User Interference Channel Research Articles

Beyond TIN: GDoF of K-User Interference Channel with Successive Interference Cancellation and Power Control

Beyond TIN: GDoF of <i>K</i>-User Interference Channel with Successive Interference Cancellation and Power Control

On the Generalized Degrees of Freedom of the Noncoherent Interference Channel

We study the generalized degrees of freedom (gDoF) of the block-fading <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">noncoherent</i> 2-user interference channel (IC) with a coherence time of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> symbol durations and symmetric fading statistics. We demonstrate that a standard training-based scheme for the noncoherent IC is suboptimal in several regimes. We study and analyze several alternate schemes: the first is a new noncoherent scheme using rate-splitting. We also consider a scheme that treats interference-as-noise (TIN) and a time division multiplexing (TDM) scheme. We show that a standard training-based scheme for the noncoherent IC is outperformed by one of these schemes in several regimes: our results demonstrate that in the very weak interference regime, the TIN scheme is the best; in the strong interference regime, the TDM scheme and the noncoherent rate-splitting scheme give better performance; in other cases either of the TIN, TDM or noncoherent rate-splitting scheme could be preferred. We also study the noncoherent IC with feedback and propose another noncoherent rate-splitting scheme. Again for the feedback case, our results demonstrate that a standard training-based scheme can be outperformed by other schemes.

Degrees of Freedom of the K-User Interference Channel Assisted by Active and Passive IRSs

In this paper, we study the degrees of freedom (DoF) region and sum DoF of the time-selective <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user interference channel in the presence of intelligent reflecting surfaces (IRSs). We consider both active and passive IRSs. While both types of IRS can attenuate the amplitude and change the phase of a reflected electromagnetic wave, active IRSs are also capable of amplifying the wave. We derive inner and outer bounds for the DoF region and lower and upper bounds for the sum DoF of the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user interference channel in the presence of an active IRS and prove that the maximum value of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> for the sum DoF can be achieved if the number of IRS elements exceeds a certain finite value. The analysis framework developed for active IRSs forms the basis for our analysis of passive IRS-assisted systems. In particular, we present probabilistic inner and outer bounds for the DoF region and probabilistic lower and upper bounds for the sum DoF of the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user interference channel in the presence of a passive IRS and prove that the lower bound for the sum DoF asymptotically approaches <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> as the number of IRS elements grows large.

Interference Nulling Using Reconfigurable Intelligent Surface

This paper investigates the interference nulling capability of reconfigurable intelligent surface (RIS) in a multiuser environment where multiple single-antenna transceivers communicate simultaneously in a shared spectrum. From a theoretical perspective, we show that when the channels between the RIS and the transceivers have line-of-sight and the direct paths are blocked, it is possible to adjust the phases of the RIS elements to null out all the interference completely and to achieve the maximum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> degrees-of-freedom (DoF) in the overall <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user interference channel, provided that the number of RIS elements exceeds some finite value that depends on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> . Algorithmically, for any fixed channel realization we formulate the interference nulling problem as a feasibility problem, and propose an alternating projection algorithm to efficiently solve the resulting nonconvex problem with local convergence guarantee. Numerical results show that the proposed alternating projection algorithm can null all the interference if the number of RIS elements is only slightly larger than a threshold of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2K(K-1)$ </tex-math></inline-formula> . For the practical sum-rate maximization objective, this paper proposes to use the zero-forcing solution obtained from alternating projection as an initial point for subsequent Riemannian conjugate gradient optimization and shows that it has a significant performance advantage over random initializations. For the objective of maximizing the minimum rate, this paper proposes a subgradient projection method which is capable of achieving excellent performance at low complexity.

Energy‐efficient alternating current computing‐enabled receiver design for K‐user interference channel simultaneous wireless information and power transfer networks

SummaryEnergy efficiency is one of the key challenges in fifth generation (5G) and beyond wireless communication systems. Recently, simultaneous wireless information and power transfer (SWIPT) systems are usually adopted to enhance energy efficiency. The harvested energy through power transfer is first rectified to generate the direct current (DC) voltage that is used to power the communication devices. This rectification reduces the energy efficiency due to losses in conversion to DC voltages. In this work, we consider integrated information decoding and energy harvesting receiver architecture through power splitting SWIPT network that enables alternating current (AC) computational logic. The AC computing method is used to supply the computing block of receivers to further enhance the energy efficiency. Multiuser multiple input single output (MISO) interference channel (IC) is considered, where receivers are required to compromise between quality of service (QoS) and energy consumption. The system sum rate is maximized under sum harvested energy and total transmit power constraints through joint beamforming and power splitting factors design. For the problem tractability in the proposed AC computing‐enabled receiver, standard beamforming schemes are deployed, namely, zero forcing (ZF), regularized zero forcing (RZF), maximum ratio transmission (MRT), and a hybrid scheme between MRT and ZF beamforming (MRT‐ZF). Moreover, the power splitting ratios design problem is transformed into a one dimension search problem. Simulation results show that different beamforming designs exhibit a great trade‐off between the achieved rate and the harvested energy.

