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Effects of Partial-Band Noise Interference on the Hybrid DS/SFH MSK System in Rayleigh Fading Channel Heung-Gyoon Ryu, Member, IEEE, Yun-Young Kim Abstract – In Rayleigh fading channel, effects of the partial-band Electronic Engineering, Chungbuk National University, Cheong-ju, noise interference on the performance of a hybrid DS/SFH MSK 361-763, Rep. of Korea. system are analyzed, and the interference environments that cause the worst BER are investigated. Results show that, in Rayleigh fading channel, the full-band interference always causes the worst performance, independent of the average SNR or average SIR. On the other hand, in AWGN channel, the full-band interference in low SIR and the partial-band interference in high SIR result in the worst case BER, respectively, for all SNR. Index Terms- hybrid, Rayleigh, AWGN, DS, SFH, BER, SNR, SIR. I. INTRODUCTION T O DATE, the studies on spread-spectrum multiple access systems have been performed according to the various modulation techniques. In the literature, there was a paper on < Transmitter Structure> the performance analysis of the hybrid DS/SFH MSK system in AWGN channel with multi-tone jamming [1]. However, it did not consider the fading channel environment. Also, there has been no paper on the hybrid DS/SFH MSK system in Rayleigh fading channel with the partial-band noise interference (PBNI). In this Letter, a novel analysis on the above system is presented. After the numerical analysis, the interference environments that cause the worst case BER performance are investigated. II. SYSTEM MODEL < Partial-band Noise Interference > For the MSK modulation, the transmitted signal takes the form t sMSK (t ) 2 P c1 (t )d1 (t ) cos 2 ( f c f h (t )) Tc t c2 (t )d 2 (t ) sin 2 ( f c f h (t )) (1) Tc where f c is carrier frequency, P is the power of the information signal, d1 (t ) and d 2 (t ) of the duration T s are data < Receiver Structure > sequences of I and Q channels, and c1 (t ) and c 2 (t ) of duration T c are DS spreading sequences of I and Q NI WI W , fI f fI I channels. It is assumed that there are N chips in T s , S( f ) 2 2 2 (2) i.e., N Ts / Tc . The f h (t ) of the duration T h is hopping 0, el sew here frequency derived from a set of N FH frequencies equally where f I and WI are the center frequency and the spaced, and the number bandwidth of the PBNI, respectively. Denoting PI as the of transmitted data per hop is a positive integer. is the received total interference power, then the psd of PBNI is random phase in the transmitter and uniformly distributed in N I / 2 P I / 2Wss , where is the interference fractional ratio, [0,2]. Assuming that the considered I/Q decision statistics are and Wss is the total spread-spectrum bandwidth. Because WI independent, it is true that the analysis on the I-channel can be is very small compared with f I , the PBNI is the narrow-band sufficient for giving the system BER. Thus, only I channel is bandpass process[3]. Thus, considered for simplicity of analysis. The PBNI is band-limited white Gaussian noise and its power spectral density(PSD) is defind as [2] nI (t ) 2 ni (t ) c o s2( f I t ) nq (t ) s i n2( f I t ) (3) where ni (t ) and nq (t ) are inphase and quadrature com- Heung-Gyoon Ryu and Yun-Young Kim are with the department of ponents of nI (t ) , respectively, and these psds are equal to that 1 of nI (t ) . Zd Z I Z M Zn . (10) In this paper, the frequency-nonselective Rayleigh fading channel with L paths is considered and its impulse response In eq. (10), a desired signal term takes the