1720 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.54, NO.10, OCTOBER 2011

Performance of an Ultra-Wideband Communication System in the Presence ofNarrowband BPSK- and QPSK-Modulated OFDM Interference

Bo Hu, Member, IEEE, and Norman C. Beaulieu, Fellow, IEEE

Abstract—An analysis is derived for calculating the bit-errorprobability of an ultra-wideband (UWB) communication systemoperating with binary phase-shift keying and quaternaryphase-shift keying narrowband interference in additive whiteGaussian noise. The analytical expressions are valid when phasetransitions of the interfering symbols can be ignored. The accuracyof the Gaussian approximation is assessed, and several modulationschemes proposed for UWB communication are evaluated in termsof capability of interference suppression.

Index Terms—Interference, multiaccess communication,orthogonal frequency-division multiplexing (OFDM), ultra-wide-band (UWB), wireless.

I. INTRODUCTION

THE Federal Communication Commission (FCC) has re-cently introduced restrictions on the power spectral den-

sity (PSD) of ultra-wideband (UWB) systems [1]. This specifi-cation reduces the potential for interference to other coexistingwireless user systems. Since the PSD of conventional commu-nication signals is much higher than that of UWB signals, theinterference from other wireless applications to UWB systemsbecomes more severe and critical. Therefore, the performanceof UWB signals in the presence of interference from other com-munication systems in the same frequency band must be care-fully investigated before commercial applications. As a result,the performance of UWB in the presence of various narrow-band interference (NBI) was studied in [2]–[5]. All these re-sults were obtained using simplified models of real interference,owing to the difficulty of the analysis for more accurate models.An expression for evaluating the bit-error rate (BER) perfor-mance of a time-hopping pulse position modulation (TH-PPM)system corrupted by interference from orthogonal frequency-di-vision multiplexing (OFDM) signals was developed in [6], inwhich a Gaussian approximation was used for modeling binaryphase-shift keying (BPSK) OFDM interference. However, pub-lished work [7] has shown that Gaussian approximations maysometimes be inaccurate in UWB applications.

In this letter, we provide an analysis for the performance ofdifferent UWB systems operating in additive white Gaussiannoise (AWGN) in the presence of BPSK and quadrature PSK(QPSK) OFDM interference, accurate when the phase transi-tions of the interfering signals can be ignored; such is the case

Paper approved by A. Zanella, the Editor for Wireless Systems of the IEEECommunications Society. Manuscript received September 14, 2009; revisedFebruary 4, 2011 and March 29, 2011.This paper was presented in part at theIEEE International Conference on Communications, Seoul, South Korea, May2010

The authors are with Department of Electrical and Computer Engineering,University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail: bohu@ee.ual-berta.ca; beaulieu@ee.ualberta.ca).

Digital Object Identifier 10.1109/TCOMM.2006.881338

when the symbol duration of the interfering signals is muchgreater than the bit duration of the UWB system. Particularly,PPM and BPSK using TH or direct sequence (DS) are con-sidered. A closed-form expression for the interference can beobtained without using any bandlimited Gaussian assumptionor approximation, for UWB systems employing pulse-shapingfor which the inverse Fourier transform exists. We consideronly BPSK and QPSK interference for brevity and clarity, butthe analysis can be extended to all quadrature modulationsfor which the in-phase and quadrature data streams can bedemodulated independently. We also investigate the accuracyof the Gaussian approximation, and show that the Gaussianapproximation for BPSK OFDM interference is not reliable,contrary to the conclusions drawn in [6].

II. SYSTEM MODELS

Assume users are transmitting on an AWGN channel inthe presence of narrowband BPSK or QPSK OFDM interfer-ence. The received signal at the UWB receiver is written as

(1)

where is additive noise with two-sided PSD ,can be TH-PPM, TH-BPSK, or DS-BPSK signals. The signalformats of TH-PPM, TH-BPSK, and DS-BPSK are those de-scribed in [7]. The set represents the received signalamplitudes, and represent time shifts (delays) forUWB signals. Additionally, and represents the received am-plitude and the time shift of the NBI signal , respec-tively.

