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**11 - 19**of**19**### λPI2,

, 2012

"... The degrees of freedom (DoF) of the two-user multiple-input single-output (MISO) broad-cast channel (BC) are studied under the assumption that the form, Ii, i = 1, 2, of the channel state information at the transmitter (CSIT) for each user’s channel can be either perfect (P), delayed (D) or not avai ..."

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The degrees of freedom (DoF) of the two-user multiple-input single-output (MISO) broad-cast channel (BC) are studied under the assumption that the form, Ii, i = 1, 2, of the channel state information at the transmitter (CSIT) for each user’s channel can be either perfect (P), delayed (D) or not available (N), i.e., I1, I2 ∈ {P,N,D}, and therefore the overall CSIT can alternate between the 9 resulting states I1I2. The fraction of time associated with CSIT state I1I2 is denoted by the parameter λI1I2 and it is assumed throughout that λI1I2 = λI2I1, i.e., λPN = λNP, λPD = λDP, λDN = λND. Under this assumption of symmetry, the main contri-bution of this paper is a complete characterization of the DoF region of the two user MISO BC with alternating CSIT. Surprisingly, the DoF region is found to depend only on the marginal probabilities (λP, λD, λN) =

### 1The Degrees of Freedom Region of Temporally-Correlated MIMO Networks with Delayed CSIT

"... We consider the temporally-correlated Multiple-Input Multiple-Output (MIMO) broadcast channels (BC) and interference channels (IC) where the transmitter(s) has/have (i) delayed channel state information (CSI) obtained from a latency-prone feedback channel as well as (ii) imperfect current CSIT, obta ..."

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We consider the temporally-correlated Multiple-Input Multiple-Output (MIMO) broadcast channels (BC) and interference channels (IC) where the transmitter(s) has/have (i) delayed channel state information (CSI) obtained from a latency-prone feedback channel as well as (ii) imperfect current CSIT, obtained, e.g., from prediction on the basis of these past channel samples based on the temporal correlation. The degrees of freedom (DoF) regions for the two-user broadcast and interference MIMO networks with general antenna configuration under such conditions are fully characterized, as a function of the prediction quality indicator. Specifically, a simple unified framework is proposed, allowing to attain optimal DoF region for the general antenna configurations and current CSIT qualities. Such a framework builds upon block-Markov encoding with interference quantization, optimally combining the use of both outdated and instantaneous CSIT. A striking feature of our work is that, by varying the power allocation, every point in the DoF region can be achieved with one single scheme. As a result, instead of checking the achievability of every corner point of the outer bound region, as typically done in the literature, we propose a new systematic way to prove the achievability. I.

### Minimum CSIT to achieve Maximum Degrees of Freedom for the MISO BC∗

, 2014

"... Channel state information at the transmitter (CSIT) is a key ingredient in realizing the multiplexing gain provided by distributed MIMO systems. For a downlink multiple-input single output (MISO) broadcast channel, with M antennas at the transmitters and K single antenna receivers, the maximum multi ..."

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Channel state information at the transmitter (CSIT) is a key ingredient in realizing the multiplexing gain provided by distributed MIMO systems. For a downlink multiple-input single output (MISO) broadcast channel, with M antennas at the transmitters and K single antenna receivers, the maximum multiplexing gain or the maximum degrees of freedom (DoF) is min(M,K). The optimal DoF of min(M,K) is achievable if the transmitter has access to perfect, instantaneous CSIT from all receivers. In this paper, we pose the question that what is minimum amount of CSIT required per user in order to achieve the maximum DoF of min(M,K). By minimum amount of CSIT per user, we refer to the minimum fraction of time that the transmitter has access to perfect and instantaneous CSIT from a user. Through a novel converse proof and an achievable scheme, it is shown that the minimum fraction of time, perfect CSIT is required per user in order to achieve the DoF of min(M,K) is given by min(M,K)/K. 1

### Index Terms

"... We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i = 1, 2,...,K) may be either perfect (P), delayed (D) or not known (N) at the transmitter with probabilities λiP, λ i D and λ i N, respectively. In this channel, accor ..."

