EE-SE Tradeoff Research Articles

On the Secure Spectral-Energy Efficiency Tradeoff in Random Cognitive Radio Networks

Spectrum efficiency (SE) and energy efficiency (EE) in secure communications have attracted much attention recently due to the fact that future wireless networks need to address the issues of high throughput, low power consumption, and high level of security. However, maximizing EE and SE are conflicting objectives, which can hardly be achieved simultaneously. In this paper, we develop a framework to study the SE and EE for secure transmission in underlay random cognitive radio (CR) networks where the primary, secondary, and eavesdropper nodes are randomly distributed according to Poisson point processes. We first analyze the connection outage probability and the secrecy outage probability of the typical links in the random CR network. Then, we evaluate the secure SE and EE in the secondary network based on the outage probability analysis. It is demonstrated that the scheduling scheme of the secondary network (i.e., the transmission power and the intensity of secondary transmitters arouses a tradeoff between the secure SE and EE. Furthermore, applying a unified secure SE-EE tradeoff metric, which condenses the secure SE and EE into a single utility function with a tradeoff factor, we formulate the joint secure SE and EE optimization problem with respect to the scheduling scheme of the secondary network. An iterative algorithm is proposed based on the separation optimization of the transmission power and the intensity. The analytical and simulation results show the effects of system parameters on the optimal solutions and secure SE-EE tradeoff. We also verify that the optimal scheduling scheme can improve the secure SE-EE tradeoff. Using these results, one can easily understand and make the secure SE-EE tradeoff in random CR networks.

On the Spectral-Energy Efficiency and Rate Fairness Tradeoff in Relay-Aided Cooperative OFDMA Systems

In resource constrained wireless systems, achieving higher spectral efficiency (SE) and energy efficiency (EE), and greater rate fairness are conflicting objectives. Here, a general framework is presented to analyze the tradeoff among these three performance metrics in cooperative OFDMA systems with decode-and-forward relaying, where subcarrier pairing and allocation, relay selection, choice of transmission strategy, and power allocation are jointly considered. In our analytical framework, rate fairness is represented utilizing the α-fairness model, and the resource allocation problem is formulated as a multi-objective optimization problem. We then propose a cross-layer resource allocation algorithm across application and physical layers, and further devise a heuristic algorithm to tackle the computational complexity issue. The SE-EE tradeoff is characterized as a Pareto optimal set, and the efficiency and fairness tradeoff is investigated through the price of fairness. Simulations indicate that higher fairness results in a worse SE-EE tradeoff. It is also shown imposing fairness helps to reduce the outage probability. For a fixed number of relays, by increasing circuit power, the performance of SE-EE tradeoff is degraded. Interestingly, by increasing the number of relays, although the total circuit power is increased, the SE-EE tradeoff is not necessarily degraded. This is thanks to the extra degree of freedom provided in relay selection.

On the Energy Efficiency–Spectral Efficiency Tradeoff in MIMO-OFDMA Broadcast Channels

This paper investigates the fundamental energy efficiency–spectral efficiency (EE–SE) relationship in a multiple-input–multiple-output (MIMO) orthogonal frequency-division multiple-access (OFDMA) broadcast channel with a practical power model considering the power consumption due to the number of admitted users, as well as the number of active transmit antennas. However, with this power model, the EE–SE tradeoff optimization problem, which jointly optimizes the transmit covariance matrices while determining the optimal admitted user set and the active transmit antenna set, is nonconvex, and hence, it is extremely difficult to solve directly. As a result, we propose an algorithm that decouples the multicarrier EE optimization problem to a set of single-carrier EE optimization problems. For the single-carrier EE optimization problem, we first investigate the EE–SE tradeoff problem with a fixed admitted user set and transmit antenna set. Under this setup, we prove that the EE–SE relationship is a quasiconcave function. Furthermore, EE is proved to be either strictly decreasing with SE or first strictly increasing and then strictly decreasing with SE. Based on these findings, we propose a two-layer resource allocation algorithm to tackle the comprehensive EE–SE tradeoff problem. Meanwhile, since admitting more users and activating more transmit antennas can achieve a higher sum rate at the cost of larger transmit-independent power consumption, there exists a tradeoff between sum-rate gain and power consumption. We therefore study the user and antenna selection approach to further explore the optimal tradeoff. Both the optimal exhaustive search and the Frobenius-norm-based dynamic selection schemes are developed to further improve the achievable EE. To further reduce the computational complexity, a strategy that chooses a fixed admitted user set for all the subcarriers is developed. Simulation results confirm the theoretical findings and demonstrate that the proposed resource allocation algorithm can efficiently approach the optimal EE–SE tradeoff.

