Abstract—In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter’s data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters ’ points of view) and two multiple-access channels (from the receivers ’ points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multipleaccess subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the

Abstract — We explore the concept of cooperative spatial multiplexing for use in MIMO multicell networks. One key application of this is the transmission of independent streams jointly by several multipleantenna access points toward multiple single antenna user terminals located in neighboring cells. To augment the realism of this setting, we further introduce a constraint on hybrid channel state information (HCSI) in which any given transmitter know its own CSI perfectly while it only has statistical information about other transmitter’s channels. This yield a game situation in which each cooperating transmitter makes a guess about the behavior of the other transmitter. We show different transmission strategies in under this setting and compare them with fully cooperative (full CSI) and non cooperative schemes. Our results show a substantial cooperation gain despite the lack of instantaneous information. I.

It has been shown recently that the dirty-paper coding is the optimal strategy for maximizing the sum rate of multiple-input multiple-output Gaussian broadcast channels (MIMO BC). Moreover, by the channel duality, the nonconvex MIMO BC sum rate problem can be transformed to the convex dual MIMO multiple-access channel (MIMO MAC) problem with a sum power constraint. In this paper, we design an efficient algorithm based on conjugate gradient projection (CGP) to solve the MIMO BC maximum sum rate problem. Our proposed CGP algorithm solves the dual sum power MAC problem by utilizing the powerful concept of Hessian conjugacy. We also develop a rigorous algorithm to solve the projection problem. We show that CGP enjoys provable convergence, nice scalability, and great efficiency for large MIMO BC systems. 1

Abstract—We study a distributed algorithm for adapting transmit beamforming vectors in a multi-antenna peer-to-peer wireless network. The algorithm attempts to maximize a sum of per-user utility functions, where each user’s utility is a function of his transmission rate, or equivalently the received signalto-interference plus noise ratio (SINR). This is accomplished by exchanging interference prices, each of which represents the marginal cost of interference to a particular user. Given the interference prices, users update their beamforming vectors to maximize their utility minus the cost of interference. For a two-user system, we show that this algorithm converges for a suitable class of utility functions. Convergence of the algorithm with more than two users is illustrated numerically. I.

Abstract—We study distributed algorithms for allocating powers and/or adjusting beamforming vectors in a peer-to-peer wireless network which may have multiple-input-single-output (MISO) links. The objective is to maximize the total utility summed over all users, where each user’s utility is a function of the received signal-to-interference-plus-noise ratio (SINR). Each user (receiver) announces an interference price, representing the marginal cost of interference from other users. A particular user (transmitter) then updates its power and beamforming vector to maximize its utility minus the interference cost to other users, which is determined from their announced interference prices. We show that if each transmitter update is based on a current set of interference prices and the utility functions satisfy certain concavity conditions, then the total utility is non-decreasing with each update. The proof is based on the convexity of the utility functions with respect to received interference, and applies to rate utility functions, and an arbitrary number of interfering MISO links. The extension to multi-carrier links is discussed as well as algorithmic variations in which the prices are not immediately updated after power or beam updates. I.

Abstract—We study distributed algorithms for updating transmit precoding matrices for a two-user Multi-Input/Multi-Output (MIMO) interference channel. Our objective is to maximize the sum rate with linear Minimum Mean Squared Error (MMSE) receivers, treating the interference as additive Gaussian noise. An iterative approach is considered in which given a set of precoding matrices and powers, each receiver announces an interference price (marginal decrease in rate due to an increase in interference) for each received beam, corresponding to a column of the precoding matrix. Given the interference prices from the neighboring receiver, and also knowledge of the appropriate cross-channel matrices, the transmitter can then update the beams and powers to maximize the rate minus the interference cost. Variations on this approach are presented in which beams are added sequentially (and then fixed), and in which all beams and associated powers are adjusted at each iteration. Numerical results are presented, which compare these algorithms with iterative water-filling (which requires no information exchange), and a centralized optimization algorithm, which finds locally optimal solutions. Our results show that the distributed algorithms perform close to the centralized algorithm, and by adapting the rank of the precoder matrices, achieve the optimal high-SNR slope. I.

Abstract—This paper addresses the problem of source and relay transmit covariance optimization on the Gaussian MIMO relay channel with full channel state information (CSI), i.e., assuming perfect knowledge of all channels. For full-duplex relaying, we show that the cut-set bound on capacity can be computed as the solution of a convex problem, thus providing a tighter bound than previously published. For time division duplex (TDD) relaying, both upper and lower bounds on capacity are derived, and the transmit covariance matrices are optimized for decode-and-forward (DF) strategies with either partial or full decoding at the relay. A generic procedure is introduced to formulate these problems into a standard convex form, and to solve them efficiently. Suboptimum precoders are also proposed which have a specific matrix structure that either leads to a closed-form expression or at least reduces the dimension of the optimization problem. Practical aspects related to transmit power constraints and CSI availability are then discussed. Finally, simulations in a cellular downlink scenario show that the partial DF strategy can achieve a rate very close to capacity for realistic values of the source to relay SNR, and that the rate loss due to suboptimum precoder structures remains small for typical antenna configurations. Index Terms—Cooperative, relay, channel state information (CSI), MIMO. I.

Abstract—In this paper, source and relay precoders are derived which optimize upper and lower bounds on the Gaussian MIMO relay channel capacity. First, the prior art on the cut-set upperbound on capacity is extended by showing that the optimization of the source and relay codebooks can be formulated as a convex problem without having to introduce a scalar parameter that captures their cross-correlation. Both the Full-Duplex and Time Division Duplex (TDD) relay channels are addressed, assuming perfect knowledge of all channels, and two procedures are proposed which solve the problem efficiently by relying on analytical expressions of gradients, subgradients and projection operators: the first one solves the dual problem while the second one applies the barrier method. Similar techniques are then used to maximize the achievable rate of Decode-and-Forward (DF) TDD MIMO relaying strategies with either partial or full decoding at the relay. Sub-optimum precoders are also proposed which have a closed-form expression that can be obtained from the KKT conditions, thus reducing the computational complexity at the expense of a lower rate. Simulations in a cellular downlink scenario show that the partial DF strategy can achieve a rate very close to capacity for realistic values of the Source to Relay signalto-noise ratio. Finally, the availability of Channel State Information (CSI) in a real system is discussed.

Abstract—We study a distributed algorithm for adjusting beamforming vectors in a peer-to-peer wireless network with multiple-input multiple-output (MIMO) channels. Each transmitter precoding matrix has rank one, and a linear minimum mean squared error (MMSE) filter is applied at each receiver. Our objective is to maximize the total utility summed over all users, where each user’s utility is a function of the received signal-to-interference-plus-noise ratio (SINR). Given all users ’ beamforming vectors and receive filters, each receiver announces an interference price, representing the marginal cost of interference from other users. A particular transmitter updates its beamforming vector to maximize its utility minus the interference cost to other users. We show that if the utility functions satisfy certain concavity conditions, then the total utility is non-decreasing with each update. We also present numerical results that illustrate the effect of ignoring interference prices from all but the closest users, and relaxing requirements on the frequency of beam and price updates. I.

Abstract—We consider the uplink of a backhaul-constrained, MIMO coordinated network. That is, a single-frequency network with