The Degrees of Freedom (DoF) of a K-User MISO Broadcast Channel (BC) is studied when the Transmitter (TX) has access to a delayed channel estimate in addition to an imperfect estimate of the current channel. The current estimate could be for example obtained from prediction applied on past estimates, in the case where feedback delay is within the coherence time. Building on previous recent works on this setting with two users, the estimation error of the current channel is characterized by its scaling as P at the exponent α, where α=1 (resp. α=0) corresponds to an estimate being essentially perfect (resp. useless) in terms of DoF. In this work, we contribute to the characterization of the DoF region in such a setting by deriving an outerbound for the DoF region and by providing an achievable DoF region. The achievable DoF is obtained by developing a new alignment scheme, called the Kα-MAT scheme, which builds upon both the principle of the MAT alignment scheme from Maddah-Ali and Tse and Zero-Forcing to achieve a larger DoF when the delayed CSIT received is correlated with the instantaneous channel state.
Channel state information at the transmitter affects the degrees of freedom of the wireless networks. In this paper, we analyze the DoF for the K-user multiple-input single-output (MISO) broadcast channel (BC) with synergistic alternating channel state information at the transmitter (CSIT). Specifically, the CSIT of each user alternates between three states, namely, perfect CSIT (P), delayed CSIT (D) and no CSIT (N) among different time slots. For the K-user MISO BC, we show that the total achievable degrees of freedom (DoF) are given by $\frac{K^{2}}{2K-1}$ through utilizing the synergistic b…
The channel state information at the transmitter (CSIT) play an important role in the performance of wireless networks. The CSIT model can be delayed and imperfect-quality, since the feedback link has a delay and the channel state information (CSI) feedback has distortion. In this paper, we thus characterize the degrees-of-freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) broadcast channel with delayed imperfect-quality CSIT, where the antenna configurations can be arbitrary. The converse proof of DoF region is based on the enhancement of physically degraded channel. T…
This work analyses the Generalized Degrees-of-Freedom (GDoF) of the 2-User Multiple-Input Single-Output (MISO) Broadcast Channel (BC) in the so-called Distributed CSIT regime, with application to decentralized wireless networks. This regime differs from the classical limited CSIT one in that the CSIT is not just noisy but also imperfectly shared across the transmitters (TXs). Hence, each TX precodes data on the basis of local CSIT and statistical quality information at other TXs. We derive the GDoF result and obtain the surprising outcome that by specific accounting of the pathloss information…
This paper theoretically characterizes the degrees-of-freedom (DoF) region of order-$(K-1)$ messages for the $K$-user multiple-input multiple-output (MIMO) broadcast channel with delayed channel state information at the transmitter (CSIT) and arbitrary antenna configurations, where the transmitter has $M$ antennas and the receiver $i=1,2,\cdots,K$ has $N_i$ antennas. For the converse, we first derive the DoF region of order-$(K-1)$ messages for the $K$-user MIMO broadcast channel with no CSIT and arbitrary antenna configurations with the aid of the proposed Genie-bound, and then establish the …
We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form $mD_1 + D_2 \leq m$. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless …
In this paper, we propose a new retrospective interference alignment for two-cell multiple-input multiple-output (MIMO) interfering multiple access channels (IMAC) with the delayed channel state information at the transmitters (CSIT). It is shown that having delayed CSIT can strictly increase the sum-DoF compared to the case of no CSIT. The key idea is to align multiple interfering signals from adjacent cells onto a small dimensional subspace over time by fully exploiting the previously received signals as side information with outdated CSIT in a distributed manner. Remarkably, we show that th…
This work studies the optimal Degrees-of-Freedom (DoF) of the $K$-User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the current channel estimation error scales in~$P^{-α}$ for $α\in[0,1]$. This papers establishes for the first time the optimal DoF in this setting thanks to a new transmission scheme which achieves the elusive DoF-optimal combining of the Maddah-Ali and Tse scheme (MAT) introduced in their seminal work in $2010$ with Zero-Forcing (ZF) for an arbitrary number of users. The derived sum DoF…
The degrees of freedom (DoF) region is characterized for the $2$-user multiple input multiple output (MIMO) broadcast channel (BC), where the transmitter is equipped with $M$ antennas, the two receivers are equipped with $N_1$ and $N_2$ antennas, and the levels of channel state information at the transmitter (CSIT) for the two users are parameterized by $β_1, β_2$, respectively. The achievability of the DoF region was established by Hao, Rassouli and Clerckx, but no proof of optimality was heretofore available. The proof of optimality is provided in this work with the aid of sum-set inequaliti…
For the two-user multiple-input multiple-output (MIMO) broadcast channel with delayed channel state information at the transmitter (CSIT) and arbitrary antenna configurations, all the degrees-of-freedom (DoF) regions are obtained. However, for the three-user MIMO broadcast channel with delayed CSIT and arbitrary antenna configurations, the DoF region of order-2 messages is still unclear and only a partial achievable DoF region of order-1 messages is obtained, where the order-2 messages and order-1 messages are desired by two receivers and one receiver, respectively. In this paper, for the thre…
