Wideband model of HF atmospheric radio noise

Transcription

1 Radi Science, Vlume 36, Number 6, Pages , Nvember-December 2001 Wideband mdel f HF atmspheric radi nise Jhn J. Lemmn Institute fr Telecmmunicatin Sciences, U.S. Department f Cmmerce, Bulder, Clrad, USA Abstract. A mdel f the wavefrm generated by high-frequency atmspheric radi nise is presented. Cumulative prbability distributins f the nise envelpe are derived and shwn t be in gd agreement with a large database cllected frm a wide range f nise envirnments. The mdel includes crrelatins in the wavefrms that simulate the burst structure f measured atmspheric nise. The bandwidth dependence f the vltage deviatin parameter, which parameterizes the impulsiveness f the nise, shws behavir that is qualitatively similar t a limited amunt f measured data. 1. Intrductin f received atmspheric nise in the HF band (3-30 Mtivated by the applicatin f spread spectrum MHz). Here the term "wideband" is used in the sense technlgy and digital signal prcessing techniques t that ne is bserving the nise ver a bandwidth n high-frequency (HF) cmmunicatin systems, adthe rder f 1 MHz. Hwever, it is assumed that the vanced HF systems that perate ver wide band- center frequency is sufficiently large relative t the widths (n the rder f 1 MHz r mre) are being bandwidth t allw the nise prcess t be characterdevelped. Since many uncertainties exist cncerning ized by a well-defined envelpe and phase. Thus the the perfrmance f such systems, it is imprtant t received nise vltage can be written as have channel mdels fr theretical predictins f system perfrmance and fr labratry measure- V(t) cs [ 0t + b(t)], ments f system perfrmance using channel simulatrs. New HF channel mdels have been develped that (1) are accurate ver bandwidths n the rder f 1 MHz, (2) can be validated with measured data, and where 0 is the RF center frequency. Atmspheric nise bursts arise frm numerus distinct prcesses in lightning discharges and can exhibit a wide variety f extremely cmplex structures [Uman, 1987]. The vlt- (3) are suitable fr implementatin in a channel age envelpe V(t) and phase b(t) are therefre simulatr. These new mdels have been develped treated as randm variables. because the HF channel simulatrs currently in wide- The develpment f the man-made nise and spread use implement a mdel f the HF channel that interference wavefrm mdel was based n examinhas nly been verified fr narrwband (less than 12 khz) stable channels [Wattersn et al., 1970]. ing statistical characteristics btained frm analyses f measured wavefrms and develping a mdel f The new wideband mdels f HF sky wave prpa- the wavefrm that exhibited thse same characterisgatin and f man-made nise and interference have been discussed by Vgler and Hffrneyer [1993] and by Lemmn [1997], respectively. These papers pinted ut that the mdel develpment has been mtivated tics. Hwever, nne f the measured wavefrms that were examined revealed the presence f atmspheric nise bursts in the raw data; the pulse width and spacing distributins f the burst nise that were by the need fr mdels that can be implemented in a bserved were nt cnsistent with thse f atmchannel simulatr. The nise and interference mdels spheric nise [Lemmn and Behm, 1993]. Presumare therefre mdels f the nise and interference ably, this was because any atmspheric nise that was wavefrms that are cmbined with the desired signal in a channel simulatr. This paper describes a wideband wavefrm mdel present was dminated by the narrwband interference, which was nt excised frm the data. Therefre the validity f the atmspheric (as ppsed t the man-made) nise mdel has been investigated by This paper is nt subject U.S. cpyright. Published in 2001 by the American Gephysical Unin. Paper number 2000RS cmparing the statistical characteristics f simulated wavefrms with the characteristics f measured atm- spheric nise that have been reprted in the literature.

