Performance of FH-MFSK cellular mobile radio in the presence of nonsynchronous users

he p o ile exhibi s wo dis inc 'slow e ching' c ys al planes: (Oil) and (lll)B. This obse a ion is consis en wi h he wo k o Cold en e a/.4 on he sensi i i y o he e ch a e o InP in HC1 o he c ys al o ien a ion. The p o ile in Fig. 2 was ob ained using a mix u e o 1(HC1): 3(H3POJ (again he g a ing o ien a ion is (Oil)), In his case he p o ile is ec angula wi h a dep h o c*2000 A. He e, he e ched dep h is no limi ed by he o ma ion o in e sec ing slow-e ching planes, and he ec angula p o ile p oduced is pa icula ly a ac i e o use in second-o de DFB lase s since a s aigh o wa d Fou ie analysis shows i o con ain =s: 1270 A o he desi ed 0-23 jum pe iod ha monic componen ( he ma k/space a io was aken o be =* 1/3). By compa ison he commonly used iangula p o ile3 con ains only 666 A o his componen . Fig. 3 As Fig. 1, e ched in 1{HCI): l(CH3C00H) Dep h =a 2000 A A ec angula p o ile was also achie ed using 1(HC1): 1(CH3COOH) as he e chan . Fig. 3 shows he c oss-sec ion o a g a ing o med in his e chan —again he dep h is ^2000 A. A pa icula ad an age o he use o elec on-beam-exposed g a ings is ha , by a ying he exposu e dose, di e en g oo e ma k/space a ios can be ob ained. Toge he wi h con olled o e -e ching o he SiO2, his has allowed us o ab ica e nea ly saw oo h g a ings, con aining i ually no second- ha monic Fqu ie componen (Fig. 4). The e chan used was l(HB ):l(CH3COOH) and in his case he g a ings we e aligned in he (Oil) di ec ion. The g a ing dep h, which is limi ed by he o ma ion o (111)A planes, is ^3200 A. IA12/4I Fig. 4 As Fig. 1, e ched in l(HB ):(CH3COOH) Dep h a 3000 A in conclusion, we ha e demons a ed a submic ome e bile el p ocess o he p oduc ion o semiconduc o di ac ion g a ings and ha e ab ica ed a ange o new g a ing p o iles in InP using his echnique. These p o iles, ha ing a ied Fou ie ha monic spec a, should pe mi he p oduc ion o mo e e i- cien op oelec onic g a ing de ices. Acknowledgmen s: The au ho s hank C. Dix o elec on- beam exposu e o he g a ing pa e ns, P. Rodge s o assis - ance wi h he d y e ching and B. Wake ield o SEM e alua ion. They also acknowledge he Di ec o o Resea ch, B i ish Telecom, o pe mission o publish his le e . L. D. WESTBROOK 9 h No embe 1983 A. W. NELSON P. J. FIDDYMENT B i ish Telecom Resea ch Labo a o ies Ma lesham Hea h, Ipswich, Su olk IP5 7RE, England Re e ences 1 UTAKA, K., AKIBA, S., SAKAI, K., and MATSUSHIMA, Y.: 'Room- empe a u e CW ope a ion o dis ibu ed- eedback bu ied* he e os uc u e InGaAsP/InP lase s emi ing a 1-57 (mC, Elec on. Le ., 1981,17, pp. 961-962 2 TANBUN-EK, T., ARM, S., KOYAMA, F., KISHINO, K., YOSHIZAWA, S., WATANABE, T., and SUEMATSU, Y.:* 'Low- h eshold cu en CW ope a ion o GalnAsP/InP bu ied-he e os uc u e dis ibu ed* B agg- e lec o lase emi ing a 1-5-1-6 .im ibid., 1981, 17, pp. 967-968 3 WESTBROOK, L. D., NELSON, A. w., and DIX, c: 'High-quali y InP su ace co uga ions o 1-55 /Am InGaAsP DFB lase s ab ica ed by elec on-beam li hog aphy', ibid., 1982,18, pp. 863-865 4 COLDREN, L. A., FURAYA, K., MILLER, B. I., and RBNTSCHLER, J. A.: 'Combined d y and we e ching echniques o o m plana (011) ace s in InGaAsP/InP double-he e os uc u es', ibid., 1982, 18, pp. 235-237 PERFORMANCE OF FH-MFSK CELLULAR MOBILE RADIO IN