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1 Ftton, M. P., Nx, A. R., & Beach, M. A. (1997). Propagaton aspects of frequency hoppng spread spectrum. n Proceedngs of the 8th EEE Personal and ndoor Moble Rado Conference, Helsnk, Fnland. (Vol. 2, pp ). nsttute of Electrcal and Electroncs Engneers (EEE). DO: /PMRC Peer revewed verson Lnk to publshed verson (f avalable): /PMRC Lnk to publcaton record n Explore Brstol Research PDF-document Unversty of Brstol - Explore Brstol Research General rghts Ths document s made avalable n accordance wth publsher polces. Please cte only the publshed verson usng the reference above. Full terms of use are avalable:

2 ~ ~ Propagaton Aspects of Frequency Hoppng Spread Spectrum M.P. Ftton, A.R. Nx, and M.A. Beach Centre for Communcatons Research, Unversty of Brstol, Brstol. BS8 ltr, Unted Kngdom Tel: , Fax: e-mal: Mke.Ftton@brstol.ac.uk!! Abstract Frequency Hoppng Spread Spectrum (FH-SS) has found a number of applcatons n both CDMA and TDMA cellular systems, wreless local loop, and wreless Local Area Networks. n ths paper, the effect of FH-SS on moble channel characterstcs s evaluated. Employng propagaton studes, statstcal analyss and smulaton models, t s shown that the frequency hopped channel dsplays mproved characterstcs when compared to the non-hopped case. The short term fadng statstcs are mproved, whch ca,n be exploted to provde an overall ncrease n qualtyof-servce. The short-term statstcs of the frequencyhopped channel are derved, enablng predcton of the performance of an FH system. 1 ntroducton F requency Hoppng Spread Spectrum (FH-SS) has been recevng a great deal of attenton for a varety of ap plcatons n the feld of wreless communcatons. The GSM worldwde dgtal standard ncorporates frequency hoppng to mprove performance and ease frequency plannng requrements []. Furthermore, the nature of the frequency-hopped channel s applcable n other areas, such as Specal Moble Rado [2], wreless local loop, and wreless Local Area Network technology [3]. n partcular, Slow Frequency Hoppng Code Dvson Multple Access (FH-CDMA) has been found sutable as an ar nterface technque for flexble thrd generaton wreless networks [41- The hoppng parameters assocated wth an FH-SS system, such as hop rate and system bandwdth, are defned. The mplcatons of these parameters axe explored, n terms of provdng optmum performaace wth codng and nterleavng, or an Automatc Repeat Request scheme. n Slow Frequency-Hopped Spread Spectrum, a number of symbols are transmtted on each hop frequency. The performance of a Forward Error Correcton (FEC) codng scheme can be maxmsed by nterleavng the data, and transmttng each symbol of the codeword on a dfferent hop frequency, affordng nherent codeword dversty. The nterleavng/de-nterleavng operaton randomses the po- 1 ston of the errors, and mproves the lkelhood of the codng scheme correctng the errors whch are present. n Automatc Repeat Request (ARQ) schemes, when a 1 partcular frame s detected as corrupted, then that frame s retransmtted. The nature of the frequency-hopped channel s hghly suted to the applcaton of an ARQ 1 scheme [5]. Provded the hoppng statstcs are appropr- ate, the system wll exhbt uncorrelated fadng between hop frames, renderng the channel effectvely memoyless over hop boundares. Consequently, t s lkely that any packet retransmsson wll experence uncorrelated channel statstcs. Theoretcal and practcal nvestgatons of the frequency hopped moble channel are employed n ths paper to 1 characterse the mpact of hoppng parameters on overall statstcs. n partcular, the relatonshp between hop rate and short-term channel parameters s explored, and the mplcatons of a lmted system bandwdth are evaluated. Furthermore, mathematcal expressons governng the short-term statstcs of the frequency-hopped channel are derved, enablng predcton of the overall performance of an FH system. A more detalled analyss of these parameters s defned n [6]. Ths analyss s based towards provson of a thrd generaton wreless network wth nequency Hoppng CDMA, supportng a flexble set of servces n a varety of ndoor and outdoor envronments. However, the hopped channel statstcs developed here are equajly applcable to other frequency hoppng systems. 