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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION 1

Link Energy Minimization inIR-UWB Based Wireless Networks

Tianqi Wang, Student Member, IEEE, Wendi Heinzelman, Senior Member, IEEE,and Alireza Seyedi, Member, IEEE

Abstract—Impulse Radio Ultra WideBand (IR-UWB) commu-nication has proven to be an important technique for supportinghigh-rate, short-range, and low-power communication. In thispaper, using detailed models of typical IR-UWB transmitterand receiver structures, we model the energy consumption perinformation bit in a single link of an IR-UWB system, consideringpacket overhead, retransmissions, and a Nakagami-m fadingchannel. Using this model, we minimize the energy consumptionper information bit by finding the optimum packet length andthe optimum number of RAKE fingers at the receiver fordifferent transmission distances, using Differential Phase-shiftkeying (DBPSK), Differential Pulse-position Modulation (DPPM)and On-off Keying (OOK), with coherent and non-coherentdetection. Symbol repetition schemes with hard decision (HD)combining and soft decision (SD) combining are also comparedin this paper. Our results show that at very short distances,it is optimum to use large packets, OOK with non-coherentdetection, and HD combining, while at longer distances, it isoptimum to use small packets, DBPSK with coherent detection,and SD combining. The optimum number of RAKE fingers arealso found for given transmission schemes.

Index Terms—Impulse radio ultra wideband, link energyminimization, energy consumption, packetization, ARQ, RAKEreceiver.

I. INTRODUCTION

IMPULSE radio ultra wideband (IR-UWB) communica-tions is regarded as an attractive solution to provide high

bandwidth and low radiated power, especially for short-rangewireless network applications [1]-[4]. Wireless sensor net-works (WSNs) have been used for applications ranging fromenvironmental monitoring and health monitoring to securityand surveillance [5][6]. These different applications for WSNshave vastly different bandwidth requirements. Take, for ex-ample, visual sensor networks (VSNs) for surveillance orhealth monitoring. These networks require a relatively largebandwidth to transmit and receive images or video in a timelymanner, and a low radiated power to avoid interference withcoexisting wireless systems. IR-UWB technology, in this case,has a great potential to facilitate the application of VSNs.

Manuscript received July 14, 2009; revised December 19, 2009 and May2, 2010; accepted June 29, 2010. The associate editor coordinating the reviewof this paper and approving it for publication was P. Popovski.

The authors are with the Department of Electrical and ComputerEngineering, University of Rochester, USA (e-mail: {tiwang, wheinzel,alireza}@ece.rochester.edu).

This work was supported in part by the National Science Foundation undergrant # ECS-0428157 and in part by a Young Investigator grant from theOffice of Naval Research, # N00014-05-1-0626.

Digital Object Identifier 10.1109/TWC.2010.072110.091038

Energy consumption is a very important design considera-tion in any IR-UWB based system. Unlike in traditional com-munications systems, where transmit power can be flexiblyadjusted to minimize the energy consumption [7][8], there isa strict limit on the effective isotropic radiated power (EIRP)in IR-UWB systems due to their overlay nature. Regulationsmandate that the spectrum of the signal be limited to −41.25dBm/MHz [1]. Since the IR-UWB system needs to operate ator near this limit to achieve a reasonable range, the traditionaloptimization techniques, which mainly operate by adjustingthe transmit power, cannot be used for IR-UWB systems.However, there are other parameters of the IR-UWB systemthat can be adjusted, such as the number of RAKE fingers, thepacket length, the modulation scheme, the detection scheme,and the coding or spreading scheme.

In IR-UWB communications, the channel delays are oftenresolvable due to the narrow width of the IR-UWB pulse.Therefore, a RAKE receiver structure can achieve considerablediversity gain [9][10]. Another important utility of the RAKEreceiver structure is that it can increase the collection of thetransmitted power through multiple paths. The diversity gainand collected power will be increased by adding more RAKEfingers (correlator taps), which in turn will increase the powerconsumption of the receiver. Therefore, the tradeoff betweenthe diversity gain as well as the power collection and the powerconsumption at the receiver must be evaluated.

Packet length is another important factor that influences theenergy consumption of a communication link. A long packetwill increase the packet error probability; thereby increasingthe average number of transmissions in an automatic-repeat-request (ARQ) system. On the other hand, a short packet willlower the system efficiency due to the packet overhead. Thus,an optimum packet length should be found to minimize theenergy consumption.

Binary modulation schemes, such as DBPSK, OOK, andDPPM, are usually used in IR-UWB systems due to theirsimplicity and good performance. Among the three mod-ulation schemes considered in this paper (DBPSK, OOK,and DPPM), DBPSK is the most robust, but also the mostenergy consuming. Compared with DBPSK, OOK requiresless energy to transmit each bit, but has a lower performance.The performance of DPPM is between DBPSK and OOK. Thecomparison and evaluation of these modulation schemes areimportant for the design of energy-efficient IR-UWB systems.

In our previous work, we proposed an energy consumptionmodel of an IR-UWB based communication link, and we

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2 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION

compared the energy consumption features of DBPSK/OOKmodulations with coherent/noncoherent detections schemes[11]. Compared with the preliminary work in [11], here wecomprehensively analyze the theoretic energy consumptioncharacteristics of an IR-UWB communication link and providean extensive comparison of practical schemes. Moreover, weuse a more realistic Nakagami-m fading channel model todescribe the wireless channel in an IR-UWB system.

In this paper, we provide detailed power consumptionmodels of a typical IR-UWB transmitter and both coherentand noncoherent receivers. The optimization model considersthese detailed power consumption models as well as thepacket structure and the ARQ procedure. Using this modelwe optimize packet length and the number of RAKE fingersat different transmission distances for DBPSK, OOK, andDPPM, with both coherent (CO) and noncoherent (NC) detec-tion. Moreover, in IR-UWB systems, to increase the effectiveenergy per bit, repetition coding schemes are commonly used.At the receiver, hard decision (HD) based combining or softdecision (SD) based combining may be used. HD combiningprovides relatively low performance but it can be operatedusing a low-power, one bit analog-to-digital converter (ADC).On the other hand, SD combining provides good performancewhile demanding a high-resolution ADC and memory units.The tradeoffs between these combining methods are alsoevaluated in this paper.

The remainder of this paper is organized as follows. SectionII surveys related work. Section III introduces the packetstructure, transceiver power model, and channel model used inthis paper. In Section IV, after deriving a lower bound on theenergy consumption per information bit in IR-UWB systems,we minimize the energy consumption per information bit overpacket length and number of RAKE fingers. Numerical resultsare presented in Section V. Section VI concludes this paper.

II. RELATED WORK

Some related work has been conducted on the improvementof link energy efficiency for battery-powered networks. Cuiet al. studied the energy per information bit minimizationproblem for narrowband systems, considering the dependencyof circuit power consumption due to modulation and codingschemes and the time duration of a packet containing 𝐿information bits for different coding schemes [8]. The authorsproposed detailed power models of a typical narrowband trans-mitter and receiver and clearly pointed out the dependencyof the power consumption on physical layer configurations,such as modulation schemes and coding schemes. They alsoextended their work to energy minimization in cooperativeMIMO based networks, considering increased spectral effi-ciency and circuit power consumptions [12]. However, theeffects of an ARQ scheme or the optimum selection of targetbit error probability were not considered.

In [13], Ammer and Rabaey proposed the energy-per-useful-bit (EPUB) metric to measure the PHY efficiency of wirelessnetworks. The authors conclude that to minimize EPUB, highdata rates, low carrier frequencies, and simple modulationschemes are preferred. The authors also point out that thepacket header plays an important role in evaluating EPUB and

should be fully studied. The authors limited their research tolow order modulations and assumed variable signal bandwidth,which may constrain the application of their results.

Lu et al. find an optimal configuration of source encoder,channel encoder and transmitter for a fixed end-to-end sourcedistortion to minimize the power consumption of a multime-dia communication link over an AWGN channel [14]. Theoptimization parameters in [14] are source coding rates andchannel coding rates.

Besides modulation schemes, coding rates and carrier fre-quencies, the impact of packet size on the performance ofwireless networks has also been investigated and proven to besignificant [15][16]. The investigation of energy minimizationover a frequency-selective channel that requires a more com-plicated receiver structure, such as a RAKE receiver, has notbeen studied in the literature. In this paper, we focus on IR-UWB systems and jointly consider the effects of the repetitioncoding, the modulation scheme, the detection scheme, thecombining scheme, the packet length, and the number ofRAKE fingers.