THE PRESENCE OF NONSYNCHRONOUS USERS Indexing e ms: Telecommunica ion, Synch onisa ion, Mobile adio sys ems Mon e Ca lo simula ion o an FH-MFSK sp ead«spec um cellula mobile adio sys em in he p esence o nonsyn- ch onous use s is p esen ed. Impai men s such as sho - e m and shadow ading a e in oduced. Pe o mance cu es showing he numbe o simul aneous use s he sys em can accep a e gi en. Bo h clus e ing and no-clus e ing s a egies a e conside ed. In oduc ion: A mul ile el equency-shi -keying (FH-MFSK) sp ead-spec um communica ion sys em has been ecen ly p oposed1 o cellula mobile- adio elephony. This sys em appea s o pe o m be e han o he FH-DPSK sys ems, i s p oposed in Re e ence 2, when only one isola ed cell is con- side ed. Howe e , a mo e ealis ic assessmen o he FH-MFSK sys em calls o an analysis o i s pe o mance in a m-ul icell con ex . An a emp o e alua e he numbe o simul- aneous use s ha could be handled a a bi e o a e o 10"3 was unde aken in Re e ence 3. In his pape 3 a mobile- o- base ansmission model was p oposed and sys em impai - men s such as in acell in e e ence om nonsynch onous use s and adjacen equency channels in he p esence o ma ched uned ecei e il e s we e analysed. Fo in e cell in e e ence, a Gaussian app oxima ion was used and only quali a i e esul s we e gi en wi hou any quan i a i e assess- men being p esen ed so a . In his le e we p esen a compu e simula ion o he FH-MFSK ansmission model men ioned3 abo e, allowing a mo e p ecise e alua ion o he numbe o simul aneous use s ha he sys em can ole a e when in e cell in e e ence is con- side ed. Mon e Ca lo simula ion: I was shown in Re e ence 1 ha he sys em bi e o a e Pb could be eadily ob ained om he inse ion p obabili y P, and miss p obabili y PM ss. These alues we e o mula ed in Re e ence 3 as P, = p ob (| ( )n/x) > Co) and (| Re-jeS0( ) ELECTRONICS LETTERS 8 h Decembe 1983 Vol. 19 No. 25/26 ) < Co) 1077 whe e x is he sampling ime, ( ) is he in acell in e e ence signal, n ( ) is he ecei ed Gaussian noise, Co is a h eshold decision alue, Re~jeS0{ ) is he desi ed signal, 10 S0( ) 0 < < X - + 2x x< <2x R and 0 a e andom a iables, namely he Rayleigh and uni o m dis ibu ions, espec i ely, and //c( ) is he in e cell in e e ence. De ails abou he na u e o ( ) and IIC( ) a e gi en in Re e ence 3. The abo e o mulas a e main ained i clus e ing is used, bu in his case he bandwid h a ailable o each cell is he whole bandwid h a ailable di ided by he numbe o hexagonal cells which compose a single clus e (see Fig. 1). Fig. 1 Hexagonal cell layou wi h clus e s o se en cells The beha iou o P and PMISS can be eadily de e mined by Mon e Ca lo ials. I is me ely necessa y o gene a e inde- penden uni o mly dis ibu ed a iables; hen, by using he adequa e ans o ma ions, samplings o ( ), M/T), //C(T) and Re~jeS0(x) can be ob ained. This p ocess is epea ed N imes, and ul ima ely we ha e N P'**W whe e 1 i | {x) + //C(T) + n/x) | > Co |0 o he wise N MlSS — N whe e { Re-»SQ{x) + {x) 0 o he wise n (x) | < Co 1 id1 I bi < 10 M=20 o =3 5 ^>>%((^ 40 ^-^^^ 35 "^^^ 30 }-& Fig. 3 Bi e o a e in a mul icell sys em assuming Gaussian in e - e ence (do s ep esen Mon e Ca lo simula ion poin s) N = 10000 was aken. Inc easing his alue p oduced a negli- gible change in he esul s bu ma kedly inc eased un ime. I can be obse ed ha he e may