We focus on the investigation of interference from narrow-band BPSK and QPSK OFDM signals. These interfering signalscould be the lower data-rate formats in an IEEE 802.11a systememploying OFDM. Our restriction to BPSK and QPSK permitsa tractable analytical study. We assume that the symbol durationof the interfering signals is much greater than the bit duration ofthe UWB system, which is common in practical systems. There-fore, phase transitions of the BPSK/QPSK OFDM signal can beneglected, and the transmitted OFDM signal can be written as

(2)

where is the number of subcarriers in the OFDM signal,represents the subcarrier frequency spacing, is the carrier fre-quency, and is the transmitted data symbol, which can rep-resent BPSK and QPSK.

0090-6778/$20.00 © 2011 IEEE

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.54, NO.10, OCTOBER 2011 1721

III. INTERFERENCE ANALYSIS

A. TH-UWB

Define the correlation of the templatewith the UWB pulse as

(3)

where is the time shift associated with binary PPM.The decision statistic of the correlation receiver is obtained as

, where is a Gaussianrandom variable (RV) with variance ,

is the desired signal component,is the total multiple-access interference (MAI), andis the interference from the OFDM signal, given by

(4)

where is the real part of . Definingand substituting into (4) yields [6]

(5)

where the second equality comes from left-shifting the pulseto create a symmetric pulse , which has the identical

shape to with pulse width , but is symmetric about .Defining

and considering the pulse is limited on , wecan approximate the integral by changing the integrationinterval to . Then can be interpreted as the in-verse Fourier transform of , and we can conclude that theinterference from the OFDM signal has a closed-formexpression, as long as the inverse Fourier transform of ex-ists.

We restrict our analysis of UWB systems to the second-orderGaussian monocycle, given by

(6)

where represents a time-normalization factor, and is intro-duced to normalize the energy of the pulses, . Our ana-lytical method, however, can be generalized to UWB systemsusing other pulses as long as their inverse Fourier transformsexist, with the adoption of numerical integration.

For the second-order Gaussian monocycle, the integralcan be calculated as

(7)

(8)

Therefore, has a closed-form expression as

(9)

where is defined as

(10)for BPSK signaling, where takes with equal proba-bility. Similarly, the expression for can be obtained forQPSK signaling as

(11)

in which and represents the in-phase and quadrature partsof the data symbol , respectively, having values chosen from

independently. As seen, for OFDM QPSK sig-naling can be regarded as the sum of two independent BPSKsignals.

Considering the uniform distribution of the symbol andletting represent expectation, we can calculate the charac-teristic function (CF) of conditioned on and as [8]

(12)

Assuming are independent, and using the uniformdistribution of on , we can express the CF of

conditioned on as [8]

(13)

1722 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.54, NO.10, OCTOBER 2011

Owing to the independence of , the CF of the OFDMinterference, , when conditioned on , is [8]

(14)

Note that (14) is a closed-form expression for the CF ofwhen the interfering OFDM signal is synchronized to

the desired UWB signal, i.e., . When the OFDM signal isnot transmitted simultaneously with the reference UWB signal,

, the conditional CF of , needs to be averagedover . Without loss of generality, assume that the time shift

is uniformly distributed on a bit duration of the UWB signal. Then, the CF of the OFDM interference to the

TH-PPM system in the asynchronous scenario is given by

(15)

Similar to the analysis described, we can also obtain the CFof conditioned on in the TH-BPSK system as

(16)

and the CF of the OFDM interference in TH-BPSK is calculatedby averaging across .

B. DS-UWB

A DS-BPSK UWB signal can be expressed as [7]

(17)

where is the number of chips per information bit. The signalcomponent in the decision statistic for the DS-UWB system is

, and is the interference to theDS-BPSK system from the OFDM signal, expressed as

(18)

where .Following similar steps as those employed in the analysis of

TH-UWB systems, we obtain the CF of the total interferencein the DS-UWB system as

(19)

TABLE IPARAMETERS OF THE EXAMPLE TH/DS-UWB AND OFDM SYSTEMS

C. Bit-Error Probability

Owing to the symmetry of the OFDM interference, the MAI,and the noise, the average probability of error for the UWBsystem is given by

(20)

where is the signal component, is AWGN, and representsthe MAI.

