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28
Degrees of Freedom of the Network MIMO Channel With Distributed CSI
, 2013
"... Abstract—In this work, we discuss the joint precoding with finite rate feedback in the socalled network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the ove ..."
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Abstract—In this work, we discuss the joint precoding with finite rate feedback in the socalled network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the overall multiuser MIMO channel and must make a precoding decision solely based on the available local CSI. We refer to this channel as the DCSIMIMO channel and the precoding problem as distributed precoding. We extend to the DCSI setting the work from Jindal in [1] for the conventional MIMO Broadcast Channel (BC) in which the number of Degrees of Freedom (DoFs) achieved by Zero Forcing (ZF) was derived as a function of the scaling in the logarithm of the SignaltoNoise Ratio (SNR) of the number of quantizing bits. Particularly, we show the seemingly pessimistic result that the number of DoFs at each user is limited by the worst CSI across all users and across all TXs. This is in contrast to the conventional MIMO BC where the number of DoFs at one user is solely dependent on the quality of the estimation of his own feedback. Consequently, we provide precoding schemes improving on the achieved number of DoFs. For the twouser case, the derived novel precoder achieves a number of DoFs limited by the best CSI accuracy across the TXs instead of the worst with conventional ZF. We also advocate the use of hierarchical quantization of the CSI, for which we show that considerable gains are possible. Finally, we use the previous analysis to derive the DoFs optimal allocation of the feedback bits to the various TXs under a constraint on the size of the aggregate feedback in the network, in the case where conventional ZF is used.
Bit Allocation Laws for MultiAntenna Channel Feedback Quantization: MultiUser Case
"... This paper addresses the optimal design of limitedfeedback downlink multiuser spatial multiplexing systems. A multipleantenna basestation is assumed to serve multiple singleantenna users, who quantize and feed back their channel state information (CSI) through a shared ratelimited feedback cha ..."
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Cited by 15 (5 self)
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This paper addresses the optimal design of limitedfeedback downlink multiuser spatial multiplexing systems. A multipleantenna basestation is assumed to serve multiple singleantenna users, who quantize and feed back their channel state information (CSI) through a shared ratelimited feedback channel. The optimization problem is cast in the form of minimizing the average transmission power at the basestation subject to users’ target signaltointerferenceplusnoise ratios (SINR) and outage probability constraints. The goal is to derive the feedback bit allocations among the users and the corresponding channel magnitude and direction quantization codebooks in a highresolution quantization regime. Toward this end, this paper develops an optimization framework using approximate analytical closedform solutions, the accuracy of which is then verified by numerical results. The results show that, for channels in the real space, the number of channel direction quantization bits should be (M−1) times the number of channel magnitude quantization bits, where M is the number of basestation antennas. Moreover, users with higher requested qualityofservice (QoS), i.e. lower target outage probabilities, and higher requested downlink rates, i.e. higher target SINR’s, should use larger shares of the feedback rate. It is also shown that, for the target QoS parameters to be feasible, the total feedback bandwidth should scale logarithmically with the geometric mean of the target SINR values and the geometric mean of the inverse target outage probabilities. In particular, the minimum required feedback rate is shown to increase if the users ’ target parameters deviate from the corresponding geometric means. Finally, the paper shows that, as the total number of feedback bits B increases, the performance of the limitedfeedback system approaches the perfectCSI system as 2 −B/M2
An analytical framework for heterogeneous partial feedback design in heterogeneous multicell ofdma networks
 IEEE Transactions on Signal Processing
, 2013
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Large system analysis of cooperative multicell downlink transmission via regularized channel inversion with imperfect CSIT
 IEEE Trans. Wireless Commun
, 2013
"... Abstract—In this paper, we analyze the ergodic sumrate of a multicell downlink system with base station (BS) cooperation using regularized zeroforcing (RZF) precoding. Our model assumes that the channels between BSs and users have independent spatial correlations and imperfect channel state info ..."
