In the setting of the time-selective two-user multiple-input single-output (MISO) broadcast channel (BC), recent work by Tandon et al. considered the case where - in the presence of error-free delayed channel state information at the transmitter (delayed CSIT) - the current CSIT for the channel of user 1 and of user 2, alternate between the two extreme states of perfect current CSIT and of no current CSIT.
Motivated by the problem of having limited-capacity feedback links which may not allow for perfect CSIT, as well as by the need to utilize any available partial CSIT, we here deviate from this `all-or-nothing' approach and proceed - again in the presence of error-free delayed CSIT - to consider the general setting where current CSIT now alternates between any two qualities. Specifically for $I_1$ and $I_2$ denoting the high-SNR asymptotic rates-of-decay of the mean-square error of the CSIT estimates for the channel of user~1 and of user~2 respectively, we consider the case where $I_1,I_2 \in\{γ,α\}$ for any two positive current-CSIT quality exponents $γ,α$. In a fast-fading setting where we consider communication over any number of coherence periods, and where each CSIT state $I_1I_2$ is present for a fraction $λ_{I_1I_2}$ of this total duration, we focus on the symmetric case of $λ_{αγ}=λ_{γα}$, and derive the optimal degrees-of-freedom (DoF) region. The result, which is supported by novel communication protocols, naturally incorporates the aforementioned `Perfect current' vs. `No current' setting by limiting $I_1,I_2\in\{0,1\}$.
Finally, motivated by recent interest in frequency correlated channels with unmatched CSIT, we also analyze the setting where there is no delayed CSIT.
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…
We study the degrees of freedom (DoF) of a $K$-user parallel MISO broadcast channel with arbitrary levels of partial CSIT over each subchannel. We derive a sum-DoF upperbound which depends on the average CSIT quality of each user. This upperbound is shown to be tight under total order, i.e. when the order of users with respect to their CSIT qualities is preserved over all subchannels. In this case, it is shown that separate coding over each subchannel is optimum in a sum-DoF sense.
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…
A required feature for the next generation of wireless communication networks will be the capability to serve simultaneously a large number of devices with heterogeneous CSIT qualities and demands. In this paper, we consider the overloaded MISO BC with two groups of CSIT qualities. We propose a transmission scheme where degraded symbols are superimposed on top of spatially-multiplexed symbols. The developed strategy allows to serve all users in a non-orthogonal manner and the analysis shows an enhanced perfomance compared to existing schemes. Moreover, optimality in a DoF sense is shown.
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…
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…
For the $K=2$ user MISO BC, i.e., the wireless broadcast channel where a transmitter equipped with $K=2$ antennas sends independent messages to $K=2$ receivers each of which is equipped with a single antenna, the sum generalized degrees of freedom (GDoF) are characterized for arbitrary channel strength and channel uncertainty levels for each of the channel coefficients. The result is extended to $K>2$ users under additional restrictions which include the assumption of symmetry.
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…
We consider the $K$-User Multiple-Input-Single-Output (MISO) Broadcast Channel (BC) where the transmitter, equipped with $M$ antennas, serves $K$ users, with $K \leq M$. The transmitter has access to a partial channel state information of the users. This is modelled by letting the variance of the Channel State Information at the Transmitter (CSIT) error of user $i$ scale as $O(P^{-α_i}$) for the Signal-to-Noise Ratio (SNR) $P$ and some constant $α_i \geq 0$. In this work we derive the optimal Degrees-of-Freedom (DoF) region in such setting and we show that Rate-Splitting (RS) is the key scheme…
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 …
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 …
Recently, the Degrees-of-Freedom (DoF) region of multiple-input-single-output (MISO) networks with imperfect channel state information at the transmitter (CSIT) has attracted significant attentions. An achievable scheme is known as rate-splitting (RS) that integrates common-message-multicasting and private-message-unicasting. In this paper, focusing on the general $K$-cell MISO IC where the CSIT of each interference link has an arbitrary quality of imperfectness, we firstly identify the DoF region achieved by RS. Secondly, we introduce a novel scheme, so called Topological RS (TRS), whose nove…
This paper considers the Sum-Rate (SR) maximization problem in downlink MU-MISO systems under imperfect Channel State Information at the Transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This Rate-Splitting (RS) approach was shown to boost the achievable Degrees of Freedo…
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 provide a fresh perspective on the problem of characterizing the DoF region of the $K$-user MISO BC with arbitrary levels of partial CSIT. In a previous achievability proof, Piovano and Clerckx characterized all faces describing a polyhedral outer bound region, and then with the aid of mathematical induction, prescribed a scheme based on rate-splitting with flexible assignment of common DoF and power levels to achieve each such face. We propose an alternative approach in which we deal directly with the region achievable through rate-splitting and employ a Fourier-Motzkin procedure to elimin…
On the Synergistic Benefits of Alternating CSIT for the MISO BC