The K-user multiple-input and multiple-output (MIMO) broadcast channel (BC) with no channel state information at the transmitter (CSIT) is considered, where each receiver is assumed to be equipped with reconfigurable antennas capable of choosing a subset of receiving modes from several preset modes. Under general antenna configurations, the sum linear degrees of freedom (LDoF) of the K-user MIMO BC with reconfigurable antennas is completely characterized, which corresponds to the maximum sum DoF achievable by linear coding strategies. The LDoF region is further characterized for a class of ant…
The degrees of freedom (DoF) of the $K$-user multiple-input multiple-output (MIMO) interference channel are studied when perfect, but delayed channel state information is available at the transmitter side (delayed CSIT). Recent works have proposed schemes that achieve increasing DoF values, but at the cost of long communication delays. This work proposes three linear precoding strategies, formulated in such a way that the achievable DoF can be derived as a function of the transmission delay, thus elucidating its achievable DoF-delay trade-off. All strategies are based on the concept of interfe…
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 (DoF) of such network. We first focus on the $3$-user MISO BC; and we completely characterize the DoF region for all possible heterogeneous C…
Rate-splitting multiple access (RSMA) has appeared as a powerful transmission and multiple access strategy for multi-user multi-antenna communications. Uniquely, this paper studies the optimization of the sum-rate of RSMA with imperfect channel state information (CSI) at the transmitter (CSIT) and the receivers (CSIR). The robustness of the RSMA approach against imperfect CSIT has been investigated in the previous studies while there has been no consideration for the effects of imperfect CSIR. This motivates us to develop a robust design relying on RSMA in the presence of both imperfect CSIT a…
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 diversity-multiplexing 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 …
We consider communication over heterogeneous parallel channels, where a transmitter is connected to two users via two parallel channels: a MIMO broadcast channel (BC) and a noiseless rate-limited multicast channel. We characterize the optimal degrees of freedom (DoF) region of this setting when the transmitter has delayed channel state information (CSIT) regarding the MIMO BC. Our results show that jointly coding over the two channels strictly outperforms simple channel aggregation and can even achieve the instantaneous CSIT performance with completely outdated CSIT on the MIMO BC in the sum D…
The Maddah-Ali and Tse (MAT) scheme is a linear precoding strategy that exploits Interference Alignment and perfect, but delayed, channel state information at the transmitters (delayed CSIT), improving the degrees of freedom (DoF) that can be achieved for the broadcast channel (BC). Since its appearance, many works have extended the concept of Retrospective Interference Alignment (RIA) to other multi-user channel configurations. However, little is known about the broadcast channel with multiple cells, i.e. the interference broadcast channel (IBC). In this work, the DoF are studied for the $K$-…
In this paper, we investigate the generalized degrees-of-freedom (GDoF) of the asymmetric interference channel with delayed channel state information at the transmitter (CSIT), where each transmitter has two antennas, each receiver has one antenna, and the strength for each interfering link can vary. The optimal sum-GDoF is characterized by matched converse and achievability proof. Through our results, we also reveal that in our antenna setting, the symmetric GDoF lower bound in [Mohanty et. al, TIT 2019] can be elevated, and the symmetric GDoF upper bound in [Mohanty et. al, TIT 2019] is tigh…
This paper proposes an interference alignment method with distributed and delayed channel state information at the transmitter (CSIT) for a class of interference networks. The core idea of the proposed method is to align interference signals over time at the unintended receivers in a distributed manner. With the proposed method, achievable trade-offs between the sum of degrees of freedom (sum-DoF) and feedback delay of CSI are characterized in both the X-channel and three-user interference channel to reveal the impact on how the CSI feedback delay affects the sum-DoF of the interference networ…
This paper focuses on linear beamforming design and power allocation strategy for ergodic rate optimization in a two-user Multiple-Input-Single-Output (MISO) system with statistical and delayed channel state information at the transmitter (CSIT). We propose a transmission strategy, denoted as Statistical Alternative MAT (SAMAT), which exploits both channel statistics and delayed CSIT. Firstly, with statistical CSIT only, we focus on statistical beamforming (SBF) design that maximizes a lower bound on the ergodic sum-rate. Secondly, relying on both statistical and delayed CSIT, an iterative alg…
We consider a $K$-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user $i(i=1,2,\ldots,K)$ may be instantaneously perfect (P), delayed (D) or not known (N) at the transmitter with probabilities $λ_P^i$, $λ_D^i$ and $λ_N^i$, respectively. In this setting, according to the three possible CSIT for each user, knowledge of the joint CSIT of the $K$ users could have at most $3^K$ states. In this paper, given the marginal probabilities of CSIT (i.e., $λ_P^i$, $λ_D^i$ and $λ_N^i$), we derive an outer bound for the DoF region of the $K$-user …