Distributed Algorithms for Spectral and Energy-Efficiency Maximization of K-User Interference Channels

In this paper, we propose a cooperative distributed framework to optimize a variety of rate and energy-efficiency (EE) utility functions, such as the minimum-weighted rate or the global EE, for the K-user interference channel. We focus on the single-input multiple-output (SIMO) case, where each user, based solely on local channel state information (CSI) and limited exchange information from other users, optimizes its transmit power and receive beamformer, although the framework can also be extended to the multiple-output multiple-input (MIMO) case. The distributed framework combines an alternating optimization approach with majorization-minimization (MM) techniques, thus ensuring convergence to a stationary point of the centralized cost function. Closed-form power update rules are obtained for some utility functions, thus obtaining very fast convergence algorithms. The receivers treat interference as noise (TIN) and apply the beamformers that maximize the signal-to-interference-plus-noise (SINR). The proposed cooperative distributed algorithms are robust against channel variations and network topology changes and, as our simulation results suggest, they perform close to the centralized solution that requires global CSI. As a benchmark, we also study a non-cooperative distributed framework based on the so-called “signal-to-leakage-plus-noise ratio” (SNLR) that further reduces the overhead of the cooperative version.

Exploiting Coherence Time Variations for Opportunistic Blind Interference Alignment

The observed coherence times associated with different wireless transmitters at any given user may vary at different rates. We demonstrate how these variations can be exploited for interference management. More precisely, we propose a new opportunistic blind interference alignment (BIA) strategy in the context of $K$ -user interference channels that exploits these variations in coherence times and provides significant data rate gains. We first provide a proof-of-concept setup in which the information about coherence time variations is available non-causally to the transmitters, and we demonstrate how transmitters and receivers can perform pre-coding and post-processing, respectively, to align a considerable part of the interference signal power. We note that in this non-causal scenario, no channel state information is available to the transmitters, and we make no specific assumption on the channel distributions. We take the key ideas of this scenario and consider a $K$ -user interference channel in which the direct links vary at a higher pace compared to the cross links. This assumption is motivated by considering mobile users, or by using our proposed transmit antenna for stationary or low-mobility users. We show how to eliminate the need for non-causal knowledge of coherence time variations, and still provide significant capacity gains.

Balanced-Switching-Oriented Blind Interference-Alignment Scheme for 2-User MISO Interference Channel

This letter considers the number of mode-switching associated with reconfigurable-antenna-based blind interference alignment (BIA) scheme for a 2-user MISO interference channel (IC). It is assumed that each user is equipped with a single reconfigurable antenna, which can switch among multiple independent modes. The switching-oriented BIA (S-BIA) scheme was proposed to minimize the overall mode-switching operations of reconfigurable antennas at the receivers. However, in S-BIA, the receivers can have a significantly different number of mode-switching operations, thus some users may experience longer delays, resulting in unfairness on their QoS. In this letter, we consider a 2-user MISO interference channel and propose a balanced-switching-based BIA (BS-BIA) scheme, which balances the individual mode-switching operations of the two users while reserving the same number of overall mode-switching operations as that in systems with S-BIA. Mathematical proofs and simulations results concur and show that the proposed BS-BIA scheme can reduce the differences in the numbers of mode-switching operations between the 2 users while keeping the overall mode-switching operation numbers close to that of systems with S-BIA.

Communicating Correlated Sources Over MAC and Interference Channels I: Separation-Based Schemes

We consider the two scenarios of communicating a pair S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> of distributed correlated sources over 2-user multiple access (MAC) and interference channels (IC), respectively. While in the MAC problem, the receiver needs to reconstruct both sources, in the IC problem, receiver j needs to reconstruct S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3.</sub> We undertake a Shannon theoretic study and focus on characterizing sufficient conditions. Building on Dueck's findings (1981), we propose a coding scheme based on fixed block-length (B-L) codes. We characterize its information theoretic performance and characterize a new set of sufficient conditions. We identify examples of the MAC and IC problems for which the latter conditions are proven to be strictly weaker than the current known tightest.

