We address a fundamental question in wireless networks that, surprisingly, has not been studied before: what is the maximum density of concurrently active links that satisfy a certain outage constraint? We call this quantity the spatial outage capacity (SOC), give a rigorous definition, and analyze it for Poisson bipolar networks with ALOHA. Specifically, we provide exact analytical and approximate expressions for the density of links satisfying an outage constraint and give simple upper and lower bounds on the SOC. In the high-reliability regime where the target outage probability is close to zero, we obtain an exact closed-form expression of the SOC, which reveals the interesting and perhaps counter-intuitive result that all transmitters need to be always active to achieve the SOC, i.e., the transmit probability needs to be set to 1 to achieve the SOC.
The meta distribution @math for Poisson bipolar networks with ALOHA and cellular networks is calculated in @cite_10 , where a closed-form expression for the moments of @math is obtained, and an exact integral expression and simple bounds on @math are provided. A key result in @cite_10 is that, for constant transmitter density @math , as the Poisson bipolar network becomes very dense ( @math ) with a very small transmit probability ( @math ), the disparity among link success probabilities vanishes and all links have the same success probability, which is the mean success probability @math . For the Poisson cellular network, the meta distribution of the SIR is calculated for the downlink and uplink scenarios with fractional power control in @cite_14 , with base station cooperation in @cite_5 , and for D2D networks underlaying the cellular network (downlink) in @cite_3 . Furthermore, the meta distribution of the SIR is calculated for millimeter-wave D2D networks in @cite_15 and for D2D networks with interference cancellation in @cite_6 . * -1mm
@cite_14 @cite_3 @cite_6 @cite_5 @cite_15 @cite_10
2963262497 2605261135 2755230429 2769047447 1640283668
The meta distribution of the signal-to-interference ratio (SIR) provides fine-grained information about the performance of individual links in a wireless network. This paper focuses on the analysis of the meta distribution of the SIR for both the cellular network uplink and downlink with fractional power control. For the uplink scenario, an approximation of the interfering user point process with a non-homogeneous Poisson point process is used. The moments of the meta distribution for both scenarios are calculated. Some bounds, the analytical expression, the mean local delay, and the beta approximation of the meta distribution are provided. The results give interesting insights into the effect of the power control in both the uplink and downlink. Detailed simulations show that the approximations made in the analysis are well justified. We study the performance of device-to-device (D2D) communication underlaying cellular wireless network in terms of the meta distribution of the signal-to-interference ratio (SIR), which is the distribution of the conditional SIR distribution given the locations of the wireless nodes. Modeling D2D transmitters and base stations as Poisson point processes (PPPs), moments of the conditional SIR distribution are derived in order to calculate analytical expressions for the meta distribution and the mean local delay of the typical D2D receiver and cellular downlink user. It turns out that for D2D users, the total interference from the D2D interferers and base stations is equal in distribution to that of a single PPP, while for downlink users, the effect of the interference from the D2D network is more complicated. We also derive the region of transmit probabilities for the D2D users and base stations that result in a finite mean local delay and give a simple inner bound on that region. Finally, the impact of increasing the base station density on the mean local delay, the meta distribution, and the density of users reliably served is investigated with numerical results. This letter presents a theoretical framework for the analysis of the meta distribution of the SIR for Poisson networks with interference cancellation (IC) enabled at the receivers, which gives deep insight into the network performance on a link-wise basis. A simple but insightful IC model named C-IC is studied for which the exact @math th moment of the meta distribution and its beta distribution approximation and some useful bounds are validated. The conditions for the mean local delay to be finite are also stated. The results show that IC improves the performance not only in terms of the mean but also in terms of the variance of the meta distribution. The meta distribution provides fine-grained information on the signal-to-interference ratio (SIR) compared with the SIR distribution at the typical user. This paper first derives the meta distribution of the SIR in heterogeneous cellular networks with downlink coordinated multipoint transmission reception, including joint transmission (JT), dynamic point blanking (DPB), and dynamic point selection dynamic point blanking (DPS DPB), for the general typical user and the worst-case user (the typical user located at the Voronoi vertex in a single-tier network). A more general scheme called JT-DPB, which is the combination of JT and DPB, is studied. The moments of the conditional success probability are derived for the calculation of the meta distribution and the mean local delay. An exact analytical expression, the beta approximation, and simulation results of the meta distribution are provided. From the theoretical results, we gain insights on the benefits of different cooperation schemes and the impact of the number of cooperating base stations and other network parameters. 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 focuses on the meta distribution of the SIR, which is the distribution of the conditional success probability @math 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 @math is reduced while increasing the network density @math such that the density of concurrent transmitters @math stays constant as @math , @math 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 @math , the variance of @math approaches a non-zero constant when @math is reduced to 0 while keeping the mean success probability constant.