The concept of Ultra Dense Networks (UDN) is often seen as a key enabler of the next generation mobile networks. However, existing analysis of UDNs, including Stochastic Geometry, has not been able to fully determine the potential gains and limits of densification. In this paper we study performance of UDNs in downlink and provide new insights on the impact of antenna height and careful site selection on the network performance. We focus our investigation on the probability of coverage, average cell rate and average area spectral efficiency for networks with regular and random BS deployments. We show that under a path-loss model which considers antenna height there exists an upper limit on network performance which is dependent on the path-loss model parameters. Our analysis shows an interesting finding that even for over-densified networks a non-negligible system performance can be achieved.
One of the first works investigating the relationship between network density and system performance is due to @cite_12 . The work shows surprising results where coverage probability as well as mean achievable data rate per cell, do not depend on BS density (also known as SINR invariance property @cite_2 ). The constant mean achievable data rate per cell implies that continuingly increasing the number of BSs in wireless networks could lead to limitless overall network performance improvements. Their conclusions are based on the assumptions of simple unbounded path-loss model, noise-less networks and BS locations following a Poisson point process. Under these assumptions, as BS density increases, the change in aggregated interference power is counter-balanced by the change in signal power, and thus the SINR remains unchanged regardless of network density @cite_12 . Following the same assumptions, @cite_20 shows SINR invariance property for HetNets.
@cite_20 @cite_12 @cite_2
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In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a unique transmit power, path loss exponent, spatial density, and bias towards admitting users. We implicitly assume every BS has full queues. From this model, we derive the outage probability of a typical user in the network, which can be viewed as a spatial average of SINR over all users in the network. We observe that deploying more or less BSs does not change the outage probability in interference-limited HCN with unbiased cell association, and observe how biasing affects the metric. The rate distribution in heterogeneous networks (HetNets) greatly benefits from load balancing, by which mobile users are pushed onto lightly-loaded small cells despite the resulting loss in SINR. This offloading can be made more aggressive and robust if the macrocells leave a fraction of time frequency resource blank, which reduces the interference to the offloaded users. We investigate the joint optimization of this technique - referred to in 3GPP as enhanced intercell interference coordination (eICIC) via almost blank subframes (ABSs) - with offloading in this paper. Although the joint cell association and blank resource (BR) problem is nominally combinatorial, by allowing users to associate with multiple base stations (BSs), the problem becomes convex, and upper bounds the performance versus a binary association. We show both theoretically and through simulation that the optimal solution of the relaxed problem still results in an association that is mostly binary. The optimal association differs significantly when the macrocell is on or off; in particular the offloading can be much more aggressive when the resource is left blank by macro BSs. Further, we observe that jointly optimizing the offloading with BR is important. The rate gain for cell edge users (the worst 3-10 ) is very large - on the order of 5-10x - versus a naive association strategy without macrocell blanking. Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given , adding more tiers and or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR. For small cell technology to significantly increase the capacity of tower-based cellular networks, mobile users will need to be actively pushed onto the more lightly loaded tiers (corresponding to, e.g., pico and femtocells), even if they offer a lower instantaneous SINR than the macrocell base station (BS). Optimizing a function of the long-term rate for each user requires (in general) a massive utility maximization problem over all the SINRs and BS loads. On the other hand, an actual implementation will likely resort to a simple biasing approach where a BS in tier j is treated as having its SINR multiplied by a factor Aj ≥ 1, which makes it appear more attractive than the heavily-loaded macrocell. This paper bridges the gap between these approaches through several physical relaxations of the network-wide association problem, whose solution is NP hard. We provide a low-complexity distributed algorithm that converges to a near-optimal solution with a theoretical performance guarantee, and we observe that simple per-tier biasing loses surprisingly little, if the bias values Aj are chosen carefully. Numerical results show a large (3.5x) throughput gain for cell-edge users and a 2x rate gain for median users relative to a maximizing received power association.