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Fundamentals of Energy-Efficient Wireless Links: Optimal Ratios and Scaling Behaviors

Anders Enqvist, Özlem Tuğfe Demir, Cicek Cavdar, Emil Björnson

TL;DR

A novel algorithm is presented that jointly optimizes these variables to achieve maximum EE, while fulfilling constraints on the variable ranges, and discovers a new relationship between the radiated power and the passive transceiver power consumption.

Abstract

In this paper, we examine the energy efficiency (EE) of a base station (BS) with multiple antennas. We use a state-of-the-art power consumption model, taking into account the passive and active parts of the transceiver circuitry, including the effects of radiated power, signal processing, and passive consumption. The paper treats the transmit power, bandwidth, and number of antennas as the optimization variables. We provide novel closed-form solutions for the optimal ratios of power per unit bandwidth and power per transmit antenna. We present a novel algorithm that jointly optimizes these variables to achieve maximum EE, while fulfilling constraints on the variable ranges. We also discover a new relationship between the radiated power and the passive transceiver power consumption. We provide analytical insight into whether using maximum power or bandwidth is optimal and how many antennas a BS should utilize.

Fundamentals of Energy-Efficient Wireless Links: Optimal Ratios and Scaling Behaviors

TL;DR

A novel algorithm is presented that jointly optimizes these variables to achieve maximum EE, while fulfilling constraints on the variable ranges, and discovers a new relationship between the radiated power and the passive transceiver power consumption.

Abstract

In this paper, we examine the energy efficiency (EE) of a base station (BS) with multiple antennas. We use a state-of-the-art power consumption model, taking into account the passive and active parts of the transceiver circuitry, including the effects of radiated power, signal processing, and passive consumption. The paper treats the transmit power, bandwidth, and number of antennas as the optimization variables. We provide novel closed-form solutions for the optimal ratios of power per unit bandwidth and power per transmit antenna. We present a novel algorithm that jointly optimizes these variables to achieve maximum EE, while fulfilling constraints on the variable ranges. We also discover a new relationship between the radiated power and the passive transceiver power consumption. We provide analytical insight into whether using maximum power or bandwidth is optimal and how many antennas a BS should utilize.
Paper Structure (13 sections, 7 theorems, 28 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 7 theorems, 28 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Prior Work and Motivations
  3. Contributions
  4. System Model
  5. Power Consumption
  6. Energy Efficiency
  7. EE-Optimal Parameter Ratios
  8. Power per Bandwidth
  9. Power per Antenna
  10. Single Variable Optimization
  11. Computational efficiency does not affect the solution
  12. Algorithm for optimizing the EE
  13. Conclusion

Key Result

Theorem 1

When the term $\mu/B + D_0 M/B$ is negligible, the $\mathrm{EE}$ in eq:EEdivB is maximized when $P$ and $B$ satisfy the ratio where and $W (\cdot)$ denotes the Lambert W function, defined by the equation $x = W(x)e^{W(x)}$ for any $x \in \mathbb{C}$.

Figures (4)

  • Figure 1: We have that the maximum energy efficiency $\mathrm{EE}_\mathrm{max}$ as defined in \ref{['eq:EE_max']} is attained for a finite number $M_\mathrm{opt}$ at an optimal ratio $P/B$.
  • Figure 2: The EE is shown as a function of $P$ and $B$. In black, we have the optimal $P$ for a given $B$ as in Lemma \ref{['maximum-EE-P']}. In red, we have optimal $B$ for a given $P$ as in Lemma \ref{['maximum-EE-B']}. $P$ and $B$ converge to the optimal ratio $P/B$ given in Theorem 1. We consider $M=20$.
  • Figure 3: The optimal $M$ as given in Lemma \ref{['maximum-EE-M']} as a function of the bandwidth and transmit power. The optimal value is shown on the vertical axis for different $P$ and $B$ values.
  • Figure 4: The EE is shown as a function of $P$ and $M$. It converges to the optimum point as detailed in Algorithm 1. Encircled in red we have the algorithm's updates of $P$ and $M$ and the corresponding $\mathrm{EE}$.

Theorems & Definitions (7)

  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Corollary 1
  • Theorem 3