In random machine-to-machine (M2M) networks, the network topology along with the variation of the wireless channel are the main sources of uncertainty that affect the network performance. Unlike most prior works, which assume a reference receiver such as aggregator located at a certain fixed point, this paper discusses a more general case where the intended receiving node can be any randomly-located node distributed uniformly in a circle. Each machine node transmits a backlog of data in time duration based on slotted-synchronous ALOHA multiple access control (MAC) scheme. A closed-form expression for the order statistics of the interference power produced by a randomly located interfering node for Nakagami-m fading channel model is obtained. Due to the dependency of the inter-node distances in uniform deployment, deriving a closed-form expression for outage probability from randomly-selected node's perspective is demanding. Using the order statistics notion, a tractable lower bound is derived for the outage probability seen from any randomly-located node's perspective inside the network region. The numerical results validate the accuracy of analytical ones and tightness of the lower bound for the broad range of the network parameters.

Using stochastic geometry, the downlink (DL) and uplink (UL) coverage probabilities are derived for co-channel packet multi-tier heterogeneous cellular networks (HCNs). The spatial locations of base stations (BSs) as well as user equipments (UEs) are modeled as independent spatial homogeneous Poisson point processes. The decoupled association is evaluated where the UE may connect to different BSs in the UL and DL transmissions. Unlike most of the existing works, the packet transmission slots are not synchronized, that is, the starting and ending points of the slots are not aligned. We investigate fundamental performance metrics of dynamic packet HCN for two traffic models, namely, the slotted-asynchronous and exponential-interarrival. Furthermore, tight lower bounds for the DL and UL coverage probabilities for two traffic models are obtained. The derived bounds are tight especially in high data rate regimes. The analysis provided herein enables us to determine the performance limits of packet-based HCNs with possible asynchronous time-slots. Simulation results are conducted to verify the analytical derivations. Furthermore, the performance comparison between pure synchronous and asynchronous packet-based systems is provided. The results confirm that the synchronous case outperforms the asynchronous one in terms of the UL and DL coverage probabilities at the cost of higher computational complexity.

Using stochastic geometry, downlink (DL) coverage probability in slot-based two-tier heterogeneous cellular networks (HCNs) is studied. Two traffic patterns namely slotted-asynchronous and exponential-interarrival are introduced to capture user activity, and the DL coverage probability based on max-SINR association is derived. In contrast to many works, the transmission slots of base stations (BS) are not synchronous. This causes a packet transmitted in one slot to experience varying levels of interference during the time slot interval. The SINR statistical distribution during one slot is derived for both traffic patterns. The numerical results are presented to illustrate the analytical ones. The comparison between asynchronous and conventional synchronous HCNs is provided to illustrate the asynchronous effect on DL performance. It is shown that to meet high coverage requirements, synchronizing slots from different BSs help to boost the coverage performance. Furthermore, it is shown that densifying networks with low-power BSs improves coverage performance and the improvement is more pronounced at higher path-loss exponents.

Random wireless networks with finite number of nodes distributed uniformly in a circular-shaped finite region are considered. A closed-form expression for the complimentary cumulative distribution function (CCDF) of Euclidean distance between a randomly selected node and its ith nearest node is derived. In contrast to most of the existing literature, the node observed is not necessarily required to be located at the centre of the network region nor located at fixed point. Moreover, the joint distribution of the distances between the ith and jth nearest nodes is derived. Finally, a tractable and quite tight lower bound on outage performance of the uniform network based on the dominant interferer node is derived. Using our derived lower bound, we can determine the maximum number of nodes that should be deployed to satisfy the required QoS. Computer simulation illustrates the validity of the theoretical analysis.

Random wireless networks with finite number of nodes distributed uniformly in a square-shaped finite region are considered. The transmission channels are assumed to experience Nakagami-m fading. A closed-form expression for the cumulative distribution function (CDF) of the interference power imposed on two randomly-located communicating nodes is derived. In contrast to most of the existing literature, the receiving node is not necessarily required to be located at the center of the network region. Two packet traffic patterns, viz., slotted-synchronous and slotted-asynchronous are considered and closed-form expressions for the CDF of the interference is obtained for each traffic pattern. Computer simulation illustrates the validity of the theoretical analyses.