On the Spectrum- and Energy-Efficiency Tradeoff in Cognitive Radio Networks

Increasing spectrum-efficiency (SE) as well as energy-efficiency (EE) has attracted much attention recently due to the fact that the future wireless networks need to address the issues of high throughput and low power consumption. However, the objective for optimizing SE sometimes conflicts with the one for optimizing EE, and the methods for improving EE may result in a decrease in SE. In this paper, we consider the SE-EE tradeoff for cognitive radio (CR) networks with co-operative spectrum sensing (CSS). First, we formulate the general problem, and analyze two special cases: the SE maximization problem and the EE maximization problem. The SE and EE are optimized separately via joint optimization of sensing duration and final decision threshold in CSS. Based on the solutions of the two special cases, the general problem for SE-EE tradeoff is solved. Then, we consider the tradeoff of SE and EE from two perspectives: (1) maximizing EE while satisfying SE requirement; and (2) maximizing SE while satisfying EE requirement. Efficient algorithms for sensing strategy design are proposed for each scenario. Finally, we demonstrate the effectiveness of the proposed sensing strategies and illustrate the tradeoff between SE and EE via simulations.

Optimal Resource Allocation and EE-SE Trade-Off in Hybrid Cognitive Gaussian Relay Channels

Recent literature has suggested the benefits of integrating licensed radio and cognitive radio into a hybrid cooperative communication system. The fundamental properties of such hybrid systems, however, have not been thoroughly investigated. This paper studies the hybrid cognitive Gaussian relay channel (HCGRC), which uses licensed radio resource (RR) and cognitive/unlicensed RR for forward and relay transmissions, respectively. HCGRC fundamentally differs from conventional relay channels in that the licensed and cognitive RRs are not subject to a total resource constraint and that the cognitive RR is opportunistic in nature. With respect to both the upper and lower bounds, we derive the optimal power-bandwidth allocation strategies for the cognitive relay to maximize the capacity, spectrum efficiency (SE), and energy efficiency (EE). The Pareto-optimal EE-SE tradeoff curve is also derived analytically. Our study leads to two key observations. First, the multi-objective power-bandwidth allocation problem is characterized by five regions, each representing a unique performance tradeoff. Second, the reliability of cognitive RR has no impact on the EE-SE tradeoff given unlimited bandwidth and power.

Flexible Resource Allocation for Joint Optimization of Energy and Spectral Efficiency in OFDMA Multi-Cell Networks

The radio resource allocation problem is studied, aiming to jointly optimize the energy efficiency (EE) and spectral efficiency (SE) of downlink OFDMA multi-cell networks. Different from existing works on either EE or SE optimization, a novel EE-SE tradeoff (EST) metric, which can capture both the EST relation and the individual cells' preferences for EE or SE performance, is introduced as the utility function for each base station (BS). Then the joint EE-SE optimization problem is formulated, and an iterative subchannel allocation and power allocation algorithm is proposed. Numerical results show that the proposed algorithm can exploit the EST relation flexibly and optimize the EE and SE simultaneously to meet diverse EE and SE preferences of individual cells.

Analysis of Spectrum Efficiency and Energy Efficiency of Heterogeneous Wireless Networks with Intra-/Inter-RAT Offloading

Offloading the users from capacity-strained macrocells in a cellular network to small cells is an effective strategy to support the increasing mobile data traffic, but a key challenge is how to simultaneously achieve high spectrum efficiency (SE) and energy efficiency (EE) in the heterogeneous radio access technology (RAT) environment. This paper develops an analytical framework for studying the performance of a two-RAT heterogeneous network (HetNet) comprising cellular and wireless local area network (WLAN) RATs. Using the developed framework, the feasibility of enhancing the SE and EE via the implementation of biased intra- and inter-RAT offloading techniques is investigated. Findings from the analysis reveal that the performance gain for SE and EE is strongly dependent on the load level and the base station (BS) power consumption attributes. A multiobjective optimization problem that maximizes the SE and EE subject to quality-of-service (QoS) constraints is formulated and solved to give the Pareto-optimal operational regime specified in terms of the small-cell BS densities and biasing factors. The novelty of this paper is the quantification of the SE-EE tradeoff as an opportunity cost measure, which is defined by the constrained Pareto-optimal regime. The insight gained from analyzing the opportunity cost is used to formulate a strategy that exploits the varying load conditions to achieve a good balance in the SE-EE tradeoff. Numerical results show that, although the potential to reduce the performance gap between SE and EE is marginal under low and high load conditions, it is feasible to significantly improve the network performance by balancing the SE-EE tradeoff during the medium load condition, as well as satisfy the users' QoS requirements by optimally adapting the small-cell BS density and offloading biasing factors.