form [4] ( n 1) Ts Z d nT s P / 2 1 c1 (t )c1 (t t 1 )d 1 (t t 1 ) L h(t ) k (t tk ) (4) cos(t / Tc ) cos(t / Tc 1 (t )) dt k 1 P / 8 1Ts d 1, n (11a) where t k and k are the time delay and the path gain, respectively, and the path gain k has Rayleigh distribution where d1,n is the n th data symbol of I channel. A term due to given by [3] the multi-path is given by 2 k p( k ) / k 2 e k (5) L ( n 1)Ts k Z M nT P / 2 k c1 (t )c1 (t tk )d1 (t tk ) k 2 s where k is the second moment of k . cos(t / Tc ) cos(t / Tc k (t )dt L (11b) Assume that the receiver is to be in synchronous with only P / 8 k cos( k ) the first path, but discards the others. Then, k can be assumed k 2 ( n 1)Ts to be related to the second moment of the reference path nT s c1 (t )c1 (t tk )d1 (t tk )dt . gain 1 , and its relation is given by [5] A term due to the PBNI is Z I . In eq. (9b), the psd of k 1 e ( k 1) (6) xI (t ) is uniformly distributed in the bandwidth of W DS , and, after the despreading procedure, the bandwidth of xI (t ) is the where is the decay rate of k . In this paper, we assume same as that of the demodulation signal. Therefore, Z I is that the path delay t k is uniformly distributed in [0, T s ]. ( n 1)Ts Z I nT s xI (t )c1 (t ) cos(t / Tc )dt III. ANALYSIS OF DECISION STATISTICS N 1 1 c1,i iT ( i 1)Tc ni (t ) cos( 2ft ) 2 i 0 c . (11c) Passing through the first BPF with the bandwidth of Wss , the received signal is given by nq (t ) sin(2ft ) cos(t / Tc )dt 1 N 1 ( i 1)Tc r (t ) rs (t ) nI (t ) n(t ) (7) nI (t )dt. c1,i iT 2 2 i 0 c L where rs (t ) k s MSK (t t k ) and n(t ) is the band-limted The last term is due to AWGN and given by k 1 ( n 1) Ts version of AWGN with a double-sided PSD of N 0 / 2 . Also, Z n nT s x n (t )c1 (t ) cos(t / Tc )dt. (11d) because the PBNI typically interfers the total spread-spectrum bandwidth with the probability of , which denotes the From eq. (11a) to (11d), the variances are as follows. var Z d 1PTs / 8 interference fracitonal ratio, nI (t ) is equal to the form of the 2 . (12) eq. (3). Denoting x1 (t ) as I channel output of the second BPF, it is var{ Z M } L k 2 P 16 2 ( n 1)T E{ k } var nT c1 (t )c1 (t tk )d1 (t tk )dts s written as (13) L PT 2 s 1e ( k 1) x1 (t ) BPF r (t ) cos 2 ( fc f h,1 (t ))t h,1 (t ) k 2 24 N xs (t ) xI (t ) xn (t ) . (8) 1 N 1N 1 ( i 1)T ( m 1)T var{ Z I } E c1,i c1, m iT mT ni (t )ni ( )dtd c c 8 i 0 m0 where f h,1 (t ) and h,1 (t ) are the dehopping frequency and c c 1 N 1 ( i 1)T ( i 1)T iT iT Eni (t )ni ( )dtd c c the phase generated from the frequency dehopper, respectively. 8 i 0 c c In eq. (8), NT 2 PW c I DS (14) 8Wss L x s (t ) P / 2 k f h,1 (t ), f h, k (t t k ) k 1 NN 0Tc c1 (t tk )d (t tk ) cost / Tc k (t ) (9a) var{ Z n } . (15) 8 xI (t ) BPF nI (t ) cos 2 ( fc f h,1 (t ))t k From the above variances, the signal-to-total interference power ratio is given by 1 n (t ) cos( 2ft ) n (t ) cos( 2ft ) i k q k (9b) zI 1 1 (16) 1 2 2Eb 2Eb 1 ( k 1) L e where f fc f h,1 (t ) f I . And, x n (t ) is the band-limited 3N k 2 NI N0 AWGN component. where Eb 1P / R, NI PI / Wss , and R is the bit rate. In eq. After despreading, the I channel correlator output Z 1 is (16), P / PI and Eb / N 0 denotes the average signal-to- ( n 1)Ts interference power ratio (SIR) and the average signal-to-noise Z 1 nT s x1 (t )c1 (t ) cos(t / Tc )dt ratio (SNR), respectively. Also, in case there is no interference, 2 the desired signal-to-total interference power ratio is 1 zn 1 . (17) 1 L ( k 1) 2E e b 3N k 2 N0 In the general fading channel, that is, the Rician fading channel, the pdf of the instantaneous signal-to-noise