How would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a "massive MIMO" fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.
The EE analysis of multi-cellular networks is much more involved than in the single-cell case due to the complicated network topology and the arising inter-cell interference. The simplest approach is to rely on heavy Monte Carlo simulations. Attempts in this direction can be found in @cite_36 and @cite_37 . Unfortunately, Monte Carlo simulated results are often anecdotal since one cannot separate fundamental properties from behaviors induced by parameter selection. Alternatively, simplified network topologies can be considered, such as the Wyner model @cite_31 or the symmetric grid-based deployment @cite_42 . While attractive for its analytical simplicity, the Wyner model does not well capture the essential characteristics of real and practical networks @cite_7 . Similarly, the symmetric grid-based models cannot capture the irregular structure of small-cell network deployments.
@cite_37 @cite_7 @cite_36 @cite_42 @cite_31
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Energy efficiency (EE) is becoming an important design goal for wireless communication systems providing high spectral efficiency (SE). Both massive multi-input multi-output (MIMO) and small cell network (SCN) are expected to achieve high EE for high throughput cellular networks, though using different mechanisms. Massive MIMO improves EE by exploiting a large array gain, while SCN improves EE by deploying a large number of low-power base stations (BSs) to reduce the propagation loss and increase the opportunity of BS sleep. In this paper, we compare the EEs as well as the SEs of Massive MIMO and SCN. For a fair comparison, we consider a multi-cell network with the same user density, antenna density and average cell-edge signal-to-noise-ratio (SNR). Perfect channel information is assumed, and three BS sleep strategies are considered. Our analysis shows that the EE of SCN increases with the cell size shrinking, and the achievable SEs of SCN and Massive MIMO increase with the cell-edge SNR. When the number of cells is large, SCN is always more energy efficient than Massive MIMO. On the other hand, when the number of cells is small, Massive MIMO achieves higher EE than SCN when the circuit power consumptions of Massive MIMO are much lower than SCN. 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 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. Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios. 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. >