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Cited by 7 (0 self)
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Abstract—In this paper, we analyze the ergodic sumrate of a multicell downlink system with base station (BS) cooperation using regularized zeroforcing (RZF) precoding. Our model assumes that the channels between BSs and users have independent spatial correlations and imperfect channel state information at the transmitter (CSIT) is available. Our derivations are based on large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the BS and users approach to infinity with some fixed ratios. In particular, a deterministic equivalent expression of the ergodic sumrate is obtained and is instrumental in getting insight about the joint operations of BSs, which leads to an efficient method to find the asymptoticoptimal regularization parameter for the RZF. In another application, we use the deterministic channel rate to study the optimal feedback bit allocation among the BSs for maximizing the ergodic sumrate, subject to a total number of feedback bits constraint. By inspecting the properties of the allocation, we further propose a scheme to greatly reduce the search space for optimization. Simulation results demonstrate that the ergodic sumrates achievable by a subspace search provides comparable results to those by an exhaustive search under various typical settings. Index Terms—Large dimensional RMT, multicell cooperation, regularized zeroforcing, feedback bit allocation. I.
TwoStage Channel Feedback for Beamforming and Scheduling in Network MIMO Systems
"... Abstract—This paper proposes an efficient twostage beamforming and scheduling algorithm for the limitedfeedback cooperative multipoint (CoMP) systems. The system includes multiple basestations cooperatively transmitting data to a pool of users, which share a ratelimited feedback channel for sen ..."
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Cited by 6 (2 self)
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Abstract—This paper proposes an efficient twostage beamforming and scheduling algorithm for the limitedfeedback cooperative multipoint (CoMP) systems. The system includes multiple basestations cooperatively transmitting data to a pool of users, which share a ratelimited feedback channel for sending back the channel state information (CSI). The feedback mechanism is divided into two stages that are used separately for scheduling and beamforming. In the first stage, the users report their best channel gain from all the basestation antennas and the basestations schedule the best user for each of their antennas. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. The paper proposes an analytical framework to derive the bit allocation between the two feedback stages and the bit allocation for quantizing each user’s CSI. For a total number of feedback bits B, it is shown that the number of bits assigned to the second feedback stage should scale as log B. Furthermore, in quantizing channel vectors from different basestations, each user should allocate its feedback budget in proportion to the logarithm of the corresponding channel gains. These bit allocation are then used to show that the overall system performance scales doublelogarithmically with B and logarithmically with the transmit SNR. The paper further presents several numerical results to show that, in comparison with other beamformingscheduling algorithms in the literature, the proposed scheme provides a consistent improvement in downlink sum rate and network utility. Such improvements, in particular, are achieved in spite of a significant reduction in the beamformingscheduling computational complexity, which makes the proposed scheme an attractive solution for practical system implementations. I.
L.: Cognitive interference alignment for OFDM twotiered networks
 In: IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC
, 2012
"... In this contribution, we introduce an interference alignment scheme that allows the coexistence of an orthogonal frequency division multiplexing (OFDM) macrocell and a cognitive smallcell, deployed in a twotiered structure and transmitting over the same bandwidth. We derive the optimal linear s ..."
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In this contribution, we introduce an interference alignment scheme that allows the coexistence of an orthogonal frequency division multiplexing (OFDM) macrocell and a cognitive smallcell, deployed in a twotiered structure and transmitting over the same bandwidth. We derive the optimal linear strategy for the single antenna secondary base station, maximizing the spectral efficiency of the opportunistic link, accounting for both signal subspace structure and power loading strategy. Our analytical and numerical findings prove that the precoder structure proposed is optimal for the considered scenario in the face of Rayleigh and exponential decaying channels. 1.
Distributed adaptation of quantized feedback for downlink network MIMO systems
 IEEE Trans. Wireless Commun
, 2011
"... Abstract—This paper focuses on quantized channel state information (CSI) feedback for downlink network MIMO systems. Specifically, we propose to quantize and feedback the CSI of a subset of BSs, namely the feedback set. Our analysis reveals the tradeoff between better interference mitigation with l ..."