1.1 Measurement Technques A campagn of frequency hoppng propagaton measurements was undertaken n an urban envronment n the cty of Brstol, at 1.823GHz [?. The transmtter, wth a half-wavelength dpole antenna, was placed on approxmately 30Om from the measurement ste, wth no le-ofsght component and a street-canyon type envronment. The moble recever operated at a constant Doppler frequency of approxmately 20&, over a loom secton. The coherence bandwdth of the channel was recovered from receved data, and corresponds to 1040 khz for a threshold of 0.5, and 250 khz for a threshold of 0.9 [7]. Furthermore, a smulaton study was undertaken, to char. acterse the narrowband frequency-hopped channel. Tc /97/$ EEE 640

3 accomplsh ths, a Raylegh channel model was employed as an approxmaton to the real narrowband channel statstcs. 2 Hoppng Parameters 2.1 Number of Hop Bns The number of hop frequences (or hop bns ) avalable for use s determned by the overall system bandwdth avalable, and the separaton between bns. n the case of an FEC scheme, f the codeword length exceeds the number of hop bns, t then becomes necessary for more than one symbol to be transmtted on a gven frequency, resultng n a performance degradaton n the codng scheme. 2.2 Hop Rate The hop rate s used to characterse the number of transtons between frequences whch occur each second. Ths parameter mpacts on overall performance n two man crtera. Frst, the hop rate wll nfluence the nstantaneous channel parameters, such as mean fade duraton and level crossng rate [S. Furthermore, the hop rate affects the trade-off between nterleavng depth and throughput delay n a hopped system. f the modem s not hoppng at a fast enough rate, the m ax nterleavng depth whch s allowed for ntellgble voce transmsson wll not allow for suffcent uncorrelated symbols n the de-nterleaved code word. Ths wll then lmt the effectveness of any codng scheme whch s employed. For optmal operaton, t s necessary for the hop rate to be suffcent for all symbols n a gven codeword to be transmtted on dfferent hop frequences, whlst observng the lmtatons on throughput delay. 2.3 Hop Bn Separaton and Hop Pattern The hop bn separaton defnes the frequency separaton between adjacent frequences n an FH system, and s partcularly mportant n determnng the degree of correlaton between hop frames n a partcular hop pattern. nsuffcent hop bn separaton wll lmt the mprovement n nstantaneous statstcs assocated wth a frequencyhopped channel. For example, hoppng between frequences whch exhbt hghly correlated fadng wll result n lttle mprovement n the mean fade duraton over the non-hopped case. Furthermore, f the separaton between hop frequences employed n a gven codeword does not provde uncorrelated fadng, the effcency of any nterleavng and FEC codng wll be mpared. deally, all symbols should be transmtted on dfferent frequences, separated by greater than the coherence bandwdth [9]. 3 Hopped Channel Statstcs Prevous propagaton work [7] has ndcated that frequency hoppng does not alter the long term statstcs of the channel. n ths secton, the mportant short-term tme doman statstcs of a frequency-hopped moble channel are analysed. 3.1 Channel Coherence Tme The coherence tme s an mportant statstc n terms of predctng the performance of a moble system) as t characterses the mean duraton of any error bursts. The coherence tme parameter ndcates the tme span over whch the channel can be assumed to be constant. Ths s defned as the tme offset requred for the correlaton coeffcent to fall below a certan threshold (0.9 n ths case). f the hop frame duraton exceeds the coherence tme of the channel, the overall coherence tme perceved for the frequency-hopped channel wll be largely determned by the system hop rate. Provded that adjacent hop frequences are separated by greater than the coherence bandwdth, fadng at the Merent frequences wll be uncorrelated. Consequently) the hopped channel s unlkely to exhbt correlated fadng over a hop boundary. Therefore, the coherence tme s fxed at a level