arXiv subjects

Martin Haenggi

Publications and source records attributed to Martin Haenggi.

At least 55 records · Page 3Linked to original sources

arXiv2016

SIR Asymptotics in General Network Models

In the performance analyses of wireless networks, asymptotic quantities and properties often pro- vide useful results and insights. The asymptotic analyses become especially important when complete analytical expressions of the performance metrics of interest are not available, which is often the case if one departs from very specific modeling assumptions. In this paper, we consider the asymptotics of the SIR distribution in general wireless network models, including ad hoc and cellular networks, simple and non-simple point processes, and singular and bounded path loss models, for which, in most cases, finding analytical expressions of the complete SIR distribution seems hopeless. We show that the lower tails of the SIR distributions decay polynomially with the order solely determined by the path loss exponent or the fading parameter, while the upper tails decay exponentially, with the exception of cellular networks with singular path loss. In addition, we analyze the impact of the nearest interferer on the asymptotic properties of the SIR distributions, and we formulate three crisp conjectures that -if true- determine the asymptotic behavior in many cases based on the large-scale path loss properties of the desired signal and/or nearest interferer only.

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arXiv2016

Unique coverage in Boolean models

Consider a wireless cellular network consisting of small, densely scattered base stations. A user $u$ is {\em uniquely covered} by a base station $b$ if $u$ is the only user within distance $r$ of $b$. This makes it possible to assign the user $u$ to the base station $b$ without interference from any other user $u'$. We investigate the maximum possible proportion of users who are uniquely covered. We solve this problem completely in one dimension and provide bounds, approximations and simulation results for the two-dimensional case.

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arXiv2015

Asymptotics and Approximation of the SIR Distribution in General Cellular Networks

It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift (or gain) of the distribution of the most tractable model, the Poisson point process (PPP). To study and explain this behavior, this paper focuses on general single-tier network models with nearest-base station association and studies the asymptotic gain both at 0 and at infinity. We show that the gain at 0 is determined by the so-called mean interference-to-signal ratio (MISR) between the PPP and the network model under consideration, while the gain at infinity is determined by the expected fading-to-interference ratio (EFIR). The analysis of the MISR is based on a novel type of point process, the so-called relative distance process, which is a one-dimensional point process on the unit interval [0,1] that fully determines the SIR. A comparison of the gains at 0 and infinity shows that the gain at 0 indeed provides an excellent approximation for the entire SIR distribution. Moreover, the gain is mostly a function of the network geometry and barely depends on the path loss exponent and the fading. The results are illustrated using several examples of repulsive point processes.

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arXiv2015

Interference Functionals in Poisson Networks

We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expected values of sum-products of functions. In proving the theorem, we present a variant of the Campbell-Mecke theorem from stochastic geometry. We proceed to apply our result in the calculation of expected values involving interference in wireless Poisson networks. Based on this, we derive outage probabilities for transmissions in a Poisson network with Nakagami fading. Our results extend the stochastic geometry toolbox used for the mathematical analysis of interference-limited wireless networks.

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arXiv2015

The Meta Distribution of the SIR in Poisson Bipolar and Cellular Networks

The calculation of the SIR distribution at the typical receiver (or, equivalently, the success probability of transmissions over the typical link) in Poisson bipolar and cellular networks with Rayleigh fading is relatively straightforward, but it only provides limited information on the success probabilities of the individual links. This paper introduces the notion of the meta distribution of the SIR, which is the distribution of the conditional success probability $P$ given the point process, and provides bounds, an exact analytical expression, and a simple approximation for it. The meta distribution provides fine-grained information on the SIR and answers questions such as "What fraction of users in a Poisson cellular network achieve 90% link reliability if the required SIR is 5 dB?". Interestingly, in the bipolar model, if the transmit probability $p$ is reduced while increasing the network density $λ$ such that the density of concurrent transmitters $λp$ stays constant as $p\to 0$, $P$ degenerates to a constant, i.e., all links have exactly the same success probability in the limit, which is the one of the typical link. In contrast, in the cellular case, if the interfering base stations are active independently with probability $p$, the variance of $P$ approaches a non-zero constant when $p$ is reduced to $0$ while keeping the mean success probability constant.

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arXiv2015

A Stochastic Geometry Analysis of Inter-cell Interference Coordination and Intra-cell Diversity

Inter-cell interference coordination (ICIC) and intra-cell diversity (ICD) play important roles in improving cellular downlink coverage. Modeling cellular base stations (BSs) as a homogeneous Poisson point process (PPP), this paper provides explicit finite-integral expressions for the coverage probability with ICIC and ICD, taking into account the temporal/spectral correlation of the signal and interference. In addition, we show that in the high-reliability regime, where the user outage probability goes to zero, ICIC and ICD affect the network coverage in drastically different ways: ICD can provide order gain while ICIC only offers linear gain. In the high-spectral efficiency regime where the SIR threshold goes to infinity, the order difference in the coverage probability does not exist, however the linear difference makes ICIC a better scheme than ICD for realistic path loss exponents. Consequently, depending on the SIR requirements, different combinations of ICIC and ICD optimize the coverage probability.