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Abstract—This paper focuses on quantized channel state information (CSI) feedback for downlink network MIMO systems. Specifically, we propose to quantize and feedback the CSI of a subset of BSs, namely the feedback set. Our analysis reveals the tradeoff between better interference mitigation with large feedback set and high CSI quantization precision with small feedback set. Given the number of feedback bits and instantaneous/longterm channel conditions, each user optimizes its feedback set distributively according to the expected SINR derived from our analysis. Simulation results show that the proposed feedback adaptation scheme provides substantial performance gain over nonadaptive schemes, and is able to effectively exploit the benefits of network MIMO under various feedback bit budgets. Index Terms—Network MIMO, base station coordination, limited feedback, cochannel interference. I.
Adaptive Limited Feedback for MISO Wiretap Channels With Cooperative Jamming
"... Abstract—This paper studies a multiantenna wiretap channel with a passive eavesdropper and an external helper, where only quantized channel information regarding the legitimate receiver is available at the transmitter and helper due to finiterate feedback. Given a fixed total bandwidth for the two ..."
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Cited by 2 (1 self)
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Abstract—This paper studies a multiantenna wiretap channel with a passive eavesdropper and an external helper, where only quantized channel information regarding the legitimate receiver is available at the transmitter and helper due to finiterate feedback. Given a fixed total bandwidth for the two feedback channels, the receiver must determine how to allocate its feedback bits to the transmitter and helper. Assuming zeroforcing transmission at the helper and random vector quantization of the channels, an analytic expression for the achievable ergodic secrecy rate due to the resulting quantization errors is derived. While direct optimization of the secrecy rate is difficult, an approximate upper bound for the mean loss in secrecy rate is derived and a feedback bit allocation method that minimizes the average upper bound on the secrecy rate loss is studied. A closedform solution is shown to be possible if the integer constraint on the bit allocation is relaxed. Numerical simulations indicate the significant advantage that can be achieved by adaptively allocating the available feedback bits. Index Terms—Cooperative jamming, feedback bits allocation, limited feedback, MISO wiretap channel. I.
Base station cooperation with feedback optimization: a large system analysis
, 2014
"... In this paper, we study feedback optimization problems that maximize the users ’ signal to interference plus noise ratio (SINR) in a twocell multipleinput multipleoutput broadcast channel. Assuming the users learn their direct and interfering channels perfectly, they can feed back this informat ..."
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In this paper, we study feedback optimization problems that maximize the users ’ signal to interference plus noise ratio (SINR) in a twocell multipleinput multipleoutput broadcast channel. Assuming the users learn their direct and interfering channels perfectly, they can feed back this information to the base stations (BSs) over the uplink channels. The BSs then use the channel information to design their transmission scheme. Two types of feedback are considered: 1) analog and 2) digital. In the analog feedback case, the users send their unquantized and uncoded channel state information (CSI) over the uplink channels. In this context, given a user’s fixed transmit power, we investigate how he/she should optimally allocate it to feed back the direct and interfering (or cross) CSI for two types of BS cooperation schemes, namely, multicell processing (MCP) and coordinated beamforming. In the digital feedback case, the direct and cross link channel vectors of each user are quantized separately, each using the random vector quantization scheme, with different size codebooks. The users then send the index of the quantization vector in the corresponding codebook to the BSs. Similar to the feedback optimization problem for the analog feedback, we investigate the optimal bit partitioning for the direct and interfering link for both types of cooperation. We focus on regularized channel inversion precoding structures and perform our analysis in the large system limit in which the number of users per cell (K) and the number of antennas per BS (N) tend to infinity with their ratio β = (K/N) held fixed. We show that for both types of cooperation, for some values of interfering channel gain, usually at low values, no cooperation between the BSs is preferred. This is because, for these values of cross channel gain, the channel estimates for the cross link are not accurate enough for their knowledge to contribute to improving the SINR and there is no benefit in doing BS cooperation under that condition. We also show that for the MCP scheme, unlike in the perfect CSI case, the SINR improves only when the interfering channel gain is above a certain threshold.