less than the hop frame duraton. Due to the dffculty of analysng the coherence tme of a hopped channel, a smulaton study of the moble envronment was undertaken, ncorporatng the effects of multpath fadng and frequency hoppng. n ths model, a Raylegh channel was employed, and the velocty and hop rate were altered. n all cases, the coherence tme was calculated wth a correlaton threshold of 0.9, and a data wndow of greater than fve wavelengths was employed. The parameter was averaged over a run of greater than 100 wavelengths. The smulaton results are shown n fgure 1, along wth the! predcted coherence tme for a two-ray model [9]. Doppler Frequency (Hz) Fgure 1: Hopped and Non-hopped Coherence Tme 64 1

4 Examnng the smulaton results contaned n fgure 1, t can be seen that frequency hoppng provdes a sgmfcant mprovement n the channel coherence tme. At Doppler frequences exceedng a certan level (say, 100Hz) hoppng provdes a small mprovement. However, at lower Doppler frequences, the effects of frequency hoppng domnate the mult-path fadng. Consequently, the hopped systems provde a coherence tme whch s largely ndependent of Doppler frequency. For example, a system operatng at 500 hops per second exhbts a maxmum coherence tme of 0.34ms at low values of Doppler frequency. For a non-hopped system to demonstrate comparable performance, a Doppler frequency of approxmately 211Hz would be requred at all tmes (from fgure 1). At the PCS frequency of 1.8GH2, ths corresponds to a velocty exceedng 148km/h at all tmes. Ths s an mportant result n the provson of hgh qualty servce, snce outage duraton wll be determned by hop rate, rather than the Doppler frequency. t s demonstrated above that a non-hopped system can experence consderable perods of outage n a slowly changng channel. Conversely, a hopped system provdes a coherence tme whch wll not exceed a certan level, rrespectve of the Doppler frequency Coherence Tme Propagaton Results Propagaton studes were employed to test the valdty of the smulaton results presented n secton 3.1. Furthermore, the mpact of correlated fadng between adjacent hop frequences s examned. Separatng hop frequences by at least the coherence bandwdth provdes optmum, uncorrelated fadng n a gven codeword. However, t s problematc achevng ths when the coherence bandwdth s large, for example n an ndoor envronment. The coherence tme of the hopped channel s shown n fgure 2 for a varety of hop bn separatons. A correlaton threshold of 0.9 was employed, wth a data wndow of approxmately 5 wavelengths. The measured value wthout hoppng was 4.3ms, at a Doppler frequency of approxmately 20Hz. Ths agrees well wth analyss of a twway model whch predcts a coherence tme of 3.6ms (fgure 1). The acton of frequency hoppng sets the coherence tme of the channel at a level determned by the hop rate, approxmately 0.3ms, n ths case. As ndcated n secton 3.1 the value predcted by smulaton s approxmately 0.34ms, demonstratng good agreement. Examnaton of the coherence tme statstc n fgure 2 ndcates that a hop bn separaton consderably less than the coherence bandwdth can stll provde sgnfcant performance enhancement. 3.2 Level Crossng Rate The level crossng rate (NR) [S s defned as the number of postve gong transtons of the sgnal magntude wth h v E g f U" B 3 O.MX)5 coherence bandwdth ,000 1,500 2,000 Frequency Fgure 2: Hopped Channel Coherence Tme (500 hps) respect to a certan threshold. A hgh level crossng rate mples a rapdly changng channel, wth problems arsng from statc nulls becomng statstcally unlkely. To smplfjr the analyss of level crossng rate n a frequency-hopped channel, t s assumed that the channel s constant over a hop perod, so that the nstantaneous characterstcs due to channel varatons can be neglected. For ths assumpton to be vald, t s necessary for the coherence tme of the narrowband channel to exceed the hop frame duraton. f the channel s not statonary over the hop perod, the short term statstcs whch are experenced wll be a combnaton of the effects of frequency hoppng and multpath fadng. Employng the assumpton that the channel s constant over a sngle hop perod mples that the