Among the numerous enabling communication technologiesfor wireless networks, IR-UWB is intriguing due to its low-power high-rate feature. The performance of IR-UWB hasbeen extensively studied [17]-[19]. Some work on the op-timization of IR-UWB systems considering antenna design,synchronization and channel capacity are also present in theliterature [20]-[23]. However, none of these optimizations isaimed at minimizing the energy consumption in IR-UWBsystems. The energy capture effect of a RAKE receiver inIR-UWB systems was first studied by Win et al. in [24]. Theauthors analyze the relationship between the diversity leveland captured energy. Although no power model is assumed in[24], the authors have concluded that there exists a thresholdnumber of RAKE fingers in IR-UWB systems such thatadding more RAKE fingers does not significantly improveperformance. Despite the fact that much research has beenconducted on IR-UWB systems, a detailed study on linkenergy minimization in IR-UWB based networks is lacking.

An effective channel model is critical in evaluating the per-formance of any communication system. Numerous researchefforts have been made towards establishing an effective IR-UWB channel model [25]-[27]. In particular, Molisch et al.proposed comprehensive IR-UWB channel models for bothfrequency ranges from 3− 10 GHz and below 1 GHz in 2006[26]. A single-slope power decay law is adopted to describethe path loss feature of the IR-UWB channel, and Nakagami-distributed amplitude is used to describe the small-scale fadingof the IR-UWB channel [26]. This model has been accepted bythe IEEE 802.15.4a Task Group as a standard model to evaluteUWB systems, and is also used in this paper to evaluate theenergy consumption of different schemes.

III. SYSTEM AND CHANNEL MODELS

We consider an IR-UWB system with a symbol repetitionscheme. The coding rate 𝑅𝑐 = 1/𝑁𝑝, where 𝑁𝑝, which is anodd number, is the coding parameter. Moreover, in order toavoid inter symbol interference (ISI), the maximum pulse rateis limited. Also, perfect knowledge of the channel is assumedat the receiver.


WANG et al.: LINK ENERGY MINIMIZATION IN IR-UWB BASED WIRELESS NETWORKS 3

RX data

BasebandProcessor

Synchronizer and Clock Generator

ADC

LNA

TemplatePulse Generator

Integrator

MixerVGAMRCFinger 1

23

4

PulseGenerator

Clock Generator and SynchronizerBaseband

Processor

TX data Pulse Modulator DA

MultipathChannel

Transmitter

Receiver

ChannelEstimator

Fig. 1. The transmitter and receiver structure in an IR-UWB system.

A. IR-UWB Transceiver Power Consumption Model

A typical IR-UWB transmitter and a typical IR-UWBreceiver with four RAKE fingers and maximal ratio combining(MRC) are shown in Fig. 1. When DBPSK, DPPM, and OOKare used at the transmitter, the power consumption of thetransmitter can be modeled as

𝑃𝑡 = 𝑃SYN + 𝐸𝑝𝑅𝑝, (1)

where 𝐸𝑝 is the fixed energy per pulse and 𝑅𝑝 is thepulse rate. The pulse rate 𝑅𝑝 = 𝜌𝑡𝑅𝑏, where 𝜌𝑡 = 1 forDBPSK and DPPM, 𝜌𝑡 = 0.5 for OOK, and 𝑅𝑏 is the bitrate. We have assumed that an information bit may be 0 or1 with equal probability. Furthermore, 𝑃SYN represents thepower consumption of the transmitter components that areindependent from the data transmission, namely the clockgenerator and synchronizer.

In our model, the power consumption of an IR-UWBtransmitter, as described by equation (1), is grouped into twoparts: the power consumption from the circuit componentsthat are not related to pulse generating (𝑃SYN), and the powerconsumption from the ones that are related to pulse generating(𝐸𝑝𝑅𝑝). That is, 𝐸𝑝𝑅𝑝 includes the power consumptions ofthe pulse generator, pulse modulator and digital amplifier(DA), while 𝑃SYN is simply the power consumption of theclock generator and synchronizer.

As shown in Fig. 1, the power consumption of an IR-UWBreceiver can be modeled as

𝑃𝑟 =𝑀𝑃COR + 𝜌𝑐𝑃ADC + 𝑃LNA + 𝑃VGA

+𝜌𝑟(𝑃GEN + 𝑃SYN + 𝑃EST),(2)

where 𝑃COR, 𝑃ADC, 𝑃LNA, 𝑃VGA, 𝑃GEN, 𝑃SYN, and 𝑃EST respec-tively represent: the power consumptions of one correlatorbranch (mixer and integrator), the analog-to-digital converter(ADC), the low noise amplifier (LNA), the variable gainamplifier (VGA), the pulse generator, the synchronizer, and thechannel estimator. 𝑀 represents the number of RAKE fingersat the receiver. 𝜌𝑟 is determined by the receiver structure.That is, 𝜌𝑟 = 1 for coherent demodulation and 𝜌𝑟 = 0 fornoncoherent demodulation. This is because for a noncoherent

UWB receiver, the pulse generator, clock generator, synchro-nizer, and channel estimator are not necessary. Moreover,𝜌𝑐 = 1 for SD combining and 𝜌𝑐 = 0 for HD combining.For SD combining, a 5-bit ADC is assumed [28], while forHD combining, the power consumption of the ADC (one-bitADC) is assumed to be negligible.

At the receiver, we consider an IR-UWB receiver that isable to choose the coherent or noncoherent demodulation afterthe signal passed through RAKE fingers and MRC. When theIR-UWB receiver uses the coherent detection, the receivedsignal will pass through a matched filter and a template pulseneeds to be generated to configure the matched filter. When theIR-UWB receiver adopts the noncoherent detection, neither amatched filter nor a template pulse is needed. The receivedsignal will be either correlated with the previously receivedsignal, or simply be multiplied by itself (envelop detection).A differential modulation scheme can cooperate with eitherthe coherent detection or noncoherent detection. For example,a DBPSK modulated signal can be noncoherently detected bya correlation with the previously received signal so that onlythe difference between the two signals will be at output ofthe ADC, or each DBPSK modulated signal can be coher-ently detected individually through a matched filter and thedifference between two adjacent bits can be measured in thedigital domain. In general, the coherent detection provides abetter performance than the noncoherent detection in terms ofbit error probability. However, the coherent detection requiresmore circuit components (template pulse generator, synchro-nizer, and etc.) and thereby consumes more power than thenoncoherent detection.

As with the transmitter, we also group the power con-sumption of an IR-UWB receiver into two parts: the powerconsumption of the circuit components that are not related tothe detection schemes (𝑀𝑃COR + 𝜌𝑐𝑃ADC + 𝑃LNA + 𝑃VGA),and the power consumption of the circuit components that arerelated to the detection schemes (𝜌𝑟(𝑃GEN + 𝑃SYN + 𝑃EST)).That is, 𝑀𝑃COR + 𝜌𝑐𝑃ADC + 𝑃LNA + 𝑃VGA represents thepower consumption of 𝑀 correlator branches, the ADC,the LNA, and the VGA. These components need to beactive whether coherent or noncoherent detection is used atthe receiver. However, the pulse generator, the synchronizer,and the channel estimator are only active during coherentdetection, where a template pulse has to be generated tocorrelate with the received pulse and the channel informationis required. During noncoherent detection, the pulse generator,the synchronizer and the channel estimator are not necessarybecause no template pulse is needed and the received signalpulse is only correlated with the previously received pulse.The power consumption of the MRC is not considered, sincea MRC is simply an adder.

B. Packet Structure

The packet structure consists of three components: synchro-nization preamble (SP), PHY-header (PHR), and payload. Weassume that there are 𝐿𝐿 bits in the payload, 𝐿PHR bits inthe PHR, and 𝐿SP symbols in the SP. Correspondingly, thetime durations to deliver the payload, the PHR, and the SPare denoted by 𝑇onL, 𝑇PHR, and 𝑇SP, respectively. The energy



consumption to transmit a packet once is the summation oftwo parts: 𝐸𝑂 , the energy consumed on delivering the SP andPHR, and 𝐸𝐿, the energy consumed on the payload.

We assume that the synchronization preamble has values{-1, 1}. Moreover, the PHR is modulated using DBPSK andalways received coherently. This is to ensure that the PHRis transmitted using the modulation and detection schemeswith the highest performance, since the PHR carries importantinformation. Also for the sake of simplicity, we assumethat the PHR is coded in the same manner as the payload.Therefore, the overhead energy consumption is

𝐸𝑂 = 𝐸(TX)𝑂 + 𝐸(RX)

𝑂

= (𝐿SP + 𝐿PHR/𝑅𝑐)𝐸𝑝 + 𝑃SYN𝑇𝑂 + 𝑃𝑟𝑇𝑂,(3)

where 𝐿SP is the number of SP symbols, 𝐿PHR is the numberof PHR bits, and 𝑇𝑂 = 𝑇SP + 𝑇PHR = (𝐿SP + 𝐿PHR

𝑅𝑐)/𝑅base,

where 𝑅base is the fixed base data rate. In this paper, afrequency selective slow fading channel is assumed. Therefore,the channel estimation block consumes 𝑃EST amount of poweronly during the reception of the overhead.