Toward an Extremal Network Theory—Robust GDoF Gain of Transmitter Cooperation Over TIN

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 theory, i.e., a study of extremal networks within particular regimes of interest. As our test application, we study the GDoF benefits of transmitter cooperation in a K user IC over the simple scheme of power control and treating interference as Gaussian noise (TIN) for three regimes of interest - a TIN regime identified by Geng et al. where TIN was shown to be GDoF optimal for the K user interference channel, a CTIN regime identified by Vi and Caire where the GDoF region achievable by TIN is convex without time-sharing, and an SLS regime identified by Davoodi and Jafar where a simple layered superposition (SLS) scheme is shown to be optimal in the K user MISO BC, albeit only for K ≤ 3. The SLS regime includes the CTIN regime, and the CTIN regime includes the TIN regime. As our first result, we show that under finite precision CSIT, TIN is GDoF optimal for the K user IC throughout the CTIN regime. Furthermore, under finite precision CSIT, appealing to extremal network theory we obtain the following results. In the TIN regime as well as the CTIN regime, we show that the extremal GDoF gain from transmitter cooperation over TIN is bounded regardless of the number of users. In fact, the gain is exactly a factor of 3/2 in the TIN regime, and 2 - 1/K in the CTIN regime, for arbitrary number of users K > 1. However, in the SLS regime, the gain is ⊖(log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (K)), i.e., it scales logarithmically with the number of users.

Sum-GDoF of 2-User Interference Channel With Limited Cooperation Under Finite Precision CSIT

The Generalized Degrees of Freedom (GDoF) of the two user interference channel are characterized for all parameter regimes under the assumption of finite precision channel state information at the transmitters (CSIT), when a limited amount of (half-duplex or full-duplex) cooperation is allowed between the transmitters in the form of $\pi $ DoF of shared messages. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either $0, 1, 1/2$ or $1/3$ . The most interesting aspect of the result is the $1/3$ slope, which appears only under finite precision CSIT and strong interference, and as such has not been encountered in previous studies that invariably assumed perfect CSIT. Indeed, the achievability and converse for the parameter regimes with $1/3$ slope are the most challenging aspects of this work. In particular, the converse relies on non-trivial applications of Aligned Images bounds.

BIA for the K-User Interference Channel Using Reconfigurable Antenna at Receivers

In this paper, we consider the problem of data transmission for ${K}-$ user interference channel (IC) with no channel state information (CSI) at transmitters. Each pair of transceivers with the aid of a particular precoder and a switching pattern structure tries to place its desired signal in a subspace which is linearly independent of interference signals. We show that if the channel values are known only to the receivers, the sum degrees-of-freedom (DoF) of the linear interference alignment (IA) with reconfigurable antenna at receivers is $\frac {{ { Kr}}}{ {r}^{2}- {r}+ {K}}$ , where $ {r} = \left \lceil{ {\frac {\sqrt {1+4 {K}}-1}{2}} }\right \rceil $ . For previous methods when $3 \leq {K} \leq 10^{4}$ , the number of solvable problems to achieve maximum sum DoF is less than 2% of different cases while in our work there is not any limitation on the number of users. In comparison with the previous related works in our proposed method, there is no limit on the number of users and the reception modes. The result indicates that the maximum sum DoF for the ${K}-$ user IC with asymptotically large values of K is $\frac {\sqrt { {K}}}{2}$ . Thus, the sum DoF of such networks using the reconfigurable antenna at receivers grows sublinearly with the number of users, whereas it grows linearly in the case where transmitters have access to CSI.

Blind Interference Alignment With ISI: A New Look at OFDM for $K$-User Interference Channels

This paper considers a $K$ -user single-input-single-output (SISO) interference channel with inter-symbol interference (ISI), in which the channel coefficients are assumed to be linear time-invariant with finite-length impulse response. The key finding of this paper is that, with no channel state information at the transmitter (CSIT), the sum-spectral efficiency can be made to scale linearly with $K$ , provided that the desired links have longer impulse responses than do the interfering links. This linear gain can be achieved (up to the maximum gain of $\frac{K}{2}$ for a particular case) by a novel multi-carrier communication scheme, termed interference-free orthogonal frequency division multiplexing (IF-OFDM) . Besides, when a transmitter is able to acquire CSIT from its paired receiver only, i.e., local CSIT, a higher sum-spectral efficiency can be achieved by a two-stage transmission method that concatenates IF-OFDM and vector coding based on singular value decomposition with a water-filling power allocation. A major implication of the derived results is that separate encoding across subcarriers per link is sufficient to linearly increase the sum-spectral efficiency with $K$ in the interference channel with ISI. Furthermore, we discuss several key ideas to facilitate the proposed IF-OFDM from a practical perspective even when the desired links do not have sufficiently long impulse responses. Various numerical results are also provided to support this theoretical analysis.

