Analysis on Interference Rejection of DS/SS Systems Using a Complex FIR Filter

Transcription

1 3026 IEICE TRANS. FUNDAMENTALS, VOL.E89 A, NO.11 NOVEMBER 2006 PAPER Special Section on Wide Band Systems Analysis on Interference Rejection of DS/SS Systems Using a Complex FIR Filter Yuki SHIMIZU a), Nonmember and Yukitoshi SANADA b), Member SUMMARY In this paper, the performance of narrow band interference (NBI) rejection scheme for direct sequence spread spectrum (DS/SS) isanalyzed. A single-tapped complex FIR filter is used for filtering a chip code to suppress NBI. In this system, the spectrum of transmitted signal has a null at an arbitrary frequency. By choosing filter coefficients, we place this null at NBI center frequency to mitigate the effect of NBI. The performance of this scheme is theoretically analyzed and validated by simulation. We also compare the effectiveness against BPSK interference between the chip code filtering and received signal filtering. The results indicate the chip code filtering is effective against single-tone and BPSK interference, and gains better performance than the received signal filtering at certain level of SNR. key words: spread spectrum, direct sequence, narrow band interference, FIR 1. Introduction Recently, DS/SS has achieved major popularity in wireless communication systems such as IEEE802.11b Wireless LAN, UWB, or IMT-2000 Cell Phone. Due to its large bandwidth, some of them have to share the same spectrum with narrow band systems. Although DS/SS has its own resistance against NBI, an extremely powerful interference is still a problem [1], [2]. A number of studies on NBI suppression for DS/SS have been reported. One of these approaches is to change chip code encoding [3]. Chip code interleaving and singletapped FIR filtering are also proposed [4]. In addition, suppression scheme with an adaptive line enhancer (ALE) is available [5]. The spectral shape of a DS/SS signal depends on its chip code spectrum. Therefore, by selecting chip code encoding, the spectrum collision between a DS/SS signal and NBI of a specific frequency can be decreased [3]. Since the number of code encoding is finite, however, this scheme is not able to combat NBI of an arbitrary frequency. Interleaving chip code introduces spectral nulls by certain interval into the spectrum of a DS/SS signal. If the center frequency of NBI is located at one of these nulls, the effect of NBI can be softened. This scheme is effective against such NBI, yet unable to deal with NBI of totally arbitrary Manuscript received March 2, Manuscript revised May 17, Final manuscript received July 11, The authors are with the Department of Electronics and Electrical Engineering, Keio University, Yokohama-shi, Japan. a) smz@snd.elec.keio.ac.jp b) sanada@elec.keio.ac.jp DOI: /ietfec/e89 a frequency. In [4] and [5], an FIR filter or an ALE is used to the received signal to notch out the effect of NBI. Although both of these schemes are capable of rejecting NBI of any frequency, they also damage the signal by filtering and cause performance loss by itself. Besides, the scheme employng an ALE is slow due to its Wiener filter component. In this paper, an FIR filter is used to modify the chip code instead of filtering the signal. Hence, this scheme does not deteriorate the performance by itself, and has the ability to mitigate NBI of an arbitrary frequency. The FIR filtering of received signal has already been shown to be useful in the presence of single-tone interferer by simulation [4]. In this paper, we investigate the performance of chip code FIR filtering via theoretical analysis. In addition to single-tone interference, we consider BPSK interference as well. Futhermore, we compare the performance of the chip code filtering with those of the received signal filtering by simulation. 