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18
Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback sche ..."
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Cited by 114 (8 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded AWGN feedback channel with orthogonal access and then the case of fading MIMO multiaccess (MIMOMAC). We show that by exploiting the MIMOMAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
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.
Multiuser MIMO Downlink Made Practical: Achievable Rates with Simple Channel State Estimation and Feedback Schemes
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) ..."
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Cited by 22 (6 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) channel feedback are analyzed, and digital feedback is shown to be potentially superior when the feedback channel uses per channel coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a relatively minor effect even if simple uncoded modulation is used on the feedback channel. We extend our analysis to the case of fading MIMO Multiaccess Channel (MIMOMAC) in the feedback link, as well as to the case of a timevarying channel and feedback delay. We show that by exploiting the MIMOMAC nature of the uplink channel, a fully scalable system with both downlink multiplexing gain and feedback redundancy proportional to the number of base station antennas can be achieved. Furthermore, the feedback strategy is optimized by a nontrivial combination of timedivision and spacedivision multipleaccess. For the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Joint spatial division and multiplexing: Opportunistic beamforming and user grouping,” arXiv preprint arXiv:1305.7252
, 2013
"... Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a tw ..."
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Cited by 17 (4 self)
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Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a two stage downlink beamforming: a prebeamformer that depends on the channel covariances and minimizes interference across groups and a multiuser MIMO precoder for the effective channel after prebeamforming, to counteract interference within a group. We first focus on the regime of a fixed number of antennas and large number of users, and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated “isotropic ” channel result of [1]. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of prebeamformers achieves the optimal sumrate scaling, albeit with a constant gap from the upper bound. Next, we consider the regime of large number of antennas and users, where user selection does not provide significant gain. In the presence of a large number of antennas, the design of prebeamformers reduces to choosing the columns of a Discrete Fourier Transform matrix based on the angles of arrival and angular spreads of the user channel covariance, when the base station (BS) is equipped with a uniform linear antenna array. Motivated by this result, we propose a simplified user grouping algorithm to cluster users into groups when the number
Optimal Allocation of Feedback Bits for Downlink OFDMA
 Systems”, in Proc. IEEE ISIT
, 2008
"... Abstract — This paper studies the downlink Orthogonal Frequency Division Multiplexing (OFDM) setup with a single Base Station (BS) serving many users. The BS is assumed to have limited Channel State Information (CSI) obtained by feedback in a Time Division Duplexing (TDD) manner. Given that the feed ..."
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Cited by 12 (2 self)
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Abstract — This paper studies the downlink Orthogonal Frequency Division Multiplexing (OFDM) setup with a single Base Station (BS) serving many users. The BS is assumed to have limited Channel State Information (CSI) obtained by feedback in a Time Division Duplexing (TDD) manner. Given that the feedback rate and the coherence time of the channel are fixed, the question asked in this paper is: how to allocate the feedback resources optimally? Specifically, what is the optimal number of tones grouped as a subchannel, the number of users that feedback for any subchannel and the number of bits used for quantization of CSI? Analytical expressions are derived for the i.i.d. Rayleigh fading case and it is shown that there is a definite hierarchy in the importance of the three design variables. Feedback resources are first allocated to create the maximum number of subchannels possible, then to allow for more users to feedback for any subchannel and lastly to increase the precision of the channel value. MonteCarlo simulations are performed to verify the accuracy of the derived analytical expressions. I.
Compressive Sensing for Feedback Reduction in MIMO Broadcast Channels 1
, 2009
"... We propose a generalized feedback model and compressive sensing based opportunistic feedback schemes for feedback resource reduction in MIMO Broadcast Channels under the assumption that both uplink and downlink channels undergo block Rayleigh fading. Feedback resources are shared and are opportunist ..."