The energy consumption for the payload can be modeledas

𝐸𝐿 = 𝐸(TX)𝐿 + 𝐸(RX)

𝐿 , (4)

where 𝐸(TX)𝐿 and 𝐸(RX)

𝐿 represent the energy consumption totransmit/receive the payload containing 𝐿𝐿 information bits,respectively. For 𝐸(TX)

𝐿 , we have

𝐸(TX)𝐿 = 𝜌𝑡𝐸𝑝𝐿𝐿/𝑅𝑐 + 𝑃SYN𝑇onL, (5)

where 𝑇onL = 𝐿𝐿/𝑅𝑏𝑅𝑐, is the time duration to transmit thepayload containing 𝐿𝐿 bits, and 𝑅𝑐 is the coding rate.

The energy consumption to receive 𝐿𝐿 information bits isgiven by

𝐸(RX)𝐿 = 𝜌𝑡(𝑀𝑃COR + 𝜌𝑐𝑃ADC + 𝑃LNA + 𝑃VGA)𝑇onL

+𝜌𝑟(𝑃GEN + 𝑃SYN)𝑇onL.(6)

The receiver does not consume power on channel estimationduring the reception of information bits when using either co-herent or noncoherent detection, since the channel informationhas been estimated during the reception of the overhead bits.

C. Channel Model

The channel model consists of a path loss model and afrequency selective fading model. In this paper, we focus ourresearch on the frequency range from 3-10 GHz.

1) Path Loss Model: The UWB path loss model is bothdistance and frequency dependent and can be modeled as [26]

𝐺𝑑 = 𝐺0 − 20(𝜅+ 1) log10(𝑓

𝑓𝑐)− 10𝑛 log10 𝑑− 3, (7)

where 𝑑 is the transmission distance, 𝐺0 is the path gain at thereference distance (𝑑 = 1 m), 𝑛 is the path loss exponent, 𝑓is the UWB transmission center frequency, 𝑓𝑐 is the referencefrequency, and 𝜅 is the frequency dependency decaying factor.Both 𝐺𝑑 and 𝐺0 are expressed in dB.

2) Frequency Selective Fading: In an IR-UWB system, thetransmitted signal inevitably encounters frequency selectivefading. The baseband channel impulse response of a frequencyselective fading channel in UWB systems consists of clustersand rays and can be represented as [26]

𝑐(𝑡) =𝐿∑𝑙=0

𝐾∑𝑘=0

𝛼𝑘,𝑙𝑒−𝜃𝑘,𝑙𝛿[𝑡− 𝑇𝑙 − 𝜏𝑘,𝑙], (8)

where 𝜃𝑘,𝑙 follows a uniform distribution (over [0, 2𝜋]) and𝛼𝑘,𝑙 is the amplitude gain of the kth ray in the lth cluster. 𝐿and 𝐾 represent the number of clusters and rays, respectively.𝑇𝑙 is the arrival time of the lth cluster, and 𝜏𝑘,𝑙 is the arrivaltime of the kth ray in the lth cluster. 𝑇𝑙 and 𝜏𝑘,𝑙 followthe following independent interarrival exponential probabilitydensity functions, the details of which can be found in [26].

The average power gain of the kth ray in the lth cluster ismodeled as

E[𝛼2𝑘,𝑙] = E[𝛼2

0,0]𝑒−𝑇𝑙/Γ𝑒−𝜏𝑘,𝑙/𝛾 , (9)

where Γ and 𝛾 are power-delay time constraints for the clustersand rays, respectively. E[𝛼2

0,0] is the average power gain ofthe first ray of the first cluster, which is expressed as

E[𝛼20,0] =

𝐺𝑑

𝛾𝜆. (10)

The parameter 𝛼𝑘,𝑙 follows a Nakagami distribution de-scribed as

𝑝(𝛼𝑘,𝑙) =2

Γ(𝑚)

(𝑚

E[𝛼2𝑘,𝑙]

)𝑚

𝛼2𝑚−1𝑘,𝑙 𝑒

− 𝑚𝛼2𝑘,𝑙

E[𝛼2𝑘,𝑙

] , (11)

where 𝑚 > 0.5 is the Nakagami m-factor and Γ(𝑚) is thegamma function.

IV. LINK ENERGY MINIMIZATION

A. Lower Bound on Average Energy Consumption per Infor-mation Bit

1) Lower bound based on channel capacity: The transmitpower is strictly limited in IR-UWB systems to avoid interfer-ing with pre-existing communication systems. In the followinganalysis, we assume the transmit power is a constant denotedby 𝑃tx. Considering the power consumption at the transmitterand receiver and the channel capacity, the lower bound ofenergy consumption per information bit is modeled as

𝐸𝑏 ≥ 𝑃𝑡+𝑃𝑟

𝐵 log(1+∑𝑀

𝑖=1∣𝛼𝑖∣2𝑃tx

𝐺𝑑𝜎2 ),

=𝑃SYN+𝐸𝑝𝑅𝑝+𝑀𝑃COR+𝑃CNST

𝐵 log(1+∑𝑀

𝑖=1∣𝛼𝑖∣2𝑃tx

𝐺𝑑𝜎2 ),

(12)

where 𝑃CNST = 𝜌𝑐𝑃ADC + 𝑃LNA + 𝑃VGA + 𝜌𝑟(𝑃GEN + 𝑃SYN)represents the receiver power consumption that is independentof the number of RAKE fingers, and ∣𝛼𝑖∣2 represents theaverage power gain of the ith selected path. Note that thepower consumption of the channel estimator is not considered,since the channel estimator is not involved in the actual datacommunication. We assume that the positioning of the RAKEfingers is ideal and therefore ∣𝛼𝑖∣2 are the largest 𝑀 valuesof E[∣𝛼𝑘,𝑙∣2] from (9). 𝑀 is the number of RAKE fingers,and 𝐵 is the signal bandwidth. Correspondingly, 𝐵 log(1 +∑𝑀

𝑖=1 ∣𝛼𝑖∣2𝑃tx/𝐺𝑑𝜎2) represents the channel capacity [29].



Equation (12) can be minimized through proper selectionof the number of RAKE fingers, 𝑀 . As transmission distanceincreases, the optimum number of RAKE fingers increasesand eventually converges to a certain value. In other words,when received SNR approaches zero, there exists an opti-mum number of RAKE fingers that minimizes the energyconsumption in IR-UWB systems. This optimum number isonly a function of the power delay profile of the channeland the power consumption values of the components of thetransceiver.

Removing the integer constraint on 𝑀 , we can determinethis convergence by finding the discrete derivative of the righthand side of (12) with respect to 𝑀 and setting the resultingequation to zero, i.e.,

(log2 𝑒)∑𝑀∗

𝑖=1 ∣𝛼𝑖∣2∣𝛼𝑀∗ ∣2 (1 +

∑𝑀∗𝑖=1 ∣𝛼𝑖∣2𝑃tx

𝐺𝑑𝜎2 )

=𝑃CNST+𝑃SYN+𝑅𝑝𝜌𝑡𝐸𝑝

𝑃COR+𝑀∗,

(13)

where 𝑒 is the natural number. As distance increases,𝑀∗ will eventually converge to a particular value as∑𝑀∗

𝑖=1 ∣𝛼𝑖∣2𝑃tx/𝐺𝑑𝜎2 → 0. The convergence value of 𝑀∗ ,

which is denoted by 𝑀∗CONV, can be found from:

(log2 𝑒)∑𝑀∗

CONV𝑖=1 ∣𝛼𝑖∣2∣𝛼𝑀∗

CONV∣2 − 𝑃CNST+𝑃SYN+𝑅𝑝𝜌𝑡𝐸𝑝

𝑃COR=𝑀∗

CONV.

(14)In general, there is no closed form solution for (14), since thedistribution of ∣𝛼𝑖∣2 directly determines the solvability of thisequation and 𝑀 has to be chosen in the positive discrete do-main. For the doubly exponential decay of E[∣𝛼𝑘,𝑙∣2], 𝑀∗

CONVexists and can always be easily found through an exhaustivesearch.

2) Lower bound based on data rate: During the modelingin (12), the data rate is bounded by the channel capacity, whichimplies a linear channel (such as an AWGN channel), infinitelylong codewords, and arbitrarily low bit error rates (i.e., noretransmissions). Most of the above assumptions do not hold inpractical communication systems. Thus, the practical data rateis usually much lower than the channel capacity. The lowerbound from (12) is, therefore, a very loose lower bound. Inthe following analysis, instead of using channel capacity, wederive the lower bound energy consumption per informationbit by using achievable data rates. In particular, the data rateneeds to consider the penalty caused by retransmission andpacketization.

