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
1995382207 2130228237 2952813714
We study an interference network where equally-numbered transmitters and receivers lie on two parallel lines, each transmitter opposite its intended receiver. We consider two short-range interference models: the "asymmetric network," where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a "symmetric network," where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the @math transmitters to its left, and the messages of the @math transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the @math receive antennas to its left, and the @math receive antennas to its right. For such networks we provide upper and lower bounds on the multiplexing gain, i.e., on the high-SNR asymptotic logarithmic growth of the sum-rate capacity. In some cases our bounds meet, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter side-information parameters @math and the receiver side-information parameters @math in the sense that increasing decreasing @math or @math by a positive integer @math has the same effect on the multiplexing gain as increasing decreasing @math or @math by @math . Moreover---even in asymmetric networks---there is an equivalence between the left side-information parameters @math and the right side-information parameters @math . 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 transmitters caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receivers 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 study the degrees of freedom (DoF) of the @math -user interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by @math successive transmitters, and is jointly received by @math successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of @math and receive cooperation order of @math . Since the channel has a total of @math transmit antennas and @math receive antennas, the maximum possible DoF is equal to @math . We show that the CoMP channel has @math DoF if and only if @math . The key idea is that the zero forcing of the interference corresponding to the @math message at the decoder of the @math message, where @math , can be viewed as a shared responsibility between the @math transmitters carrying the @math message, and the @math receivers decoding the @math message. For the general case, we derive an outer bound that states that the DoF is bounded above by @math . For the special case with only CoMP transmission, i.e, @math , we propose a scheme that can achieve @math DoF for all @math K @math M_ t @math M_ t -1$ receivers, thereby allowing each of these receivers to enjoy 1 DoF, and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space. The achievability proofs are based on the notion of algebraic independence from algebraic geometry.