2 1386 LEMMON: HF ATMOSPHERIC NOISE MODEL _ uj A rn Percent f Time Ordinate Exceeded Figure 1. Set f amplitude prbability distributins f atmspheric radi nise fr varius V,/values frm ITU-R [1986]. 2. First-Order Statistics distributins are parameterized by the vltage devia- The first-rder statistics f a randm prcess de- tin parameter Va (the db difference between the scribe the time-averaged behavir f the prcess. rms and mean values f the nise vltage envelpe). These statistics have been described fr atmspheric Unlike Gaussian nise, the characteristics f atmnise by a mdel develped by Spaulding and Wash- spheric nise are a functin f receiver bandwidth. burn [1985] and apprved by the Internatinal Tele- Herman and DeAngelis [1987] have given results n cmmunicatins Unin, Radicmmunicatins Assem- the effect f bandwidth n Va, shwn in Figure 2. bly [ITU-R, 1986]. This mdel specifies cumulative These results are based n medium-frequency data prbability distributins f the received nise vltage (450-kHz center frequency). Hwever, it was pinted envelpe and assumes unifrmly distributed phase. ut by the authrs that preliminary analysis f sme The mdel is shwn in Figure 1, in which the prbability limited HF data indicated similar behavir, s that

3 LEMMON: HF ATMOSPHERIC NOISE MODEL Vde=l 22 2O Vd 10 Vd 8 Vd 6 Vd Vde= 2 Gaussian Vde= K Bandwidth Rati = (BWn/200) Figure 2. Translatin f V a frm a 200-Hz bandwidth t ther bandwidths, based n measured medium frequency data [Herman and DeAngelis, 1987]. the results were assumed, with cautin, t be applicable t the HF band. bands bserved ver bandwidths n the rder f 1 khz. It will be shwn in the present paper that this mdel is als in gd agreement with the measured first-rder envelpe statistics f atmspheric nise ver much wider bandwidths. In accrdance with the Hall mdel it is assumed that the phase tb(t) is unifrmly distributed and the prbability density functin œ,(v) f the vltage envelpe V(t) is given by (0-1) /ø-iv pv(v) (V 2 +,y2) (0+1)/2 ' (1) where 0 and 7 are free parameters (with the cnstraint that 0 > 1, s that p (V) is nrmalizable). A set f amplitudes distributed accrding t (1) can be generated by integrating (1) t btain the cumulative prbability P(V), 0-1 In this paper the first-rder statistics f the atmspheric nise wavefrm are characterized by the Hall [1966] mdel. This mdel was develped t describe atmspheric radi nise and was shwn t be in gd inverting the result t btain V(P), agreement with the first-rder envelpe statistics f measured atmspheric nise in the VLF, LF, and HF P(V) = 1 - (V 2 + /2)(0- )/2, (2) V(P) = 'y (1- p)2/(- )- 1 ) 1/2 1, (3) and treating the cumulative prbability P as a randm variable unifrmly distributed between 0 and 1. Values f 0 and 7 can be determined by relating them t values f Vtt and the mean nise pwer measured at the terminals f a lssless, shrt mn- ple antenna, which have been specified fr varius gegraphical lcatins, times f day, seasns, and frequencies [Spaulding and Washburn, 1985; ITU-R, 1986]. Frm (3) it can be seen that values f a randm variable V(t) distributed accrding t (1) are prprtinal t 7; therefre Vtt, which is prprtinal t the lgarithm f a vltage rati, is independent f 7 and depends nly upn 0. The relatinship between Vtt and 0 was determined

