In an Ultra-dense network (UDN) where there are more base stations (BSs) than active users, it is possible that many BSs are instantaneously left idle. Thus, how to utilize these dormant BSs by means of cooperative transmission is an interesting question. In this paper, we investigate the performance of a UDN with two types of cooperation schemes: non-coherent joint transmission (JT) without channel state information (CSI) and coherent JT with full CSI knowledge. We consider a bounded dual-slope path loss model to describe UDN environments where a user has several BSs in the near-field and the rest in the far-field. Numerical results show that non-coherent JT cannot improve the user spectral efficiency (SE) due to the simultaneous increment in signal and interference powers. For coherent JT, the achievable SE gain depends on the range of near-field, the relative densities of BSs and users, and the CSI accuracy. Finally, we assess the energy efficiency (EE) of cooperation in UDN. Despite costing extra energy consumption, cooperation can still improve EE under certain conditions.
 Existing cellular network analyses, and even simulations, typically use the standard path loss model where received power decays like @math over a distance @math . This standard path loss model is quite idealized, and in most scenarios the path loss exponent @math is itself a function of @math , typically an increasing one. Enforcing a single path loss exponent can lead to orders of magnitude differences in average received and interference powers versus the true values. In this paper, we study multi-slope path loss models, where different distance ranges are subject to different path loss exponents. We focus on the dual-slope path loss function, which is a piece-wise power law and continuous and accurately approximates many practical scenarios. We derive the distributions of SIR, SNR, and finally SINR before finding the potential throughput scaling, which provides insight on the observed cell-splitting rate gain. The exact mathematical results show that the SIR monotonically decreases with network density, while the converse is true for SNR, and thus the network coverage probability in terms of SINR is maximized at some finite density. With ultra-densification (network density goes to infinity), there exists a phase transition in the near-field path loss exponent @math : if @math unbounded potential throughput can be achieved asymptotically; if $ 0 , ultra-densification leads in the extreme case to zero throughput. This paper addresses the following question: how reliable is it to use the unbounded path-loss model G(d) = d-alpha, where alpha is the path-loss exponent, to model the decay of transmitted signal power in wireless networks? G(d) is a good approximation for the path-loss in wireless communications for large values of d but is not valid for small values of d due to the singularity at 0. This model is often used along with a random uniform node distribution, even though in a group of uniformly distributed nodes some may be arbitrarily close to one another. The unbounded path-loss model is compared to a more realistic bounded path-loss model, and it is shown that the effect of the singularity on the total network interference level is significant and cannot be disregarded when nodes are uniformly distributed. A phase transition phenomenon occurring in the interference behavior is analyzed in detail. Several performance metrics are also examined by using the computed interference distributions. In particular, the effects of the singularity at 0 on bit error rate, packet success probability and wireless channel capacity are analyzed. Dense deployment which brings small base stations (BS) closer to mobile devices is considered as a promising solution to the booming traffic demand. Meanwhile, the utilization of new frequency bands and spectrum aggregation techniques provide more options for spectrum choice.Whether to increase BS density or to acquire more spectrum is a key strategic question for mobile operators. In this paper, we investigate the relationship between BS density and spectrum with regard to individual user throughput target. Our work takes into account load-dependent interference model and various traffic demands. Numerical results show that densification is more effective in sparse networks than in already dense networks. In sparse networks, doubling BS density results in almost twofold throughput increase. However, in dense networks where BSs outnumber users, more than 10 times of BS density is needed to double user throughput. Meanwhile, spectrum has a linear relationship with user throughput for a given BS density. The impact of traffic types is also discussed. Even with the same area throughput requirement, different combination of user density and individual traffic amount leads to different needs for BS density and spectrum. There have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the network performance. Moreover, tractable analysis can be performed only for a fixed location user (e.g., cell center or edge user). In this paper, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process. We also consider the user density, and derive the user outage probability that an arbitrary user is under outage owing to low signal-to-interference-plus-noise ratio or high congestion by multiple users. Using the result, we calculate the density of success transmissions in the downlink cellular network. An interesting observation is that the success transmission density increases with the base station density, but the increasing rate diminishes. This means that the number of base stations installed should be more than @math -times to increase the network capacity by a factor of @math . Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of network-level simulations.