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Transmitter Optimization for the MultiAntenna Downlink with PerAntenna Power Constraints
 IEEE Transactions on Signal Processing
, 2007
"... Abstract—This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the basestation. In contrast to the conventional sumpower constraint on the transmit antennas, this paper adopts a more realistic perantenna power constraint, bec ..."
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Cited by 52 (5 self)
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Abstract—This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the basestation. In contrast to the conventional sumpower constraint on the transmit antennas, this paper adopts a more realistic perantenna power constraint, because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier. Assuming perfect channel knowledge at the transmitter, this paper investigates two different transmission schemes under the perantenna power constraint: a minimumpower beamforming design for downlink channels with a single antenna at each remote user and a capacityachieving transmitter design for downlink channels with multiple antennas at each remote user. It is shown that in both cases, the perantenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise. This generalizes previous uplink–downlink duality results and transforms the perantenna transmitter optimization problem into an equivalent minimax optimization problem. Further, it is shown that various notions of uplink–downlink duality may be unified under a Lagrangian duality framework. This new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink perantenna transmitter optimization problem. Index Terms—Beamforming, broadcast channel, capacity region, dirtypaper coding, Lagrangian duality. I.
Exploiting multiantennas for opportunistic spectrum sharing in cognitive radio networks
 IEEE J. Select. Topics in Signal Processing
, 2008
"... ..."
MultiCell MIMO Cooperative Networks: A New Look at Interference
 J. Selec. Areas in Commun. (JSAC
, 2010
"... Abstract—This paper presents an overview of the theory and currently known techniques for multicell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacitylimiting factor, multicell cooperation can dramatically improv ..."
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Cited by 42 (18 self)
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Abstract—This paper presents an overview of the theory and currently known techniques for multicell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacitylimiting factor, multicell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit intercell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multicell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental informationtheoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and systemlevel integration. A few promising and quite fundamental research avenues are also suggested. Index Terms—Cooperation, MIMO, cellular networks, relays, interference, beamforming, coordination, multicell, distributed.
An introduction to convex optimization for communications and signal processing
 IEEE J. Sel. Areas Commun
, 2006
"... Abstract—Convex optimization methods are widely used in the ..."
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Cited by 29 (2 self)
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Abstract—Convex optimization methods are widely used in the
Sum Rate Characterization of Joint Multiple CellSite Processing
, 2005
"... The sumrate capacity of a cellular system model is analyzed, considering the uplink and downlink channels, while addressing both nonfading and flatfading channels. The focus is on a simple Wynerlike multicell model, where the system cells are arranged on a circle, assuming the cellsites are lo ..."
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Cited by 26 (9 self)
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The sumrate capacity of a cellular system model is analyzed, considering the uplink and downlink channels, while addressing both nonfading and flatfading channels. The focus is on a simple Wynerlike multicell model, where the system cells are arranged on a circle, assuming the cellsites are located at the boundaries of the cells. For the uplink channel, analytical expressions of the sumrate capacities are derived for intracell TDMA scheduling, and a “WideBand ” (WB) scheme (where all users are active simultaneously utilizing all bandwidth for coding). Assuming individual percell power constraints, and using the Lagrangian uplinkdownlink duality principle, an analytical expression for the sumrate capacity of the downlink channel is derived for nonfading channels, and shown to coincide with the corresponding uplink result. Introducing flatfading, lower and upper bounds on the average percell sumrate capacity are derived. The bounds exhibit an O(loge K) multiuser diversity factor for a number of users percell K ≫ 1, in addition to the array diversity gain. Joint multicell processing is shown to eliminate outofcell interference, which is traditionally considered to be a limiting factor in highrate reliable communications. This paper was presented in part at the 9
Convex conic formulations of robust downlink precoder designs with quality of service constraints
 IEEE J. Select. Topics Signal Processing
, 2007
"... 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 deterministicallybounded model for the channel uncertainty of each u ..."
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Cited by 11 (1 self)
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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 deterministicallybounded 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 computationallyefficient restrictions of the original design problem. The three approaches yield semidefinite program (SDP) formulations that offer different tradeoffs between the degree of conservatism and the size of the SDP. We will also show how these conservative approaches can be used to derive efficientlysolvable quasiconvex restrictions of some related design problems, including the robust counterpart to the problem of maximizing the minimum signaltointerferenceplusnoiseratio (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.
Shitz), “Zeroforcing precoding and generalized inverses
 in Proc. IEEE Int. Symp
, 2008
"... Abstract—We consider the problem of linear zeroforcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudoinverse. We begin with the standard design under the assumption ..."