2. System Model 2.1 System Model Figure 1 shows a system used in this paper. The sequence d(n) is spread by filtered chip code c(n) and then transmitted at frequency f c as s(t). During the transmission, a signal from other wireless devices i(t) is added as interference. Then AWGN n(t) is added to the received signal due to LNA at the receiver. These signalsr(t) are firstly brought down to the base band. The base band signal b(t) is then sampled at the chip interval T c, and is despread to recover the sequence ˆd(n). Note that in this system, the chip code is filtered at the transmitter. Therefore, it is necessary that the transmitter detect the center frequency of the interference, and inform the receiver of it. This may lead the transmitter system to Fig. 1 System model. Copyright c 2006 The Institute of Electronics, Information and Communication Engineers

2 SHIMIZU and SANADA: ANALYSIS ON INTERFERENCE REJECTION OF DS/SS SYSTEMS USING A COMPLEX FIR FILTER 3027 from 0 to 2π. Being converted down to the base band, the sampled interference is written as Fig. 2 Normailized gain response of FIR filter. be complex. In this paper, however, we assume both the receiver and the transmitter already know the center frequency of the interference. 2.2 The Effect of FIR Filtering In this paper, we use a single-tapped FIR filter for spectral shaping. The filter delay time T d is set to the chip interval T c, and the filter coeficients are h 0 = 1, h 1 = e jθ.thefir filter with these paramters has the gain response shown in Fig. 2. The X axis of Fig. 2 means the frequency which is normalized with 1 T d. Especially, the gain response of the FIR filter has a null at a specific frequency f null. (2p + 1) π + θ f null = (1) 2πT c where p is an integer. It is possible to shift this null to any desired frequency by choosing the phase θ of h 1. In the DS/SS system, first the original chip code c o (n) is filtered by the FIR filter. The filter output is taken as the spreading chip code c(n). According to the gain response of the filter, the spectrum of c(n) has a null. Therefore, the signal spread by c(n) has also a spectral null at f null. By setting this null to the center frequency of NBI, the spectrum friction between DS/SS and NBI can be reduced. As a consequence, the effect of NBI is suppressed. 2.3 Interference Model Single-Tone Interference One of the most popular interferer is single-tone interference. This type of interference is unmodulated, and has single center frequency. Here, single-tone interference at frequency f I is given as follows. i tone (t) = A e j(2π f It ξ) Note that A is the amplitude of interference. ξ is the phase of the single-tone interference and is uniformly distributed (2) î tone (n) = A e j(2π f dnt c ξ) where f d is a frequency difference defined as f d = f c f I. Despreading î tone (n)forthel-th DS/SS bit duration, we get I tone (l, f d ) = l M 1 n=(l 1) M (3) î tone (n)c (n mod M) (4) where M is the length of the despreading chip code c (n). Therefore, the absolute value of Eq. (4) is M 1 I e ( f d ) = î tone (n)c (n) (5) n=0 which is irrelevant to l. Using Eqs. (4), (5), and the variance 2σ 2 n of the base band noise n(n)e ( jπ2 f cnt c ), the bit error rate of the DS/SS system is P t (I e ( f d ),φ e (l)) = 1 ( ) 2 erfc Eb + I e ( f d )cosφ e (l) (6) 2σn where E b is the bit energy of the DS/SS system, and φ e (l) = arg {I tone (l, f d )} is uniformly distributed from 0 to 2π as ξ is. Because of the distribution of φ e (l), we need to average Eq. (6) on φ e (l). 1 2π 2π 0 = 1 2π P t (I e ( f d ),φ e (l))dφ e 2π 0 ( ) 1 2 erfc Eb + I e ( f d )cosφ e (l) dφ e, (7) 2σn According to the analysis of Glave and Rosenbaum [6], we take the Taylor series of Eq. (7) on γ = E b 2σn. 1 2π ( ) 1 γ 2π 0 2 erfc I e ( f d ) + γ cos φ e (l) dφ e Eb = 1 2 erfc ( γ ) + e γ π q=1 ( 1) q H q 1 (γ) q! γ q [ ] q Ie ( f d ) 1 2π cos q φ e (l)dφ e (8) Eb 2π 0 Note that H q is the Hermite polynomial defined as H q (x) = ( 1) q e x2 q x e x2. Since φ e (l) is uniformly distributed, the expectation E {cos q φ e (l)} has the following values. E {cos q φ e (l)} = 1 2π cos q φ e (l)dφ e 2π 0 2 = q q 2 0, (q : odd), (q : even) (9)

