Gaussian Interference Channel Research Articles

On the Optimum Diversity–Multiplexing Tradeoff of the Two-User Gaussian Interference Channel With Rayleigh Fading

In this paper, the optimum tradeoff between diversity and multiplexing gains in a two-user quasi-static Rayleigh fading interference channel (IC) is studied. The diversity and multiplexing gains are two basic performance measures in wireless networks which characterize the transmission reliability and the data rate, respectively. It would be of interest to investigate the optimal tradeoff between these two measures. First, we develop a coding scheme for the two-user quasi-static Rayleigh fading Gaussian IC with interference level α := log INR/log SNR ≥ 1. Then, for this coding scheme the achievable diversity-multiplexing tradeoff (DMT) is characterized. Our achievable DMT coincides with its outer bound. In the low and high rate regions (to be defined later), the proposed coding scheme is a one-level Gaussian code, independent of the channel state information (CSI). In the middle rate region (to be defined later), the proposed coding scheme, depending on the partial CSI, can be a one-level or a two-level Gaussian code. We show that the relevant partial CSI can be represented by only one bit determined by the absolute value of the channel gain. In the middle rate region, we assume that the single-bit partial CSI for all the four channel gains of the Gaussian IC are available at both transmitters.

Two-User Gaussian Interference Channel with Finite Constellation Input and FDMA

In the two-user Gaussian Strong Interference Channel (GSIC) with finite constellation inputs, it is known that relative rotation between the constellations of the two users enlarges the Constellation Constrained (CC) capacity region. In this paper, a metric for finding the approximate angle of rotation to maximally enlarge the CC capacity is presented. It is shown that for some portion of the Strong Interference (SI) regime, with Gaussian input alphabets, the FDMA rate curve touches the capacity curve of the GSIC. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, at high powers, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve for the constellations BPSK, QPSK, 8-PSK, 16-QAM and 64-QAM. It is known that, with Gaussian input alphabets, the FDMA inner-bound at the optimum sum-rate point is always better than the simultaneous-decoding inner-bound throughout the Weak Interference (WI) regime. For a portion of the WI regime, it is shown that, with identical finite constellation inputs for both the users, the simultaneous-decoding inner-bound enlarged by relative rotation between the constellations can be strictly better than the FDMA inner-bound.

Relaying in the Presence of Interference: Achievable Rates, Interference Forwarding, and Outer Bounds

The smallest network model that captures relaying in the presence of multiple communicating pairs causing interference to each other is the interference channel with a relay. In this paper, an achievable rate region for the interference channel with a relay is derived. Special cases of strong interference under which this region is the capacity region are presented. The results obtained demonstrate the benefits of interference forwarding at a relay. By forwarding interfering messages, the relay can improve their reception at unintended receivers and, thus, facilitate interference cancellation. We show that intentionally forwarding interfering messages can improve the achievable rates. The achievable rates and interference forwarding gains are also illustrated by numerical results in Gaussian channels. Finally, a sum-rate outer bound to the capacity region of the Gaussian interference channel with a relay is derived and compared with the achievable rate region. The cut-set bound for this channel is also derived and shown to be much looser than the new sum-rate outer bound.

On the Maximum Achievable Sum-Rate With Successive Decoding in Interference Channels

In this paper, we investigate the maximum achievable sum-rate of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We provide two algorithms to translate the optimal schemes in the deterministic channel model to the Gaussian channel model. We also derive two upper bounds on the maximum achievable sum-rate of the Gaussian Han-Kobayashi schemes, which automatically upper bound the maximum achievable sum-rate using successive decoding of Gaussian codewords. Numerical evaluations show that, similar to the deterministic channel results, the maximum achievable sum-rate with successive decoding in the Gaussian channels oscillates between that with Han-Kobayashi schemes and that with single message schemes.