4 1388 LEMMON: HF ATMOSPHERIC NOISE MODEL numerically by simulating wavefrms using (3) with varius values f 0 and calculating Va fr each wavefrm. The results are shwn in Figure 3, in which Va is pltted versus 0. Fr each value f 0, 100 wavefrms (each cnsisting f 32,000 samples) were simulated. The three values f Va that are pltted fr each value f 0 are the mean value and the mean value _+1 standard deviatin fr the 100 wavefrms. Having determined 0 frm Va, 7 can be determined frm 0 and the mean nise pwer as fllws. If P is the nise pwer at the antenna terminals and V is the received nise vltagenvelpe, then P - V2/R, where R is the receiver lad. Transfrming variables frm vltage V t pwer P, the prbability density functin f pwer pp(p) crrespnding t the prbability density functin f vltage in (1) is (0-1)(72/R) 0-1)/2 Pc(P) = 2(P + 72/R) (ø+1)/2 ' (4) Denting the mean pwer by Pm, it fllws that f ø Ppp(P) dp= Pm. (5) Substituting (4) int (5), carrying ut the integratin, and slving fr 7 results in -Pm-t- P2 m -t (6),s 20 ß 0-20 Vd:1.01 Vdl =5.02 Vd2=10.12 Vd3=15.00 Vd4:20.13 Vd5:25.10 Vd6=29.82 Vd7= Percent f the Time Ordinate Exceeded Figure 4. Set f amplitude prbability distributins f simulated atmspheric radi nise fr varius V,i values Average - Ave + std 0 I I 1 I llllllll III I I I I Figure 3. Relatinship between Vii and 0 fr the atmspheric radi nise simulatin mdel. As indicated abve, it has been shwn that the prbability distributin functin f the nise envelpe given by the Hall mdel is in general agreement with a limited amunt f narrwband HF atmspheric nise data [Hall, 1966]. Hwever, it is f interest t cmpare the Hall mdel with the ITU-R mdel, which is based n a wide range f measured data and which relates varius envirnments t specific values f Vd and Pm' Using the relatinship between 0 and Vd shwn in Figure 3, nise wavefrms (4 millin samples) with varius values f Vd were simulated. The cumulative distributin functins f their vltage envelpes are pltted in Figure 4. Cmparisn f Figures 1 and 4 indicates that the prbabilities f the simulated nise envelpes generally agree with thse given by the ITU-R fr exceedance prbabilities greater than 10-4 (0.01%). Thus the first-rder statistics f the mdel are cnsistent with thse f measured data

5 LEMMON: HF ATMOSPHERIC NOISE MODEL 1389 ver a large range f values f the nise envelpe. Mrever, the relatinships between the mdel parameters 0 and / and the parameters Va and Pm enable ne t determine specific values f the mdel parameters fr varius envirnments. the vltage envelpe exclusively frm the quiet (r burst) set during the quiet (r burst) time intervals. Samples f time duratins distributed accrding t (7) were generated by integrating (7) t btain the cumulative distributin P(T), 3. Higher-Order Statistics Atmspheric nise bursts are well knwn t be clustered in time, because f the presence f numerus individual lightning strkes within a single flash [Uman, 1987]. These crrelatins have been studied by Fishman et al. [1991], wh have develped a mdel fr burst duratin and time between bursts based n and time between bursts are f the frm pt(t) = (Cie -c2r + C3) ß exp - 22 (1- e -c2r) - C3T, (7) where C1, C2, and C3 are free parameters and T is the burst duratin r time between bursts in secnds. P(T) = 1 - exp - 22 (1- e r) _ C3T, (8) inverting (8) t btain T(P), and treating P as a unifrmly distributed randm variable between 0 and 1. The inversin f (8) was perfrmed numerically by cnstructing a lkup table fr T(P). The threshld separating the burst and quiet sam- ples was determined by requiring the fractin f measured data. The data were cllected by the Mitre samples in the quiet set t equal the fractin f time Crpratin in Bedfrd, Massachusetts, and cnsist in the quiet state. The quiet and burst time duratins f successive 1-ms averages f nise pwer ver a are randm variables. Hwever, the expected value f wideband (1 MHz) channel with center frequencies in the fractin f quiet time fr a recrd f