3 3028 IEICE TRANS. FUNDAMENTALS, VOL.E89 A, NO.11 NOVEMBER 2006 From Eqs. (6), (7), (8), and (9), the bit error rate of the DS/SS system in the presence of single-tone interference is given as follows. P tone ( f d ) = 1 2 erfc( γ) + e γ H 2q 1 ( γ)γ q π 2 2q q!q! q= BPSK Interference [ Ie ( f d ) Eb ] 2q (10) Next BPSK interference is investigated. BPSK transmits data by alternating its phase from 0 to π,orviceversa.when the BPSK interference is present, its phase alternation may occur within a bit duration of the DS/SS system. Therefore the effect of the phase alternation must be considered. There are 2 possible cases. case1: No phase alternation occurs within a bit duration of the DS/SS system case2: Phase alternation occurs within a bit duration of the DS/SS system Thus, to acquire the total bit error rate of the DS/SS system, it is required to average the bit error rate in either case above. In this paper, it s assumed that the symbol duration of the BPSK interference T s = M s T c is longer than the bit duration of the DS/SS system T b = M T c. It s also assumed that BPSK phase alternation may occur at any moment within the DS/SS bit duration in equal probability. According to the assumptions above, the probability of each case is p 1 = 1 M 1, (11) p 2 = M 1. (12) Suppose BPSK interference has amplitude A and its frequency f I. Since a part of BPSK interference without phase alternation can be regarded as single-tone interferer, the bit error rate of case 1 is given as follows. P e1 ( f d ) = P tone ( f d ) (13) To obtain the bit error rate of case 2, it is first clarified how BPSK interference is despread when phase alternation is present. Suppose BPSK interference î(m, n) has its phase alternation at the m-th sample (1 m M 1) within DS/SS bit duration. We then let c (m, n) denote a chip code with phase alternation at the m-th sample. { c c (m, n) = (n), 0 n m 2 c (14) (n), m 1 n M 1 As shown in Fig. 3, despreading î(m, n) by c (n) is equivalent to despreading single-tone interference by c (m, n). Next I b ( f d, m) is introduced to denote the absolute Fig. 3 Despreading of BPSK interference. value of despread i(m, n). M 1 I b ( f d, m) = c (m, n) A e j2π f dnt c (15) n=0 Using I b ( f d, m), the bit error rate of the DS/SS system in such case can be written in the following form. P e2 ( f d, m) = 1 2 erfc( γ) (16) + e γ H 2q 1 ( γ)γ q [ ] 2q Ib ( f d, m) π 2 2q q!q! Eb q=1 From Eqs. (11), (12), (13), and (16), we get the average bit error rate of the DS/SS system in the presence of BPSK interference as the following. P BPS K ( f d ) = ( 1 M 1 + M m=2 3. Numerical Results ) P e1 ( f d ) 3.1 The Effect of Chip Code Filtering 1 P e2 ( f d, m) (17) In this paper, we define SIR as the following. SIR= E b (18) A 2 T b Note that A is the amplitude of the interference. E b and T b is the bit energy and the bit duration of DS/SS signal, respectively. Table 1 shows the simulation parameters used to validate the results of analysis. As shown in Fig. 1, the data is modulated with BPSK at the bit rate of 100 Mbps. The modulated signal is then spread by the filtered DS-UWB Ternary code (length:25) at the chip rate 2.5 Gcps. During transmission at the baseband, the noise and the interference is added to the signal. The received signal is then despread by the

4 SHIMIZU and SANADA: ANALYSIS ON INTERFERENCE REJECTION OF DS/SS SYSTEMS USING A COMPLEX FIR FILTER 3029 Table 1 Simulation parameters. 1st Mod. BPSK 2nd Mod. DS/SS Bit rate of DS/SS R b 100 Mbps Chip rate of DS/SS R c 2.5 Gcps Chip code c(n) Filtered DS-UWB Ternary code (M:25) Filter delay T d T c Filter coefficients h 0 = 1,h 1 = i Spectral null of DS/SS signal GHz Fig. 6 The effect of BPSK symbol duration change. Fig. 4 Fig. 5 BER vs. E b /N 0 (Single-tone interference). BER vs. E b /N 0 (BPSK interference). filtered chip code to recover the data sequence. An FIR filter with coefficients h 0 = 1andh 1 = i is used for chip code filtering. With the DS-UWB Ternary code input into this filter, we take the output sequence of length 25 as the chip code for this system. Due