Capacity Region of Vector Gaussian Interference Channels With Generally Strong Interference

An interference channel is said to have strong interference if a certain pair of mutual information inequalities are satisfied for all input distributions. These inequalities assure that the capacity of the interference channel with strong interference is achieved by jointly decoding the signal and the interference. This definition of strong interference applies to discrete memoryless, scalar and vector Gaussian interference channels. However, there exist vector Gaussian interference channels that may not satisfy the strong interference condition but for which the capacity can still be achieved by jointly decoding the signal and the interference. This kind of interference is called generally strong interference. Sufficient conditions for a vector Gaussian interference channel to have generally strong interference are derived. The sum-rate capacity and the boundary points of the capacity region are also determined.

Sum-rate optimal power policies for energy harvesting transmitters in an interference channel

This paper considers a two-user Gaussian interference channel with energy harvesting transmitters. Different than conventional battery powered wireless nodes, energy harvesting transmitters have to adapt transmission to availability of energy at a particular instant. In this setting, the optimal power allocation problem to maximize the sum throughput with a given deadline is formulated. The convergence of the proposed iterative coordinate descent method for the problem is proved and the short-term throughput maximizing offline power allocation policy is found. Examples for interference regions with known sum capacities are given with directional waterfilling interpretations. Next, stochastic data arrivals are addressed. Finally, online and/or distributed near-optimal policies are proposed. Performance of the proposed algorithms are demonstrated through simulations.

Achieving Global Optimality for Weighted Sum-Rate Maximization in the K-User Gaussian Interference Channel with Multiple Antennas

Characterizing the global maximum of weighted sum-rate (WSR) for the K-user Gaussian interference channel (GIC), with the interference treated as Gaussian noise, is a key problem in wireless communication. However, due to the users' mutual interference, this problem is in general non-convex and thus cannot be solved directly by conventional convex optimization techniques. In this paper, by jointly utilizing the monotonic optimization and rate profile techniques, we develop a new framework to obtain the globally optimal power control and/or beamforming solutions to the WSR maximization problems for the GICs with single-antenna transmitters and single-antenna receivers (SISO), single-antenna transmitters and multi-antenna receivers (SIMO), or multi-antenna transmitters and single-antenna receivers (MISO). Different from prior work, this paper proposes to maximize the WSR in the achievable rate region of the GIC directly by exploiting the facts that the achievable rate region is a "normal" set and the users' WSR is a "strictly increasing" function over the rate region. Consequently, the WSR maximization is shown to be in the form of monotonic optimization over a normal set and thus can be solved globally optimally by the existing outer polyblock approximation algorithm. However, an essential step in the algorithm hinges on how to efficiently characterize the intersection point on the Pareto boundary of the achievable rate region with any prescribed "rate profile" vector. This paper shows that such a problem can be transformed into a sequence of signal-to-interference-plus-noise ratio (SINR) feasibility problems, which can be solved efficiently by existing techniques. Numerical results validate that the proposed algorithms can achieve the global WSR maximum for the SISO, SIMO or MISO GIC.

A Coordinate System for Gaussian Networks

This paper investigates network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are considered. It is shown that in these problems, non-Gaussian code ensembles can achieve higher rates than the Gaussian ones. It is also shown that the strong Shamai-Laroia conjecture on the Gaussian ISI channel does not hold. In order to analyze non-Gaussian code ensembles over Gaussian networks, a geometrical tool using the Hermite polynomials is proposed. This tool provides a coordinate system to analyze a class of non-Gaussian input distributions that are invariant over Gaussian networks.

On Asymmetric Interference Channels with Cooperating Receivers

This paper studies a model for communications in wireless networks supported by designated cooperation links. In particular, a 2-user Gaussian one-sided interference channel with two rate-limited and orthogonal communication links between the receivers is considered. A communication protocol for the channel is proposed, which combines rate-splitting and superposition encoding techniques with the conventional decode-forward and compress-forward strategies. It is shown that a careful design of codebooks and coding scheme, which is obtained from intuition based on superposition coding, can greatly reduce the complexity of the strategy. Analytical and numerical results show that the proposed scheme, although not universally optimal, can achieve the capacity region or sum capacity exactly or asymptotically in certain scenarios. Various limits of sum capacity gain due to cooperation are also discussed.