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Cited by 11 (0 self)
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Abstract—We consider the problem of linear zeroforcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudoinverse. We begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudoinverse are optimal among the generalized inverses in this setting. Then, we proceed to examine individual perantenna power constraints. In this case, the pseudoinverse is not necessarily the optimal inverse. In fact, finding the optimal matrix is nontrivial and depends on the specific performance measure. We address two common criteria, fairness and throughput, and show that the optimal generalized inverses may be found using standard convex optimization methods. We demonstrate the improved performance offered by our approach using computer simulations. Index Terms—Beamforming, generalized inverses, perantenna constraints, semidefinite relaxation, zeroforcing precoding. I.
Coordinated beamforming for the multicell multiantenna wireless system
 IEEE Trans. Wireless Commun
"... Abstract—In a conventional wireless cellular system, signal processing is performed on a percell basis; outofcell interference is treated as background noise. This paper considers the benefit of coordinating basestations across multiple cells in a multiantenna beamforming system, where multiple ..."
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Cited by 10 (3 self)
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Abstract—In a conventional wireless cellular system, signal processing is performed on a percell basis; outofcell interference is treated as background noise. This paper considers the benefit of coordinating basestations across multiple cells in a multiantenna beamforming system, where multiple basestations may jointly optimize their respective beamformers to improve the overall system performance. This paper focuses on a downlink scenario where each remote user is equipped with a single antenna, but where multiple remote users may be active simultaneously in each cell. The design criterion is the minimization of the total weighted transmitted power across the basestations subject to signaltointerferenceandnoiseratio (SINR) constraints at the remote users. The main contribution is a practical algorithm that is capable of finding the joint optimal beamformers for all basestations globally and efficiently. The proposed algorithm is based on a generalization of uplinkdownlink duality to the multicell setting using the Lagrangian duality theory. The algorithm also naturally leads to a distributed implementation. Simulation results show that a coordinated beamforming system can significantly outperform a conventional system with percell signal processing. I.
Distributed Downlink Beamforming with Cooperative Base Stations
"... We consider a cellular network where base stations can cooperate to determine the signals to be transmitted on the downlink. In such a scenario, it would be possible to use “macrodiversity ” transmit beamforming to improve system performance. The downlink beamformer of interest is generalised from s ..."
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Cited by 8 (1 self)
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We consider a cellular network where base stations can cooperate to determine the signals to be transmitted on the downlink. In such a scenario, it would be possible to use “macrodiversity ” transmit beamforming to improve system performance. The downlink beamformer of interest is generalised from some transmit beamformers that have been shown to meet various optimality criteria in the literature. The particular downlink beamformer structure enables us to recast our downlink beamforming problem as a virtual LMMSE estimation problem. Based on this virtual set up, we exploit the structure of the channel and develop distributed beamforming algorithms using local message passing between neighbouring base stations. We design distributed downlink beamforming algorithms for onedimensional and twodimensional cellular networks. For onedimensional cellular network, two algorithms are outlined, both of which are based on the Kalman smoothing framework. The first algorithm is a forwardbackward algorithm that produces optimal performance, but it has the disadvantage of a delay that grows linearly with array size. The second algorithm, which is a limited extent algorithm, solves the delay problem by using only local information. For the twodimensional cellular network, we remodel the network as a factor graph and present a distributed algorithm based on the sumproduct algorithm. We show that despite the presence of loops in the factor graph, the algorithm produces optimal results if convergence occurs. Convergence is demonstrated using simulation results. Index Terms Downlink beamforming; multicell processing; cooperative base stations; multipleinputmultipleoutput (MIMO); distributed algorithm; localised interference; message passing; linear mean square error (LMMSE); Kalman smoothing; sumproduct algorithm. 1 I.
Quality of service and maxminfair transmit beamforming to multiple cochannel multicast groups
 IEEE Trans. Signal Processing
, 2008
"... Abstract—The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signaltointerferenceplusnoise ratio (SINR) at ..."
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Cited by 8 (6 self)
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Abstract—The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signaltointerferenceplusnoise ratio (SINR) at each receiver; and a “fair ” approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the multiuser downlink beamforming problem; the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of the emerging WiMAX and UMTSLTE wireless networks. The joint problem also contains singlegroup multicast beamforming as a special case. The latter (and therefore also the former) is NPhard. This motivates the pursuit of computationally efficient quasioptimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient highquality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings. Index Terms—Broadcasting, convex optimization, downlink beamforming, multicasting, semidefinite relaxation. I.