In this work, we study the generalized degrees-of-freedom (GDoF) of downlink and uplink cellular networks, modeled as Gaussian interfering broadcast channels (IBC) and Gaussian interfering multiple access channels (IMAC), respectively. We focus on regimes of low inter-cell interference, where single-cell transmission with power control and treating inter-cell interference as noise (mc-TIN) is GDoF optimal. Recent works have identified two relevant regimes in this context: one in which the GDoF region achieved through mc-TIN for both the IBC and IMAC is a convex polyhedron without the need for time-sharing (mc-CTIN regime), and a smaller (sub)regime where mc-TIN is GDoF optimal for both the IBC and IMAC (mc-TIN regime). In this work, we extend the mc-TIN framework to cellular scenarios where channel state information at the transmitters (CSIT) is limited to finite precision. We show that in this case, the GDoF optimality of mc-TIN extends to the entire mc-CTIN regime, where GDoF benefits due to interference alignment (IA) are lost. Our result constitutes yet another successful application of robust outer bounds based on the aligned images (AI) approach.
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…
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…
We study the generalized degrees-of-freedom (GDoF) of cellular networks under finite precision channel state information at the transmitters (CSIT). We consider downlink settings modeled by the interfering broadcast channel (IBC) under no multi-cell cooperation, and the overloaded multiple-input-single-output broadcast channel (MISO-BC) under full multi-cell cooperation. We focus on three regimes of interest: the mc-TIN regime, where a scheme based on treating inter-cell interference as noise (mc-TIN) was shown to be GDoF optimal for the IBC; the mc-CTIN regime, where the GDoF region achievabl…
Aligned-Images Sumset Inequalities are used in this work to study the Generalized Degrees of Freedom (GDoF) of the symmetric layered multi-hop interference channel under the robust assumption that the channel state information at the transmitters (CSIT) is limited to finite precision. First, the sum-GDoF value is characterized for the $2\times 2\times 2$ setting that is comprised of $2$ sources, $2$ relays, and $2$ destinations. It is shown that the sum-GDoF do not improve even if perfect CSIT is allowed in the first hop, as long as the CSIT in the second hop is limited to finite precision. Th…
This contribution investigates the Degrees-of-Freedom region of a two-user frequency correlated Multiple-Input-Single-Output (MISO) Broadcast Channel (BC) with imperfect Channel State Information at the transmitter (CSIT). We assume that the system consists of an arbitrary number of subbands, denoted as $L$. Besides, the CSIT state varies across users and subbands. A tight outer-bound is found as a function of the minimum average CSIT quality between the two users. Based on the CSIT states across the subbands, the DoF region is interpreted as a weighted sum of the optimal DoF regions in the sc…
This work obtains the first bound that is provably sensitive to network coherence time, i.e., coherence time in an interference network where all channels experience the same coherence patterns. This is accomplished by a novel adaptation of the aligned image sets bound, and settles various open problems noted previously by Naderi and Avestimehr and by Gou et al. For example, a necessary and sufficient condition is obtained for the optimality of 1/2 DoF per user in a partially connected interference network where the channel state information at the receivers (CSIR) is perfect, the channel stat…
This paper considers dynamic transmit covariance design in point-to-point MIMO fading systems with unknown channel state distributions and inaccurate channel state information subject to both long term and short term power constraints. First, the case of instantaneous but possibly inaccurate channel state information at the transmitter (CSIT) is treated. By extending the drift-plus-penalty technique, a dynamic transmit covariance policy is developed and is shown to approach optimality with an $O(δ)$ gap, where $δ$ is the inaccuracy measure of CSIT, regardless of the channel state distribution …
In this paper, a new optimization framework is presented for the joint design of user selection, power allocation, and precoding in multi-cell multi-user multiple-input multiple-output (MU-MIMO) systems when imperfect channel state information at transmitter (CSIT) is available. By representing the joint optimization variables in a higher-dimensional space, the weighted sum-spectral efficiency maximization is formulated as the maximization of the product of Rayleigh quotients. Although this is still a non-convex problem, a computationally efficient algorithm, referred to as generalized power i…
In this paper, we look at the problem of treating interference as noise (TIN) in the Gaussian interfering multiple access channel (IMAC). The considered network comprises $K$ mutually interfering multiple access channels (MACs), each consisting of two transmitters communicating independent messages to one receiver. We define the TIN scheme for this channel as one in which each MAC performs a power controlled version of its capacity-achieving strategy while treating interference from all other MACs as noise. We characterize an achievable generalized degrees-of-freedom (GDoF) region under the TI…