be some ques ion ega ding he accu acy o hese esul s, pa icula ly o Pb alues smalle han 10"3. Fo una ely hese Pb alues a e no usually handled in mobile- adio elephony. Resul s: Fig. 2 shows he FH-MFSK sys em pe o mance in he p esence o six adjacen in e e ing cells. E e y hexagonal cell con ains M simul aneous use s, he ansmission a e pe use is 32 kbi /s, and he bandwid h conside ed in each cell is he whole 20 MHz a ailable. Powe con ol in he mobileSj a mean pa h loss exponen a o —3-5 and a logno mal dis ibu- ion modelling he shadow ading wi h 8 dB s anda d de i- a ion ha e been aken in o accoun . Finally, op imum h es- hold decision alues we e ound a each signal/noise a io. Fig. 3 shows he esul s ob ained in Re e ence 3 by using he Gaussian app oxima ion o he in e cell in e e ence. Compa - ing Figs. 2 and 3 leads o he ealisa ion ha he Gaussian app oach is oo pessimis ic and a be e pe o mance could be expec ed. The do ed line o Fig. 3 also shows he FH-MFSK sys em pe o mance using he Mon e Ca lo simula ion and he Gaussian app oxima ion o he in e cell in e e ence o M = 20 simul aneous use s pe cell. This analysis se es as a check on he alidi y o he Mon e Ca lo echniques. In Re e ence 3 clus e ing was sugges ed as a s a egy o imp o e he mul icell pe o mance. In o de o gain insigh on 1 1030 c< =3 5 2530 15 20 25^ 30 5 1Q 15 20 |371/2| Ec/N0.dB Ec/N0.dB Fig. 2 Bi e o a e in a mul icell sys em om Mon e Ca lo simula ion Fig. 4 Bi e o a e in a mul icell sys em wi h a clus e o se en cells 1078 ELECTRONICS LETTERS 8 h Decembe 1983 Vol.19 No. 25/26 i s e ec s, he desi ed cell and i s six adjacen ones we e con- side ed o be a clus e o basic cell o epe i ion. The o he clus e s appea ing in he mul icell sys em we e no aken in o accoun because in a i s app oach he in e cell in e e ence a ising wi h he clus e ing s a egy was supposed negligible. The esul s plo ed in Fig. 4 show ha clus e ing wo sens he mul icell e iciency and consequen ly i s p esence in he FH-MFSK sys em is appa en ly no o be ecommended. The indica ion is ha he gains om sp ead-spec um p ocessing a e o se by inc eased in acell in e e ence, when his ac o is aken in o accoun . R. AGUST1-COMES 31s Oc obe 1983 F. CASADEVALL-PALACIO G. JUNYENT-GIRALT ETS1 Telecomunicacibn Apdo. 30 002, Ba celona, Spain Re e ences 1 GOODMAN, D. J., HENRY, p. s., and PRABHU, . K.: 'F equency- hopped mul ile el FSK o mobile adio', Bell Sys . Tech. J., 1980, 59, pp.1257-1275 2 COOPER, G. R., and NETTLETON, R. W. : 'A sp ead spec um echnique o high-capaci y mobile communica ions', IEEE T ans., 1978, VT-27, pp. 264-275 3 AGUSTI, R., and JUNYENT, G.: 'Pe o mance o FH mul ile el FSK o mobile adio in an in e e ence en i onmen ', ibid., 1983, •JOM-31, pp. 840-846 using he a e age alue and he a iance o he ecei ed signal 3 as MODE PARTITION NOISE CAUSED BY WAVELENGTH-DEPENDENT ATTENUATION IN LIGHTWAVE SYSTEMS Indexing e ms: Lase s and applica ions, Lase diodes, Op ical ansmission Powe luc ua ions among he longi udinal modes o lase diodes cause noise in he ecei ed signal a e being il e ed by a wa eleng h-dependen a enua ion mechanism. We ha e de eloped a heo e ical model o cha ac e ise his noise and s udied deg ada ion in ligh wa e sys em pe o mance. Powe penal ies obse ed in a 432 Mbi /s wa eleng h di ision mul iplexing sys em expe imen ag