1
Abstract— This paper presents the basic metric related to energy efficiency (EE) of a radio communication link. The link model includes power consumption of the baseband modules, such as coding and adaptive modulation and of the radio-frequency frontend. Simulation results show that there exist an optimal operation point for a given link distance to maximize the EE1.
Index Terms—Energy efficiency, OFDM, adaptive modulation, coding
I. INTRODUCTION
HE power consumption problem in wireless communication has become very important. It has been noted that Information and Communication Technologies (ICT) have significantly contributed to global warming, and energy consumed by the ICT infrastructure is more than 3-5% of the world-wide consumed energy. In the same time, the network data volume is expected to increase by a factor of one thousand in ten years [1], resulting in even larger ICT-related CO2 footprint. It is envisioned for the future 5G
communication that energy efficiency (EE) of wireless systems has to be improved by the factor of 10.
Traditionally, wireless systems are optimized by taking into account only the signal transmission energy, while the power consumption of analog and digital processing is usually neglected. The breakdown of the power consumption of the example short-range wireless communication system for a transmitter and a receiver is presented in Table I and II. Note that the main source of energy consumption at the transmitter is a power amplifier used to amplify the emitted signal. RF front-end and baseband signal processing is also a major source of energy consumption. On the other hand, digital signal processing and in particular error-correcting decoding are key energy-consuming modules at the receiver.
For longer-distances communication, e.g. cellular networs, around 50-80% of the total power consumed by a base-station is the power consumed by the transmit power amplifier [2]. Similar results we can derived for a mobile terminals [3]. It is well-known that the power amplifiers are nonlinear elements.
1 The presented work has been supported by the National Science Centre in Poland within the OPUS project no. 2013/11/B/ST7/01168 “EcoNets”.
This means that signal of a high amplitude is distorted and the signal energy spilling out of the nominal band to the adjacent bands, and thus, inefficiency of the signal energy in-band concentration and energy loss.
In this paper we look at the optimal power allocation between baseband signal processing including error-correcting coding and transmit power to obtain the highest EE for a single link in the frequency-selective Rayleigh-fading channel. In Section II, the key sources of the energy consumption in a wireless system are discussed. In Section III, the considered system model is presented, and the energy efficiency metric is defined. Simulation parameters and results are presented in Section IV. The paper ends with conclusions.
II. WIRELESS LINK POWER CONSUMPTION
The total power consumption for a given transmission link consists of transmitted, radio-frequency and baseband processing power [5][6]. The transceiver system has two types of circuit: analog and digital circuits. Digital circuits perform digital signal processing and operate at baseband frequency e.g. source and channel coding, equalization, digital modulation and decoding processes. Analog circuits include a digital to analog converter, a power amplifier, a mixer, an intermediate frequency amplifier, a low-noise amplifier, an
Energy Efficiency of coded multicarrier
transmission in wireless frequency selective
fading channels
Bartosz Bossy, Student member, IEEE, Hanna Bogucka, Senior Member, IEEE
T
TABLEI
BREAKDOWN OF THE TRANSMITTER POWER CONSUMPTION OF WLANS [3] Transmitter components Percentage of power consumption – typical value
Power amplifier RF front-end
Digital signal processing and MAC Local oscillator Digital-to-analog converters 44% 24% 22% 4% 3% Baseband front-end 3% TABLEII
BREAKDOWN OF THE RECEIVER POWER CONSUMPTION OF WLANS [3] Transmitter components Percentage of power consumption – typical value
Analog-to-digital converter Error correction decoding Digital signal processing and MAC Baseband front-end RF front-end 27% 24% 24% 10% 8% Local oscillator 7%
2 analog to digital converter, active filters and a frequency
synthesizer.
The total energy consumption E also consist of five main components [6]:
ܧ ൌ ܲ௧ܶ ܲܶ ܲ௧ܶ௧ ܲ௦ܶ௦ ܲௗܶ௧ (1) where Pont and Ponr is the power consumption of the
transmitter and receiver analog circuits respectively in the active mode, Ptr and Psm is the power consumption of the
transmitter in the transient mode and the sleep mode respectively, and Pdc is the power consumed at digital circuits.
Moreover, Ton, Ttr, Tsm and Ttc is the time of being in active,
transient and sleep mode and of using digital processing respectively. The power consumption Psm is dominated by the
leaking current of the switching transistors and this term is often neglected (Psm = 0). The analog circuits power terms can
be described by formula [4]:
ܲ௧ൌ ܲ௧ ܲ ܲ௧ൌ ሺͳ ߞሻܲ௧ ܲ௧ (2) ܲൌ ܲ (3) where Pt is a transmitted power, Pct and Pcr is the power
consumption of analog components and consist of the frequency synthesizer power consumption, the LNA power consumption, the active filter power consumption and the IFA power consumption. Pamp is the PA power consumption, ߞ ൌ
ߦ ߟΤ െ ͳwith ξ and η begin the drain efficiency and the peak-to-average ratio, respectively. The value ξ is equal to ͵൫ξܯ െ ͳ൯Ȁ൫ξܯ ͳ൯ for M-QAM modulation [7].