The problem of dirty paper coding (DPC) over the (multi-antenna) fading dirty paper channel (FDPC) Y = H(X + S) + Z is considered when there is imperfect knowledge of the channel state information H at the transmitter (CSIT). The case of FDPC with positive definite (p.d.) input covariance matrix was studied by the authors in a recent paper, and here the more general case of positive semi-definite (p.s.d.) input covariance is dealt with. Towards this end, the choice of auxiliary random variable is modified. The algorithms for determination of inflation factor proposed in the p.d. case are then …
The simple scheme of treating interference as noise (TIN) is studied in this paper for the 3 x 2 X channel. A new sum-capacity upper bound is derived. This upper bound is transformed into a generalized degrees-of-freedom (GDoF) upper bound, and is shown to coincide with the achievable GDoF of scheme that combines TDMA and TIN for some conditions on the channel parameters. These conditions specify a noisy interference regime which extends noisy interference regimes available in literature. As a by-product, the sum-capacity of the 3 x 2 X channel is characterized within a constant gap in the giv…
In a K-user Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees-of-freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this work, we show that for such TIN-optimal interference channels, even if the message set is expanded to include an independent message fro…
Despite the simplicity of the scheme of treating interference as noise (TIN), it was shown to be sum-capacity optimal in the Gaussian 2-user interference channel in \cite{ShangKramerChen,MotahariKhandani,AnnapureddyVeeravalli}. In this paper, an interference network consisting of a point-to-point channel interfering with a multiple access channel (MAC) is considered, with focus on the weak interference scenario. Naive TIN in this network is performed by using Gaussian codes at the transmitters, joint decoding at the MAC receiver while treating interference as noise, and single user decoding at…
In this paper, we explore the information-theoretic optimality of treating interference as noise (TIN) in cellular networks. We focus on uplink scenarios modeled by the Gaussian interfering multiple access channel (IMAC), comprising $K$ mutually interfering multiple access channels (MACs), each formed by an arbitrary number of transmitters communicating independent messages to one receiver. We define TIN for this setting as a scheme in which each MAC (or cell) performs a power-controlled version of its capacity-achieving strategy, with Gaussian codebooks and successive decoding, while treating…
This article studies a novel distributed precoding design, coined team minimum mean-square error (TMMSE) precoding, which rigorously generalizes classical centralized MMSE precoding to distributed operations based on transmitter-specific channel state information (CSIT). Building on the so-called theory of teams, we derive a set of necessary and sufficient conditions for optimal TMMSE precoding, in the form of an infinite dimensional linear system of equations. These optimality conditions are further specialized to cell-free massive MIMO networks, and explicitly solved for two important exampl…
It is shown that in the K-user interference channel, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then the simple scheme of using point to point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron…
The problem of Dirty Paper Coding (DPC) over the Fading Dirty Paper Channel (FDPC) Y = H(X + S)+Z, a more general version of Costa's channel, is studied for the case in which there is partial and perfect knowledge of the fading process H at the transmitter (CSIT) and the receiver (CSIR), respectively. A key step in this problem is to determine the optimal inflation factor (under Costa's choice of auxiliary random variable) when there is only partial CSIT. Towards this end, two iterative numerical algorithms are proposed. Both of these algorithms are seen to yield a good choice for the inflatio…
We study the capacity region of the two-user Binary Fading (or Erasure) Interference Channel where the transmitters have no knowledge of the channel state information. We develop new inner-bounds and outer-bounds for this problem. We identify three regimes based on the channel parameters: weak, moderate, and strong interference regimes. Interestingly, this is similar to the generalized degrees of freedom of the two-user Gaussian interference channel where transmitters have perfect channel knowledge. We show that for the weak interference regime, treating interference as erasure is optimal whil…
It has been shown recently by Geng et al. that in a $K$ user Gaussian interference network, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all signal strengths measured in dB scale), then power control and treating interference as noise (TIN) is sufficient to achieve the entire generalized degrees of freedom (GDoF) region. Motivated by the intuition that the deterministic model of Avestimehr et al. (ADT deterministic model) is particularly suited for exploring the op…
Despite the simplicity of the scheme of treating interference as noise (TIN), it was shown to be sum-capacity optimal in the Gaussian interference channel (IC) with very-weak (noisy) interference. In this paper, the 2-user IC is altered by introducing an additional transmitter that wants to communicate with one of the receivers of the IC. The resulting network thus consists of a point-to-point channel interfering with a multiple access channel (MAC) and is denoted PIMAC. The sum-capacity of the PIMAC is studied with main focus on the optimality of TIN. It turns out that TIN in its naive varian…