In this paper, we only consider binary modulation schemes.Also, to avoid ISI, the maximum pulse rate is limited by themaximum excess delay of the multipath channel, 𝐷𝑠. That is,the maximum pulse rate is 1/𝐷𝑠. In addition, considering theimpacts of packetization, retransmission and overheads, thelower bound of the energy consumption per information bitcan be further tightened as

𝐸𝑏 ≥(𝑃𝑟+𝑃SYN+𝜌𝑡𝐸𝑝𝑅𝑝

1/𝐷𝑠

)𝑁 𝑇on+2𝑇IPS+𝑇ACK

𝑇onL, (15)

where 𝑁 is the total number of transmissions. (𝑇on +2𝑇IPS +𝑇ACK)/𝑇onL denotes the rate penalty caused by packetization,where 𝑇IPS denotes inter packet space and 𝑇ACK representsthe time duration the transmitter listens for acknowledgementfrom the receiver. The detailed formulas of 𝑇IPS and 𝑇ACK

(m-1)

(RX)trE

trT onT IPST ACKT onT ACKT trT

LNE(RX)ACKE

trT onT ACKT onT ACKT trT

0

IPST IPST IPST

IPST IPST IPST IPST(RX)IPSE

(TX)trE

(TX)IPSE(TX)

LE

(RX)LE

(TX)IPSE

(RX)IPSE

(TX)LE

(RX)LE

(TX)IPSE (TX)

IPSE (TX)trE

(TX)ACKE (RX)

trE(RX)IPSE (RX)

IPSE

Fig. 2. The transmission and reception of one packet using 𝑁 totaltransmissions.

can be found in the following section. The above parametersare determined by the detailed packet structure, channel condi-tions, and modulation schemes. Although (15) implies an idealwideband channel with no multipath and omits the possibleenergy losses due to circuit start-up, this model tightens thebound from (12) and better represents practical scenarios sinceboth 𝑁 and (𝑇on+2𝑇IPS+𝑇ACK)/𝑇onL are greater than or equalto 1.

B. Practical Average Energy Consumption Per InformationBit

Although (15) provides a lower bound on the energyconsumption per information bit, it does not consider manypractical issues. For example, it does not consider the energyspent on the packet overhead and listening. In practice, weneed to consider the detailed procedure of transmitting onepacket instead of one bit [7].

1) Energy Consumption per Packet with Retransmissions:To guarantee the successful reception of one packet, anautomatic repeat request (ARQ) protocol is used. A deliveryprocedure involving 𝑁 − 1 retransmissions is shown in Fig.2. The inter packet space (IPS) is denoted by 𝑇IPS. The powerconsumption during 𝑇IPS is mainly due to the clock generatorand synchronizer. Therefore, the corresponding energy con-sumption at the transmitter is 𝐸(TX)

IPS = 𝑃SYN𝑇IPS, while thereceiver consumes 𝐸(RX)

IPS = 𝜌𝑟𝑃SYN𝑇IPS.We assume that before transmission or reception of a packet,

the transmitter and receiver spend 𝑇tr amount of time to gofrom the off (sleep) state to an on (active) state. We refer to thistime duration as the “transient session”. During the transientsession, the transmitter consumes 𝐸(TX)

tr = 𝑃SYN𝑇tr amount ofenergy to start the front end clock generator and synchronizer.Similarly, the receiver consumes 𝐸(RX)

tr = 𝜌𝑟𝑃SYN𝑇tr.𝑇on is the time duration for the transmission of one packet.

That is

𝑇on = 𝑇SP + 𝑇PHR + 𝑇onL,

= (𝐿SP +𝐿PHR𝑅𝑐

)/𝑅base +𝐿𝐿

𝑅𝑏𝑅𝑐.

(16)

The energy consumptions at the transmitter and receiverduring 𝑇on are

𝐸(TX) = 𝐸(TX)𝐿 + 𝐸(TX)

𝑂 ,

𝐸(RX) = 𝐸(RX)𝐿 + 𝐸(RX)

𝑂 .(17)

where 𝐸(TX)𝐿 , 𝐸(TX)

𝑂 , 𝐸(RX)𝐿 and 𝐸(RX)

𝑂 are given in (3), (4), (5)and (6), respectively.



𝑇ACK is the time period when the transmitter listens for anacknowledgement. We set 𝑇ACK = 𝑇𝑂. Overall, the defini-tions of the energy consumptions within one transmission aresummarized as follows

𝐸IPS = 2𝐸(TX)IPS + 2𝐸(RX)

IPS ,𝐸LN = 𝜌𝑟𝑃SYN𝑇ACK,

𝐸TRAN = 2𝐸(TX)tr + 2𝐸(RX)

tr ,

𝐸(RX)ACK = 𝑃𝑟𝑇ACK,

𝐸(TX)ACK = (𝐿SP + 𝐿PHR/𝑅𝑐)𝐸𝑝 + 𝑃SYN𝑇ACK,

𝐸(TX) = 𝐸(TX)𝐿 + 𝐸(TX)

𝑂 ,

𝐸(RX) = 𝐸(RX)𝐿 + 𝐸(RX)

𝑂 ,

(18)

where 𝐸IPS is the total energy consumed by the receiver andthe transmitter in IPSs within one transmission. 𝐸TRAN is thetotal energy consumption of the receiver and the transmitterduring the transient sessions. In both IPSs and transientsessions, only the frequency synthesizers consume energy.𝐸LN denotes the energy consumption of the transmitter

on listening to the media for the ACK from the receiver inthe first 𝑁 − 1 unsuccessful transmissions. Therefore, 𝐸LN

is the energy consumption of idle listening during 𝑇ACK.𝐸(RX)

ACK, 𝐸(TX)ACK are the energy consumption of the transmitter

for receiving the ACK and the energy consumption of thereceiver for transmitting the ACK. In this paper, we assume theACK message is simply a packet containing only the PHR andthe SP. Since the PHR and the SP always consist of {−1, 1}symbols and only coherent detection with SD combining isused, 𝐸(RX)

ACK and 𝐸(TX)ACK are constant for a given repetition

coding scheme.The decomposition of the energy consumption during each

packet transmission session has been shown in Section IV-B1.Therefore, the average energy consumption for successfuldelivery of a packet can be expressed as

𝐸 = (𝐸(TX) + 𝐸(RX) + 𝐸LN + 𝐸IPS)𝑁

−𝐸LN + 𝐸TRAN + 𝐸(TX)ACK + 𝐸(RX)

ACK ,(19)

where 𝑁 is the average number of transmissions/receptions re-quired to successfully deliver one packet. The average numberof transmissions 𝑁 = 1/(1−𝑃𝑏)𝐿𝐿 , where 𝑃𝑏 is the averageBEP. Note that (1 − 𝑃𝑏)

𝐿𝐿 is the probability that a packetis received correctly. As shown in the following subsection,the average BEP 𝑃𝑏 is closely related to the modulation type,detection schemes, repetition coding/combing schemes, andnumber of Rake fingers.

2) Average BEP over Independent Nakagami Fading Chan-nels: The average BEP can be obtained utilizing the charac-teristic function of the pdf of the output SNR after the MRC[30][31][32]. The instantaneous SNR at the ith finger is

𝛾𝑖 =∣𝛼𝑖∣2𝑃tx

𝐺𝑑𝜎2, (20)

where 𝑃tx is the transmit power, 𝐺𝑑 denotes the path lossat distance 𝑑, and 𝜎2 represents the noise power at thereceiver. Also, 𝛼𝑖 represents the attenuation of the selectedpath preserving the ith largest power. The instantaneous SNRat the output of the MRC is 𝛾 =

∑𝑀𝑖=1 𝛾𝑖.

The average bit error probability of DBPSK-CO can befound by averaging the BEP of DBPSK-CO over an AWGNchannel, with the pdf of 𝛾 which is indicated by 𝑝(𝛾). By

using an alternate representation of the Q-function, we havethe BEP of DBPSK-CO over an AWGN channel as [33][34]

𝑃𝑏,DBPSK-CO,AWGN ≈ 2𝑄(√2𝛾)[1−𝑄(√2𝛾)].

≈ 2𝑄(√2𝛾),

= 2𝜋

∫ 𝜋2

0 𝑒− 2𝛾

sin2 𝜙 𝑑𝜙.(21)

The average BEP can be expressed as

𝑃𝑏,DBPSK-CO =∫∞0𝑃𝑏,DBPSK-CO,AWGN𝑝(𝛾)𝑑𝛾,

=∫∞0

{2𝜋

∫ 𝜋2

0𝑒− 2𝛾

sin2 𝜙 𝑑𝜙}𝑝(𝛾)𝑑𝛾,

= 2𝜋

∫ 𝜋2

0

{∫∞0𝑒− 2𝛾

sin2 𝜙 𝑝(𝛾)𝑑𝛾}𝑑𝜙,

= 2𝜋

∫ 𝜋2

0

{∫∞0 𝑒

− 2𝛾

sin2 𝜙 𝑝(𝛾)𝑑𝛾}𝑑𝜙.

