Sina Lashgari

Linear Degrees of Freedom of the MIMO X-Channel With Delayed CSIT

We establish the degrees of freedom (DoF) of the two-user X-channel with delayed channel knowledge at transmitters [i.e., delayed channel state information at the transmitters (CSIT)], assuming linear coding strategies at the transmitters. We derive a new upper bound and characterize the linear DoF of this network to be 6/5. The converse builds upon our development of a general lemma that shows that, if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. As a byproduct, we also apply this general lemma to the three-user interference channel with delayed CSIT, thereby deriving a new upper bound of 9/7 on its linear DoF. This is the first bound that captures the impact of delayed CSIT on the DoF of this network, under the assumption of linear encoding strategies.

Timely Throughput of Heterogeneous Wireless Networks: Fundamental Limits and Algorithms

The proliferation of different wireless access technologies, together with the growing number of multi-radio wireless devices suggest that the opportunistic utilization of multiple connections at the users can be an effective solution to the phenomenal growth of traffic demand in wireless networks. In this paper, we consider the downlink of a wireless network with N access points (APs) and M clients, where each client is connected to several out-of-band APs, and requests delay-sensitive traffic (e.g., real-time video). We adopt the framework of Hou and study the maximum total timely throughput of the network, denoted by CT3, which is the maximum average number of packets delivered successfully before their deadline. Solving this problem is challenging since even the number of different ways of assigning packets to the APs is NM. We overcome the challenge by proposing a deterministic relaxation of the problem, which converts the problem to a network with deterministic delays in each link. We show that the additive gap between the capacity of the relaxed problem, denoted by Cdet and CT3 is bounded by 2√(N(Cdet + [N/4])), which is asymptotically negligible compared to Cdet, when the network is operating at high-throughput regime. In addition, our numerical results show that the actual gap between CT3 and Cdet is in most cases much less than the worst-case gap proven analytically. Moreover, using LP rounding methods we prove that the relaxed problem can be approximated within additive gap of N. We extend the analytical results to the case of time-varying channel states, real-time traffic, prioritized traffic, and optimal online policies. Finally, we generalize the model for deterministic relaxation to consider fading, rate adaptation, and multiple simultaneous transmissions.

Blind wiretap channel with delayed CSIT

We consider the Gaussian wiretap channel with a transmitter, a legitimate receiver, and k eavesdroppers (k ∈ ℕ), where the secure communication is aided via a jammer. We focus on the setting where the transmitter and the jammer are blind with respect to the state of channels to eavesdroppers, and only have access to delayed channel state information (CSI) of the legitimate receiver, which is referred to as “blind cooperative wiretap channel with delayed CSIT”. We show that a strictly positive secure Degrees of Freedom (DoF) of 1 over 3 is achievable irrespective of the number of eavesdroppers (k) in the network, and further, 1 over 3 is optimal assuming linear coding strategies at the transmitters. The converse proof is based on two key lemmas. The first lemma, named Rank Ratio Inequality, shows that if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear sub-spaces at the two receivers cannot exceed 3/2, due to delayed CSI. The second lemma implies that once the transmitters in a network have no CSI with respect to a receiver, the least amount of alignment will occur at that receiver, meaning that transmit signals will occupy the maximal signal dimensions at that receiver. Finally, we show that once the transmitter and the jammer form a single transmitter with two antennas, which we refer to as MISO wiretap channel, 1 over 2 is the optimal secure DoF when using linear schemes.

A rank ratio inequality and the linear degrees of freedom of X-channel with delayed CSIT

We establish the degrees of freedom of the X-channel with delayed channel knowledge at transmitters (i.e., delayed CSIT), assuming linear coding strategies at the transmitters. We derive a new upper bound and characterize the linear degrees of freedom of this network to be 6/5. The converse builds upon our development of a general lemma for wireless networks consisting of two transmitters and two receivers, with delayed CSIT. The lemma states that, if the two transmitters employ linear strategies, then the ratio of the rank of received signal subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. This lemma can also be applied to any arbitrary network, in which a receiver decodes its desired message in the presence of two interferers.

MISO Broadcast Channel With Hybrid CSIT: Beyond Two Users

We study the impact of heterogeneity of channel-state-information available at the transmitters (CSIT) on the capacity of broadcast channels with a multiple-antenna transmitter and k single-antenna receivers (MISO BC). In particular, we consider the k-user MISO BC, where the CSIT with respect to each receiver can be either instantaneous/perfect, delayed, or not available; and we study the impact of this heterogeneity of CSIT on the degrees-of-freedom (DoFs) of such network. We first focus on the three-user MISO BC, and we completely characterize the DoF region for all possible heterogeneous CSIT configurations, assuming linear encoding strategies at the transmitters. The result shows that the state-of-the-art achievable schemes in the literature are indeed sum-DoF optimal, when restricted to linear encoding schemes. To prove the result, we develop a novel bound, called interference decomposition bound, which provides a lower bound on the interference dimension at a receiver which supplies delayed CSIT based on the average dimension of constituents of that interference, thereby decomposing the interference into its individual components. Furthermore, we extend our outer bound on the DoF region to the general k-user MISO BC, and demonstrate that it leads to an approximate characterization of linear sum-DoF to within an additive gap of 0.5 for a broad range of CSIT configurations. Moreover, for the special case where only one receiver supplies delayed CSIT, we completely characterize the linear sum-DoF.