to this filtering, a null is inserted at GHz in the spectrum of DS/SS signal spread by the filtered chip code. Note that the delay time between each filter tap is equal to the chip duration of the DS/SS system, T c = 0.4ns. Figures 4 and 5 show the BER performance of DS/SS when the center frequency of the interference is right at the spectral null, GHz. In this case, the symbol duration of the BPSK interference T s is fixed to 0.1µs which is as 10 times longer as the bit duration of DS/SS T b. As shown in Figs. 4 and 5, the effect of Single-tone interference is perfectly suppressed by FIR filtering, while BPSK interference still causes performance degradation. Because of the bandwidth of BPSK interference BW = 2 T s, the spectra of DS/SS and BPSK have slight overlap. This is why the FIR filtering is less effective against BPSK interference. Figure 6 show how the performance improves as the symbol duration of BPSK interference gets longer.r is the ratio between BPSK symbol duration T s and DS/SS bit duration T b,definedasr = T s T b. Greater R means narrower BW, and less spectrum overlap between DS/SS and BPSK interference. Figures 7 and 8 show the performance of when the interference frequency is not at the spectral null. f null means the frequency of the spectral null introduced by chip code filtering. In this case, f null is located at GHz. The X axes of both figures mean the frequency gap between f null and the center frequency of the interference. The gap is normalized with the chip rate of DS/SS, R c. In both results the performance against frequency gap has similar tendency. In addition to f null, the performance is improved at 2 independent frequencies. This is due to the spectral shape of the filtered chip code. Figure 9 shows the spectrum of the filtered chip code. The spectrum has a null inserted by filtering. In addition to this null, the spectrum gets low at two distinct frequencies, (A) and (B). This is why the system shows fine BER at frequencies other than f null. In all cases above, the theoretical and simulated bit error rate suit well together. 3.2 Comparison with Received Signal Filtering Here, we have investigated how the performance of the chip code filtering differes from that of received signal filtering. In the received signal filtering system, the chip code is unmodified,

5 3030 IEICE TRANS. FUNDAMENTALS, VOL.E89 A, NO.11 NOVEMBER 2006 Fig. 7 BER vs. Frequency gap (Single-tone interference). Fig. 10 Performance comparison against BPSK interference (R=10). Fig. 8 BER vs. Frequency gap (BPSK inteference). Fig. 11 Performance comparison against BPSK interference (R=100). Fig. 9 The spectrum of the filtered chip code. Fig. 12 Performance comparison against BPSK interference (R=1000). the received signal is filtered before despreading. For received signal filtering, we have employed FIR filters whose bandwidth is equal to that of the filter used for chip code filtering. We have evaluated 2 different number of filter taps, 1 and 20, for comparison. The target interference here is BPSK signal of the center frequency of GHz, and the parameters in Table 1 are used for the chip code filtering. The original (unfiltered) DS-UWB Ternary chip code is used in the received signal filtering system. In addition, we assume the amount of phase

6 SHIMIZU and SANADA: ANALYSIS ON INTERFERENCE REJECTION OF DS/SS SYSTEMS USING A COMPLEX FIR FILTER 3031 shift due to receivd signal filtering is known to the system. As shown in Figs. 10, 11, and 12, the chip code filtering marks superior performance to the received signal filtering when E b /N 0 is less than 10 db. When E b /N 0 is greater than 10 db, however, the received signal filtering with singletapped FIR filter stands out the rest. The effect of 20-tapped FIR filtering appears to be the worst at all time. The reasons for this are the following. 