(22)On the other hand, the moment generating function (MGF)

of the pdf of 𝛾 is defined as Ψ𝛾(𝜈) =∫∞0𝑒𝜈𝛾𝑝(𝛾)𝑑𝛾.

Therefore,

𝑃𝑏,DBPSK-CO =2

𝜋

∫ 𝜋2

0

Ψ𝛾(𝜈)∣𝜈=− 2sin2 𝜙

𝑑𝜙. (23)

Since 𝛼𝑘,𝑙 follows a Nakagami-m distribution from thechannel model, the MGF of the pdf of 𝛾 has been establishedas [30]

Ψ𝛾(𝜈) =

𝑀∏𝑖=1

1

(1− 𝜈𝛾𝑖/𝑚𝑖)𝑚𝑖

(24)

where 𝛾𝑖 = E[∣𝛼𝑖∣2]𝑃tx𝐺𝑐/𝐺𝑑𝜎2 is the average received SNR

at the ith finger. E[∣𝛼𝑖∣2] represents the average power ofthe ith selected path, that is E[∣𝛼𝑖∣2] = E[∣𝛼𝑘,𝑙∣2], where∣𝛼𝑘,𝑙∣2 has the ith largest expectation among all paths. 𝑚𝑖 isthe Nakagami m-factor for the ith selected path. As shownin [26], for the first ray of each cluster, 𝑚𝑖 is assumedto be deterministic and independent of delay; while for theremaining paths, 𝑚𝑖 follows a delay-dependence lognormaldistribution.

Moreover, if we consider repetition coding with parameter𝑁𝑝 and SD combining, the average SNR will increase 𝑁𝑝

times compared with the corresponding uncoded modulations.That is, the eventual average BEP for DBPSK with coherentdetection and SD combining (DBPSK-CO-SD) is

𝑃𝑏,DBPSK-CO-SD = 2𝜋

∫ 𝜋2

0 Ψ𝛾(𝜈)∣𝜈=− 2𝑁𝑝

sin2 𝜙

𝑑𝜙. (25)

Instead, if HD combining is used, the average BEP forDBPSK with coherent detection and HD combining (DBPSK-CO-HD) 𝑃𝑏,DBPSK-CO-HD can be expressed ass

𝑃𝑏,DBPSK-CO-HD

=𝑁𝑝∑

𝑘=𝑁𝑝+1

2

(𝑁𝑝

𝑘

)𝑃 𝑘

𝑏,DBPSK-CO(1− 𝑃𝑏,DBPSK-CO)𝑁𝑝−𝑘,

(26)where 𝑃𝑏,DBPSK-CO is given in (22). A similar procedurecan be directly applied to OOK with coherent detectionand DPPM with coherent detection, using either HD or SDcombining.

In the case of DBPSK-NC, the average bit error probabilityof DBPSK-CO can be found by directly utilizing the MGF of



the pdf of 𝛾. First, we have the BEP of DBPSK-NC over anAWGN channel as [34]

𝑃𝑏,DBPSK-NC,AWGN ≈ 12𝑒

−𝛾 (27)

The average BEP can then be expressed as

𝑃𝑏,DBPSK-NC =∫∞0𝑃𝑏,DBPSK-NC,AWGN𝑝(𝛾)𝑑𝛾,

=∫∞0

12𝑒

−𝛾𝑝(𝛾)𝑑𝛾,= 1

2Ψ𝛾(𝜈)∣𝜈=−1,

= 12

𝑀∏𝑖=1

1(1+𝛾𝑖/𝑚𝑖)

𝑚𝑖

(28)Correspondingly, we have

𝑃𝑏,DBPSK-NC-SD =1

2

𝑀∏𝑖=1

1

(1 +𝑁𝑝𝛾𝑖/𝑚𝑖)𝑚𝑖, (29)

and

𝑃𝑏,DBPSK-NC-HD

=𝑁𝑝∑

𝑘=𝑁𝑝+1

2

(𝑁𝑝

𝑘

)𝑃 𝑘

𝑏,DBPSK-NC(1− 𝑃𝑏,DBPSK-NC)𝑁𝑝−𝑘.

(30)The average bit error probabilities of DPPM and OOK withnon-coherent detection, using either HD or SD combing, canbe obtained following a similar procedure. Moreover, to avoidexcessive requirements of memory units, only HD combiningis considered for noncoherent detections.

3) Energy per Information Bit Minimization: From (19),the energy consumption per information bit is

𝐸𝑏 = (𝐸(TX)+𝐸(RX)+𝐸LN+𝐸IPS)

𝐿𝐿(1−𝑃𝑏)𝐿𝐿

+𝐸TRAN+𝐸

(TX)𝐴𝐶𝐾+𝐸(RX)

ACK−𝐸LN

𝐿𝐿.

(31)

Our goal is to find an optimum combination of the modulationscheme, the detection scheme, the repetition coding parameter𝑁𝑝, the combining scheme, the packet length, 𝐿𝐿, and thenumber of RAKE fingers at the receiver, 𝑀 , over a slowfrequency-selective channel for a given transmission distance,that minimizes the effective energy consumption per informa-tion bit denoted by (31). Removing the integer constraint on𝐿𝐿, it is straight forward to find the closed form optimumpacket length by solving ∂𝐸𝑏/∂𝐿𝐿 = 0. At high SNR, theresult is

𝐿∗𝐿 ≈ −𝑃𝑏(𝐴+𝐵)+

√𝑃 2

𝑏(𝐴+𝐵)2+4(𝐴+𝐵)𝐶𝑃𝑏

2𝐶𝑃𝑏, (32)

where

𝐴 = 𝐸TRAN + 𝐸(TX)𝐴𝐶𝐾 + 𝐸(RX)

ACK − 𝐸LN,

𝐵 = 𝐸IPS + 𝐸LN + 𝐸(TX)𝑂 + 𝐸(RX)

𝑂 + 𝐸(RX)𝐿 ,

𝐶 = (𝜌𝑡𝐸𝑝 + 𝑃SYN/𝑅𝑏)/𝑅𝑐+[𝜌𝑡(𝑀𝑃COR + 𝜌𝑐𝑃ADC + 𝑃LNA + 𝑃VGA)+𝜌𝑟(𝑃GEN + 𝑃SYN)]/(𝑅𝑏𝑅𝑐).

As indicated by (32), 𝐿∗𝐿 will decrease as BEP increases. In

a real application of this model, the packet length can alwaysbe selected as the nearest integer of the resulting 𝐿∗

𝐿.In this paper, we have assumed that the data rate is

fixed at the maximum allowable data rate that avoids ISI.Correspondingly, the transmit power, as shown in (1), is also

fixed. Therefore, the average BEP at a given transmissiondistance for a given modulation scheme is only determined bythe modulation and detection schemes, repetition coding andcombining schemes, and the number of RAKE fingers at thereceiver. For a given combination of the modulation/detectionscheme and the repetition coding/combining scheme, the BEPfollows a non-increasing function of the number of RAKEfingers. Thus, 𝐿∗

𝐿 follows a non-decreasing function of thenumber of RAKE fingers.

The optimum number of RAKE fingers reflects the tradeoffbetween the power consumption cost,𝑀𝑃COR and the receivedpower gain, E[∣𝛼𝑖∣2]𝑃tx/𝐺𝑑. The optimum selection of mod-ulation/detection schemes and repetition coding/combiningschemes reflects the tradeoff between the performance andthe power consumption at the transceiver, since higher perfor-mance is often accompanied by higher power consumption.Unlike the optimum packet length, there are no closed formexpressions for the optimum modulation/detection schemes,repetition coding/combining schemes and number of RAKEfingers. However, numerical optimizations can be performedover these parameters, and the optimization results will begiven in the following section.

