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

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

Performance of an Ultra-Wideband Communication System in the Presence of Narrowband 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-error probability of an ultra-wideband (UWB) communication system operating with binary phase-shift keying and quaternary phase-shift keying narrowband interference in additive white Gaussian noise. The analytical expressions are valid when phase transitions of the interfering symbols can be ignored. The accuracy of the Gaussian approximation is assessed, and several modulation schemes proposed for UWB communication are evaluated in terms of capability of interference suppression. Index Terms—Interference, multiaccess communication, orthogonal frequency-division multiplexing (OFDM), ultra-wideband (UWB), wireless.

I. INTRODUCTION

when the symbol duration of the interfering signals is much greater than the bit duration of the UWB system. Particularly, PPM and BPSK using TH or direct sequence (DS) are considered. A closed-form expression for the interference can be obtained without using any bandlimited Gaussian assumption or approximation, for UWB systems employing pulse-shaping for which the inverse Fourier transform exists. We consider only BPSK and QPSK interference for brevity and clarity, but the analysis can be extended to all quadrature modulations for which the in-phase and quadrature data streams can be demodulated independently. We also investigate the accuracy of the Gaussian approximation, and show that the Gaussian approximation for BPSK OFDM interference is not reliable, contrary to the conclusions drawn in [6].

T

HE Federal Communication Commission (FCC) has recently introduced restrictions on the power spectral density (PSD) of ultra-wideband (UWB) systems [1]. This specification reduces the potential for interference to other coexisting wireless user systems. Since the PSD of conventional communication signals is much higher than that of UWB signals, the interference from other wireless applications to UWB systems becomes more severe and critical. Therefore, the performance of UWB signals in the presence of interference from other communication systems in the same frequency band must be carefully investigated before commercial applications. As a result, the performance of UWB in the presence of various narrowband interference (NBI) was studied in [2]–[5]. All these results 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) performance of a time-hopping pulse position modulation (TH-PPM) system corrupted by interference from orthogonal frequency-division multiplexing (OFDM) signals was developed in [6], in which a Gaussian approximation was used for modeling binary phase-shift keying (BPSK) OFDM interference. However, published work [7] has shown that Gaussian approximations may sometimes be inaccurate in UWB applications. In this letter, we provide an analysis for the performance of different UWB systems operating in additive white Gaussian noise (AWGN) in the presence of BPSK and quadrature PSK (QPSK) OFDM interference, accurate when the phase transitions of the interfering signals can be ignored; such is the case Paper approved by A. Zanella, the Editor for Wireless Systems of the IEEE Communications Society. Manuscript received September 14, 2009; revised February 4, 2011 and March 29, 2011.This paper was presented in part at the IEEE International Conference on Communications, Seoul, South Korea, May 2010 The authors are with Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TCOMM.2006.881338

II. SYSTEM MODELS Assume users are transmitting on an AWGN channel in the presence of narrowband BPSK or QPSK OFDM interferat the UWB receiver is written as ence. The received signal (1) is additive noise with two-sided PSD , where can be TH-PPM, TH-BPSK, or DS-BPSK signals. The signal formats of TH-PPM, TH-BPSK, and DS-BPSK are those derepresents the received signal scribed in [7]. The set amplitudes, and represent time shifts (delays) for UWB signals. Additionally, and represents the received amplitude and the time shift of the NBI signal , respectively. We focus on the investigation of interference from narrowband BPSK and QPSK OFDM signals. These interfering signals could be the lower data-rate formats in an IEEE 802.11a system employing OFDM. Our restriction to BPSK and QPSK permits a tractable analytical study. We assume that the symbol duration of the interfering signals is much greater than the bit duration of the UWB system, which is common in practical systems. Therefore, phase transitions of the BPSK/QPSK OFDM signal can be neglected, 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 frequency, and is the transmitted data symbol, which can represent BPSK and QPSK.

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

III. INTERFERENCE ANALYSIS

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where represents a time-normalization factor, and is introduced to normalize the energy of the pulses, . Our analytical method, however, can be generalized to UWB systems using other pulses as long as their inverse Fourier transforms exist, with the adoption of numerical integration. For the second-order Gaussian monocycle, the integral can be calculated as

A. TH-UWB Define the correlation of the template with 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 Gaussian , random variable (RV) with variance is the desired signal component, is the total multiple-access interference (MAI), and is the interference from the OFDM signal, given by

(7)

(8) Therefore,

has a closed-form expression as

(9) where

is defined as

(4) where is the real part of . Defining and substituting into (4) yields [6] takes for BPSK signaling, where bility. Similarly, the expression for QPSK signaling as

(10) with equal probacan be obtained for

(5) (11) where the second equality comes from left-shifting the pulse to create a symmetric pulse , which has the identical with pulse width , but is symmetric about . shape to Defining

and considering the pulse is limited on , we can approximate the integral by changing the integration interval to . Then can be interpreted as the inverse Fourier transform of , and we can conclude that the interference from the OFDM signal has a closed-form expression, as long as the inverse Fourier transform of exists. We restrict our analysis of UWB systems to the second-order Gaussian monocycle, given by (6)

in which and represents the in-phase and quadrature parts of the data symbol , respectively, having values chosen from independently. As seen, for OFDM QPSK signaling can be regarded as the sum of two independent BPSK signals. Considering the uniform distribution of the symbol and letting represent expectation, we can calculate the characteristic function (CF) of conditioned on and as [8]

