A Novel High Capacity Frequency Hopping Spread Spectrum System Suited to Power-line Communications

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A Novel High Capacity Frequency Hopping Spread Spectrum System Suited to Power-line Communications Gen Marubayashi SOKA University 1-236 Tangi-cho Hachioji-shi Tokyo Japan Fax : +81-426-91-9312

1 A Novel High Capacity Frequency Hopping Spread Spectrum System Suited to Power-line Communications Gen Marubayashi SOKA University Tangi-cho Hachioji-shi Tokyo Japan Fax : marugen@t.soka.ac.jp Abstruct A novel multilevel FSK frequency hopping system in which informations are transformed to both levels and hopping patterns to achieve high transmission capacity is proposed. The system is an extention of the FWMultilevel FSK system proposed by Goodman et.al. to two dimensional scheme. n principle close analogy may be seen between the M-ary DS system and the proposed system when replacing hopping patterns in the proposed system by PN sequences. Analytical results verify the effectiveness of this system for the power-line communications. 1. ntroduction Frequency Hopping Systems(FH) andlor Frequency Shift Keying System(FSK) are considered to be extremely suited to power-line signal transmission because of its robustness to impulsive noise disturbances. An impulsive noise will directly affect the information bits in a time domain system such as Direct Sequence Spread Spectrum System(DS) however in a frequency keyed system informations are carried always by narrow frequency spectrum and only a small portion of the impulsive noise frequency spectrum affects the information signals during small duration of time. n a FSK system when we want to decrease the bit error rate of the system we must narrower the frequency spectrum of each frequency t6ne which lead to decrease the transmission rate. To increase the transmission rate M-ary FSK systems are invented. However in this system several information bits are allocated to each frequency tone so that a single tone disturbance cause burst errors and strong error correction is needed. FWMultilevel FSK system proposed by Goodman, Henry, Prabhu improves the above mentioned defect of the M-ary FSK system by applying fast frequency hopping scheme and majority decision technique and achieved high spectral efficiency with good reliability. n this paper a modified version of the FWMultilevel FSK system is proposed which enables about twice rate transmission. The system is conveniently named as FWM-ary Multilevel FSK system. As suggested by this name close analogy may be seen between the M-ary Direct Sequence Spread Spectrum system and the proposed system when replacing PN sequences in the M-ary DS system by hopping patterns in the proposed system. The effectiveness of the proposed system can easily be understood from the above analogy. Characteristic feature of the proposed system is that in a conventional frequency hopping system each system in a multiple access system uses only one hopping pattern as their address, in contrast, in a proposed system each system in a multiple access system uses plural number of hopping patterns and an information symbol can be determined by designating both the frequency level and the hopping pattern. n the following system principle and analytic formulas for the single channel transmission and several results of calculations for the impulsive noise environments transmission are given. 2. System principle System configuration of the proposed system is shown in Fig.l. n the transmitter incoming first K, data bits are transformed to levels by the encoder and next K2 data bits are sent to the data selector which selects a corresponding hopping pattern. Transformed levels and the selected hopping patterns are added by a modulo 2 adder chip by chip as shown in Fig.2. These operations are just the same as that of the FWMultilevel FSK system except that the hopping pattern is not fixed. n the proposed system hopping patterns are used to carry informations so that some means to give address are needed. n Fig.2 an illustrative method of giving address using scrambler is shown. Each system has its own particular scramble rule and can be used as a hidden key. Methad of giving address is not confined to this example. After getting address levels are transformed to tones by a tone generator and transmitted to the line. At the receiver received tones are first transformed to levels by a spectrum analyzer and then descrambled by, a descrambler(fig.3). The descrambler acts just the reverse operation as the scrambler. From the descrambled levels each hopping pattern in the receiver is subtracted by modulo2 base. Finally subtracted outputs are put into the decision circuit and the decision circuit finds in what pattern in what level transmitted information exists and finally decides the transmitted information bit, i.e. K=K+K2. The FWMultilevel FSK is considered to be the special case in which K2=0. K2 directly relates to the obtainable number of hopping patterns and to the error probability and requires further study, however, with a rule of them it is safe to assume K OK2. n the following

2 analysis K, is set equal to K2. When we postulates K=K2 we can transmit twice bit rates as high as that of the FWMultilevel FSK system for the same number of L shown if Fig.2 and 3, however, in the proposed system slightly larger numbers of L will be needed to achieve the same bit error rate because of increased number of probability elements. 3. mpulsive noise environment considerations n the power-line signal transmissions impulsive noise disturbances is considered to be the major problem. mpulsive noise in a power-line can be classified as 1. mpulses arose from switches on off of the electric appliances connected to the line. 2. mpulses occurring in synchronous to the electric source voltage zero-crossings. Frequency of occurrence of class 1 impulse is small and its average power is low. Class 2 impulse is the major problem. Consider an impulsive noise with the peak voltage VN and width At in a period T as shown in Fig.4(a). Fig.4(b) shows its power spectral density. n which No represents the average power spectral density over the transmission bandwidth W. Let Pa represents the average power in which R is the line impedance. Then Next consider a FSK signal of peak amplitude Vs and duration Th as shown in Fig.S(a). When we use n such frequency tones in a system then Spectral width of a tone is about 2W/n. Fig.S(b) shows the spectral relationship between signal and noise. Signal power is and noise power is calculated as then signal to noise ratio is obtained as Now consider the class 2 impulsive noise. Assuming 50 Hz electric source the time interval between successive zero-crossings is 10 msec. For the power-line impulsive noise it was reported that VN sometimes exceeds looov however these may considered to be the class 1 type noise otherwise the average power becomes unreasonably large. For the cyclic impulsive noise average power of below 1 watt seems to be reasonable. As for the values of At according to various measurement results almost all pulses At can be assumed to lie between 1OOlOO psec. These figures in mind as an typical example let suppose a cyclic impulsive noise of At=SOps, VN=lOOV, T=lOms. Suppose we use 100 tones (n=100) and let S/N=l, then from equation(6) we get Vs=V. f we postulate W=400kHz then from equation(3) T,,=250ps. This means that only a portion of 115 of a tone suffers from the impulsive noise disturbance of S/N=l. These figures may enough suggest the reliability of the system. 4. Error rate formulae The proposed system can be applied for mobile radio also. n that case it will be used as a multiple access system. For the power-line transmission usual way of application will be a single channel packet communication scheme so that it may not be necessary to consider multiple users at a time, however in the following, error rate formulae for the multiple access system will be shown for completeness. Parameters Number of bits in a symbol : K Number of chips in a symbol : L Number of frequencies(number of levels) : n Number of hopping patterns : h