V. NUMERICAL RESULTS

In this section, we demonstrate the results of minimizingthe effective energy consumption per information bit modeledby equation (31). We assume that 𝐵 = 500 MHz, 𝐿SP = 1024symbols, 𝐿PHR = 16 symbols [1], coding rate 𝑅𝑐 = 1/𝑁𝑝, and𝑁𝑝 = 1, 3, 5, ..., 15. The maximum excess delay is 𝐷𝑆 = 40ns, which limits the maximum pulse rate to 𝑅𝑝 ≈ 1/𝐷𝑠 = 25Mbps to avoid inter symbol interference. The power con-sumptions of the transmitter and receiver components areas follows [28],[35]-[38]: 𝑃SYN = 30.6 mW, 𝑃ADC = 2.2mW, 𝑃GEN = 2.8 mW, 𝑃VGA = 22 mW, 𝑃LNA = 9.4 mW,𝑃COR = 10.08 mW. To the best of our knowledge, there isno existing literature providing specific power consumptionevaluations of the channel estimation block in an IR-UWBreceiver. Therefore, in this paper we assume the IR-UWBreceiver uses the data-aided estimation method from [39],which can essentially be implemented as a correlator. Thus,we assume 𝑃EST = 𝑃COR = 10.08 mW.

The fixed emitted energy per pulse is 𝐸𝑝 = 4.5 pJ/pulse.Therefore, the maximum amount of transmit power is 𝑃tx =𝐸𝑝𝑅𝑝 = 0.113 mW. Also, we assume 𝑇IPS = 200 𝜇s and𝑇tr = 400 𝜇s. Moreover, 𝑅base = 1 Mbps, where 𝑅base denotesthe data rate to transmit the header and preamble symbols, andthe path loss parameter is set to 𝐿𝑤 = 0.7 dB/m.

The parameters of the channel model for an office envi-ronment with no line of sight (NLOS) are used [26]. That is,the path loss exponent 𝑛 = 3.07, the frequency dependencydecaying factor 𝜅 = 0.71, reference path gain 𝐺0 = −59.9dB, transmission center frequency 𝑓 = 3.1 GHz, the referencefrequency 𝑓𝑐 = 5 GHz. The distance range of interest is𝑑 ∈ [3, 27] meters. We used exhaustive search to solve theoptimization model. The quality of service (QoS) is assumedto be error free. That is, the expected number of total trans-missions is 1/(1− 𝑃𝑏)𝐿𝐿 .



3 5 7 9 11 13 15 17 19 21 23 25 27

10−10

10−8

10−6

10−4

10−2

100

Pb*

d (meters)

DPPM−CO−HD DPPM−NC−HD DPPM−CO−SD DBPSK−CO−HD DBPSK−NC−HD DBPSK−CO−SD OOK−CO−HD OOK−NC−HD OOK−CO−SD

Fig. 3. The optimum target BEP versus distance (𝑁𝑝 = 3).

3 5 7 9 11 13 15 17 19 21 23 25 2710

0

101

102

103

104

105

106

107

108

L L* (in

bits

)

d (meters)


Fig. 4. The optimum packet length versus distance (𝑁𝑝 = 3).

A. Optimization with Fixed 𝑁𝑝

To better understand the influence of the packetlength, the number of RAKE fingers, and the modula-tion/combining/detection schemes, first, we consider a fixed𝑁𝑝 = 3 to isolate the impact of repetition coding from therest of the parameters.

The optimum BEPs and optimum packet lengths of differentmodulation/combining/detection schemes with 𝑁𝑝 = 3 areshown in Figs. 3 and 4, respectively. As shown in Fig. 3,as the transmission distance increases, the optimum BEP willincrease since it will require increasingly more power at thereceiver to maintain a low BEP as 𝑑 increases. Therefore, theoptimum choice is to lower the target BEPs to avoid a dramaticincrease in the number of RAKE fingers. Correspondingly, asshown in Fig. 4, the optimum packet length will decrease as𝑑 increases to avoid costly retransmissions caused by higherBEP, since a short packet length results in a lower packet errorprobability.

Note that, at short transmission distances, there are highvariations of 𝑃 ∗

𝑏 and 𝐿∗𝐿. This is because at short distances

3 5 7 9 11 13 15 17 19 21 23 25 270

5

10

15

20

25

Opt

imal

num

ber

of R

ake

finge

rs

d (meters)

DPPM−CO−HD DPPM−NC−HD DPPM−CO−SD DBPSK−CO−HD DBPSK−NC−HD DBPSK−CO−SD OOK−CO−HD OOK−NC−HD OOK−CO−SDFrom (12)

Fig. 5. The optimum number of RAKE fingers versus distance (𝑁𝑝 = 3).

where 𝑃 ∗𝑏 is very low, 𝑃 ∗

𝑏 is very sensitive to a change inthe number of RAKE fingers. That is, at short distances,additional RAKE fingers will provide a considerable amountof collected power gain. Correspondingly, 𝐿∗

𝐿 will changesignificantly as the number of RAKE fingers changes at shortdistances. On the other hand, at large distances, additionalRAKE fingers only provide a small amount of collected powergain. Therefore, 𝑃 ∗

𝑏 and 𝐿∗𝐿 are not sensitive to a change in the

number of RAKE fingers. The curves of 𝑃 ∗𝑏 and 𝐿∗

𝐿 therebybecome smooth as distances increase.

Fig. 5 shows the optimum number of RAKE fingers atthe receiver versus distance. As the transmission distanceincreases, the optimum number of RAKE fingers will increaseand converge to a certain value. This is due to the change ofbalance between the diversity gain and the power cost inducedby each additional RAKE finger. The absolute value of theincrease in collected energy by an additional RAKE fingerdecreases with distance. This diminishing gain incurs a fixedcost, namely 𝑃COR. Consequently, as distance increases, toavoid excessive retransmissions, the number of RAKE fingersshould increase to collect more received power. However,when distance increases beyond a certain level, path lossbecomes very large, and increasing the number of RAKEfingers does not lead to the collection of considerably morereceived power. However, more RAKE fingers will incur morepower consumption at the receiver. Thus, at large transmissiondistances, increasing the number of RAKE fingers does notimprove the energy efficiency. The optimum receiver powerconsumptions of different modulation schemes at differenttransmission distances follow the trend of the optimum num-ber of RAKE fingers shown in Fig. 5. The optimum num-ber of RAKE fingers from (12) is also shown in Fig. 5.Since (12) does not include the imperfection of repetitioncoding/modulation and the overhead caused by packetizationand retransmissions, the received power that is collected by theRAKE fingers at the receiver reaches the theoretical maximumefficiency (no waste on overhead).

The overall minimized energy consumption per information



3 5 7 9 11 13 15 17 19 21 23 25 27−80

−70

−60

−50

−40

−30

−20

−10

0

10

20

Eb* (d

Bm

J)

d (meters)

DPPM−CO−HD DPPM−NC−HD DPPM−CO−SD DBPSK−CO−HD DBPSK−NC−HD DBPSK−CO−SD OOK−CO−HD OOK−NC−HD OOK−CO−SDLower bound by (12)Lower bound by (15)

Fig. 6. The minimum energy consumption per information bit versus distance(𝑁𝑝 = 3).

3 5 7 9 11 13 15 17 19 21 23 25 27−52

−50

−48

−46

−44

−42

−40

−38

−36

−34

Eb* (d

Bm

J)

d (meters)


Fig. 7. The overall minimum energy consumption per information bit andcorresponding modulation/decoding/detection schemes (𝑁𝑝 = 3).

bit is shown in Fig. 6. OOK-NC-HD consumes the leastamount of energy when 𝑑 < 6m, while DBPSK-NC-HD offersthe lowest energy consumption per information bit when 6m ≤𝑑 < 11m. DBPSK-CO-HD is the most energy efficient schemewhen 11m ≤ 𝑑 < 16m. DBPSK-CO-SD is the most energyefficient scheme when the distance is greater than 16 meters.This trend reflects the balance between the transmitter energyconsumption and the receiver energy consumption. At a shorttransmission distance, the less robust schemes (OOK-NC-HD)require less power consumption at the transmitter/receiver andprovide a BEP low enough to avoid excessive retransmissions.Therefore, the OOK scheme, noncoherent detection, and HDcombining have a high energy efficiency at short transmissiondistances. However, as transmission distance increases, theabove schemes require a large number of RAKE fingers tomaintain a low BEP, thereby the receiver power consumptionwill increase dramatically if using schemes like OOK-NC-HD.On the other hand, the more robust schemes (such as DBPSK-CO-HD, DBPSK-CO-SD) consume much less power at the

3 7 12 17 22 27−55

−50

−45

−40

−35

−30

−25

−20

−15

d (meters)

Eb* (

dBm

J)

NP = 1

NP = 3

NP = 5

NP = 7

NP = 9

NP = 11

NP = 13

NP = 15

Fig. 8. The overall minimum energy consumption per information bitfor different repetition coding parameters with optimized 𝐿𝐿, 𝑀 , andmodulation/repetition coding/detection schemes.

