Spectrally Shaped Generalized MC-DS-CDMA with Dual Band Combining for Increased Diversity

Transcription

1 Unversty of South Carolna Scholar Commons Faculty Publcatons Electrcal Engneerng, Department of 5-28 Spectrally Shaped Generalzed MC-DS-CDMA wth Dual Band Combnng for Increased Dversty Wenhu ong Davd W. Matolak Unversty of South Carolna - Columba, matolak@cec.sc.edu Follow ths and addtonal works at: Part of the Sgnal Processng Commons, and the Systems and Communcatons Commons Publcaton Info Postprnt verson. Publshed n IEEE Transactons on Wreless Communcatons, Volume 7, Issue 5, 28, pages IEEE Transactons on Wreless Communcatons, 28, IEEE ong, W., Matolak, D. 28. Spectrally Shaped Generalzed MC-DS-CDMA wth Dual Band Combnng for Increased Dversty. IEEE Transactons on Wreless Communcatons, 75, Ths Artcle s brought to you for free and open access by the Electrcal Engneerng, Department of at Scholar Commons. It has been accepted for ncluson n Faculty Publcatons by an authorzed admnstrator of Scholar Commons. For more nformaton, please contact SCHOLARC@malbox.sc.edu.

2 1676 IEEE TRASACTIOS O WIRELESS COMMUICATIOS, VOL. 7, O. 5, MAY 28 Spectrally Shaped Generalzed MC-DS-CDMA wth Dual Band Combnng for Increased Dversty Wenhu ong and Davd W. Matolak, Senor Member, IEEE Abstract A new multcarrer spread spectrum modulaton scheme s proposed n ths paper. Ths scheme uses snusodal chp waveforms to shape the spectrum of each subcarrer of a multcarrer drect sequence spread spectrum DS-SS sgnal. As a result, each subcarrer has two dstnct spectral lobes, one a lower sdeband LSB and the other an upper sdeband USB. By properly selectng the parameters of the snusodal chp waveforms, the two sdeband sgnals can be made to undergo ndependent fadng n a dspersve fadng channel. These two ndependently-faded sdeband sgnals, when combned at the recever, provde dversty gan to the system. Our analyss and smulaton results show that by properly selectng the chp waveform parameter and the ntersubcarrer frequency separaton, the bt error rato BER performance of the proposed scheme s superor to that of the conventonal MC-DS-CDMA system n dspersve fadng channels. In addton, spectral sdelobes are naturally reduced by our scheme. Index Terms Drect sequence spread spectrum, multcarrer. I. ITRODUCTIO DIRECT sequence spread spectrum DS-SS s wdely used n both cvlan and mltary applcatons for ts well known advantages, such as multple access, low probablty of ntercepton and resstance to nterference [1]. One of the attractve features of DS-SS, when used n a wreless envronment, s that the wde sgnal bandwdth helps the recever to resolve channel echoes, or multpath. These echoes, when combned n a maxmal rato combnng MRC fashon, provde the system so called multpath dversty, whch mproves system error probablty performance. Recent research has addressed the combnaton of spread spectrum and multcarrer modulaton, resultng n the multcarrer spread spectrum MC-SS sgnalng schemes [2]. There are at least three types of multcarrer spread spectrum schemes: MC-CDMA, MC-DS-CDMA, and MT-DS-CDMA. In MC-CDMA [3-5], the spreadng s performed n the frequency doman, where the chps of the DS spreadng sgnal are transmtted va dfferent subcarrers, yeldng frequency dversty. For MC/MT-DS-CDMA systems [6-1], spreadng s performed n the tme doman, whch brngs multpath dversty to the system when channel echoes are combned va MRC. The only dfference between the MC-DS-CDMA and Manuscrpt receved September 24, 26; revsed September 15, 27 and ovember 22, 27; accepted January 1, 28. The assocate edtor coordnatng the revew of ths paper and approvng t for publcaton was A. Stefanov. W. ong s wth Qualcomm Inc., 5775 Morehouse Dr. San Dego CA e-mal: wenhux@qualcomm.com. D. W. Matolak s wth Oho Unversty, School of Electrcal Engneerng and Computer Scence, Athens, OH 4571 e-mal: matolak@ohou.edu. Dgtal Object Identfer 1.119/TWC /8$25. c 28 IEEE MT-DS-CDMA schemes s the frequency separaton between adjacent subcarrers [2]. For MT-DS-CDMA the frequency separaton s the data rate of each subcarrer, whereas the frequency separaton for MC-DS-CDMA s the chp rate of each subcarrer. It was also shown n [11] that these two types of schemes are actually specal cases of a generalzed multcarrer DS-SS sgnalng scheme, whose performance n dspersve fadng channels can be analyzed under a common frame work. In [12] the authors proposed an MC-SS system that spreads the sgnal n both tme and frequency domans, where the same data bt s DS-SS spread, and transmtted through orthogonal subcarrers. By spreadng n both tme and frequency domans, the system can obtan hgher dversty order at the prce of lower system throughput compared wth the MC-DS-CDMA type systems we are consderng. The spectral sdelobes of any transmtted sgnal may act as nterference to sgnals n adjacent bands, and tradtonally these sdelobes are suppressed va flterng, e.g., usng a rased cosne flter. In [13], the MC-SS sdelobe levels were reduced by concentratng more energy n the central, or man lobe. Ths concentraton can be acheved by adjustng the data rate, chp rate and frequency separatons between adjacent subcarrers. In addton to sdelobe suppresson, the transmsson scheme n [13] can shape the spectrum of the transmtted sgnal by approprate selecton of the aforementoned parameters. Spectral shapng can also be acheved usng dfferent chp waveforms. In [14] the spectrum of a sngle carrer DS-CDMA sgnal was shaped to have a flat spectrum wthn a specfed band by usng a band lmted chp waveform. The purpose of ths band lmted chp waveform was to mnmze multple access nterference MAI n a CDMA applcaton when the channel s the addtve whte Gaussan nose AWG channel. Followng ths work, authors n [15] and [16] used numercal methods to fnd the optmal tme-lmted chp waveform that mnmzes both the MAI and the out-of-band sgnal energy, agan n the AWG channel. In [17], the authors nvestgated the bt error performance of generalzed MC-DS-CDMA [11] wth dfferent chp waveforms,.e., rectangular, half-sne, and rased cosne chp waveforms. Ther results showed that for a gven ntersubcarrer spacng there exsts an optmal choce of chp waveform. The effects of chp waveform selecton on the performance of MC-DS-CDMA were nvestgated n [18]. The author demonstrated that the performance of MC-DS-CDMA systems s nsenstve to the chp waveform shapng, but ths nvestgaton, as well as the work done by [17], dd not nclude our two-sdeband approach. In ths paper, we propose a new multcarrer modulaton scheme that uses snusodal chp waveforms to shape the