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arXiv2015

Bounding the Bethe and the Degree-$M$ Bethe Permanents

It was recently conjectured that the permanent of a ${P}$-lifting $θ^{\uparrow{P}}$ of a matrix $θ$ of degree $M$ is less than or equal to the $M$th power of the permanent perm$(θ)$, i.e., perm$(θ^{\uparrow{P}})\leq(\text{perm}(θ))^M$ and, consequently, that the degree-$M$ Bethe permanent $\text{perm}_{M,\mathrm{B}} (θ)$ of a matrix $θ$ is less than or equal to the permanent perm$(θ)$ of $θ$, i.e., perm$_{M, \mathrm{B}} (θ)\leq \text{perm}(θ)$. In this paper, we prove these related conjectures and show in addition a few properties of the permanent of block matrices that are lifts of a matrix. As a corollary, we obtain an alternative proof of the inequality perm$_{\mathrm{B}} (θ)\leq \text{perm}(θ)$ on the Bethe permanent of the base matrix $θ$ that uses only the combinatorial definition of the Bethe permanent.

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arXiv2015

Throughput Analysis for Full-Duplex Wireless Networks with Imperfect Self-interference Cancellation

This paper investigates the throughput for wireless network with full-duplex radios using stochastic geometry. Full-duplex (FD) radios can exchange data simultaneously with each other. On the other hand, the downside of FD transmission is that it will inevitably cause extra interference to the network compared to half-duplex (HD) transmission. Moreover, the residual self-interference has negative effects on the network throughput. In this paper, we focus on a wireless network of nodes with both HD and FD capabilities and derive and optimize the throughput in such a network. Our analytical result shows that if the network is adapting an ALOHA protocol, the maximal throughput is achieved by scheduling all concurrently transmitting nodes to work in either FD mode or HD mode depending on one simple condition. Moreover, the effects of imperfect self-interference cancellation on the signal-to-interference ratio (SIR) loss and throughput are also analyzed based on our mathematical model. We rigorously quantify the impact of imperfect self-interference cancellation on the throughput gain, transmission range, and other metrics, and we establish the minimum amount of self-interference suppression needed for FD to be beneficial.

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arXiv2014

Throughput Analysis for Wireless Networks with Full-Duplex Radios

This paper investigates the throughput for wireless network with full-duplex radios using stochastic geometry. Full-duplex (FD) radios can exchange data simultaneously with each other. On the other hand, the downside of FD transmission is that it will inevitably cause extra interference to the network compared to half-duplex (HD) transmission. In this paper, we focus on a wireless network of nodes with both HD and FD capabilities and derive and optimize the throughput in such a network. Our analytical result shows that if the network is adapting an ALOHA protocol, the maximal throughput is always achieved by scheduling all concurrently transmitting nodes to work in FD mode instead of a mixed FD/HD mode or HD mode regardless of the network configurations. Moreover, the throughput gain of using FD transmission over HD transmission is analytically lower and upper bounded.

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arXiv2014

The Mean Interference-to-Signal Ratio and its Key Role in Cellular and Amorphous Networks

We introduce a simple yet powerful and versatile analytical framework to approximate the SIR distribution in the downlink of cellular systems. It is based on the mean interference-to-signal ratio and yields the horizontal gap (SIR gain) between the SIR distribution in question and a reference SIR distribution. As applications, we determine the SIR gain for base station silencing, cooperation, and lattice deployment over a baseline architecture that is based on a Poisson deployment of base stations and strongest-base station association. The applications demonstrate that the proposed approach unifies several recent results and provides a convenient framework for the analysis and comparison of future network architectures and transmission schemes, including amorphous networks where a user is served by multiple base stations and, consequently, (hard) cell association becomes obsolete.

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arXiv2014

User-Centric Intercell Interference Nulling for Downlink Small Cell Networks

Small cell networks are regarded as a promising candidate to meet the exponential growth of mobile data traffic in cellular networks. With a dense deployment of access points, spatial reuse will be improved, and uniform coverage can be provided. However, such performance gains cannot be achieved without effective intercell interference management. In this paper, a novel interference coordination strategy, called user-centric intercell interference nulling, is proposed for small cell networks. A main merit of the proposed strategy is its ability to effectively identify and mitigate the dominant interference for each user. Different from existing works, each user selects the coordinating base stations (BSs) based on the relative distance between the home BS and the interfering BSs, called the interference nulling (IN) range, and thus interference nulling adapts to each user's own interference situation. By adopting a random spatial network model, we derive an approximate expression of the successful transmission probability to the typical user, which is then used to determine the optimal IN range. Simulation results shall confirm the tightness of the approximation, and demonstrate significant performance gains (about 35%-40%) of the proposed coordination strategy, compared with the non-coordination case. Moreover, it is shown that the proposed strategy outperforms other interference nulling methods. Finally, the effect of imperfect channel state information (CSI) is investigated, where CSI is assumed to be obtained via limited feedback. It is shown that the proposed coordination strategy still provides significant performance gains even with a moderate number of feedback bits.