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We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i = 1, 2,...,K) may be either perfect (P), delayed (D) or not known (N) at the transmitter with probabilities λiP, λ i D and λ i N, respectively. In this channel, according to the three possible CSIT for each user, joint CSIT of the K users could have at most 3K realizations. Although the results by Tandon et al. show that the Degrees of Freedom (DoF) region for the two user MISO BC with symmetric marginal probabilities (i.e., λiQ = λQ∀i ∈ {1, 2,...,K}, Q ∈ {P,D,N}) depends only on the marginal probabilities, we show that this interesting result does not hold in general when the number of users is more than two. In other words, the DoF region is a function of the CSIT pattern, or equivalently, all the joint probabilities. In this paper, given the marginal probabilities of CSIT, we derive an outer bound for the DoF region of the K-user MISO BC. Subsequently, the achievability of these outer bounds are considered in certain scenarios. Finally, we show the dependence of the DoF region on the joint probabilities.

### Communications over the Broadcast Channel with Limited and Delayed Feedback: Fundamental Limits and Novel Encoders and Decoders

, 2013

"... It is my pleasure to express my thanks to all the people who contributed in many ways to the success of this dissertat ion. Many thanks must begin with my advisers, Prof. Petros Elia and Prof. Raymond Knopp. This dissertat ion would not have been possible without their guidance, support and encourag ..."

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It is my pleasure to express my thanks to all the people who contributed in many ways to the success of this dissertat ion. Many thanks must begin with my advisers, Prof. Petros Elia and Prof. Raymond Knopp. This dissertat ion would not have been possible without their guidance, support and encouragement. My first and sincere apprecia-t ion goes to Prof. Pet ros Elia. I appreciate his cont inuing interact ions and helps, in all stages of this thesis, which made my Ph.D. experience produc-t ive and st imulat ing. I remember that he used to work on a paper with me overnight in the offi ce, and that he used to discuss on a paper with me in a McDonald’s store during the weekend. His at t itude and enthusiasm to re-search inspired me to become a bet ter researcher. I am also thankful to Prof. Raymond Knopp, whose advices and supports were invaluable to me. In addit ion, I would like to thank Prof. Sheng Yang and Prof. Syed Ali Jafar for the insight ful technical discussions on my topic, as well as my the-sis jury members Prof. Daniela Tuninet t i, Prof. Mari Kobayashi, Prof. Dirk

### On the DoF Region of K-user MISO . . .

"... An outer bound for the degrees of freedom (DoF) region of the K-user multiple-input single-output (MISO) broadcast channel (BC) is developed under the hybrid channel state information at transmitter (CSIT) model, in which the transmitter has instantaneous CSIT of channels to a subset of the receiver ..."

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An outer bound for the degrees of freedom (DoF) region of the K-user multiple-input single-output (MISO) broadcast channel (BC) is developed under the hybrid channel state information at transmitter (CSIT) model, in which the transmitter has instantaneous CSIT of channels to a subset of the receivers and delayed CSIT of channels to the rest of the receivers. For the 3-user MISO BC, when the transmitter has instantaneous CSIT of the channel to one receiver and delayed CSIT of channels to the other two, two new communication schemes are designed, which are able to achieve the DoF tuple of

### Space-Time Encoded MISO Broadcast Channel with Outdated CSIT: An Error Rate and Diversity Performance Analysis

"... Abstract-Studies of the MISO Broadcast Channel (BC) with delayed Channel State Information at the Transmitter (CSIT) have so far focused on the sum-rate and Degrees-of-Freedom (DoF) region analysis. In this paper, we investigate for the first time the error rate performance at finite SNR and the di ..."

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Abstract-Studies of the MISO Broadcast Channel (BC) with delayed Channel State Information at the Transmitter (CSIT) have so far focused on the sum-rate and Degrees-of-Freedom (DoF) region analysis. In this paper, we investigate for the first time the error rate performance at finite SNR and the diversitymultiplexing tradeoff (DMT) at infinite SNR of a space-time encoded transmission over a two-user MISO BC with delayed CSIT. We consider the so-called MAT protocol obtained by Maddah-Ali and Tse, which was shown to provide 33% DoF enhancement over TDMA. While the asymptotic DMT analysis shows that MAT is always preferable to TDMA, the Pairwise Error Probability analysis at finite SNR shows that MAT is in fact not always a better alternative to TDMA. Benefits can be obtained over TDMA only at very high rate or once concatenated with a full-rate full-diversity space-time code. The analysis is also extended to spatially correlated channels and the influence of transmit correlation matrices and user pairing strategies on the performance are discussed. Relying on statistical CSIT, signal constellations are further optimized to improve the error rate performance of MAT and make it insensitive to user orthogonality. Finally, other transmission strategies relying on delayed CSIT are discussed.