(12) Assuming distribution of

are independent, and using the uniform on , we can express the CF of conditioned on as [8] (13)

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

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

(14) Note that (14) is a closed-form expression for the CF of when the interfering OFDM signal is synchronized to the desired UWB signal, i.e., . When the OFDM signal is not transmitted simultaneously with the reference UWB signal, , the conditional CF of , needs to be averaged over . 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)

of

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

C. Bit-Error Probability Owing to the symmetry of the OFDM interference, the MAI, and the noise, the average probability of error for the UWB system is given by (20)

(16)

where is the signal component, is AWGN, and represents the MAI. Considering the relationship between the cumulative distribution function (CDF) and the CF of an RV, we can calculate the average probability of error for the desired user in the UWB systems as

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

(21)

B. DS-UWB

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

A DS-BPSK UWB signal can be expressed as [7] (17) where is the number of chips per information bit. The signal component in the decision statistic for the DS-UWB system is , and is the interference to the DS-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 interference in the DS-UWB system as

(19)

IV. NUMERICAL RESULTS AND COMPARISONS We use our analytical results to study the average BER performance of TH-UWB and DS-UWB in the presence of IEEE 802.11a BPSK/QPSK OFDM interference. The parameters of the example UWB systems and the OFDM system are listed in Table I. Fig. 1 shows the BERs of a TH-BPSK system operating with BPSK/QPSK OFDM interference. In the Gaussian approximation, the expression for the signal-to-interference-plus-noise ratio (SINR) is given by

(22) where the variance of the OFDM interference, , can be obtained from (9) and (18). The BER curves are presented as a function of signal-to-noise power ratio (SNR) with . For BPSK OFDM interference, we observe that the theoretical results obtained from the precise analysis and the test simulation results are in excellent agreement. It is also seen that

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

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

=

the Gaussian approximation is in good agreement with the analysis only for small and medium SNR values, say SNR 10 dB, when . However, the Gaussian approximation underestimates the BERs by an order of magnitude when the SNR is 16 dB. Unlike the analytical results, which show that the perforis better than the performance for , mance for , the Gaussian approximation proand again better for vides the same BERs for , and fails to predict the BER performance improvement achieved by using larger values of . On the other hand, we note that the exact BER curves become increasingly closer to the BER curves obtained from the Gaussian approximation as the length of the repetition code increases. This observation can be explained as follows. Considering the expression for the OFDM interference in (9), we as can see that more interfering terms will contribute to increases. Owing to the near independence between these terms, the total interference can be well-approximated as a Gaussian RV for large values of following a central limit theorem (CLT). It appears that the Gaussian approximation is valid for estimating the BER of the TH-BPSK system operating with BPSK OFDM interference for large values of , but it underestimates the BERs for large values of SNR and small values of . Also, when the TH-BPSK system is operating with QPSK OFDM interference, the Gaussian approximation provides accurate BER estimates for all SNR values considered, and does not show the differences for small values of seen in the BPSK case. This is explained by the fact that the convergence to the normal distribution is faster in the QPSK case than in the BPSK case, because the QPSK case has more levels. Fig. 2 shows the performance of the DS-BPSK UWB system in the presence of BPSK OFDM interference. In order to fairly compare the BER performance of DS-UWB systems, we is used for all TH assume that the same data rate [7]. In this figure, and DS systems, which requires the Gaussian approximation provides almost the same BER estimates for different values of . However, unlike the results seen in Fig. 1 for BPSK OFDM interference, the Gaussian

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

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

approximation is in excellent agreement with the CF analysis for all values of SNR. This behaviour can also be explained using a CLT. Checking the expression for in (18) for the DS-UWB system, we note that many more terms than is the case in TH-UWB systems contribute to the total interference to normalize the DS-UWB system. when we use In this case, the OFDM interference more closely approximates a Gaussian-distributed RV, and the Gaussian approximation is highly accurate for estimating the BER. In consequence, as long as the value of is large enough to make the interference AWGN-like, the BER performance will no longer be improved by using a longer repetition code. These results corroborate the . In observations obtained from Fig. 1 for large values of contrast to the behaviour of UWB systems in the presence of MAI, as obtained in [7], increasing the length of the repetition code will not suppress more narrowband OFDM interference, and the UWB system performance will not be improved, or is large enough that the Gaussian when the value of

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. Note that DS-BPSK and large SNR values when and TH-BPSK achieve the same BER performance when the interference closely follows the Gaussian distribution as increases. Fig. 4 shows the BERs of these systems operating with QPSK OFDM interference. Unlike the result observed in Fig. 3, where DS-BPSK outperforms TH-BPSK for large SNR values with small , DS-BPSK and TH-BPSK achieve similar BERs for all SNR values with arbitrary values of when corrupted by QPSK OFDM interference. Again, it appears that convergence to the normal distribution happens sooner for QPSK than BPSK. REFERENCES

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

approximation can be used for predicting the error probability reliably. In Fig. 3, BERs of TH-PPM, TH-BPSK, and DS-BPSK corrupted by BPSK OFDM interference are compared. We observe that TH-BPSK outperforms TH-PPM for all values of SNR. TH-BPSK provides similar BERs to DS-BPSK for small 8 dB. In contrast to the results obSNR values, say SNR tained using the Gaussian approximation, which indicate that TH-BPSK achieves the same performance as DS-BPSK when both systems are operated in OFDM interference, the DS-BPSK system actually outperforms the TH-BPSK system for moderate

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