Spectral Efficiency and Energy Efficiency of OFDM Systems: Impact of Power Amplifiers and Countermeasures

In wireless communication systems, the nonlinear effect and inefficiency of power amplifier (PA) have posed practical challenges for system designs to achieve high spectral efficiency (SE) and energy efficiency (EE). In this paper, we analyze the impact of PA on the SE-EE tradeoff of orthogonal frequency division multiplex (OFDM) systems. An ideal PA that is always linear and incurs no additional power consumption can be shown to yield a decreasing convex function in the SE-EE tradeoff. In contrast, we show that a practical PA has an SE-EE tradeoff that has a turning point and decreases sharply after its maximum EE point. In other words, the Pareto-optimal tradeoff boundary of the SE-EE curve is very narrow. A wide range of SE-EE tradeoff, however, is desired for future wireless communications that have dynamic demand depending on the traffic loads, channel conditions, and system applications, e.g., high-SE-with-low-EE for rate-limited systems and high-EE-with-low-SE for energy-limited systems. For the SE-EE tradeoff improvement, we propose a PA switching (PAS) technique. In a PAS transmitter, one or more PAs are switched on intermittently to maximize the EE and deliver an overall required SE. As a consequence, a high EE over a wide range SE can be achieved, which is verified by numerical evaluations: with 15% SE reduction for low SE demand, the PAS between a low power PA and a high power PA can improve EE by 323%, while a single high power PA transmitter improves EE by only 68%.

On the Tradeoff Between Spectral Efficiency and Energy Efficiency of Homogeneous Cellular Networks With Outage Constraint

In this paper, the tradeoff relationship between the spectral efficiency (SE) and energy efficiency (EE) of homogenous cellular networks in which the BSs are arbitrarily distributed is investigated. The network performance metrics of SE and EE are assessed subject to a downlink transmission outage constraint in interference-limited operational environments. The EE is expressed in closed form as a function of SE, based on which the performance bounds of the network are derived. Unlike the traditional inverse relationship between SE and EE, it is found in this paper that there exists an operational regime for which both the SE and EE increase while satisfying the outage requirement, and the density of base stations (BSs) simultaneously sharing the spectrum is optimal. The difference in the performance achieved for the SE when operating in the EE maximizing mode as compared with the SE maximizing mode strongly depends on the received signal-to-interference ratio (SIR) threshold. In the SE-EE tradeoff regime, the analytical tools from microeconomics theory are applied to determine the optimal BS density with respect to the utility achieved by the network operator via balancing the SE and EE objectives. Numerical results show that, by tuning a preference factor toward either the SE or EE metrics, it is feasible to realize Pareto optimal performance.

Energy Efficiency Contours for Broadcast Channels Using Realistic Power Models

Energy savings are becoming a global trend, hence the importance of energy efficiency (EE) as an alternative performance evaluation metric. This paper proposes an EE based resource allocation method for the broadcast channel (BC), where a linear power model is used to characterize the power consumed at the base station (BS). Having formulated our EE based optimization problem and objective function, we utilize standard convex optimization techniques to show the concavity of the latter, and thus, the existence of a unique globally optimal energy-efficient rate and power allocation. Our EE based resource allocation framework is also extended to incorporate fairness, and provide a minimum user satisfaction in terms of spectral efficiency (SE). We then derive the generic equation of the EE contours and use them to get insights about the EE-SE trade-off over the BC. The performances of the aforementioned resource allocation schemes are compared for different metrics against the number of users and cell radius. Results indicate that the highest EE improvement is achieved by using the unconstrained optimization scheme, which is obtained by significantly reducing the total transmit power. Moreover, the network EE is shown to increase with the number of users and decrease as the cell radius increases.