The degrees of freedom (DoF) of the two-user multiple-input single-output (MISO) broadcast channel (BC) are studied under the assumption that the form, I_i, 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., I_1 and I_2 can take values of either P, D or N, and therefore the overall CSIT can alternate between the 9 resulting states, each state denoted as I_1I_2. The fraction of time associated with CSIT state I_1I_2 is denoted by the parameter λ_{I_1I_2} and it is assumed throughout that λ_…
In this paper, degrees of freedom (DoF) is investigated for the $M\times N$ single input single output (SISO) X channel with alternating channel state information at the transmitters (CSIT). It is known that the sum DoF of 2-user SISO X channel with synergistic alternating CSIT is the same as the sum DoF of 2-user $(M=N=2)$ SISO X channel with perfect CSIT [8]. In this paper, such 2-user X channel schemes are extended to the general $M\times N$ X channel. It is shown that the proposed $M\times N$ X channel schemes with synergistic alternating CSIT achieve $2M/(M+1)$ sum DoF. This DoF with $M=N…
We study the problem of secure transmission over a Gaussian two-user multi-input single-output (MISO) broadcast channel under the assumption that links connecting the transmitter to the two receivers may have unequal strength statistically. In addition to this, the state of the channel to each receiver is conveyed in a strictly causal manner to the transmitter. We focus on a two state topological setting of strong v.s. weak links. Under these assumptions, we first consider the MISO wiretap channel and establish bounds on generalized secure degrees of freedom (GSDoF). Next, we extend this model…
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…
In this paper, a new proof for the degrees of freedom (DoF) region of the K-user multiple-input multiple-output (MIMO) broadcast channel (BC) with no channel state information at the transmitter (CSIT) and perfect channel state information at the receivers (CSIR) is provided. Based on this proof, the capacity region of a certain class of MIMO BC with channel distribution information at the transmitter (CDIT) and perfect CSIR is derived. Finally, an outer bound for the DoF region of the K-user MIMO interference channel (IC) with no CSIT is provided.
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…
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…
We address the max-min fairness design problem for a MU-MISO system with partial Channel State Information (CSI) at the Base Station (BS), consisting of an imperfect channel estimate and statistical knowledge of the estimation error, and perfect CSI at the receivers. The objective is to maximize the minimum Average Rate (AR) among users subject to a transmit power constraint. An unconventional transmission scheme is adopted where the Base Station (BS) transmits a common message in addition to the conventional private messages. In situations where the CSIT is not accurate enough to perform inte…
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…
In this paper, we consider the design of robust linear precoders for MU-MISO systems where users have perfect Channel State Information (CSI) while the BS has partial CSI. In particular, the BS has access to imperfect estimates of the channel vectors, in addition to the covariance matrices of the estimation error vectors. A closed-form expression for the Average Minimum Mean Square Error (AMMSE) is obtained using the second order Taylor Expansion. This approximation is used to formulate two fairness-based robust design problems: a maximum AMMSE-constrained problem and a power-constrained probl…
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 …
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…
The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form $I_{i}$, $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf{P}, \mathsf{D}, \mathsf{N}\}$, and the forms $\mathsf{P}$, $\mathsf{D}$ and $\mathsf{N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between $9$ possible states corresponding to all possible values of $I_{1}I_{2}$, with each state occurring for $λ_…
We study the $K=3$ user multiple input single output (MISO) broadcast channel (BC) with $M=3$ antennas at the transmitter and $1$ antenna at each receiver, from the generalized degrees of freedom (GDoF) perspective, under the assumption that the channel state information at the transmitter (CSIT) is limited to finite precision. In particular, our goal is to identify a parameter regime where a simple layered superposition (SLS) coding scheme achieves the entire GDoF region. With $α_{ij}$ representing the channel strength parameter for the link from the $j^{th}$ antenna of the transmitter to the…
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 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…
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 $K$-…
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 …
This work explores coded caching in the symmetric $K$-user cache-aided MISO BC with imperfect CSIT-type feedback, for the specific case where the cache size is much smaller than the library size. Building on the recently explored synergy between caching and delayed-CSIT, and building on the tradeoff between caching and CSIT quality, the work proposes new schemes that boost the impact of small caches, focusing on the case where the cumulative cache size is smaller than the library size. For this small-cache setting, based on the proposed near-optimal schemes, the work identifies the optimal cac…
We study the $K$-user, $M$-subchannel parallel multiple-input-single-output (MISO) broadcast channel (BC) under arbitrary levels of partial channel state information at the transmitter (CSIT). We show that the parallel subchannels constituting this setting are separable from a degrees-of-freedom (DoF) region perspective if and only if the partial CSIT pattern is totally ordered. This total order condition corresponds to users abiding by the same order, with respect to their CSIT quality levels, in each of the parallel subchannels. For instance, let $α_{k}^{[l]}$ and $α_{j}^{[l]}$ be the CSIT q…