In this paper, we study the achievable degrees-of-freedom (DoF) regions of the $K$-user multiple-input-single-output (MISO) time correlated broadcast channel (BC). The time correlation induces knowledge of the current channel state information at transmitter (CSIT) with an estimation error $P^{-α}$, where $P$ is the signal-to-noise ratio (SNR). We consider the following two scenarios: $(i)$ $K$-user with $K$-antenna base station (BS) and $(ii)$ $3$-user with $2$-antenna BS. In case of symmetric DoF tuples, where all the users obtain the same DoF, we derive the total DoF equal to $\frac{K(1-α)}…
In a K-user Gaussian interference channel, it has been shown by Geng et al. that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then power control and treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this work, we generalize the optimality of TIN to compound networks. We show that for a K-user compound Gaus…
We consider the information-theoretic optimality of treating inter-cell interference as noise (multi-cell TIN) in downlink cellular networks. We focus on scenarios modeled by the Gaussian interfering broadcast channel (IBC), comprising $K$ mutually interfering Gaussian broadcast channels (BCs), each formed by a base station communicating independent messages to an arbitrary number of users. We establish a new power allocation duality between the IBC and its dual interfering multiple access channel (IMAC), which entails that the corresponding generalized degrees-of-freedom regions achieved thro…
For single-antenna Gaussian interference channels, we re-formulate the problem of determining the Generalized Degrees of Freedom (GDoF) region achievable by treating interference as Gaussian noise (TIN) derived in [3] from a combinatorial perspective. We show that the TIN power control problem can be cast into an assignment problem, such that the globally optimal power allocation variables can be obtained by well-known polynomial time algorithms. Furthermore, the expression of the TIN-Achievable GDoF region (TINA region) can be substantially simplified with the aid of maximum weighted matching…
We consider the information-theoretic optimality of treating inter-cell interference as noise in downlink cellular networks modeled as Gaussian interfering broadcast channels. Establishing a new uplink-downlink duality, we cast the problem in Gaussian interfering broadcast channels to that in Gaussian interfering multiple access channels, and characterize an achievable GDoF region under power control and treating inter-cell interference as (Gaussian) noise. We then identify conditions under which this achievable GDoF region is optimal.
The interference management technique that treats interference as noise (TIN) is optimal when the interference is sufficiently low. Scheduling algorithms based on the TIN optimality condition have recently been proposed, e.g., for application to device-to-device communications. TIN, however, has never been applied to cellular networks. In this work, we propose a scheduling algorithm for application to cellular networks that is based on the TIN optimality condition. In the proposed scheduling algorithm, each base station (BS) first randomly selects a user equipment (UE) in its coverage region, …
Significant progress has been made recently in Generalized Degrees of Freedom (GDoF) characterizations of wireless interference channels (IC) and broadcast channels (BC) under the assumption of finite precision channel state information at the transmitters (CSIT), especially for smaller or highly symmetric network settings. A critical barrier in extending these results to larger and asymmetric networks is the inherent combinatorial complexity of such networks. Motivated by other fields such as extremal combinatorics and extremal graph theory, we explore the possibility of an extremal network t…
It is well known that Multiple-Input Multiple-Output (MIMO) systems have high spectral efficiency, especially when channel state information at the transmitter (CSIT) is available. When CSIT is obtained by feedback, it is practical to assume that the channel state feedback rate is finite and the CSIT is not perfect. For such a system, we consider beamforming and power on/off strategy for its simplicity and near optimality, where power on/off means that a beamforming vector (beam) is either turned on with a constant power or turned off. The main contribution of this paper is to accurately evalu…
The Han-Kobayashi (HK) scheme achieves the best known achievable rate region for the K user interference channel (IC). Simple HK schemes are HK schemes with Gaussian signaling, no time sharing, and no private-common power splitting. The class of simple HK schemes includes the treating interference as noise (TIN) scheme and schemes that involve various levels of interference decoding and cancellation at each receiver. We derive conditions under which simple HK schemes achieve sum capacity for general K user Gaussian ICs. These results generalize existing sum capacity results for the TIN scheme …
We consider secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. The results are proved by first considering the deterministic interference channel model and identifying a regime in which a simple schem…
How to manage the interference introduced by the enormous wireless devices is a crucial issue to address in the prospective sixth-generation (6G) communications. The treating interference as noise (TIN) optimality conditions are commonly used for interference management and thus attract significant interest in existing wireless systems. Cell-free massive multiple-input multiple-output (CF mMIMO) is a promising technology in 6G that exhibits high system throughput and excellent interference management by exploiting a large number of access points (APs) to serve the users collaboratively. In thi…