nstantaneous characterstcs due to channel varatons can be neglected. Consequently, the leve crossng rate can be calculated from the cumulatve statstcs of the channel envelope dstrbuton. n ths case a Raylegh dstrbuted channel s assumed [S. The level crossng rate of a hopped channel s calculated from the channel statstcs both before and after a hop boundary. Calculatons are greatly smplfed f the envelopes before and after the hop boundary are assumed to be uncorrelated. Ths condton wll be satsfed f the hop frequency spacng exceeds the channel coherence bandwdth. The level crossng rate of a hopped channel s gven by equaton 1, where fhop s the hop rate (n hops per second). NR = fhopp[tl < R]P[T2 > E] - -R2/2u2 (1 -.-R2/2u2 - fhope ) (1) Level Crossng Rate Propagaton Results Comparson of real and predcted statstcs for nonhopped and hopped systems s shown n fgure 3. The hopped system s operatng at a rate of 500 hops per second, and adjacent frequences are separated by 1.5MHz. The dagram ndcates reasonable agreement 642

5 between real and predcted data. n partcular, the hopped performance s accurately predcted by equaton1 at hgh magntude thresholds. At lower values, the statstcs of the channel domnate, and thus the measured hoppng characterstc tends towards the non-hopped theoretcal curve. " The mean fade duraton of a frequency-hopped channel can be calculated n a smlar fashon to level crossng rate wth hoppng. t s assumed that the channel s statonary over a hop frame, and that all hop frequences exhbt uncorrelated fadng. The fade duraton s calculated from the cumulatve statstcs and the level crossng rate. The approxmaton to mean fade duraton n a hopped channel s shown n equaton 3 for a Raylegh dstrbuted channel. r 0.1lL.1..,.,.. (, ).,.,,.J Receved Sgnal Level Relatve to Mean (db) Fgure 3: Predcted and Measured Level Crossng Rate h 0 s * 0 Employng the expresson for fade duraton (equaton 3), the statstcs for a number of hop rates are plotted n fgure 5. These results llustrate the mprovement n fade duraton assocated wth hoppng. For example, a system operatng at 500 hops per second wll experence a fade duraton relatve to lodb below the mean of approxmately 2ms. Ths s a sgnfcant mprovement over the non-hopped case, wth a mean fade duraton of 7ms at a Doppler frequency of 20Hz for the same threshold. Alternatvely, for a non-hopped system to provde a smar mean fade duraton would requre a moble velocty of at least 80km/h at 1.8GHz Receved Sgnal Level Relatve to Mean (db) Fgure 4: Level Crossng Rate (100 khz spacng) Fhther propagaton measurements contaned n fgure 4 shows the mprovement n level crossng rate resultng from ncreasng the hop rate. As predcted n secton 3.2, performance s mproved wth ncreased hop rate, even at a relatvely low hop bn separaton of 1001CHz. However, the ntal performance mprovement assocated wth hop png s not reflected by a contnued ncrease n the hop rate. The trade-off between hardware complexty and mproved channel characterstcs becomes unfavourable as hop rate s ncreased too far. 3.3 Mean Fade Duraton Mean fade duraton ((Tf)) [S s defned as the tme spent wth a magntude less than a certan threshold n a partcular fade. t s possble to relate fade duraton to an ndcaton of system qualty, such as outage duraton. d *.3 e r; W E A-.., -,,,,, /,, lt.. #.., -. ~. ~ k Receved Sgnal Level Relatve to Mean (a) Fgure 5: Frequency-Hopped Channel Fade Duraton Mean Fade Duraton Propagaton Results The mean fade duraton statstc of the hopped channel was calculated from propagaton data. Fgure 6 ndcates the mean fade duraton for both narrowband and hopped systems, wth results obtaned from theory and propagaton data. There s good agreement between analytcal and measured data. The hopped system n fgure 6 s operatng at 500 hops per second. Snce the hop bn sep araton s set at 1.5MHz, and exceeds the coherence bandwdth, the fadng s largely uncorrelated wth the adjacent hop frequency, Examnaton of the results contaned n fgure 6 ndcates reasonable smlarty between theoretcal and propagaton 643