Considering the relationship between the cumulative distri-bution function (CDF) and the CF of an RV, we can calculatethe average probability of error for the desired user in the UWBsystems as

(21)

where is the CF for the noise term , andand is the CF of the interference from the OFDM signaland the MAI from interfering UWB signals, respectively.

IV. NUMERICAL RESULTS AND COMPARISONS

We use our analytical results to study the average BER per-formance of TH-UWB and DS-UWB in the presence of IEEE802.11a BPSK/QPSK OFDM interference. The parameters ofthe example UWB systems and the OFDM system are listed inTable I.

Fig. 1 shows the BERs of a TH-BPSK system operating withBPSK/QPSK OFDM interference. In the Gaussian approxima-tion, the expression for the signal-to-interference-plus-noiseratio (SINR) is given by

(22)

where the variance of the OFDM interference, , canbe obtained from (9) and (18). The BER curves are presentedas a function of signal-to-noise power ratio (SNR) with

. For BPSK OFDM interference, we observe that the the-oretical results obtained from the precise analysis and the testsimulation results are in excellent agreement. It is also seen that

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.54, NO.10, OCTOBER 2011 1723

Fig. 1. Average BER versus SNR of the TH-BPSK UWB system operatingwith BPSK/QPSK OFDM interference with A=A = 0 dB.

the Gaussian approximation is in good agreement with the anal-ysis only for small and medium SNR values, say SNR 10 dB,when . However, the Gaussian approximation underes-timates the BERs by an order of magnitude when the SNR is16 dB. Unlike the analytical results, which show that the perfor-mance for is better than the performance for ,and again better for , the Gaussian approximation pro-vides the same BERs for , and fails to predict theBER performance improvement achieved by using larger valuesof . On the other hand, we note that the exact BER curves be-come increasingly closer to the BER curves obtained from theGaussian approximation as the length of the repetition codeincreases. This observation can be explained as follows. Con-sidering the expression for the OFDM interference in (9), wecan see that more interfering terms will contribute to as

increases. Owing to the near independence between theseterms, the total interference can be well-approximatedas a Gaussian RV for large values of following a centrallimit theorem (CLT). It appears that the Gaussian approxima-tion is valid for estimating the BER of the TH-BPSK systemoperating with BPSK OFDM interference for large values of

, but it underestimates the BERs for large values of SNR andsmall values of . Also, when the TH-BPSK system is oper-ating with QPSK OFDM interference, the Gaussian approxima-tion provides accurate BER estimates for all SNR values con-sidered, and does not show the differences for small values of

seen in the BPSK case. This is explained by the fact thatthe convergence to the normal distribution is faster in the QPSKcase than in the BPSK case, because the QPSK case has morelevels.

Fig. 2 shows the performance of the DS-BPSK UWB systemin the presence of BPSK OFDM interference. In order tofairly compare the BER performance of DS-UWB systems, weassume that the same data rate is used for all THand DS systems, which requires [7]. In this figure,the Gaussian approximation provides almost the same BERestimates for different values of . However, unlike the resultsseen in Fig. 1 for BPSK OFDM interference, the Gaussian

Fig. 2. Average BER versus SNR of the DS-BPSK UWB system operatingwith BPSK OFDM interference for different A=A values.