eed wi h heo e ical p e- dic ions. Mode pa i ion noise (MPN) in ligh wa e sys ems is caused by a combina ion o ins an aneous luc ua ion o he powe dis ibu ed among he lase modes and spec al il e ing in he ansmission pa h. MPN associa ed wi h ib e dispe sion causing phase delay in each pulse has been ex ensi ely dis- cussed in he li e a u e1 and ound o se one o he pe - o mance limi a ions in high-bi - a e ligh wa e sys ems. In his le e we desc ibe MPN caused by wa eleng h- dependen a enua ion in he ansmission pa h.2 MPN o his kind is especially impo an in designing WDM sys ems, whe e ansmission cha ac e is ics nea cu o wa eleng hs o mul iplexe s and demul iplexe s a e highly wa eleng h- dependen . Wa eleng h-dependen ib e a enua ion in long- haul sys ems also can cause his ype o MPN in addi ion o he MPN associa ed wi h ib e dispe sion, especially in sys em channels ope a ing nea he OH abso p ion peaks. Le a( and/- ep esen he ins an aneous powe in he lase 's i h mode and mode-dependen a enua ion in he ansmission pa h a wa eleng h A,, espec i ely. Then he signal ampli ude o each pulse a i ing a he ecei e can be gi en by = L ai i (!) Assuming ha he powe is no malised such ha £,- a, = 1 and ha he pa i ioning is cons an o e he du a ion o each pulse bu andom om pulse o pulse, MPN can be desc ibed (2) whe e as ep esen s ime-a e aged powe o he i h mode and mode pa i ion coe icien k ep esen s a measu e o he powe which luc ua es. The coe icien k is assumed o be cons an o all modes. The noise- o-signal a io due o MPN can be gi en by N/S = a2 = <T2JP (3) The powe penal y AP, which is de ined as he inc ease in ecei ed powe necessa y o main ain an e o a e equal o he one wi hou MPN, is hen gi en by (4) whe e Qc = l/< p and Q is he Q- alue associa ed wi h a gi en bi e o a e.4 Al hough eqns. 2-4 can be calcula ed nume ically o a gi en lase spec um and il e ing cha ac e is ic, i is use ul o ob ain an analy ical o mula o e alua e sys em pe o mance by making he ollowing assump ions. The ime-a e aged en elope o he lase spec um is app ox- ima ed wi h a Gaussian cen ed a wa eleng h Xc and o hal - wid h AX: 1exp[-(/l-Ac)2/2(AA)2](5) The wa eleng h-dependen a enua ion is assumed o be linea wi h wa eleng h a ound Xc: (6) whe e A ep esen s a e o a enua ion change in dB/nm. Sub- s i u ing eqns. 5 and 6 in o eqns. 2 and 3 and app oxima ing he sums wi h in eg als yields <x2 = e2(exp [04 AA/4-34)2] - 1) (7) and om eqn. 4 he powe penal y is gi en by AP = -5 log.o {1 - e2 c2(exp [(A AA/4-34)2] - 1)} (8) T ansmission deg ada ion due o MPN was in es iga ed expe imen ally as he op ical signal was sen h ough a g a ing demul iplexe used o a single-mode wo-channel WDM sys em expe imen .5'6 The powe penal ies due o MPN we e de e mined om bi e o a e (BER) agains ecei ed powe measu emen s wi h and wi hou he demul iplexe . Bu ied- he e os uc u e (BH) InGaAsP/InP lase s we e modula ed wi h 432 Mbi /s NRZ o ma . Fig. 1 shows he spec al a enua ion o he g a ing demul iplexe and he ope a ing wa eleng hs o lase ansmi e s. Table 1 summa ises lase spec a and ansmission il e ing cha ac e is ics. Also gi en a e MPN penal ies measu ed a 10 ACB 1200 1300 1 wa eleng h ,nm [577/il Fig. 1 Spec al a enua ion o g a ing demul iplexe and lase ope a ing wa eleng hs ELECTRONICS LETTERS 8 h Decembe 1983 Vol. 19 No. 25/26 1079