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154
The Degrees of Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels with No CSIT
, 2009
"... The degrees of freedom (dof) regions are characterized for the multipleinput multipleoutput (MIMO) broadcast channel (BC), the interference channel (IC), and the cognitive radio channel (CRC) when there is perfect and no channel state information at the receivers and the transmitter(s) (CSIR and CS ..."
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Cited by 37 (8 self)
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The degrees of freedom (dof) regions are characterized for the multipleinput multipleoutput (MIMO) broadcast channel (BC), the interference channel (IC), and the cognitive radio channel (CRC) when there is perfect and no channel state information at the receivers and the transmitter(s) (CSIR and CSIT), respectively. For the Kuser MIMO BC, the exact characterization of the dof region is obtained, which shows that simple timedivisionbased transmission is dofregion optimal. Using the techniques developed during the analysis of the dof region of the twouser BC, the corresponding problems for the twouser MIMO IC and the twouser MIMO CRC are addressed. For both of these channels, the exact characterization of the dof region is provided, except in a few antenna configurations. In these cases, an outerbound on the dof region is obtained. All these results are derived for a class of distributions of the fading channel matrices and the additive noises that is more general than those considered in the earlier works such as isotropic fading or Rayleigh fading with white Gaussian noise. Furthermore, using the dof region of the Kuser MIMO BC, the dof regions of the Kuser MIMO IC and the Kuser MIMO CRC are derived in some special cases.
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 35 (2 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.
Limited Feedbackbased Block Diagonalization for the MIMO Broadcast Channel
"... Block diagonalization is a linear precoding technique for the multiple antenna broadcast (downlink) channel that involves transmission of multiple data streams to each receiver such that no multiuser interference is experienced at any of the receivers. This lowcomplexity scheme operates only a fe ..."
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Cited by 35 (1 self)
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Block diagonalization is a linear precoding technique for the multiple antenna broadcast (downlink) channel that involves transmission of multiple data streams to each receiver such that no multiuser interference is experienced at any of the receivers. This lowcomplexity scheme operates only a few dB away from capacity but requires very accurate channel knowledge at the transmitter. We consider a limited feedback system where each receiver knows its channel perfectly, but the transmitter is only provided with a finite number of channel feedback bits from each receiver. Using a random quantization argument, we quantify the throughput loss due to imperfect channel knowledge as a function of the feedback level. The quality of channel knowledge must improve proportional to the SNR in order to prevent interferencelimitations, and we show that scaling the number of feedback bits linearly with the system SNR is sufficient to maintain a bounded rate loss. Finally, we compare our quantization strategy to an analog feedback scheme and show the superiority of quantized feedback. I.
Space division multiple access with a sum feedback rate constraint
 IEEE Trans. Signal Processing
, 2007
"... Abstract—On a multiantenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, incr ..."
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Cited by 34 (7 self)
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Abstract—On a multiantenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper bounded by a constant. This design consists of algorithms for CSI quantization, thresholdbased CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded. Index Terms—Broadcast channels, feedback communication, multiuser channels, space division multiplexing. I.
Training and Feedback Optimization for Multiuser MIMO Downlink
, 2009
"... We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over timefrequency blocks that span a coherent time × a coherence bandwidth. In closedloop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base s ..."
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Cited by 32 (2 self)
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We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over timefrequency blocks that span a coherent time × a coherence bandwidth. In closedloop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In openloop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use a tight closedform lower bound on the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three timefrequency block models inspired by actual systems, we provide some useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.
On the Degrees of Freedom of Finite State Compound Wireless Networks  Settling a Conjecture by Weingarten et. al.
, 2009
"... We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multipleinput singleoutput (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weing ..."
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Cited by 32 (19 self)
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We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multipleinput singleoutput (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weingarten et. al. have found inner and outer bounds on the DoF with 2 users. The bounds have a different character. While the inner bound collapses to unity as the number of states increases, the outer bound does not diminish with the increasing number of states beyond a threshold value. It has been conjectured that the outer bound is loose and the inner bound represents the actual DoF. In the complex setting (all signals, noise, and channel coefficients are complex variables) we solve a few cases to find that the outer bound – and not the inner bound – of Weingarten et. al. is tight. For the real setting (all signals, noise and channel coefficients are real variables) we completely characterize the DoF, once again proving that the outer bound of Weingarten et. al. is tight. We also extend the results to arbitrary number of users. Second, we characterize the DoF of finite state scalar (single antenna nodes) compound X networks with arbitrary number of users in the real setting. Third, we characterize the DoF of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting. The key finding is that scalar interference networks and (real) X networks do not lose any DoF due to channel uncertainty at the transmitter in the finite state compound setting. The finite state compound MISO BC does lose DoF relative to the perfect CSIT scenario. However, what is lost is only the DoF benefit of joint processing at transmit antennas, without which the MISO BC reduces to an X network.
Finiterate feedback MIMO broadcast channels with a large number of users
 Proc. of IEEE Intl. Symposium on Info. Theory
, 2006
"... Abstract — We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to ..."
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Cited by 31 (3 self)
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Abstract — We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sumrate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load. I.
On the secure degrees of freedom of wireless X networks
 In 46th Annual Allerton Conference on Communication, Control and Computing
, 2008
"... Abstract — Previous work showed that the X network with M transmitters, N receivers has MN degrees of freedom. In this ..."
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Cited by 30 (4 self)
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Abstract — Previous work showed that the X network with M transmitters, N receivers has MN degrees of freedom. In this
MultiAntenna Broadcast Channels with Limited Feedback and User Selection
, 2006
"... We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directiona ..."
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Cited by 29 (3 self)
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We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sumrate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.
Coordinated Beamforming with Limited Feedback in the MIMO Broadcast Channel
, 2008
"... In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multipleinput multipleoutput (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past wo ..."
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Cited by 26 (8 self)
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In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multipleinput multipleoutput (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.