that this fact is taken into account. A performance criterion is derived for a frequency-nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code. The resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods. In addition, a particularly efficient solution method is developed for the special case of independently fading channel coefficients. The proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space-time block coding. Simulation results for a narrow-band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge.

Abstract-Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell interference can be coordinated and higher performance achieved, especially for terminals at cell edges. Most previous work in the area has assumed that base stations have common knowledge of both data dedicated to all terminals and full or partial channel state information (CSI) of all links. Herein, we analyze the case of distributed cooperation where each base station has only local CSI, either instantaneous or statistical. In the case of instantaneous CSI, the beamforming vectors that can attain the outer boundary of the achievable rate region are characterized for an arbitrary number of multiantenna transmitters and single-antenna receivers. This characterization only requires local CSI and justifies distributed precoding design based on a novel virtual signal-to-interference noise ratio (SINR) framework, which can handle an arbitrary SNR and achieves the optimal multiplexing gain. The local power allocation between terminals is solved heuristically. Conceptually, analogous results for the achievable rate region characterization and precoding design are derived in the case of local statistical CSI. The benefits of distributed cooperative transmission are illustrated numerically, and it is shown that most of the performance with centralized cooperation can be obtained using only local CSI.Index Terms-Coordinated multipoint (CoMP), network multiple-input-multiple-output (MIMO), base station cooperation, distributed precoding, rate region, virtual signal-to-interference noise ratio (SINR).

Abstract-In this paper, we create a framework for trainingbased channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics.The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas.

Abstract-This paper studies secrecy rate optimization in a wireless network with a single-antenna source, a multi-antenna destination and a multi-antenna eavesdropper. This is an unfavorable scenario for secrecy performance as the system is interference-limited. In the literature, assuming that the receiver operates in half duplex (HD) mode, the aforementioned problem has been addressed via use of cooperating nodes who act as jammers to confound the eavesdropper. This paper investigates an alternative solution, which assumes the availability of a full duplex (FD) receiver. In particular, while receiving data, the receiver transmits jamming noise to degrade the eavesdropper channel. The proposed self-protection scheme eliminates the need for external helpers and provides system robustness. For the case in which global channel state information is available, we aim to design the optimal jamming covariance matrix that maximizes the secrecy rate and mitigates loop interference associated with the FD operation. We consider both fixed and optimal linear receiver design at the destination, and show that the optimal jamming covariance matrix is rank-1, and can be found via an efficient 1-D search. For the case in which only statistical information on the eavesdropper channel is available, the optimal power allocation is studied in terms of ergodic and outage secrecy rates. Simulation results verify the analysis and demonstrate substantial performance gain over conventional HD operation at the destination.

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