Fig. 3. Comparison of the TH-PPM, TH-BPSK, and DS-BPSK systems withthe same data rate operating in BPSK OFDM interference.

approximation is in excellent agreement with the CF analysisfor all values of SNR. This behaviour can also be explainedusing a CLT. Checking the expression for in (18) forthe DS-UWB system, we note that many more terms than is thecase in TH-UWB systems contribute to the total interferencewhen we use to normalize the DS-UWB system.In this case, the OFDM interference more closely approximatesa Gaussian-distributed RV, and the Gaussian approximation ishighly accurate for estimating the BER. In consequence, aslong as the value of is large enough to make the interferenceAWGN-like, the BER performance will no longer be improvedby using a longer repetition code. These results corroborate theobservations obtained from Fig. 1 for large values of . Incontrast to the behaviour of UWB systems in the presence ofMAI, as obtained in [7], increasing the length of the repetitioncode will not suppress more narrowband OFDM interference,and the UWB system performance will not be improved,when the value of or is large enough that the Gaussian

1724 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.54, NO.10, OCTOBER 2011

Fig. 4. Comparison of the TH-PPM, TH-BPSK, and DS-BPSK systems withthe same data rate operating in QPSK OFDM interference.

approximation can be used for predicting the error probabilityreliably.

In Fig. 3, BERs of TH-PPM, TH-BPSK, and DS-BPSK cor-rupted by BPSK OFDM interference are compared. We ob-serve that TH-BPSK outperforms TH-PPM for all values ofSNR. TH-BPSK provides similar BERs to DS-BPSK for smallSNR values, say SNR 8 dB. In contrast to the results ob-tained using the Gaussian approximation, which indicate thatTH-BPSK achieves the same performance as DS-BPSK whenboth systems are operated in OFDM interference, the DS-BPSKsystem actually outperforms the TH-BPSK system for moderate

and large SNR values when . Note that DS-BPSKand TH-BPSK achieve the same BER performance when theinterference closely follows the Gaussian distribution as in-creases. Fig. 4 shows the BERs of these systems operating withQPSK OFDM interference. Unlike the result observed in Fig. 3,where DS-BPSK outperforms TH-BPSK for large SNR valueswith small , DS-BPSK and TH-BPSK achieve similar BERsfor all SNR values with arbitrary values of when corruptedby QPSK OFDM interference. Again, it appears that conver-gence to the normal distribution happens sooner for QPSK thanBPSK.

REFERENCES

[1] Revision of Part 15 the Commission’s Rules Regarding Ultra-Wide-band Transmission Systems FCC, ET Docket 98-153, 2002.

[2] M. Hamalainen, R. Tesi, V. Hovinen, N. Laine, and J. Iinatti, “On theUWB system performance studies in AWGN channel with interferencein UMTS band,” in Proc. IEEE Conf. Ultra-Wideband Syst. Technol.,Baltimore, MD, May 20–23, 2002, pp. 321–325.

[3] L. Zhao and A. M. Haimovich, “Performance of ultra-widebandcommunications in the presence of interference,” IEEE J. Sel. AreasCommun., vol. 20, no. 9, pp. 1684–1691, Dec. 2002.

[4] E. Baccarelli, M. Biagi, and L. Taglione, “A novel approach to in-bandinterference mitigation in ultra wide band radio systems,” in Proc.IEEE Conf. Ultra Wideband Syst. Technol., Baltimore, MD, May20–23, 2002, pp. 297–301.

[5] A. Giorgetti, M. Chiani, and M. Z. Win, “Ultrawide bandwidth RAKEreception in the presence of narrowband interference,” in Proc. IEEEVeh. Technol. Conf., May 17–19, 2004, pp. 1659–1663.

[6] B. Firoozbakhsh, T. G. Pratt, and N. Jayant, “Analysis of IEEE 802.11ainterference on UWB systems,” in Proc. IEEE Conf. Ultra WidebandSyst. Technol., Reston, VA, Nov. 16–20, 2003, pp. 473–477.

[7] B. Hu and N. C. Beaulieu, “Accurate performance evaluation of time-hopping and direct-sequence UWB systems in multiuser interference,”IEEE Trans. Commun., vol. 53, no. 6, pp. 1053–1062, Jun. 2005.

[8] B. Hu, “Performance evaluation and pulse design for ultra-widebandcommunications,” Ph.D. dissertation, Dept. Elect. Comput. Eng., Univ.Alberta, Edmonton, AB, Canada, Jan. 2006.