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.
Previous works that investigate the throughput, energy efficiency and their tradeoff have mainly focused on the point-to-point communication link or the single-cell case @cite_10 @cite_32 @cite_36 @cite_33 , while the interference from other cells are neglected. Meanwhile, the throughput analysis of conventional cellular networks has received lots of attention, and different models have been proposed, such as the Wyner model @cite_0 or the grid model @cite_35 @cite_3 . While the Wyner model is commonly used due to its tractability, it may lose the essential characteristics of real and practical networks @cite_26 . On the other hand, the regular grid model becomes intractable as the network size grows, and it cannot handle the irregular network structure in small cell networks. In general, it is quite challenging to accurately evaluate the performance of cellular networks, due to the complexity of the network topology, and effects of multi-path propagation. A more common way to evaluate cellular networks is by simulation. For example, in @cite_3 , different cellular network architectures were compared through simulation. While evaluating the network performance through simulation can provide insights on some specific settings, the results may not be extended to other scenarios and the computational complexity is rather high.
@cite_35 @cite_26 @cite_33 @cite_36 @cite_32 @cite_3 @cite_0 @cite_10
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In this paper, we present a systematic study of the uplink capacity and coverage of pico-cell wireless networks. Both the one dimensional as well as the two dimensional cases are investigated. Our goal is to compute the size of pico-cells that maximizes the spatial throughput density. To achieve this goal, we consider fluid models that allow us to obtain explicit expressions for the interference and the total received power at a base station. We study the impact of various parameters on the performance: the path loss factor, the spatial reuse factor and the receiver structure (matched filter or multiuser detector). We relate the performance of the fluid models to that of the original discrete system and show that the fluid model provides a bound for the discrete one. The Wyner model has been widely used to model and analyze cellular networks due to its simplicity and analytical tractability. Its key aspects include fixed user locations and the deterministic and homogeneous interference intensity. While clearly a significant simplification of a real cellular system, which has random user locations and interference levels that vary by several orders of magnitude over a cell, a common presumption by theorists is that the Wyner model nevertheless captures the essential aspects of cellular interactions. But is this true? To answer this question, we compare the Wyner model to a model that includes random user locations and fading. We consider both uplink and downlink transmissions and both outage-based and average-based metrics. For the uplink, for both metrics, we conclude that the Wyner model is in fact quite accurate for systems with a sufficient number of simultaneous users, e.g., a CDMA system. Conversely, it is broadly inaccurate otherwise. Turning to the downlink, the Wyner model becomes inaccurate even for systems with a large number of simultaneous users. In addition, we derive an approximation for the main parameter in the Wyner model - the interference intensity term, which depends on the path loss exponent. The dramatic increase of network infrastructure comes at the cost of rapidly increasing energy consumption, which makes optimization of energy efficiency (EE) an important topic. Since EE is often modeled as the ratio of rate to power, we present a mathematical framework called fractional programming that provides insight into this class of optimization problems, as well as algorithms for computing the solution. The main idea is that the objective function is transformed to a weighted sum of rate and power. A generic problem formulation for systems dissipating transmit-independent circuit power in addition to transmit-dependent power is presented. We show that a broad class of EE maximization problems can be solved efficiently, provided the rate is a concave function of the transmit power. We elaborate examples of various system models including time-varying parallel channels. Rate functions with an arbitrary discrete modulation scheme are also treated. The examples considered lead to water-filling solutions, but these are different from the dual problems of power minimization under rate constraints and rate maximization under power constraints, respectively, because the constraints need not be active. We also demonstrate that if the solution to a rate maximization problem is known, it can be utilized to reduce the EE problem into a one-dimensional convex problem. The energy consumption of different cellular network architectures are analyzed. In particular, a comparison of the transmit energy consumption between a single large cell with multiple co-located antennas, multiple micro-cells with a single antenna at each cell, and a large cell with a distributed antenna system are presented. The influence of different system parameters such as cell size, spatial distribution of the users, and the availability of channel state information (CSI) toward the total required transmit energy are analyzed. It is shown that the current macro-cellular architecture with co-located antennas has poor energy efficiency in the absence of CSI, but has better energy efficiency than small cells when perfect CSI is available. Moreover, macro-cells with distributed antennas have the best energy efficiency of all three architectures under perfect CSI. These results shed light on design guidelines to improve the energy efficiency of cellular network architectures. We obtain Shannon-theoretic limits for a very simple cellular multiple-access system. In our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha (0 spl les spl alpha spl les 1) times the sum of the signals transmitted from the adjacent cells plus ambient Gaussian noise. Although this simple model is scarcely realistic, it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems. We consider both a one dimensional linear cellular array and the familiar two-dimensional hexagonal cellular pattern. The discrete-time channel is memoryless. We assume that N contiguous cells have active transmitters in the one-dimensional case, and that N sup 2 contiguous cells have active transmitters in the two-dimensional case. There are K transmitters per cell. Most of our results are obtained for the limiting case as N spl rarr spl infin . The results include the following. (1) We define C sub N ,C spl circ sub N as the largest achievable rate per transmitter in the usual Shannon-theoretic sense in the one- and two-dimensional cases, respectively (assuming that all signals are jointly decoded). We find expressions for limN spl rarr spl infin C sub N and limN spl rarr spl infin C spl circ sub N . (2) As the interference parameter spl alpha increases from 0, C sub N and C spl circ sub N increase or decrease according to whether the signal-to-noise ratio is less than or greater than unity. (3) Optimal performance is attainable using TDMA within the cell, but using TDMA for adjacent cells is distinctly suboptimal. (4) We suggest a scheme which does not require joint decoding of all the users, and is, in many cases, close to optimal. >