infinite the 13- t 16-MHz range. The nise pwer was length is TQ/(TQ + TB), where TQ and TB are the recrded after suppressin f narrwband interfer- mean values f the time between bursts and the burst ence via a blck fast-furier-transfrm- (FFT)-based duratin, respectively. These values were determined peratin which sets t zer all spectral cmpnents frm (7) by evaluating exceeding a threshld. A three-parameter renewal prcess mdel was fund t prvide a gd descriptin f bth burst itpt(t) dr duratin and time between bursts. A burst event is defined t start (end) when the average nise pwer numerically. Thus, if P0 is the pwer threshld, becmes greater (less) than a specified threshld. The prbability density functins p r(t) f burst duratin PO pc(p) dp= TQ TQ ' (9) where pe(p) is the pwer prbability density functin in (4). Substituting (4) int (9), carrying ut the integratin, and slving fr P0 gives e0=- T2[(TQ) 2/(0-1) -1 ( 0) Accrdingly, it is prpsed that the burst structure f atmspheric nise be simulated by the fllwing The threshld in (10) des nt precisely crrespnd t the threshlds used by Fishman et al. [1991] t prcedure. First, independent samples f the vltage mdel the distributins f burst duratin and time envelpe with a prbability density functin given by between bursts. Hwever, this prcedure des pr- (1) are generated. The samples are then separated vide a means f crrelating the nise bursts in time in int tw sets: a "quiet" set cnsisting f sample values a way that is apprximately cnsistent with measured less than a given threshld and a "burst" set cnsist- data. Nte that the prcedure in n way depends ing f sample values greater than that threshld. upn the particular frms f the prbability density Independent samples f burst duratin and time between bursts with prbability density functins f functins in (7). Als nte that this prcedure, which amunts t generating crrelatins in a set f indethe frm (7) are generated and alternatively cncat- pendent samples f the vltage envelpe, in n way enated, s that time is partitined int intervals that alternate between quiet and burst states. The waveaffects the first-rder statistics. Thus the agreement between the prbability distributins f the mdel frm is simulated by selecting independent samples f and measured data remains intact.

6 1390 LEMMON: HF ATMOSPHERIC NOISE MODEL 2OO loo -l -2-3OO x x x10 4 Time (ms) Figure 5. Sixteen secnds f the in-phase cmpnent f a simulated atmspheric nise wavefrm. An example wavefrm that was simulated with the mdel is shwn in Figure 5. Pltted is the in-phase cmpnent f the baseband vltage, V(t) cs tk(t), sampled nce per millisecnd ver a time interval f 16 s. The values f the parameters in the vltage envelpe distributin are and 0 = 2.5 (Va = 8.9 db). The parameter values used in the distributins f burst duratin and time between bursts were taken frm an example discussed by Fishman et al. [1991]' Fr the burst duratins, C1 = 57.43, C2 = 32.23, and C3 = (Ta = 26 ms); fr the time between bursts, C 1 = 18.62, C2 = 16.62, and C3 = 1.49 (TQ = 247 ms). These parameter values prvide a gd fit t the distributins btained frm measured wideband (1 MHz) atmspheric nise at a center frequency f MHz. The effects f bandwidth n Va were investigated by filtering simulated wavefrms (4 millin samples and a sample rate f 1 MHz) with three-ple lw-pass filters and calculating the Va f the filtered wavefrms. The cutff frequencies f the filters were chsen t be 0.1, 0.01, 0.001, and times the 45 4O 35 3O 25 2O Lg f the Bandwidth Rati Figure 6, Translatin f V /frm a 1-MHz bandwidth t ther bandwidths fr the atmspheric nise simulatin mdel.