Gaussian Interference Channel Aided by a Relay with Out-of-Band Reception and In-Band Transmission

A Gaussian Interference Channel (IC) is investigated in which a relay assists two source-destination pairs. The relay is assumed to receive over dedicated orthogonal channels from the sources (e.g., over orthogonal bands or time slots, or over wired links), while it transmits in the same band as the sources. This scenario is referred to as IC assisted by an out-of-band reception/ in-band transmission relay (IC-OIR). An achievable rate region is derived for the IC-OIR that encompasses, besides the standard signal relaying, interference management via interference relaying, cancellation and precoding. The sum-capacity is found in a specific regime defined by the very strong relay-interference conditions. Numerical results validate the performance gains of interference mitigation via the relay.

Robust Rate Maximization Game Under Bounded Channel Uncertainty

We consider the problem of decentralized power allocation for competitive rate maximization in a frequency-selective Gaussian interference channel under bounded channel uncertainty. We formulate a distribution-free robust framework for the rate maximization game. We present the robust optimization equilibrium for this game and derive sufficient conditions for its existence and uniqueness. We show that an iterative waterfilling algorithm converges to this equilibrium under certain sufficient conditions. We analyze the social properties of the equilibrium under varying channel uncertainty bounds for the two-user case. We also observe an interesting phenomenon that the equilibrium moves toward a frequency-division multiple-access solution for any set of channel coefficients under increasing channel uncertainty bounds. We further prove that increasing channel uncertainty can lead to a more efficient equilibrium and, hence, a better sum rate in certain two-user communication systems. Finally, we confirm, through simulations, that this improvement in equilibrium efficiency is also observed in systems with a higher number of users.

Interference Channel with Constrained Partial Group Decoding

We propose novel coding and decoding methods for a fully connected K-user Gaussian interference channel. Each transmitter encodes its information into multiple layers and transmits the superposition of those layers. Each receiver employs a constrained partial group decoder (CPGD) that decodes its designated message along with a part of the interference. In particular, each receiver performs a twofold task by first identifying which interferers it should decode and then determining which layers of them should be decoded. Determining the layers to be decoded and decoding them are carried out in a successive manner, where in each step a group of layers with a constraint on its group size is identified and jointly decoded while the remaining layers are treated as Gaussian noise. The decoded layers are then subtracted from the received signal and the same procedure is repeated for the remaining layers. We provide a distributed algorithm, tailored to the nature of the interference channels, that determines the transmission rate at each transmitter based on some optimality measure and also finds the order of the layers to be successively decoded at each receiver. We also consider practical design of a system that employs the quadrature amplitude modulations (QAM) and rateless codes. Numerical results are provided on the achievable sum-rate under the ideal case of Gaussian signaling with random codes as well as on the system throughput under practical modulations and channel codes. The results show that the proposed multi-layer coding scheme with CPGD offers significant performance gain over the traditional un-layered transmission with single-user decoding.

Outage Analysis of Block-Fading Gaussian Interference Channels

This paper considers the asymptotic behavior of the outage probability of a two-source block-fading single-antenna Gaussian interference channel in the high-SNR regime by means of the diversity-multiplexing tradeoff. A general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated. This asymmetric scenario allows to analyze networks with “mixed” interference, i.e., when different sources are at different distance from their intended destination, that are not possible under the commonly used symmetric assumption. Inner and outer bounds for the diversity are derived. The outer bound is based on the recent “to within one bit” capacity result of Etkin for the unfaded Gaussian channel and is a re-derivation of a known bound for which an error is pointed out. The inner bound is based on the Han and Kobayashi achievable region both without rate splitting and with a rate spitting inspired by the “to within one bit” capacity result. An analytical comparison of the diversity upper and lower bounds for a general channel seems difficult; by numerical evaluations, the two bounds are shown to coincide for a fairly large set of channel parameters.