Performance Analysis of Rate Splitting in K-User Interference Channel Under Imperfect CSIT: Average Sum Rate, Outage Probability and SER

Interference alignment (IA) and rate splitting (RS) are two promising interference processing techniques to handle the interference problems in the multi-input multi-output (MIMO) multi-cell cooperation scenario. However, under the imperfect channel state information (CSIT) in the practical systems, the poor robustness of IA has become a bottleneck of its performance gain. On the other hand, RS can provide a robust solution, yet its outage performance is limited by its SIC decoding process. To make up these two schemes’ shortcomings and achieve the robust and reliable multi-cell cooperation, in this paper, we propose a novel transmission scheme, signal and interference alignment based rate splitting (SIA-RS), and provide comprehensively analyze the performance under CSIT quantization error. Closed-from expressions are derived for the average sum rate, outage probability and symbol error rate (SER) and their asymptotic versions in high signal-to-noise ratio (SNR) region. Due to signal alignment and common message, there exists certain correlation between the key variables. The nested finite weighted sum of independent and correlated Erlang random variables is used to approximate the exact expressions of performance. The relationship between “splitting” and “alignment” is revealed via the analytical derivation and numerical simulation. The simulation results show that the proposed SIA-RS achieves the best average sum rate compared with conventional IA and RS schemes, indicate that alignment would further reduce the outage probability, and suggest to the separate modulation schemes for common and private messages in terms of SER.

Interference Mitigation via Sparse Coding in ${K}$ -User Interference Channels

In this letter, we propose a signal recovery scheme for interference mitigation in ${K}$ -user interference channels. The recurrent structure of communication signals is investigated, based on which a single-user region (SUR) detection scheme involving sparse coding (SC) is proposed. A dictionary is constructed directly over SURs detected. Recovery of signal in the principal link is then implemented via a template matching step over the dictionary. Comparing with existing signal recovery schemes involving SC, main contributions include: 1) the proposed scheme is significantly more practical as it no more relies on clean signals as a prior for dictionary construction and 2) traditional time-consuming dictionary training is avoided, thus the computation complexity is remarkably lowered. Simulation results show that SURs in the received signal can be accurately recognized via the proposed SUR detection scheme. Moreover, the signal recovered by the proposed scheme is of higher quality, under lower time consumption and without clean signal as a prior , comparing with existing scheme.

$K$ –User Interference Channels With Backhaul Cooperation: DoF vs. Backhaul Load Trade–Off

In this paper, we consider $K$ –user interference channels with $M$ antennas per node and with backhaul collaboration in one side (among the transmitters or among the receivers), for $M,K\in \mathbb {N}$ , and investigate the tradeoff between the rate in the channel versus the communication load in the backhaul. In this investigation, each node is equipped with $M$ antennas and we focus on a first order approximation result, where the rate of the wireless channel is measured by the degrees of freedom (DoF) per user, and the load of the backhaul is measured by the entropy of backhaul messages per user normalized by $\log $ of transmit power, at high power regimes. This tradeoff is fully characterized for the case of even values of $K$ and approximately characterized for the case of odd values of $K$ , with vanishing approximation gap as $K$ grows. To achieve DoF of $M$ per user, this result establishes the asymptotic optimality of the most straightforward scheme, called central processing, in which the messages are collected at one of the nodes, centrally processed, and forwarded back to each node. In addition, this result shows that the gain of the schemes, relying on distributed processing, through pairwise communication among the nodes (e.g., cooperative alignment) does not scale with the size of the network. For the converse, we develop a new outer-bound on the tradeoff based on splitting the set of collaborative nodes (transmitters or receivers) into two subsets and assuming full cooperation within each group. We further present a sufficient condition on the wireless channel connectivity, which although more relaxed, guarantees the validity of the above tradeoff. Finally, we show that verifying this condition takes a polynomial time in the network size.