1. The signal power loss due to filtering 2. The spectral shape of the original chip code 3. The notch depth of the filters First, the received signal filtering does diminish the received signal power while the chip code filtering does not. Therefore, the chip code filtering has the best performance at low E b /N 0. Besides, the 20-tapped FIR filter has steeper gain response than the single-tapped one in the same frequency band. That leads to severer power decay, and the poorest performance when the E b /N 0 is less than 10 db. Secondly, the spectral shape of the original chip code allows the single-tapped signal filtering to excel the others at high E b /N 0. The original chip code has a slightly low spectrum at the center frequency of interference, GHz. Thus, besides filtering, the interference power is reduced by despreading with the original chip code. That is why the signal filtering with the single-tapped FIR is more effective when the E b /N 0 is high. Last of all, the notch depth of the 20-tapped FIR filter causes performance degradation. The gain response of the 20-tapped filter has ripples in its stop band. These ripples deterrs the filter from obliterating the interference completely. Unlike the 20-tapped filter, the single-tapped one has zero gain response right at the center frequency of the interference. Hence, both the chip code filtering, and the signal filtering with the single-tapped filter achieve better performance than the 20-tapped signal filtering. 4. Conclusion In this paper, we analyzed the performance of interference suppression scheme employing an FIR filter for chip code manipulation. Against single-tone and BPSK interference, the chip code filtering proved to be more effective than the received signal filtering when the E b /N 0 is less than 10 db. [3] K. Nishioka, W. Horie, and Y. Sanada, Wireless and battery-less high-speed communication module using spread spectrum modulation, Proc. Eighth International Symposium on Wireless Personal Multimedia Commun., vol.3, pp , Aalborg, Denmark, Sept [4] V.E. Comley, P.C.J. Hill, and R.D. Barfoot, Chip Code Manipulation for interference rejection in DS/SS systems, IEEE Mil. Commn. Conf., vol.3, pp , Oct [5] N.J. Bershad, Error probabilities for DS spread spectrum systems using an ALE for narrow-band interference rejection, IEEE Trans. Commun., vol.36, no.5, pp , May [6] A. Rosenbaum and F. Glave, An error-probability upper bound for coherent phase-shift keying with peak-limited interference, IEEE Trans. Commun., vol.22, no.1, pp.6 16, Jan Yuki Shimizu was born in Kyoto in He received his B.E. degree in electronics engineering from Keio University, Yokohama Japan in Since April 2006, he has been a graduate student in School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University. His current research interest is in DS/SS communication systems. Yukitoshi Sanada was born in Tokyo in He received his B.E. degree in electrical engineering from Keio University, Yokohama Japan, his M.A.Sc. degree in electrical engineering from the University of Victoria, B.C., Canada, and his Ph.D. degree in electrical engineering from Keio University, Yokohama Japan, in 1992, 1995, and 1997, respectively. In 1997 he joined the Faculty of Engineering, Tokyo Institute of Technology as a Research Associate. In 2000 he jointed Advanced Telecommunication Laboratory, Sony Computer Science Laboratories, Inc, as an associate researcher. In 2001 he jointed Faculty of Science and Engineering, Keio University, where he is now an assistant professor. He received the Young Engineer Award from IEICE Japan in His current research interest is in software defined radio and ultra wideband systems. Acknowledgement The first author would like to thank Mr. W. Horie, University of Keio, for his unbelievably helpful suggestion and astonishingly valueble comments. References [1] I. Howitt and F. Awad, Optimizing IEEE b packet fragmentation in collocated Bluetooth interference, IEEE Trans. Commun., vol.53, no.53, pp , June [2] Z. Zeng, B. Allen, Z. Liu, and A.H. Aghvami, Evaluation of IEEE b and Bluetooth coexistence in an office environment, IEE International Conf. on 3G Mobile Commun. Tech., pp.54 58, 2004.