This paper examines the impact of system parameters such as access point density and bandwidth partitioning on the performance of randomly deployed, interference-limited, dense wireless networks. While much progress has been achieved in analyzing randomly deployed networks via tools from stochastic geometry, most existing works either assume a very large user density compared to that of access points which does not hold in a dense network, and or consider only the user signal-to-interference-ratio as the system figure of merit which provides only partial insight on user rate, as the effect of multiple access is ignored. In this paper, the user rate distribution is obtained analytically, taking into account the effects of multiple access as well as the SIR outage. It is shown that user rate outage probability is dependent on the number of bandwidth partitions (subchannels) and the way they are utilized by the multiple access scheme. The optimal number of partitions is lower bounded for the case of large access point density. In addition, an upper bound of the minimum access point density required to provide an asymptotically small rate outage probability is provided in closed form.
 Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the over-loaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of M different RATs, each deploying up to K different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate. Interference coordination improves data rates and reduces outages in cellular networks. Accurately evaluating the gains of coordination, however, is contingent upon using a network topology that models realistic cellular deployments. In this paper, we model the base stations locations as a Poisson point process to provide a better analytical assessment of the performance of coordination. Since interference coordination is only feasible within clusters of limited size, we consider a random clustering process where cluster stations are located according to a random point process and groups of base stations associated with the same cluster coordinate. We assume channel knowledge is exchanged among coordinating base stations, and we analyze the performance of interference coordination when channel knowledge at the transmitters is either perfect or acquired through limited feedback. We apply intercell interference nulling (ICIN) to coordinate interference inside the clusters. The feasibility of ICIN depends on the number of antennas at the base stations. Using tools from stochastic geometry, we derive the probability of coverage and the average rate for a typical mobile user. We show that the average cluster size can be optimized as a function of the number of antennas to maximize the gains of ICIN. To minimize the mean loss in rate due to limited feedback, we propose an adaptive feedback allocation strategy at the mobile users. We show that adapting the bit allocation as a function of the signals' strength increases the achievable rate with limited feedback, compared to equal bit partitioning. Finally, we illustrate how this analysis can help solve network design problems such as identifying regions where coordination provides gains based on average cluster size, number of antennas, and number of feedback bits. In this paper, we adopt stochastic geometry theory to analyze the optimal macro micro BS (base station) density for energy-efficient heterogeneous cellular networks with QoS constraints. We first derive the upper and lower bounds of the optimal BS density for homogeneous scenarios and, based on these, we analyze the optimal BS density for heterogeneous networks. The optimal macro micro BS density can be calculated numerically through our analysis, and the closed-form approximation is also derived. Our results reveal the best type of BSs to be deployed for capacity extension, or to be switched off for energy saving. Specifically, if the ratio between the micro BS cost and the macro BS cost is lower than a threshold, which is a function of path loss and their transmit power, the micro BSs are preferred, i.e., deploy more micro BSs for capacity extension or switch off certain macro BSs for energy saving. Otherwise, the optimal choice is the opposite. Our work provides guidance for energy efficient cellular network planning and dynamic operation control.1