On the Energy Efficiency of Interference Alignment in the $K$ -User Interference Channel

Interference alignment (IA) is regarded as an important physical-layer interference management technique. Most research contributions on IA were focused on the analysis of its achievable spectral efficiency, either from the degrees of freedom or from the capacity perspective. Meanwhile, high energy-efficiency (EE) has become a key requirement for next-generation wireless communications. Hence, we focus our attention on the EE of IA in the fully connected $K$ -user interference channel, where each user has either a single antenna or multiple antennas. We consider both perfect and imperfect channel state information scenarios. New insights into the achievable EE of IA are obtained by investigating the impact of different precoding matrices, the number of users, the number of antennas, symbol extension values, channel estimation accuracy, total transmit power, and power allocation schemes. In particular, we demonstrate that in the single-antenna-user case, the IA schemes relying on unequal power allocation achieves higher EE than their equal power allocation counterparts. However, in the scenario where each user is equipped with multiple antennas, equal power allocation achieves higher EE than unequal power allocation for the IA. Furthermore, using non-uniform precoding-matrix-generating vector ${\boldsymbol {w}}$ is not necessarily beneficial for improving the achievable EE of IA. We also find that the EE performance of IA with smaller symbol extension values is higher than that with larger symbol extension values, the achievable EE of IA decays with the increase of the total transmit power, the EE performance of IA degrades as the channel estimation accuracy becomes low and that having a larger number of transmit/receive antennas on each user achieves a higher EE in IA.

Sum-Rate Maximization Methods for Wirelessly Powered Communication Networks in Interference Channels

In this paper, we study a wireless powered communication network (WPCN) in a general $N$ -user interference channel (IFC), where a hybrid access-point (H-AP) in each cell supports its corresponding user. In this multi-cell environment, the H-AP first sends the energy signal to charge users in the downlink (DL) phase, while in the subsequent uplink (UL) phase, each user transmits its information signal to the corresponding H-AP utilizing the previously harvested energy. For the WPCN in this IFC scenario, cross-link interference occurs due to asynchronous time allocation of the DL and the UL among $N$ cells which significantly affects the overall performance. To handle the interference issue efficiently, we jointly optimize the DL and UL time allocation of each cell as well as the transmit power allocation at the H-APs and the users so that the weighted sum-rate of UL information transmission is maximized. To tackle non-convexity of the weighted sum-rate maximization problem, we propose an iterative algorithm where the time allocation and the transmit power are updated based on the weighted minimum mean square error criteria and the gradient projection method, respectively. Furthermore, we consider two simple protocols where the DL time allocation of each cell is synchronized and present resource allocation method, respectively. In simulation results, we verify that the proposed algorithm for the asynchronous protocol outperforms conventional schemes.

RaptorQ-Based Efficient Multimedia Transmission Over Cooperative Cellular Cognitive Radio Networks

Accommodating the fast-growing multimedia traffic demands at low cost is critical to ensure the future competitiveness of cellular networks. Cognitive radio (CR) emerges as a key technology to enhance radio spectrum utilization and provides an effective solution to meet critical spectrum demands for future mobile multimedia traffics. In this paper, we investigate reliable downlink video transmission in underlay cellular CR networks by means of cooperative diversity. We use RaptorQ code as the Application Layer Forward Error Correction scheme to combat packet loss arising from the primary user interference and other channel conditions such as channel fading. For implementing cooperative diversity, we select the best relay based on the ability of successful decoding using RaptorQ and the value of signal-to-interference-plus-noise ratio at the destination node. Moreover, for efficient primary user channel utilization, the selected relay performs merging of the encoding coefficients before forwarding to the destination. We evaluate the performance of the proposed framework under various time sharing scenarios between the direct and best indirect transmission links in terms of decoding overhead, probability of decoding failure, and peak signal-to-noise ratio of the received videos. Numerical results show that the proposed scheme outperforms the baseline transmission scheme and conventional relaying schemes using Amplify-and-Forward and Decode-and-Forward transmission techniques.

Power Control by GDoF Duality of Treating Interference as Noise

In this letter, we revisit the duality of treating interference as noise from the generalized degrees-of-freedom (GDoF) perspective. Specifically, in a general $K$ -user interference channel, where interference is treated as Gaussian noise, we demonstrate, for any given GDoF tuple and its power allocation, how to derive a power allocation that yields a dominant GDoF tuple in its reciprocal channel. This finding naturally leads to a fast iterative GDoF-duality-based power control algorithm. Numerical results show that the proposed algorithm achieves competitive sum-rate performance with sophisticated signal-to-interference-plus-noise ratio-based power control scheme.