3 Number of simultaneous users : M Detection probability : PD False alarm probability : PF Probability density function P(V) of the envelope V(t) when both signal and noise exist. where : signal amplitude 0: : noise power at the output of the band pass filter o(z) : first kind zeros order modified Bessel function False alarm probability PF where b : threthold level bo : threthold level normalized by effective noise voltage Detection probability pd = 1 - Q(&J,) - SNR where y= 10 SNR : signal to noise ratio in db ~(a, P) = J X, (m)e-g2+a2)12dx... Marcum Q function (1)correct hopping pattern case Probability of interfering signals invasion P Probability of invasion of both interfering signals and the false alarm 4=P+P,-P.P, Probability of existing m tones in a level with L chips Ps(m) (rn) = rl k,l(l- p,)l-lll nz 1 Probability of existing k raws with maximum number of q error tones P(q,k) 1 ("; J-" P(q,k) = P, (dl: C P, (4 m=o when q=o P(O, n - 1) = [P, (o)j- P(0, k) = 0; k # rz - 1 when k=o \ m=o Probability of i chips among L chips have correct tone inputs Pc(i) (2)wrong hopping pattern case Probability of interfering signal invasion P1

4 Probability of invasion of both interfering signals and the false alarm P1 P =P1+PF -P1.PF Probability of existing q tones in a level with L chips Pls(q) PS (4) = jl ki: (1 - P, ) ~-q 4, Probability of existing k raws with maximum number of q error tones Pl(q,k) when q=o.. Pl(O,n) = [P, (0)1' Pl(0, k) = 0; k # n when k=o h 1 Pl(q.0) = (5.1. T u =O (u) Probability of number of hopping patterns with q inputs is h, when hopping pattern are wrong choiced Pl h(q,hq) [ h-1 Pl. (4, hq )= kplq(4))l- {Pl(q.o)~-~-~~q hq 1 (3)bit error rate Symbol error rate Pw 1 L "-' P, (i, m) "-' P(i, k) z+l P, =l-c~,(i)z i=o m=o m+l Bit error rate Pb, 1 5. Results of analysis Using analytical formulae shown in section3 numerical analysis has been made for the power-line transmission with 450kHz bandwidth. A result of calculations is shown in Fig.6. n deriving the figures equal transmission power for different n is assumed so that SNR varies in accordance with n. Similar results for FH/Multilevel FSK system is shown in Fig.7 for comparison. As shown in the figure about twice bit rate can be achieved by the proposed system compared to FWMultilevel FSK system. 6. Conclusion. n this paper a novel frequency hopping system is proposed and the effectiveness of the system for the power-line transmission is discussed. Results of analysis show its high capacity transmission features. Detailed study for the optimum design is left for future study and further improvements can well be expected. 7. Reference D:J.Goodman, P.S.Henry, V.K.Prabhu : "Frequency Hopped Multilevel FSK for Mobile Radio", Bell System Tech. J., Vo1.59, No.7, Sept Scrambler Transmit MODULO(n) signal Series Encoder -Un,.mWnn, W'"'- Data Y, Output to W,,32 selector -+ generator 0 Kbits A i G, parallel 4 vm Hopping pattern converter WML - ' 1 Pattern P Pattern 2 -- e i 1 z: 1 Xm Address ~ransrnitter(wmm~~~)

5 Received signal Descrambler Series selector converter. MODULO(n1 Pattern 1 P. detector Binary output nput dalo(q) Scrambler ~~ltput Transmit signal LM 4f ECL iiii Deleclion matrix T.,=qglH.,: h... ' T.4 n 4 cteaiun level... Fig.2 System Operation(transmitter) D 6 Signal D $ Noise Fig.3 System Operation(receiver) Fig. 1 System Configuration : Fig.4 mpulsive Noise 1 0 d) fb Burst noise spectrum (b), t b v J J N, 1 T h (a) Fig.5 0 FSK signal... 4-b AW (b) W ;:::::: 4-1 FH/M M FSK [PF=0.01]

MMFSK-EOD System Using Binary Hopping Pattern in FH/SS Communications

JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 2, MARCH 2009 119 MMFSK-EOD System Using Binary Hopping Pattern in FH/SS Communications Suguru Hasegawa Nagaoka University of Technology, Department of Electrical