3 7 12 17 22 270

5

10

15

20

25

d (meters)

M*

3 7 12 17 22 2710

0

105

1010

d (meters)

L L*

Np = 1

Np = 3

Np = 5

Np = 7

Np = 9

Np = 11

Np = 13

Np = 15

Fig. 9. The 𝑀∗ and 𝐿∗𝐿 with optimized modulation/combining/detection

schemes for different 𝑁𝑝.

receiver since they need fewer RAKE fingers to achieve a lowBEP. Thus, as transmission distance increases, these schemeswill become the energy efficient schemes. The lower boundon 𝐸𝑏 from (12) and the packetized lower bound on 𝐸𝑏 from(15) are also shown in Fig. 6. The packetized bound from(15) is larger than (12), especially for large distances. This iscaused by the decrease of 𝐿∗

𝐿 as distance increases, as shownin Fig. 4, which in turn increases the packetization overhead.

The overall minimum 𝐸𝑏 and corresponding modulation,repetition coding and detection schemes are shown in Fig. 7.This figure, together with Fig. 5, reveals that, at short distances(high SNRs), low complexity and low performance mod-ulation/repetition coding/detection schemes, such as OOK-NC-HD with a small number of RAKE fingers, are energyefficient; while at large distances (low SNRs), higher com-plexity and higher performance modulation/repetition cod-ing/detection schemes, such as DBPSK-CO-SD with a largenumber of RAKE fingers, become energy efficient.



TABLE IOVERALL OPTIMUM CONFIGURATIONS

Distance (m) Modulation Detection 𝑁𝑝 Combining 𝑀∗ 𝐿∗𝐿 (Kbit)

3 7

4OOK

10

5 NC 66 7

7 8∼ 1500

8 7

9 1HD

8

10 10

11 11

12 14

13 16

14 DBPSK 21

15 23

16 12

17 14∼ 500

18CO

16

19 3 18

20 21

21 23

22 SD 1623 5 17

24 19 ∼ 50

25 16

26 7 17

27 19

B. Optimization with Variable 𝑁𝑝

Besides the optimization on packet length, number ofRAKE fingers and modulation/combining/ detection schemes,the repetition coding parameter𝑁𝑝 in repetition coding shouldalso be adjusted to minimize 𝐸𝑏. Now we assume that 𝑁𝑝

takes the values 1, 3, 5, ..., 15.Fig. 8 shows the overall minimum energy consumption

per information bit for different repetition coding parameters.To show the influence of 𝑁𝑝, the 𝐸∗

𝑏 shown in Fig. 8have been optimized over 𝐿𝐿, 𝑀 and modulation/repetitioncoding/detection schemes. Fig. 8 shows that the optimum 𝑁𝑝

increases as 𝑑 increases (SNR decreases). This observationfurther confirms that, to guarantee link level reliable commu-nication, high-complexity and high-performance transceiverstructures are energy efficient at low SNRs; while low-complexity and low-performance transceiver structures areenergy efficient at high SNRs.

Fig. 9 shows the optimum number of RAKE fingers andpacket lengths for different repetition coding parameters 𝑁𝑝,with optimized modulation/combining/detection schemes. Thecurves with different𝑁𝑝 display the same trend: as 𝑑 increases(SNR decreases), 𝑀∗ increases and converges to the samelevel, while 𝐿∗

𝐿 decreases. Fig. 9 also reveals that the effectof a large 𝑁𝑝 on the packet error probability on the expectednumber of retransmissions is equivalent to that of a small𝐿𝐿 or a large 𝑀 , and vice versa. Therefore, it is possibleto use a long repetition code to minimize energy under somecircumstances where a large number of RAKE fingers andadjustable packet lengths are not feasible.

C. Optimum Configuration Table

The results of these optimizations can enable the transceiverto adapt by selecting the overall optimum configurations(including the modulation/detection scheme, the repetitioncoding/combining scheme, the packet length and the numberof RAKE fingers) according to the expected transmission dis-tance through a lookup table. Table I is an example of such alook-up table obtained with the particular power consumptionand channel models assumed in this paper.

D. The Effects of Power Consumption Values on the OptimumConfigurations

Implementation technologies have a paramount impact onthe choice of the optimal communication schemes. For exam-ple, should 𝑃SYN become smaller, the distance range in whichcoherent detection is energy efficient becomes larger. In fact,considering an extreme case where the transceiver does notconsume any power, we shall always use the communicationscheme with the highest performance, such as DBPSK withcoherent detection, soft decoding and an all-RAKE receiver.In real applications, the overall optimum configurations shouldbe carefully evaluated using the generic energy consumptionmodel provided in this paper as summarized in (31) and thepower consumption values of the actual circuit componentsbased on the adopted production technologies. For instance,suppose we choose another set of power consumption valueswhere 𝑃SYN = 2.2 mW, while the rest of the power con-sumption values stay the same. The resulting overall optimumconfigurations are summarized in Table II. By comparing



TABLE IIOVERALL OPTIMUM CONFIGURATIONS

Distance (m) Modulation Detection 𝑁𝑝 Combining 𝑀∗ 𝐿∗𝐿 (Kbit)

3 NC 7 ∼ 3000

4OOK

9

5 46 5

7 6∼ 1500

8 7

9 1HD

8

10 9

11 11 ∼ 500

12 13

13 15

14 DBPSK 18

15 22

16 10

17 CO 11∼ 100

18 12

193

14

20 16

21 18

22 SD 1323 14

245

16 ∼ 50

25 18

26 14

277

16

Tables I and II, we find that since the difference in powerconsumption of coherent and noncoherent schemes becomessmaller, the distance range in which coherent detection isenergy efficient becomes larger. However, the general trend ofthe optimal configurations versus transmission distance staysthe same: high-complexity and high-performance transceiverstructures are energy efficient at large distances; while low-complexity and low-performance transceiver structures areenergy efficient at short distances.

VI. CONCLUSIONS

In this paper, we provided the power consumption models oftypical transmitter and receiver structures of IR-UWB systems.Then, under the assumption of a frequency selective time-invariant channel, we determine the optimum combination ofthe modulation scheme, the detection scheme, the repetitioncoding parameter, the combining scheme, the packet length,and the number of RAKE fingers at the receiver to mini-mize energy consumption per information bit. An optimumnumber of RAKE fingers exists under the assumption ofa frequency selective time-invariant channel with a doubleexponentially decaying power delay profile. The results showthat low-complexity, low-performance transmission schemesare energy efficient at high SNRs, while high-complexity,high-performance schemes are energy efficient at low SNRs.Using the specific power consumption values selected in thispaper, we provided detailed optimum transmission schemes,

including packet length, modulation, detection, repetition cod-ing, combining, and number of RAKE fingers for giventransmission distances for a typical IR-UWB link.

REFERENCES

[1] F. C. Commission, “Part 15 of the Commission’s Rules RegardingUltra-Wideband Transmission Systems Federal Communications Com-mission,” July 2008.

[2] I. Gresham, A. Jenkins, R. Egri, C. Eswarappa, N. Kinayman, N. Jain,R. Anderson, F. Kolak, R. Wohlert, S. Bawell, J. Bennett, and J. Lanteri,“Ultra-wideband radar sensors for short-range vehicular applications,”IEEE Trans. Microwave Theory and Techniques, vol. 52, pp. 2105–2122,Sep. 2004.

[3] S. Gezici, T. Zhi, G. Giannakis, H. Kobayashi, A. Molisch, H. Poor,and Z. Sahinoglu, “Localization via ultra-wideband radios: a look atpositioning aspects for future sensor networks,” IEEE Signal Process.Mag., vol. 22, pp. 70–84, July 2005.

[4] I. Oppermanz, L. Stoica, A. Rabbachin, Z. Shelby, and J. Haapola,“UWB wireless sensor networks: UWEN - a practical example,” IEEECommun. Mag., vol. 42, pp. S27–S32, Dec. 2004.

[5] A. J. Goldsmith and S. B. Wicker, “Design challenges for energy-constrained ad hoc wireless networks,” IEEE Wireless Commun., Aug.2002.

[6] I. Akyildiz, S. Weilian, Y. Sankarasubramaniam, and E. Cayirci, “Asurvey on sensor networks,” IEEE Commun. Mag., vol. 40, pp. 102–114, Aug. 2002.

[7] T. Wang, W. Heinzelman, and A. Seyedi, “Minimization of transceiverenergy consumption in wireless sensor networks with AWGN channels,”in Proc. Allerton Conference, Sep. 2008.

[8] S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-constrained modulationoptimization,” IEEE Trans. Wireless Commun., vol. 4, no. 8, pp. 2349–2360, Sep. 2005.

[9] M. Z. Win and R. A. Scholtz, “On the energy capture of ultrawidebandwidth signal in dense multipath environments,” IEEE Commun.Lett., vol. 2, no. 9, 1998.



[10] D. Cassioli, M. Z. Win, F. Vatalaro, and A. F. Molisch, “Low complex-ity Rake receivers in ultra-wideband channels,” IEEE Trans. WirelessCommun., vol. 4, pp. 1265–1275, Apr. 2007.