Because a unified model of power consumption of digital components is not available, in the remainder of this paper, we use analysis for specific systems described in the literature [8]. The power consumption for digital processing is small compared to power consumption for analog circuits e.g. in radio base stations, the power consumption for digital circuits accounts for only about 10% of the total consumed power, however, analog circuits consume about 65% power [7]. In case of simple signal processing techniques (an uncoded system and single-user communication) we can neglect the power consumption of digital signal processing. However, as more complex coding techniques are applied, the related power consumption, specially for decoding at the receiver. cannot be neglected.
III. SYSTEM MODEL AND ENERGY EFFICIENCY We consider a communication link between two wireless nodes and involving wireless frequency-selective Rayleigh-fading channel. The transmitter applies adaptive bit and power loading for the Orthogonal Frequency Division Modulation (OFDM) as well as error-correcting codes (adaptive coded modulation). For the simplicity of considerations, we assume trellis codes or more general coset codes superimposed on top of the adaptive modulation at each subcarrier (see Fig. 1). By using the subset partitioning inherent to coded modulation,
trellis or lattice codes designed for AWGN channels can be superimposed directly onto the adaptive modulation with the same approximate coding gain [4].
Fig. 1. General trellis-coded modulator.
The energy efficiency (EE) can be defined in different perspectives e.g. as the ratio of efficient output of energy to total energy. Another way to define EE is the performance per unit energy consumption. In the digital signal processor the performance is defined to Floating-Point Operations Per Second (FLOPS), Million Instruction Per Second (MIPS) in computer, and bit rate (bit/s) in communications.
We define our EE metric as the ratio of the link throughput to the total consumed power, i.e. as the number of successfully transmitted information bits (satisfying the assumed bit error probability) per unit energy consumption (Joule). In our considerations, we assume perfect knowledge of the Channel State Information (CSI), i.e. instantaneous channel characteristic. Thus, our EE metric is:
ܧܧ ൌோ
(4) where, R is the throughput expressed in bit/s, P is the total consumed power - expressed in Watts. The unit of energy efficiency is bit/s/W or bit/Joule. We consider both, a flat-fading channel and a frequency selective channel. The throughput of the band-limited channel is described by the Shannon-Hartley theorem and the rate in the flat-fading channel is expressed as:
ܴ ൌ ܤݎ݈݃ଶቀͳ ఈுீ
ேబ ቁ (5)
where, H is the channel gain (equal to ߜ݀ିఊ, where d is the TX-RX distance, ߛ is the characteristic value describing the environment, ߜ is a parameter describing radio-frequency front-ends and transmission frequency), G is the coding gain, r is the applied code rate, B is the bandwidth, N0 is the AWGN
power spectral density, α is the parameter dependent on the assumed error probability, ߙ ൌ െͳǤͷȀሺͲǤͷܲሻ for M-QAM modulation. The throughput of the frequency-selective channel is dependent on frequency response. In order to maximize the system throughput we can use water-filling algorithm. In such a case, the rate in frequency-selective channel is described by formula:
ܴ ൌ ȟ݂ݎ σ ଶቀͳ
ఈுሺሻሺሻீሺሻ
ேబ ቁ
ேିଵ
ୀ (6)
where, N is the number of discrete flat-fading channels (or subcarriers in multicarrier modulation), ο݂ is the subchannel bandwidth, D is the dependent on target bit-error probability, ܪሺ݂ሻ is the channel characteristic at frequency ݂ including the path loss: ܪሺ݂ሻ ൌ ߜ݀ିఊܪԢሺ݂ሻ, ܲ୲ሺ݂ሻ - transmit power
3 loaded to frequency ݂, ܩሺ݂ሻ - coding gain at subcarrier
frequency ݂. Specifically, by using the subset partitioning inherent to coded modulation, trellis or lattice codes designed for AWGN channels can be superimposed onto the adaptive modulation with the same approximate coding gain [4]. The basic idea of adaptive coded modulation is to exploit the separability of code and constellation design. Here, for the frequency-selective channel, it can be assumed that each data stream transmitted in subchannel n (defined around frequency fn) is separately encoded with an error-correcting code of the
coding gain ܩሺ݂ሻ. Eventually, for multicarrier modulation it is not usually the case, because the data are encoded across the set of subcarriers in order to correct symbol errors at faded subcarriers. Without further elaboration on this and without loss of generality, for the simplicity of our consideration we assume that the resulting coding gain at each subcarrier is ܩሺ݂ሻ. In such a case, the optimal power loading equals:
ܲ௧ሺ݂ሻ ൌ ቐ ܭ െ ேబ ఈȁுሺሻȁమீሺሻ݂ݎ ேబ ఈȁுሺሻȁమீሺሻ ܭ Ͳݐ݄݁ݎݓ݅ݏ݁ (7)
where K is the so-called water-level, which can be derived from the total power constraint condition:
ܭ ή ܤ ൌ ்ܲ σ
ேబ
ఈȁுሺሻȁమீሺሻ
ேିଵ
ୀ (8) where, ܲ is the total transmit in-band power. An EE metric should include all parameters pertinent to the power consumption for communication. The total consumed power in (4) for a flat-fading channel and a frequency selective channel is expressed as:
ܲ ൌ
Kఉ ܲௗ ܲ ܲ௧ ڮ (9) where K is the antenna energy conversion efficiency, ߚ is the percentage of in-band power (taking HPA nonlinearities into account). P may be dependent on all factors described above in Section II, however for the simplicity, we narrow our considerations to active mode of operation of the transmitter and the receiver.