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Cited by 4 (1 self)
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We propose a generalized feedback model and compressive sensing based opportunistic feedback schemes for feedback resource reduction in MIMO Broadcast Channels under the assumption that both uplink and downlink channels undergo block Rayleigh fading. Feedback resources are shared and are opportunistically accessed by users who are strong, i.e. users whose channel quality information is above a certain fixed threshold. Strong users send same feedback information on all shared channels. They are identified by the base station via compressive sensing. Both analog and digital feedbacks are considered. The proposed analog & digital opportunistic feedback schemes are shown to achieve the same sumrate throughput as that achieved by dedicated feedback schemes, but with feedback channels growing only logarithmically with number of users. Moreover, there is also a reduction in the feedback load. In the analog feedback case, we show that the propose scheme reduces the feedback noise which eventually results in better throughput, whereas in the digital feedback case the proposed scheme in a noisy scenario achieves almost the throughput obtained in a noiseless dedicated feedback scenario. We also show that for a fixed given budget of feedback bits, there exist a tradeoff between the number of shared channels and thresholds accuracy of the feedback SINR. Index Terms Compressed sensing, feedback, lasso, multipleinput multipleoutput (MIMO) systems, opportunistic, protocols, scheduling. I.
Receive Combining vs. MultiStream Multiplexing in Downlink Systems with MultiAntenna Users
"... Abstract—In downlink multiantenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multiantenna users is much larger than N, the maximal multiplexing gain ..."
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Cited by 3 (1 self)
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Abstract—In downlink multiantenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multiantenna users is much larger than N, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are nearorthogonal, for multistream multiplexing to users with wellconditioned channels, and/or to enable interferenceaware receive combining. In this paper, we try to answer the question if the N data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user—the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multiuser diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization. Index Terms—Multiuser MIMO, channel estimation, limited feedback, blockdiagonalization, zeroforcing, receive combining.
Adaptive Feedback Rate Control in MIMO Broadcast Systems with User Scheduling
"... Abstract — In [1], an adaptive scheme was introduced in view of optimizing the overall spectral efficiency of a multiuser MIMO wireless broadcast channel where the channel state information at the transmitting base station (CSIT), to be used for user scheduling and beamforming, is acquired over a li ..."
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Cited by 2 (0 self)
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Abstract — In [1], an adaptive scheme was introduced in view of optimizing the overall spectral efficiency of a multiuser MIMO wireless broadcast channel where the channel state information at the transmitting base station (CSIT), to be used for user scheduling and beamforming, is acquired over a limitedrate feedback channel. In this scheme, the feedback rate is no longer constant per scheduling period but rather optimized as a function of the timedependent channel quality seen at the user side. The present paper further refines this idea and elaborates on some of the associated practical concerns. I.
Fundamental limits in correlated fading mimo broadcast channels: Benefits of transmit correlation diversity,” arXiv preprint arXiv:1401.7114
, 2014
"... We investigate the impact of transmit correlation on the capacity of correlated fading MIMO broadcast channels (BCs) and establish capacity characterizations in various regimes of system parameters, with a particular interest in the largescale array (or massive MIMO) regime. It is advocated in this ..."
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Cited by 2 (1 self)
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We investigate the impact of transmit correlation on the capacity of correlated fading MIMO broadcast channels (BCs) and establish capacity characterizations in various regimes of system parameters, with a particular interest in the largescale array (or massive MIMO) regime. It is advocated in this paper that transmit correlation can be of use to increase both multiplexing gain and power gain in multiuser MIMO systems. We show the potential gains and succinctly characterize fundamental limits in correlated fading MIMO BCs, assuming an ideal condition for which transmit correlation diversity is well defined. In particular, transmit correlation is shown to improve the system multiplexing gain up to by a factor of the degrees of transmit correlation diversity. Not relying on the ideal condition on transmit correlations, we further propose a joint spatial division and multiplexing (JSDM) scheme based on opportunistic beamforming that, for a large number of users, can achieve near optimal sumrate scaling with very limited channel state feedback in realistic channels.
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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Cited by 1 (1 self)
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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.