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arXiv2014

Asymptotic Deployment Gain: A Simple Approach to Characterize the SINR Distribution in General Cellular Networks

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the outage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) is smaller than a threshold) as the threshold goes to zero. We show that, remarkably, the slope of the outage probability (in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the success probabilities of the PPP and another point process in the high-reliability regime (where the success probability is near 1). To demonstrate the usefulness of the ADG for the characterization of the SINR distribution, we investigate the outage probabilities and the ADGs for different point processes and fading statistics by simulations.

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arXiv2014

The Performance of Successive Interference Cancellation in Random Wireless Networks

This paper provides a unified framework to study the performance of successive interference cancellation (SIC) in wireless networks with arbitrary fading distribution and power-law path loss. An analytical characterization of the performance of SIC is given as a function of different system parameters. The results suggest that the marginal benefit of enabling the receiver to successively decode k users diminishes very fast with k, especially in networks of high dimensions and small path loss exponent. On the other hand, SIC is highly beneficial when the users are clustered around the receiver and/or very low-rate codes are used. Also, with multiple packet reception, a lower per-user information rate always results in higher aggregate throughput in interference-limited networks. In contrast, there exists a positive optimal per-user rate that maximizes the aggregate throughput in noisy networks. The analytical results serve as useful tools to understand the potential gain of SIC in heterogeneous cellular networks (HCNs). Using these tools, this paper quantifies the gain of SIC on the coverage probability in HCNs with non-accessible base stations. An interesting observation is that, for contemporary narrow-band systems (e.g., LTE and WiFi), most of the gain of SIC is achieved by canceling a single interferer.

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arXiv2014

The Ginibre Point Process as a Model for Wireless Networks with Repulsion

The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy, tractability and practicability tradeoffs, we introduce and promote the $β$-GPP, an intermediate class between the PPP and the GPP, as a model for wireless networks when the nodes exhibit repulsion. To show that the model leads to analytically tractable results in several cases of interest, we derive the mean and variance of the interference using two different approaches: the Palm measure approach and the reduced second moment approach, and then provide approximations of the interference distribution by three known probability density functions. Besides, to show that the model is relevant for cellular systems, we derive the coverage probability of the typical user and also find that the fitted $β$-GPP can closely model the deployment of actual base stations in terms of the coverage probability and other statistics.

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arXiv2013

Managing Interference Correlation Through Random Medium Access

The capacity of wireless networks is fundamentally limited by interference. However, little research has focused on the interference correlation, which may greatly increase the local delay (namely the number of time slots required for a node to successfully transmit a packet). This paper focuses on the question that whether increasing randomness in the MAC, such as frequency-hopping multiple access (FHMA) and ALOHA, helps to reduce the effect of interference correlation. We derive closed-form results for the mean and variance of the local delay for the two MAC protocols and evaluate the optimal parameters that minimize the mean local delay. Based on the optimal parameters, we propose the definitions of two operation regimes: correlation-limited regime and bandwidth-limited regime. Our results reveal that while the mean local delays for FHMA with N sub-bands and for ALOHA with transmit probability p are the same when p=1/N with thermal noise ignored, significant difference exists between the variances. At last, we evaluate the mean delay-jitter tradeoff and the bounds on the tail probability of the local delay, which shed key insights into the system design.

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arXiv2013

Diversity Polynomials for the Analysis of Temporal Correlations in Wireless Networks

The interference in wireless networks is temporally correlated, since the node or user locations are correlated over time and the interfering transmitters are a subset of these nodes. For a wireless network where (potential) interferers form a Poisson point process and use ALOHA for channel access, we calculate the joint success and outage probabilities of n transmissions over a reference link. The results are based on the diversity polynomial, which captures the temporal interference correlation. The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with independent Rayleigh fading over all links. We also determine the complete joint SIR distribution for two transmissions and the distribution of the local delay, which is the time until a repeated transmission over the reference link succeeds.

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arXiv2013

A Versatile Dependent Model for Heterogeneous Cellular Networks

We propose a new model for heterogeneous cellular networks that incorporates dependencies between the layers. In particular, it places lower-tier base stations at locations that are poorly covered by the macrocells, and it includes a small-cell model for the case where the goal is to enhance network capacity.

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arXiv2013

Joint Design of Channel and Network Coding for Star Networks

Channel coding alone is not sufficient to reliably transmit a message of finite length $K$ from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. In this scenario RLNC has been shown to have a throughput advantage over TDMA schemes as K and q tend to infinity. In this paper we focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel coding rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small message lengths K and small q.

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