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The effect of fading, channel inversion, and threshold scheduling on ad hoc networks
 IEEE TRANS. INF. THEORY
, 2007
"... This paper addresses three issues in the field of ad hoc network capacity: the impact of i) channel fading, ii) channel inversion power control, and iii) threshold–based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state informat ..."
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Cited by 91 (29 self)
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This paper addresses three issues in the field of ad hoc network capacity: the impact of i) channel fading, ii) channel inversion power control, and iii) threshold–based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signaltointerference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a thresholdbased transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading.
Log Gaussian Cox processes
"... Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases. The appealing properties of such models are demonstrated theoretically as well as through data examples and simulations. In particular, the first, second and thirdorder prop ..."
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Cited by 67 (5 self)
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Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases. The appealing properties of such models are demonstrated theoretically as well as through data examples and simulations. In particular, the first, second and thirdorder properties are studied and utilized in the statistical analysis of clustered point patterns. Also empirical Bayesian inference for the underlying intensity surface is considered.
On the equivalence of the tube and Euler characteristic methods for the distribution of the maximum of Gaussian fields over piecewise smooth domains
"... Consider a Gaussian random field with a finite KarhunenLoève expansion of the form Z(u) = n i=1 uizi, where zi, i =1,...,n, are independent standard normal variables and u =(u1,...,un) ′ ranges over an index set M, which is a subset of the unit sphere Sn−1 in Rn. Under a very general assumption tha ..."
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Cited by 27 (6 self)
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Consider a Gaussian random field with a finite KarhunenLoève expansion of the form Z(u) = n i=1 uizi, where zi, i =1,...,n, are independent standard normal variables and u =(u1,...,un) ′ ranges over an index set M, which is a subset of the unit sphere Sn−1 in Rn. Under a very general assumption that M is a manifold with a piecewise smooth boundary, we prove the validity and the equivalence of two currently available methods for obtaining the asymptotic expansion of the tail probability of the maximum of Z(u). One is the tube method, where the volume of the tube around the index set M is evaluated. The other is the Euler characteristic method, where the expectation for the Euler characteristic of the excursion set is evaluated. General discussion on this equivalence was given in a recent paper by Adler (2000). In order to show the equivalence we prove a version of the Morse theorem for a manifold with a piecewise smooth boundary. 1. Introduction. 1.1. Maximum of a Gaussian field. Let M be a closed subset of the unit sphere Sn−1 in Rn. We consider a random field {Z(u)  u =(u1,...,un) ′ ∈ M} defined by Z(u) =u ′ n∑
Transmission Capacity of Wireless Ad Hoc Networks: Successive Interference Cancellation vs. Joint Detection
"... Abstract—The performance benefits of two interference cancellation methods, successive interference cancellation (SIC) and joint detection (JD), in wireless ad hoc networks are compared within the transmission capacity framework. SIC involves successively decoding and subtracting out strong interfer ..."
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Cited by 26 (2 self)
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Abstract—The performance benefits of two interference cancellation methods, successive interference cancellation (SIC) and joint detection (JD), in wireless ad hoc networks are compared within the transmission capacity framework. SIC involves successively decoding and subtracting out strong interfering signals until the desired signal can be decoded, while highercomplexity JD refers to simultaneously decoding the desired signal and the signals of a few strong interferers. Tools from stochastic geometry are used to develop bounds on the outage probability as a function of the spatial density of interferers. These bounds show that SIC performs nearly as well as JD when the signaltointerference ratio (SIR) threshold is less than one, but that SIC is essentially useless for SIR thresholds larger than one whereas JD provides a significant outage benefit regardless of the SIR threshold. I.
Downlink capacity and base station density in cellular networks.” Available: http://arxiv.org/abs/1109.2992
"... AbstractThere have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the network performance. Moreover, tractable analysis c ..."
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Cited by 22 (3 self)
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AbstractThere have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the network performance. Moreover, tractable analysis can be performed only for a fixed location user (e.g., cell center or edge user). In this paper, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process. We also consider the user density, and derive the user outage probability that an arbitrary user is under outage owing to low signaltointerferenceplusnoise ratio or high congestion by multiple users. Using the result, we calculate the density of success transmissions in the downlink cellular network. An interesting observation is that the success transmission density increases with the base station density, but the increasing rate diminishes. This means that the number of base stations installed should be more than ntimes to increase the network capacity by a factor of n. Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of networklevel simulations.
Markov Chain Monte Carlo and Spatial Point Processes
, 1999
"... this paper) reversibility holds, that is f P(x, A)(,x) = f PC, B A for all A, B , whereby r is clearly invariant ..."
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Cited by 20 (5 self)
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this paper) reversibility holds, that is f P(x, A)(,x) = f PC, B A for all A, B , whereby r is clearly invariant
A geometric interpretation of fading in wireless networks: theory and applications
 IEEE Trans. Inform. Theory
, 2008
"... Abstract—In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading by incorporating the fading process into the poin ..."
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Cited by 19 (3 self)
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Abstract—In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading by incorporating the fading process into the point process model. Concretely, assuming nodes are distributed in a stationary Poisson point process in , the properties of the point processes that describe the path loss with fading are analyzed. The main applications are singlehop connectivity and broadcasting. Index Terms—Broadcasting, connectivity, fading, geometry, point process, wireless networks.
Reactiondiffusion based transmission patterns for ad hoc networks
 in 24th IEEE Conference on Computer Communications (IEEE INFOCOM 2005
, 2005
"... Abstract — We present a new scheme that mimics pattern formation in biological systems to create transmission patterns in multihop ad hoc networks. Our scheme is decentralized and relies exclusively on local interactions between the network nodes to create global transmission patterns. A transmissio ..."
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Cited by 12 (0 self)
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Abstract — We present a new scheme that mimics pattern formation in biological systems to create transmission patterns in multihop ad hoc networks. Our scheme is decentralized and relies exclusively on local interactions between the network nodes to create global transmission patterns. A transmission inhibits other transmissions in its immediate surrounding and encourages nodes located further away to transmit. The transmission patterns created by our medium access control scheme combine the efficiency of allocationbased schemes at high traffic loads and the flexibility of random access schemes. Moreover, we show that with appropriately chosen parameters our scheme converges to collision free transmission patterns that guarantee some degree of spatial reuse. I.
Effect of Spatial Interference Correlation on the Performance of Maximum Ratio Combining
 IEEE TRANS. WIRELESS COMMUN
, 2014
"... While the performance of maximum ratio combining (MRC) is well understood for a single isolated link, the same is not true in the presence of interference, which is typically correlated across antennas due to the common locations of interferers. For tractability, prior work focuses on the two extr ..."
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Cited by 11 (3 self)
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While the performance of maximum ratio combining (MRC) is well understood for a single isolated link, the same is not true in the presence of interference, which is typically correlated across antennas due to the common locations of interferers. For tractability, prior work focuses on the two extreme cases where the interference power across antennas is either assumed to be fully correlated or fully uncorrelated. In this paper, we address this shortcoming and characterize the performance of MRC in the presence of spatiallycorrelated interference across antennas. Modeling the interference field as a Poisson point process, we derive the exact distribution of the signaltointerference ratio (SIR) for the case of two receive antennas, and upper and lower bounds for the general case. Using these results, we study the diversity behavior of MRC and characterize the critical density of simultaneous transmissions for a given outage constraint. The exact SIR distribution is also useful in benchmarking simpler correlation models. We show that the fullcorrelation assumption is considerably pessimistic (up to 30 % higher outage probability for typical values) and the nocorrelation assumption is significantly optimistic compared to the true performance.