MIMO Interference Channel With Confidential Messages: Achievable Secrecy Rates and Precoder Design

We study the achievable rate regions of the multiple-input multiple-output (MIMO) interference channel with confidential messages sent to two receivers, assuming the transmitters use linear precoding. Each receiver is assumed to be an eavesdropper for the other link, and the transmitters employ various techniques to increase the secrecy rate of their own link or that of the network. We describe both cooperative and noncooperative transmission schemes for Gaussian interference channels, and derive their achievable secrecy rate regions. Cooperation is made possible if the transmitters share a portion of their channel state information, allowing them to appropriately adjust their precoders and improve the overall secrecy performance of the network. A game-theoretic formulation of the problem is adopted to allow the transmitters to find an operating point that balances network performance and fairness. The benefit of cooperation is demonstrated via several numerical examples.

Diversity-Multiplexing Tradeoff of the Two-User Interference Channel

Diversity-multiplexing tradeoff (DMT) is a coarse high SNR approximation of the fundamental tradeoff between data rate and reliability in a slow fading channel. In this paper, we characterize the fundamental DMT of the two-user single antenna Gaussian interference channel. We show that the class of multilevel superposition coding schemes universally achieves (for all fading statistics) the DMT for the two-user interference channel. For the special case of symmetric DMT, when the two users have identical rate and diversity gain requirements, we characterize the DMT achieved by the Han-Kobayashi scheme, which corresponds to two level superposition coding.

On the Average Achievable Rate of Block Fading Decentralized Interference Channel

This paper aims to explore the average achievable rate of two-user decentralized Gaussian interference channel in a non-ergodic block fading environment, assuming the channel gains are constant throughout one transmission block and vary independently for the next block. It is assumed the channel gains are not available at the transmitters, while direct and cross channel gains are perfectly available at the corresponding receivers. In this regard, under Gaussian codebook assumption and considering the signal arising from the other co-channel communication link is treated as an interference, a multi-layer coding strategy is exploited at each transmitter. Then, under individual transmit power constraints and in a Rayleigh block fading environment, the optimum power allocation across code layers is derived, showing the average achievable rate of using multi-layer coding outperforms that of using a single layer code.

Noisy-Interference Sum-Rate Capacity for Vector Gaussian Interference Channels

New sufficient conditions for a vector Gaussian interference channel to achieve the sum-rate capacity by treating interference as noise are derived, which generalize the existing results. More concise conditions for multiple-input-single-output, and single-input-multiple-output scenarios are obtained.

Price-based interference avoidance game in the Gaussian interference channel

This paper considers a distributed interference avoidance problem employing frequency assignment in the Gaussian interference channel (IC). We divide the common channel into several sub-channels and each user chooses one sub-channel for transmission in such a way that the total interference in the IC is minimum. This mechanism named interference avoidance in this paper can be modeled as a competitive game model. And a completely autonomous distributed iterative algorithm called distributed interference avoidance algorithm (DIA) is adopted to achieve the Nash equilibrium (NE) of the game. Due to the self-optimum, the DIA is a sub-optimal algorithm. Therefore, through introducing an optimal compensation (or price) into the competitive game model, we successfully develop a compensation-based game model to approximate the optimal interference avoidance problem. Moreover, an optimal algorithm called iterative optimal interference avoidance algorithm (IOIA) is proposed to reach the optimality of the interference avoidance scheme. We analyze the implementation complexity of the proposed algorithm which is only O(N), with N standing for the number of users in the IC. We also give the proof on the convergence of the proposed algorithm. The performance upper bound and lower bound are derived for the IOIA algorithm. The simulation results show that the IOIA does reach the optimality under the condition of interference avoidance mechanism.

Interference Alignment for Secrecy

This paper studies the frequency/time selective <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> )] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks.

Convergence of utility-based power control in Gaussian interference channel

The convergence of non-cooperative distributed power control in Gaussian interference channel is analysed in this study. Firstly, the existing distributed power control schemes are categorised as two types: gradient projection type and non-linear type, according to the iterative steps. A unified mathematical formulation is then provided for each type. The objective is extended from rate maximisation, which has been studied a lot in iterative water-filling game, to more general form of utility maximisation. Based on it, a set of sufficient conditions are derived for each type of the schemes, guaranteeing the uniqueness of the fixed point and the global convergence in a totally asynchronous manner. These convergence requirements can be interpreted as different degree of separation, according to the concrete form of utility function. To get insight into the derived convergence conditions, some numerical results are presented in the end.