ratio is given by [6] 1 K z z p( z ) exp K (1 K ) I 0 2 ( K 2 K ) , z0 z z z (18) where K is the Rician factor, which denotes the power ratio of the direct wave and the indirect wave, and z and z denote the Fig. 2. The effect of the interference fractional ratio on the instantaneous SNR and the average SNR, respectively. Using system performance when SIR 20dB , L 2 and 3 . the eq. (18), the average bit error probability is obtained by Pe 0 Q z p ( z )dz . (19) The effect of the fractional ratio, , on the system performance is shown in Fig. 1, when the average SNR is fixed In eq. (19), we used Q z since we just consider z as the as 20dB. In Rayleigh fading channel, the worst case is when =1 (full-band interference), independent of the average SIR. total signal-to-interference ratio, not the pure SNR. In Rayleigh On the other hand, in AWGN channel, the performance of fading channel, since no direct component is present, K=0. system is different according to the average SIR. More Therefore, specifically, the full-band interference in low SIR and the partial-band interference in high SIR cause the worst case, 1 z . Pe 1 (20) respectively. 2 2 z Fig. 2 shows the effect of the fractional ratio on the system performance, in case the SIR is fixed as 20 dB. The worst case Replacing z with eq. (16) and (17), the average bit error BER, in Rayleigh channel, is occurred by the partial-band probabilities in case of being interfered and not, Pe, I and Pe, N , interference, independent of the average SNR. On the contrary, can be obtained, respectively. Consequently, the total bit error in AWGN channel, the full-band interference causes the worst probability in fading channel is given by BER, irrespective of the average SNR. Pb Pe, I (1 ) Pe, N . (21) V. CONCLUSION In this paper, the performance of a hybrid DS/FH MSK system is analyzed in Rayleigh fading channel with the partial- IV. NUMERICAL ANALYSIS AND DISCUSSIONS band noise interference, and the interference environments that In this section, when the total processing gain is fixed as cause the worst BER performance of the above system are 1000(30dB), we evaluate the BER performance of a hybrid investigated. Results show that, in Rayleigh fading channel, the DS/SFH-MSK system full-band interference always causes the worst performance, independent of the average SNR or SIR. On the other hand, in AWGN channel, the partial-band interference the worst case for high SIR (about 20dB) and the full-band interference for low SIR (about 0dB) result in the worst BER, respectively, independent of SNR. REFERENCES [1] H. Zheng and N. Zhang, “Performance Analysis of Hybrid DS-SFH/MSK Spread-Spectrum System under Multione Jamming,” IEEE MILCOM’99, pp. 567-570, 1999. [2] S. Kondo and L. B. Milstein, ”Performance of Multi- carrier DS CDMA Systems,” IEEE Trans. on. Commun., vol. 44, no. 2, pp. 238-246., February 1996. [3] J. G. Proakis, Digital Communications, 3rd ed., McGraw- . Hill, 1995. Fig. 1. The effect of the interference fractional ratio on the [4] Z Tan and I. F. Blake, "Performance analysis of system preformance when SNR 20dB , L 2 and 3 . noncoherent DS-SFH spread spectrum multiple access for indoor wireless communications," IEEE MILCOM '92, vol.3, pp.851-855, 1992. [5] T. Eng and L. B. Milstein, "Coherent DS-CDMA 3 Performance in Nakagami Multipath Fading," IEEE Trans. on Commun., vol. 43, no. 2/3/4, pp. 1134-1143, February/March/April 1995. [6] S. Sampei, Applications of Digital Wireless Technologies to Global Wireless Communications, Prentice-Hall, 1997. 4 5

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