The SINR model for wireless networks has been extensively studied recently. It tries to model whether a particular transmitter is heard at a specific location, with @math transmitting simultaneously. The SINR diagram consists of @math regions where each transmitter can be heard and the remaining space where no one can be heard. Efficient point location in the SINR diagram, i.e., building a data structure to determine, for a query point, whether any transmitter is heard there, and if so, which one, has been recently investigated. Previous such planar data structures are constructed in time at least quadratic in @math and support logarithmic-time approximate queries. Moreover, the performance of these depends not only on the number @math of transmitters and on the approximation parameter @math , but also on some geometric parameters that cannot be bounded a priori as a function of @math or @math . We address the question of batched point location queries, i.e., answering many queries simultaneously. Specifically, in one dimension, we can answer @math queries exactly in amortized polylogarithmic time per query, while in the plane we can do it approximately. All these results can handle arbitrary power assignments to the transmitters. Moreover, the amortized query time in these results depends only on @math and @math . We also show how to speed up the preprocessing in a previously proposed point-location structure in SINR diagram for uniform-power sites, by almost a full order of magnitude. For this we obtain results on the sensitivity of the reception regions to slight changes in the reception threshold, which are of independent interest. Finally, these results demonstrate the (so far underutilized) power of combining algebraic tools with those of computational geometry and other fields.
The papers most relevant to ours are those by @cite_9 and @cite_23 discussed above. @cite_14 also considered the problem of handling queries of the following form (in the uniform-power setting): Given a transmitter @math and query point @math , does @math receive @math by successively applying interference cancellation? (Interference cancellation is a technology that enables a point @math to receive a transmitter @math , even if @math 's signal is not the strongest one received at @math ; see @cite_14 for further details.)
@cite_9 @cite_14 @cite_23
2589022566 2131089922 2091755831 2039876598
We consider a system, comprising a library of @math files (e.g., movies) and a wireless network with a @math transmitters, each equipped with a local cache of size of @math files and a @math receivers, each equipped with a local cache of size of @math files. Each receiver will ask for one of the @math files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers’ future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of @math is achievable, and this is within a factor of 2 of the optimum, under uncoded prefetching and one-shot linear delivery schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes ), (ii) the transmitters’ caches and receivers’ caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network. To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitter’s caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receiver’s caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF. 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 higher-complexity 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 signal-to-interference 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. In the interference scheduling problem, one is given a set of n communication requests described by pairs of points from a metric space. The points correspond to devices in a wireless network. In the directed version of the problem, each pair of points consists of a dedicated sending and a dedicated receiving device. In the bidirectional version the devices within a pair shall be able to exchange signals in both directions. In both versions, each pair must be assigned a power level and a color such that the pairs in each color class (representing pairs communicating in the same time slot) can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference Plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. This is commonly referred to as the "physical model" and is the established way of modelling interference in the engineering community. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We study oblivious power assignments in which the power value of a pair only depends on the distance between the points of this pair. We prove that oblivious power assignments cannot yield approximation ratios better than Ω(n) for the directed version of the problem, which is the worst possible performance guarantee as there is a straightforward algorithm that achieves an O(n)-approximation. For the bidirectional version, however, we can show the existence of a universally good oblivious power assignment: For any set of n bidirectional communication requests, the so-called "square root assignment" admits a coloring with at most polylog(n) times the minimal number of colors. The proof for the existence of this coloring is non-constructive. We complement it by an approximation algorithm for the coloring problem under the square root assignment. This way, we obtain the first polynomial time algorithm with approximation ratio polylog(n) for interference scheduling in the physical model. In this paper, we address the problem of computing the probability that r out of n interfering wireless signals are "captured," i.e., received with sufficiently large Signal to Interference plus Noise Ratio (SINR) to correctly decode the signals by a receiver with multi-packet reception (MPR) and Successive Interference Cancellation (SIC) capabilities. We start by considering the simpler case of a pure MPR system without SIC, for which we provide an expression for the distribution of the number of captured packets, whose computational complexity scales with n and r. This analysis makes it possible to investigate the system throughput as a function of the MPR capabilities of the receiver. We then generalize the analysis to SIC systems. In addition to the exact expressions for the capture probability and the normalized system throughput, we also derive approximate expressions that are much easier to compute and provide accurate results in some practical scenarios. Finally, we present selected results for some case studies with the purpose of illustrating the potential of the proposed mathematical framework and validating the approximate methods.