7 LEMMON: HF ATMOSPHERIC NOISE MODEL 1391 bandwidth f the unfiltered wavefrms. The parameter values used in the prbability density functins f burst duratin and time between bursts are the same as in the example abve. The results are shwn in Figure 6, in which Vd is pltted versus the lgarithm f the bandwidth rati f the filtered and unfiltered wavefrms. Cmparing Figures 2 and 6 reveals qualitatively similar behavir, althugh the tw sets f curves are nt in full quantitative agreement at all values f Vd and bandwidth rati. 4. Summary A wideband mdel f HF atmspheric radi nise has been develped. The mdel enables ne t sim- ulate atmspheric nise wavefrms ver bandwidths f the rder f 1 MHz, intended fr implementatin in a wideband HF channel simulatr. Cumulative prbability distributins f the vltage envelpes f simulated wavefrms are in general agreement with the mdel apprved by the ITU-R, which is based n a large database and range f nise envirnments. Values f the mdel parameters that are apprpriate fr a specific nise envirnment can be determined a priri, because these parameters have been related t the vltage deviatin parameter and the mean nise pwer, which have been specified fr varius ge- graphical lcatins, seasns, times f day, and frequencies. A prcedure has been develped fr generating crrelatins in the wavefrms that simulate the b- served burst structure f atmspheric nise. This burst structure causes the impulsiveness f the nise, parameterized by the vltage deviatin parameter, t be a functin f the bandwidth ver which the nise is bserved. The bandwidth dependence f the vltage deviatin parameter f simulated wavefrms has been investigated and is in qualitative agreement with a limited amunt f HF data analyzed by Herman and DeAngelis [ 1987]. On the ther hand, atmspheric nise is ntriusly nnstatinary, and n attempt has been made t simulate this nnstatinarity. As was pinted ut in the discussin f the man-made nise and interfer- ence mdel [Lemmn, 1997], the purpse f these mdels is t develp the capability t perfrm labratry measurements f radi perfrmance under statinary channel cnditins, s that perfrmance and channel cnditins can be crrelated. Within this cntext the lack f nnstatinarity shuld nt seriusly cmprmise the usefulness f the mdel. Acknwledgments. The authr wishes t thank J. McEvy and W. Bnser f the U.S. Air Frce Rme Labratry, D. Bdsn and G. Rekstad f the Natinal Cmmunica- tins System, and Rbert Oldham f the U.S. Army Cmmunicatin/Electrnics Cmmand fr their supprt f the wrk reprted herein. The authr als wishes t thank C. J. Behm fr his assistance in perfrming the cmputer simu- latins. References Fishman, P.M., C.-R. Liu, and P. A. Bell, A statistical mdel fr burst duratin and time between bursts fr WBHF atmspheric nise, paper presented at IEEE Military Cmmunicatins Cnference, Inst. f Electr. and Electrn. Eng., McLean, Va., Hall, H. M., A new mdel f "impulsive" phenmena: Applicatins t atmspheric nise cmmunicatins channels, Tech. Rep and , SU-SEL , Electrn. Lab., Stanfrd Univ., Stanfrd, Calif., Herman, J. R., and X. A. DeAngelis, Bandwidth expansin effects n the vltage deviatin parameter (V a) f MF and HF atmspheric radi nise, Radi Sci., 22, 26-36, Int. Telecmm. Unin, Radicmmun. Assem. (ITU-R), Characteristics and applicatins f atmspheric radi nise data, CCIR Rep , Geneva, (Reprinted as Radi nise, Recmm. P , Int. Telecmm. Unin, Radicmmun. Assem., Geneva, 1994.) Lemmn, J. J., Wideband mdel f man-made HF nise and interference, Radi Sci., 32, , Lemmn, J. J., and C. J. Behm, Wideband HF nise/ interference mdeling, part II, Higher-rder statistics, NTIA Rep , Natl. Telecmmun. and Inf. Admin., Washingtn, D.C., (Available as PB frm Natl. Tech. Inf. Serv., Springfield, Va.) Spaulding, A.D., and J. S. Washburn, Atmspheric radi nise: Wrldwide levels and ther characteristics, NTIA Rep , Natl. Telecmmun. and Inf. Admin., Washingtn, D.C., (Available as PB frm Natl. Tech. Inf. Serv., Springfield, Va.) Uman, M. A., The Lightning Discharge, Academic, San Dieg, Calif., Vgler, L. E., and J. A. Hffmeyer, A mdel fr wideband HF prpagatin channels, Radi Sci., 28, , Wattersn, C., J. Jurshek, and W. Bensema, Experimental cnfirmatin f an HF channel mdel, IEEE Trans. Cmmun. Tech., COM-18, , J. J. Lemmn, Institute fr Telecmmunicatin Sciences, U.S. Department f Cmmerce, 325 Bradway, Bulder, CO , USA. (jlemmn@its.bldrdc.gv) (Received March 31, 2000; revised February 23, 2001; accepted March 22, 2001.)