IV. SIMULATION
The computer simulation was conducted using MATLAB software. The energy efficiency versus the transmit power and the link distance has was examined. The Rayleigh flat-fading channel and a frequency-selective channel was simulated. The coding gain at each subcarrier in case of multicarrier adaptive modulation is assumed to be the same ܩሺ݂ሻ ൌ ܩ. The parameters of the simulated system are shown in Table III. Below, simulation results are presented.
In Fig. 2, energy efficiency versus transmit power is plotted for a communication link connecting two wireless nodes. This actually reflects the dependence of the EE on the link distance. The signal is single-carrier modulated and transmitted over the flat-fading channel with average attenuation is equal to 1. The energy consumption of digital circuits varies for different types of coding, modulation and other digital signal processing. In our considerations we use the parameters found in the literature [8], and convolution coding and decoding of rate r = k/(k+1) (assumed as part of the trellis encoder). The power consumption of digital circuits is expressed as:
ܲௗൌ ܧௗܴ , (10) where Edc is the energy consumption of digital signal
processing per bit, R is a throughput. In Fig. 3 and Fig. 4 the results of EE(PT) are shown for frequency-selective channel
and OFDM system. In Fig. 3, two systems are compared: a system that determines the bit and power loading using water-filling algorithm, and a system with equal power is allocated to each subchannel (OFDM subcarrier). In Fig. 4 coded and uncoded system performances are compared. In Fig. 5, three coded systems are compared: all systems use convolutional code with rate ½ but with different constraint length K=3, 5, 7. Note, that in the presented curves, there always exists an optimum point of operation (transmit power) maximizing the EE of a link. This is visible in particular for shorter distances, in which the digital circuits power consumption related to coding and decoding may be a dominating energy-consumption factor.
TABLEIII SIMULATION PARAMETERS
Parameter Symbol Value
Channel estimation Radio channel Bandwidth [kHz]
Characteristic value describing the environment B γ Ideal Rayleigh 10 3.5
Antenna energy conversion efficiency
Error probability
Percentage of in-band power Channel gain Coding gain [dB] η Pe β H G 0.35 10E-5 100% Rayleigh distribution 1,4.75 TX-RX distance[m] d [1,10]
AWGN power spectral density [dBm]
N0 -60
Transmit in-band power [W] Power consumption of transmitter analog circuit [mW] Power consumption of received analog circuit [mW]
Energy consumption of digital circuit [pJ/bit]
Constelation for flat-fading Number of subchannel PT Pct Pcr Edc M N [0:2] 98 112 1805, 532, 176 16QAM 16
4
Fig. 2. Energy-efficiency vs. the transmit power for flat-fading channel.
Fig. 3. Energy efficiency versus transmitted power for frequency-selective channel, and OFDM system with either water-filling algorithm or same-power for each subchannel.
Fig. 4. Energy efficiency versus transmitted power for frequency-selective channel, a coded OFDM system with water-filling algorithm, convolutional code (R=1/2).
Fig. 5. Energy efficiency versus transmitted power for frequency-selective channel, an OFDM system with water-filling algorithm, convolutional code (r = 1/2, K = 3,5,7).
V. CONCLUSIONS
In this paper, energy efficiency of a wireless link has been analyzed. We considered the flat-fading and the frequency selective channel, as well as coded and uncoded multicarrier modulation for our examined system. It can be observed that coding (Fig. 4) and water-filling (Fig. 3) algorithms improve energy efficiency. In figure 4. we can observe, that with the rise of coding gain improve energy efficiency. Probably, when power consumption of digital signal processing is high, energy efficiency can decrease. Moreover, there exists the optimum point for the total transmit power maximizing the EE. Further research is aimed at the improvement of energy efficiency in a network of nodes and the variety of links.
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