Small cell networks have recently been proposed as an important evolution path for the next-generation cellular networks. However, with more and more irregularly deployed base stations (BSs), it is becoming increasingly difficult to quantify the achievable network throughput or energy efficiency. In this paper, we develop an analytical framework for downlink performance evaluation of small cell networks, based on a random spatial network model, where BSs and users are modeled as two independent spatial Poisson point processes. A new simple expression of the outage probability is derived, which is analytically tractable and is especially useful with multi-antenna transmissions. This new result is then applied to evaluate the network throughput and energy efficiency. It is analytically shown that deploying more BSs or more BS antennas can always increase the network throughput, but the performance gain critically depends on the BS-user density ratio and the number of BS antennas. On the other hand, increasing the BS density or the number of transmit antennas will first increase and then decrease the energy efficiency if different components of BS power consumption satisfy certain conditions, and the optimal BS density and the optimal number of BS antennas can be found. Otherwise, the energy efficiency will always decrease. Simulation results shall demonstrate that our conclusions based on the random network model are general and also hold in a regular grid-based model.
So far, most studies that adopt the random network model to analyze cellular networks only focus on the spatial distribution of BSs, while the distribution of mobile users is largely ignored. Specifically, BSs are modeled as a PPP, and each BS always has a mobile user to serve, so the user density and the BS-user association are irrelevant. Such an assumption holds only when the user density is much larger than the BS density, which is not the case in small cell networks where the user density is comparable to the BS density. In this paper, we will explicitly consider the user density and the BS-user association. Moreover, most previous works only consider single-antenna BSs. As shown in previous works on wireless ad-hoc networks @cite_18 @cite_4 @cite_7 , random network models with multi-antenna transmission are much more challenging than single-antenna systems. In cellular networks, stochastic orders were introduced in @cite_13 to provide qualitative comparison between different multi-antenna techniques, but such method cannot be used for quantitative analysis. In our work, we will consider multi-antenna transmission in small cell networks and investigate the effect of multiple BS antennas on the system performance.
@cite_13 @cite_18 @cite_4 @cite_7
2137079066 2012396676 1565287731
This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or non-fading environments. The transmission capacity is given for interference-limited uniformly random networks on the entire plane with path loss exponent alpha > 2 in which nodes use: (1) static beamforming through M sectorized antennas, for which the increase in transmission capacity is shown to be thetas(M2) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigenbeamforming (maximal ratio transmission combining), in which the increase is shown to be thetas(M 2 alpha ); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal space-time block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagami-m fading for increasing m. It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that space-time block coding offers only marginal gains. We develop a general framework for the analysis of a broad class of point-to-point linear multiple-input multiple-output (MIMO) transmission schemes in decentralized wireless ad hoc networks. New general closed-form expressions are derived for the outage probability, throughput and transmission capacity. For the throughput, we investigate the optimal number of data streams in various asymptotic regimes, which is shown to be dependent on different network parameters. For the transmission capacity, we prove that it scales linearly with the number of antennas, provided that the number of data streams also scales linearly with the number of antennas, in addition to meeting some mild technical conditions. We also characterize the optimal number of data streams for maximizing the transmission capacity. To make our discussion concrete, we apply our general framework to investigate three popular MIMO schemes, each requiring different levels of feedback. In particular, we consider eigenmode selection with MIMO singular value decomposition, multiple transmit antenna selection, and open-loop spatial multiplexing. Our analysis of these schemes reveals that significant performance gains are achieved by utilizing feedback under a range of network conditions. This paper investigates the performance of open-loop multi-antenna point-to-point links in ad hoc networks with slotted ALOHA medium access control (MAC). We consider spatial multiplexing transmission with linear maximum ratio combining and zero forcing receivers, as well as orthogonal space time block coded transmission. New closed-form expressions are derived for the outage probability, throughput and transmission capacity. Our results demonstrate that both the best performing scheme and the optimum number of transmit antennas depend on different network parameters, such as the node intensity and the signal-to-interference-and-noise ratio operating value. We then compare the performance to a network consisting of single-antenna devices and an idealized fully centrally coordinated MAC. These results show that multi-antenna schemes with a simple decentralized slotted ALOHA MAC can outperform even idealized single-antenna networks in various practical scenarios.