This paper analyzes the connection between the protocol and physical interference models in the setting of Poisson wireless networks. A transmission is successful under the protocol model if there are no interferers within a parameterized guard zone around the receiver, while a transmission is successful under the physical model if the signal to interference plus noise ratio (SINR) at the receiver is above a threshold. The parameterized protocol model forms a family of decision rules for predicting the success or failure of the same transmission attempt under the physical model. For Poisson wireless networks, we employ stochastic geometry to determine the prior, evidence, and posterior distributions associated with this estimation problem. With this in hand, we proceed to develop five sets of results: i) the maximum correlation of protocol and physical model success indicators, ii) the minimum Bayes risk in estimating physical success from a protocol observation, iii) the receiver operating characteristic (ROC) of false rejection (Type I) and false acceptance (Type II) probabilities, iv) the impact of Rayleigh fading vs. no fading on the correlation and ROC, and v) the impact of multiple prior protocol model observations in the setting of a wireless network with a fixed set of nodes in which the nodes employ the slotted Aloha protocol in each time slot.
Several works have explored how to employ the protocol model within the context of scheduling @cite_3 @cite_2 @cite_0 . Hasan and Andrews @cite_3 study the protocol model as a scheduling algorithm in CDMA-based wireless ad hoc networks. They comment that a guard zone around each transmitter induces a natural tradeoff between interference and spatial reuse, affecting higher layer performance metrics such as transmission capacity, and they employ stochastic geometry to derive a guard zone that maximizes transmission capacity. Shi @cite_5 examine the use of the protocol model within a cross-layer optimization framework and provide a strategy for correcting infeasible schedules generated under the protocol model by allowing transmission rate-adaptation to physical model SINR. Zhang @cite_1 analyze the effectiveness of protocol model scheduling using a variety of analytical, simulation, and testbed measurements. This body of work on the protocol model as a scheduling paradigm is distinct from our focus on the protocol model as an interference model of the success or failure of attempted transmissions. Iyer @cite_6 compares several interference models via simulation and qualitatively discusses the sacrifices in accuracy associated with abstracted interference models, including the protocol model.
@cite_1 @cite_3 @cite_6 @cite_0 @cite_2 @cite_5
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Interference model is the basis of MAC protocol design in wireless networked sensing and control, and it directly affects the efficiency and predictability of wireless messaging. To exploit the strengths of both the physical and the protocol interference models, we analyze how network traffic, link length, and wireless signal attenuation affect the optimal instantiation of the protocol model. We also identify the inherent trade-off between reliability and throughput in the model instantiation. Our analysis sheds light on the open problem of efficiently optimizing the protocol model instantiation. Based on the analytical results, we propose the physical-ratio-K (PRK) interference model as a reliability-oriented instantiation of the protocol model. Via analysis, simulation, and testbed-based measurement, we show that PRK-based scheduling achieves a network throughput very close to (e.g., 95p) what is enabled by physical-model-based scheduling while ensuring the required packet delivery reliability. The PRK model inherits both the high fidelity of the physical model and the locality of the protocol model, thus it is expected to be suitable for distributed protocol design. These findings shed new light on wireless interference models; they also suggest new approaches to MAC protocol design in the presence of uncertainties in network and environmental conditions as well as application QoS requirements. In ad hoc networks, it may be helpful to suppress transmissions by nodes around the desired receiver in order to increase the likelihood of successful communication. This paper introduces the concept of a guard zone, defined as the region around each receiver where interfering transmissions are inhibited. Using stochastic geometry, the guard zone size that maximizes the transmission capacity for spread spectrum ad hoc networks is derived - narrowband transmission (spreading gain of unity) is a special case. A large guard zone naturally decreases the interference, but at the cost of inefficient spatial reuse. The derived results provide insight into the design of contention resolution algorithms by quantifying the optimal tradeoff between interference and spatial reuse in terms of the system parameters. A capacity increase relative to random access (ALOHA) in the range of 2 - 100 fold is demonstrated through an optimal guard zone; the capacity increase depending primarily on the required outage probability, as higher required QoS increasingly rewards scheduling. Compared to the ubiquitous carrier sense multiple access (CSMA) which essentially implements a guard zone around the transmitter rather than the receiver - we observe a capacity increase on the order of 30 - 100 In wireless communications, the desired wireless signal is typically decoded by treating the sum of all the other ongoing signal transmissions as noise. In the networking literature, this phenomenon is typically abstracted using a wireless channel interference model. The level of detail in the interference model, evidently determines the accuracy of the results based upon the model. Several works in the networking literature have made use of simplistic interference models, e.g., fixed ranges for communication and interference, the capture threshold model (used in the ns2 network simulator), the protocol model, and so on. At the same time, fairly complex interference models such as those based on the SINR (signal-to-interference-and-noise ratio) have also been proposed and used. We investigate the impact of the choice of the interference model, on the conclusions that can be drawn regarding the performance of wireless networks, by comparing different wireless interference models. We find that both in the case of random access networks, as well as in the case of scheduled networks (where node transmissions are scheduled to be completely conflict-free), different interference models can produce significantly different results. Therefore, a lot of caution should be exercised before accepting or interpreting results based on simplified interference models. Further, we feel that an SINR-based model is the minimum level of detail that should be employed to model wireless channel interference in a networking context. This paper tries to reconcile the tension between the physical model and the protocol model that have been used to characterize interference relationship in a multihop wireless network. The physical model (a.k.a. signal-to-interference-and-noise ratio model) is widely considered as a reference model for physical layer behavior but its application in multihop wireless networks is limited by its complexity. On the other hand, the protocol model (a.k.a. disk graph model) is simple but there have been doubts on its validity. This paper explores the following fundamental question: How to correctly use the protocol interference model? We show that, in general, solutions obtained under the protocol model may be infeasible and, thus, results based on blind use of protocol model can be misleading. We propose a new concept called "reality check” and present a method of using a protocol model with reality check for wireless networks. Subsequently, we show that by appropriate setting of the interference range in the protocol model, it is possible to narrow the solution gap between the two models. Our simulation results confirm that this gap is indeed small (or even negligible). Thus, our methodology of joint reality check and interference range setting retains the protocol model as a viable approach to analyze multihop wireless networks.