Three-user MISO broadcast channel: How much can CSIT heterogeneity help?

We study the impact of heterogeneity of channel state information available to the transmitters (CSIT) on the performance of multi-antenna multi-user wireless networks. More specifically, we consider the 3-user multiple-input single-output (MISO) broadcast channel, where the available CSIT with respect to each receiver can be instantaneous (P), delayed (D), or none (N); and we characterize the extent to which such heterogeneity of CSIT impacts its linear degrees of freedom (LDoF). In particular, we completely characterize the DoF region for all possible CSIT configurations, assuming linear encoding strategies at the transmitters. The converse, which is the main contribution of the paper, is based on a novel lemma, called Interference Decomposition Bound, which provides a lower bound on the interference dimension at a receiver with delayed CSIT, based on the dimension of constituents of that interference, thereby decomposing the interference into its individual components.

Blind MIMO wiretap channel with delayed CSIT

We study the Gaussian MIMO wiretap channel where a transmitter wishes to communicate a secure message to a legitimate receiver in the presence of eavesdroppers, while the eavesdroppers should not be able to decode the secure message. Each node in the network is equipped with arbitrary number of antennas. Furthermore, channels are time varying, and the transmitter has no channel state information (CSIT) of its channels to the eavesdroppers; and it only has access to delayed CSIT of the channel to the legitimate receiver. We completely characterize the secure degrees of freedom (SDoF) of such network, when restricted to linear encoding schemes. In particular, we strictly improve the state-of-the-art achievable schemes for this network. Furthermore, we develop a tight converse result by presenting a lemma, which states that once the transmitter(s) in a network have no CSIT of a certain receiver, and receivers have the same number of antennas, the least amount of alignment will occur at that receiver, meaning that transmit signals will occupy the maximal signal dimensions at that receiver.

Transmitter cooperation in interference channel with delayed CSIT

In this work we study the impact of limited transmitter cooperation on interference management in two-user interference channel. In particular, we consider the two-user interference channel with delayed channel state information at the transmitters (delayed CSIT). We first present a model to capture and quantify the amount of cooperation between the transmitters. In this model we denote the fraction of shared messages that are intended for Rx₁, Rx₂ by ρ₁,ρ₂, respectively, and then, characterize the degrees of freedom (DoF) region as a function of ρ₁, ρ₂. As a result, the two-user interference channel and two-user multiple-input single-output (MISO) broadcast channel become special cases of no cooperation (ρ₁ = ρ₂ = 0) and full cooperation (ρ₁ = ρ₂ = 1) in our framework. Moreover, our result indicates that the maximum benefit of cooperation from the DoF perspective is achieved by sharing only half of the messages between the transmitters.

A general outer bound for MISO broadcast channel with heterogeneous CSIT

We study the impact of heterogeneity of channel-state-information available at the transmitters (CSIT) on the capacity of broadcast channels with a multiple-antenna transmitter and k single-antenna receivers (MISO BC). In particular, we consider the k-user MISO BC, where the CSIT with respect to each receiver can be either instantaneous/perfect (P), delayed (D), or not available (N); and we study the impact of this heterogeneity of CSIT on the degrees-of-freedom (DoF) of such network. We develop a general outer bound on the DoF region of k-user MISO BC for all possible heterogeneous CSIT configurations, assuming linear encoding strategies at the transmitter. The outer bound leads to an approximate linear sum-DoF characterization to within 0.5 for a broad range of CSIT configurations. It also leads to an exact characterization of linear sum-DoF for some specific CSIT configurations. Our proof of the outer bound relies on the development of a novel lemma, called Interference Decomposition Bound, which lower bounds the interference dimension at a receiver which supplies delayed CSIT based on the average dimension of constituents of that interference, thereby decomposing it into its components.

Approximating the timely throughput of heterogeneous wireless networks

In this paper we consider the down link of a heterogeneous wireless network with N Access Points (APs) and M clients, where each client is connected to several out-of-band APs, and requests delay-sensitive traffic (e.g., real-time video). We adopt the framework of Hou, Borkar, and Kumar, and study the maximum total timely throughput of the network, denoted by C(T3), which is the maximum average number of packets delivered successfully before their deadline. We propose a deterministic relaxation of the problem, which converts the problem to a network with deterministic delays in each link. We show that the additive gap between the capacity of the relaxed problem denoted by Cdet, and C(T3) is bounded by 2√(N(Cdet + N/4)), which is asymptotically negligible compared to Cdet, when the network is operating at high-throughput regime. Moreover, using LP rounding methods we prove that the relaxed problem can be approximated in polynomial time with additive gap of N.