6 0.01 n a predcted Measured o.ooo1 Receved Sgnal Level Relatve to Mean (a) Fgure 6: Predcted and Measured Mean Fade Duraton data, partcularly at hgher magntude thresholds. At low magntude levels, the nnate channel statstcs arsg from multpath fadng have more nfluence on composte performance. Consequently, the real hopped system performance tends towards the non-hopped case. 4 Conclusons and mplcatons Ths paper explores the requrements and mpact of the hoppng parameters n a frequency-hopped system. Requency hoppng mproves the nstantaneous characterstcs of the channel, whlst leavng the long term statstcs unchanged [7]. The short-term statstcs of the hopped channel are derved, and can be employed to predct the performance enhancement assocated wth frequency hoppng. deally, a frequency-hopped channel wll become effectvely memoryless. Consequently, the effcency of an nterleaved FEC scheme wll be maxmsed. Alternatvely, the requred retransmsson tme of an ARQ approach wll be mnmsed. Results obtaned from propagaton and smulaton studes confrm the mprovement n nstantaneous channel statstcs assocated wth frequency hoppng, especally at low vehcle velocty. ncreasng the hop rate mproves the hopped channel characterstcs, although results ndcate that the mprovement becomes less sgnfcant at hgher hop rates. Consequently, the hop rate can be set at a feasbb value (say, 500 hops per second). Further propagaton studes were appled to examne the necessty for uncorrelated fadng between kames n the hop pattern. Propagaton results ndcate that, whlst t s advantageous to separate hop frequences by greater than the coherence bandwdth, t s possble to reduce ths strngent lmtaton. Results contaned n fgure 2 demonstrate that a frequency separaton of approxmately one half the coherence bandwdth can be employed wth only a slght performance degradaton. Ths s an mportant result, especally when lmted spreadng bandwdth s avalable, and t s unfeasble to provde large separaton between hop channels. Ths s especally problematc n lghtly dspersve envronments, when the coherence bandwdth s large. For example n an ndoor channel, t s not atypcal to experence delay spread n the order of 50ns, and coherence bandwdth of 3MHZ. f the hop separaton s not requred to be sgnfcant wth respect to the coherence bandwdth, the lmtatons of system bandwdth l become less strngent. t s shown that frequency hoppng sets the coherence tme at a level determned by hop rate, and largely ndependent of Doppler requency. Ths s mportant as the performance of ARQ and FEC schemes are lnked to the coherence tme, whch characterses any error bursts whch occur. Consequently, t becomes possble to characterse the performance of the transmsson protocol, rrespectve of moble speed. Hence, frequency hoppng fnds many applcatons n wreless LAN [3] and wreless local loop technology. 5 Acknowledgements The authors would lke to thank the Engneerng and Physcal Scences Research Councl (EPSRC) for ther fnancal support, and grateful acknowledge the facltes and gudance provded by Prof. J.P.McGeehan. References [l] J. Skold, B. Gudmundson, and J. F&jh, Performance and Characterstcs of GSM-based PCS, n EEE 45th Vehcular Technology Conference, July 1995, pp [2] S. Mller and M. Rtz, FHMA Appled to Modern SMR - A System Revew, n Wreless Technology 1995, September 1995, pp [3] WNFORUM, Proceedngs of the Frst Annual PCS Workshop, October [4] P.D. Rasky, G.M. Chasson, D.E. Borth, and R.L. Peterson, Slow Frequency-Hop TDMA/CDMA for Macrocellular Personal Communcatons, BEE Personal Communcatons, vol. 1, no. 2, pp , Aprl [5] N. Guo and S.D. Morgera, Fkequency-Hopped ARQ for Wreless Network Data Servces, EEE Joumal on Selected Areas n Communcatons, vol. 12, no. 8, pp , October [6] M.P. Ftton, A.R.Nx, and M.A. Beach, Propagaton Aspects of Frequency Hoppng Spread Spectrum, submtted to EE Proceedngs on Mcrowaves, Antennas and Propagaton. 171 M.P. Ftton, D.J. Purle, and M.A. Beach, The mpact of System Bandwdth on a Frequency Hopped Channel, n EE 10th nternatonal Conference 0% Antennas and Propagaton. EE, Aprl 1995, pp [S W.C. Jakes et al, Mcrowave Moble Communcatons, J. Wley & Sons, New York, USA, [9] J.G. Proaks, Dgtal Communcatons, McGraw-Hll, 2nd. edton,