We consider a $K$-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user $i(i=1,2,\ldots,K)$ may be either instantaneously perfect (P), delayed (D) or not known (N) at the transmitter with probabilities $λ_P^i$, $λ_D^i$ and $λ_N^i$, respectively. In this setting, according to the three possible CSIT for each user, knowledge of the joint CSIT of the $K$ users could have at most $3^K$ states. Although the results by Tandon et al. show that for the symmetric two user MISO BC (i.e., $λ_Q^i=λ_Q,\ \forall i\in \{1,2\}, Q\in \{P,D,N\}$), the …
We study the Gaussian MIMOME wiretap channel where a transmitter wishes to communicate a confidential message to a legitimate receiver in the presence of eavesdroppers, while the eavesdroppers should not be able to decode the confidential message. Each node in the network is equipped with arbitrary number of antennas. Furthermore, channels are time varying, and there is no channel state information available at the transmitter (CSIT) with respect to eavesdroppers' channels; and transmitter only has access to delayed CSIT of the channel to the legitimate receiver. The secure degrees of freedom …
In this paper, we consider a MU-MISO system where users have highly accurate Channel State Information (CSI), while the Base Station (BS) has partial CSI consisting of an imperfect channel estimate and statistical knowledge of the CSI error. With the objective of maximizing the Average Sum Rate (ASR) subject to a power constraint, a special transmission scheme is considered where the BS transmits a common symbol in a multicast fashion, in addition to the conventional private symbols. This scheme is termed Joint Multicasting and Broadcasting (JMB). The ASR problem is transformed into an augment…
The generalized degrees of freedom (GDoF) region of the multiple-input multiple-output (MIMO) Gaussian Z-interference channel with an arbitrary number of antennas at each node is established under the assumption of delayed channel state information at transmitters (CSIT). The GDoF region is parameterized by $α$, which links the interference-to-noise ratio (INR) to the signal-to-noise ratio (SNR) via $INR=SNR^α$. A new outer bound for the GDoF region is established by maximizing a bound on the weighted sum-rate of the two users, which in turn is obtained by using a combination of genie-aided si…
We consider the cache-aided MISO broadcast channel (BC) in which a multi-antenna transmitter serves $K$ single-antenna receivers, each equipped with a cache memory. The transmitter has access to partial knowledge of the channel state information. For a symmetric setting, in terms of channel strength levels, partial channel knowledge levels and cache sizes, we characterize the generalized degrees of freedom (GDoF) up to a constant multiplicative factor. The achievability scheme exploits the interplay between spatial multiplexing gains and coded-multicasting gain. On the other hand, a cut-set-ba…
This paper considers a K-user Multiple-Input-Single-Output (MISO) Interference Channel (IC), where the channel state information obtained by the transmitters (CSIT) is perfect, but completely outdated. A Retrospective Interference Alignment (RIA) using such delayed CSIT was proposed by the authors of [1] for the MISO Broadcast Channel (BC), but the extension to the MISO IC is a non-trivial step as each transmitter only has the message intended for the corresponding user. Recently, [7] focused on a Single-Input-Single-Output (SISO) IC and solved such bottleneck by inventing a distributed higher…
The state-dependent $K$-user memoryless Broadcast Channel~(BC) with state feedback is investigated. We propose a novel transmission scheme and derive its corresponding achievable rate region, which, compared to some general schemes that deal with feedback, has the advantage of being relatively simple and thus is easy to evaluate. In particular, it is shown that the capacity region of the symmetric erasure BC with an arbitrary input alphabet size is achievable with the proposed scheme. For the fading Gaussian BC, we derive a symmetric achievable rate as a function of the signal-to-noise ratio~(…
We study the degrees of freedom (DoF) regions of the two-user multiple-input multiple-output (MIMO) broadcast channel with a general message set (BC-CM) - that includes private and common messages - under fast fading. Nine different channel state knowledge assumptions -collectively known as hybrid CSIT models - are considered wherein the transmitter has either perfect/instantaneous (P), delayed (D) or no (N) channel state information (CSI) from each of the two receivers. General antenna configurations are addressed wherein the three terminals have arbitrary numbers of antennas. The DoF regions…
In general, the different links of a broadcast channel may experience different fading dynamics and, potentially, unequal or hybrid channel state information (CSI) conditions. The faster the fading and the shorter the fading block length, the more often the link needs to be trained and estimated at the receiver, and the more likely that CSI is stale or unavailable at the transmitter. Disparity of link fading dynamics in the presence of CSI limitations can be modeled by a multi-user broadcast channel with both non-identical link fading block lengths as well as dissimilar link CSIR/CSIT conditio…
In this paper, the sum secure degrees of freedom (SDoF) of the $K$-user Multiple Input/Single Output (MISO) Broadcast Channel with Confidential Messages (BCCM) and alternating Channel State Information at the Transmitter (CSIT) is investigated. In the MISO BCCM, a $K$-antenna transmitter (TX) communicates toward $K$ single-antenna receivers (RXs), so that message for RX $k$ is kept secret from RX $j$ with $j<k$. For this model, we consider the scenario in which the CSI of the RXs from $2$ to $K$ is instantaneously known at the transmitter while CSI of RX $1$ is known at the transmitter (i) ins…