In this work, we study the value of cooperative transmission in wireless networks if no channel state information is available at the transmitters (no CSIT). Our focus is on large locally connected networks, where each transmitter is connected to the receiver that has the same index as well as L succeeding receivers. The cases of L=1 and L=2 represent Wyner's asymmetric and symmetric network models, respectively. The considered rate criterion is the per user Degrees of Freedom (puDoF) as the number of transmitter-receiver pairs goes to infinity. For the case when L=1, it was shown in previous …
We introduce a general framework for treating channels with memory and feedback. First, we generalize Massey's concept of directed information and use it to characterize the feedback capacity of general channels. Second, we present coding results for Markov channels. This requires determining appropriate sufficient statistics at the encoder and decoder. Third, a dynamic programming framework for computing the capacity of Markov channels is presented. Fourth, it is shown that the average cost optimality equation (ACOE) can be viewed as an implicit single-letter characterization of the capacity.…
Rate-Splitting Multiple Access (RSMA) is an emerging flexible, robust and powerful multiple access scheme for downlink multi-antenna wireless networks. RSMA relies on multi-antenna Rate-Splitting (RS) strategies at the transmitter and Successive Interference Cancellation (SIC) at the receivers, and has the unique ability to partially decode interference and partially treat interference as noise so as to softly bridge the two extremes of fully decoding interference (as in Non-Orthogonal Multiple Access, NOMA) and treating interference as noise (as in Space Division Multiple Access, SDMA or Mult…
We analyze two-user single-antenna fading interference channels with perfect receive channel state information (CSI) and no transmit CSI. For the case of very strong interference, we prove that decoding interference while treating the intended signal as noise, subtracting the result out, and then decoding the desired signal, a process known as "stripping", achieves the diversity-multiplexing tradeoff (DMT) outer bound derived in Akuiyibo and Leveque, Int. Zurich Seminar on Commun., 2008. The proof is constructive in the sense that it provides corresponding code design criteria for DMT optimali…
We analyze two-user single-antenna fading interference channels with perfect receive channel state information (CSI) and no transmit CSI. We compute the diversity-multiplexing tradeoff (DMT) region of a fixed-power-split Han and Kobayashi (HK)-type superposition coding scheme and provide design criteria for the corresponding superposition codes. We demonstrate that this scheme is DMT-optimal under moderate, strong, and very strong interference by showing that it achieves a DMT outer bound that we derive. Further, under very strong interference, we show that a joint decoder is DMT-optimal and "…
The sum-capacity for specific sub-classes of ergodic fading Gaussian two-user interference channels (IFCs) is developed under the assumption of perfect channel state information at all transmitters and receivers. For the sub-classes of uniformly strong (every fading state is strong) and ergodic very strong two-sided IFCs (a mix of strong and weak fading states satisfying specific fading averaged conditions) the optimality of completely decoding the interference, i.e., converting the IFC to a compound multiple access channel (C-MAC), is proved. It is also shown that this capacity-achieving sche…
This paper adds to the understanding of the capacity region of the Gaussian interference channel. To this end, the capacity region of the one-sided Gaussian interference channel is first fully characterized. This is accomplished by introducing a new representation of the Han-Kobayashi region and providing a new outer bound on the capacity region of this channel which is tight both in the weak and strong interference regimes. In light of this capacity result, the capacity region of the degraded Gaussian interference channel is established immediately. Next, by combining the capacity regions of …
We study the capacity of discrete memoryless many-to-one interference channels, i.e., K user interference channels where only one receiver faces interference. For a class of many-to-one interference channels, we identify a noisy interference regime, i.e., a regime where random coding and treating interference as noise achieves sum-capacity. Specializing our results to the Gaussian MIMO many-to-one interference channel, which is a special case of the class of channels considered, we obtain new capacity results. Firstly, we extend the noisy interference regime, previously studied for (many-to-on…
This paper shows that for the two-user Gaussian Interference Channel (G-IC) Treating Interference as Noise without Time Sharing (TINnoTS) achieves the closure of the capacity region to within either a constant gap, or to within a gap of the order O(logln(min(S,I))) where S is the largest Signal to Noise Ratio (SNR) on the direct links and I is the largest Interference to Noise Ratio (INR) on the cross links. As a consequence, TINnoTS is optimal from a generalized Degrees of Freedom (gDoF) perspective for all channel gains except for a subset of zero measure. TINnoTS with Gaussian inputs is kno…