[11] T. Wang, W. Heinzelman, and A. Seyedi, “Minimizing energy con-sumption in IR-UWB based wireless sensor networks,” in Proc. IEEEInternational Conference on Communications (ICC), June 2009.

[12] S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-efficiency of MIMOand cooperative MIMO techniques in sensor networks,” IEEE J. Sel.Areas Commun., vol. 22, no. 6, pp. 1089–1098, Aug. 2004.

[13] J. Ammer and J. Rabaey, “The energy-per-useful-bit metric for evaluat-ing and optimizing sensor network physical layers,” 3rd Annual IEEECommunications Society on Sensor and Ad Hoc Communications andNetworks (SECON ’06), Sep. 2006.

[14] X. Lu, E. Erkip, Y. Wang, and D. Goodman, “Power efficient multimediacommunication over wireless channels,” IEEE J. Sel. Areas Commun.,vol. 21, no. 10, pp. 1738–1751, Dec. 2003.

[15] P. Lettieri and M. B. Srivastava, “Adaptive frame length control forimproving wireless link throughput, range, and energy efficiency,” inProc. INFOCOM ’98, Mar. 1998.

[16] Y. Sankarasubramaniam, I. Akyildiz, and S. McLaughlin, “Energyefficiency based packet size optimization in wireless sensor networks,” inProc. First IEEE 2003 IEEE International Workshop on Sensor NetworkProtocols and Applications, 2003.

[17] S. Cui, A. J. Goldsmith, and A. Bahai, “Exact bit error rate analysis ofTH-PPM UWB systems in the presence of multiple-access interference,”IEEE Commun. Lett., vol. 7, no. 12, pp. 572–574, Dec. 2003.

[18] Q. Zhang and J. H. Cho, “On RAKE receivers for ultra-widebandbinary block-coded PPM in dense multipath channels,” IEEE Trans.Veh. Technol., vol. 56, no. 4, pp. 1737–1747, July 2007.

[19] J. D. Choi and W. E. Stark, “Performance of ultra-wideband communi-cations with suboptimal receivers in multipath channels,” IEEE J. Sel.Areas Commun., vol. 20, no. 9, pp. 1754–1766, Dec. 2002.

[20] N. Telzhensky and Y. Leviatan, “Novel method of UWB antennaoptimization for specified input signal forms by means of geneticalgorithm,” IEEE Trans. Antennas Propag., vol. 54, no. 8, pp. 2216–2225, Aug. 2006.

[21] R. Zhang and X. Dong, “Synchronization and integration region op-timization for UWB signals with non-coherent detection and auto-correlation detection,” IEEE Trans. Commun., vol. 54, no. 5, pp. 790–798, May 2008.

[22] Y. Shi, Y. T. Hou, and H. D. Sherali, “Cross-layer optimization fordata rate utility problem in UWB-based ad hoc networks,” IEEE Trans.Mobile Computing, vol. 7, no. 6, pp. 764–777, June 2008.

[23] U. Onunkwo and Y. Li, “On the optimum pulse-position modulationindex for ultra-wideband communication,” Shanghai, China, June 2004,pp. 77–80.

[24] M. Z. Win and R. A. Scholtz, “On the energy capture of ultrawidebandwidth signals in dense multipath environments,” IEEE Commun.Lett., vol. 2, no. 9, pp. 245–247, Sep. 1998.

[25] D. Cassioli, M. Z. Win, and A. F. Molisch, “The ultra-wide bandwidthindoor channel: from statistical model to simulations,” IEEE J. Sel. AreasCommun., vol. 20, no. 6, Aug. 2002.

[26] A. F. Molisch, D. Cassioli, C.-C. Chong, S. Emami, A. Fort, B. Kannan,J. Karedal, J. Kunisch, H. G. Schantz, K. Siwiak, and M. Z. Win,“A comprehensive standardized model for ultrawideband propagationchannels,” IEEE Trans. Antennas Propag., vol. 54, pp. 3151–3166, Nov.2006.

[27] K. Siwiak and A. Petroff, “A statistical model for indoor multipathpropagation,” IEEE J. Sel. Areas Commun., vol. SAC-5, no. 2, pp. 128–137, Feb. 1987.

[28] B. Verbruggen, J. Craninckx, M. Kuijk, P. Wambacq, and G. Van derPlas, “A 2.2 mW 5b 1.75 GS/s folding flash ADC in 90 nm digitalCMOS,” in Proc. ISSCC, 2007.

[29] C. E. Shannon, “A mathematical theory of communication,” Bell Syst.Tech. J., vol. 27, pp. 379–423, 623–656, July-Oct. 1948.

[30] J. G. Proakis, Digital Communications, 4th edition. Addison-Wesley,1972.

[31] E. Al-Hussaini and A. Al-Bassiouni, “Performance of MRC diversitysystems for the detection of signals with Nakagami fading,” IEEE Trans.Commun., vol. 33, pp. 1315–1319, Dec. 1985.

[32] ——, “MRC performance for M-ary modulation in arbitrarily correlatedNakagami fading channels,” IEEE Trans. Commun., vol. 47, pp. 44–52,Jan. 1999.

[33] B. Sklar, Digital Communications: Fundamentals and Applications,2nd edition. Prentice Hall PTR, 2001.

[34] A. Goldsmith, Wireless Communications, 1st edition. CambridgeUniversity Press, 2005.

[35] A. Medi and W. Namgoong, “A high data-rate energy-efficientinterference-tolerant fully integrated CMOS frequency channelizedUWB transceiver for impulse radio,” in Proc. JSSC, 2008.

[36] H. Kao, A. Chin, K. Chang, and S. McAlister, “A low-power current-reuse LNA for ultra-wideband wireless receivers from 3.1 to 10.6 GHz,”in Proc. SiRF07, 2007.

[37] Y. Gao, K. Cai, Y. Zheng, and B.-L. Ooi, “A wideband CMOS multiplierfor UWB application,” in Proc. ICUWB, 2007.

[38] C. T. Fu and H. Luong, “A CMOS linear-in-dB high-linearity variable-gain amplifier for UWB receivers,” in Proc. ASSCC, 2007.

[39] V. Lottici, A. D’Andrea, and U. Mengali, “Channel estimation for ultra-wideband communications,” IEEE J. Sel. Areas Commun., vol. 20, no. 9,pp. 1638–1645, Dec. 2002.

Tianqi Wang received the B.E. degree in 2004in Communications Engineering, from Beijing Uni-versity of Posts and Telecommunications, Beijing,China, and the M. Eng. degree in 2007 in Elec-trical and Computer Engineering, from MemorialUniversity of Newfoundland, St. John’s, Canada.He is currently working toward a Ph.D. degree atthe Department of Electrical and Computer Engi-neering, University of Rochester, USA. His currentresearch interests include wireless communicationsand cross-layer design in wireless sensor networks.

Wendi B. Heinzelman is an associate professor inthe Department of Electricals and Computer Engi-neering at the University of Rochester, and she holdsa secondary appointment as an associate professor inthe Department of Computer Science. Dr. Heinzel-man also currently serves as Dean of GraduateStudies for Arts, Sciences and Engineering at theUniversity of Rochester. Dr. Heinzelman received aB.S. degree in Electrical Engineering from CornellUniversity in 1995 and M.S. and Ph.D. degrees inElectrical Engineering and Computer Science from

MIT in 1997 and 2000, respectively. Her current research interests lie in theareas of wireless communications and networking, mobile computing, andmultimedia communication.

Dr. Heinzelman received the NSF CAREER award in 2005 for her researchon cross-layer architectures for wireless sensor networks, and she receivedthe ONR Young Investigator Award in 2005 for her work on balancingresource utilization in wireless sensor networks. She is an Associate Editorfor the IEEE TRANSACTIONS ON MOBILE COMPUTING, an Associate Editorfor the ACM Transactions on Sensor Networks and an Associate Editor forElsevier Ad Hoc Networks Journal. Dr. Heinzelman is a senior member of theIEEE and the ACM, and she is co-founder of the 𝑁2 Women (NetworkingNetworking Women) group.

Alireza Seyedi (S’95, M’04) received his B.S. de-gree from Sharif University of Technology, Tehran,Iran, in 1997 and his M.S. and Ph.D. degrees fromRensselaer Polytechnic Institute, Troy, NY, in 2000and 2004, respectively, all in electrical engineering.Since 2007 he has been with the Faculty of theElectrical and Computer Engineering Departmentat the University of Rochester, where he currentlyis an Assistant Professor (Research). Prior to that,he was with Philips Research North America. Hisprimary research interests are in the areas of Com-

munications, Control, and their convergence. He is a Member of the IEEECommunications, Control and Signal Processing Societies.


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