3 IOG and MATOLAK: SPECTRALLY SHAPED GEERALIZED MC-DS-CDMA WITH DUAL BAD COMBIIG FOR ICREASED DIVERSITY 1677 S/P c k t cos2 π ft 1 c k t cos2 π ft 2 c k t cos2 π ft V... Fg. 1. Transmtter block dagram for user k. s k t spectrum of each subcarrer. For a gven subcarrer, the chp waveform of our proposed scheme shapes the transmtted sgnal spectrum to have two dstnct lobes, a lower sdeband LSB and an upper sdeband USB. Wth properly selected chp waveform parameters, the separaton between these two lobes can be wder than the channel s coherence bandwdth, resultng n the two sdebands undergong uncorrelated fadng. Ths uncorrelated fadng of the LSB and USB can be utlzed to greatly mprove performance by vrtue of dversty. Ths paper s organzed as follows: Secton II ntroduces the proposed system transcever waveforms and the akagamm dspersve fadng channel model we employ. Secton III provdes the analyss of recever decson statstcs requred for error probablty estmaton. In Secton IV we provde numercal results and dscusson, and Secton V contans a summary and conclusons. II. SYSTEM MODEL A. Transmtted Sgnal A block dagram of the transmtter s shown n Fg.1. For smplcty of exposton, we use bnary phase shft-keyng BPSK modulaton, but results can easly be extended to hgher order PSK. As shown n the fgure, user k s bnary data stream s frst seral to parallel converted to form V parallel data streams each wth bt duraton of. Each of the V branches of the data stream s spread by the same spreadng waveform wth chp duraton of T c. As n any CDMA system, the spreadng code s used to dstngush users, and the same random long code s used for each subcarrer of a gven user sgnal. There are K user sgnals present. After spreadng, the chps of each subcarrer modulate the subcarrer snusods, and the transmtted sgnal s formed va summng the sgnals of all subcarrers. The transmtted sgnal of user k s s k 2Eb V t = d k n/ =1 n= c k npt nt c cos2πf t 1 where E b, are respectvely the bt energy and bt duraton of each subcarrer, d k n {±1} s user k s nth transmtted data bt on the th subcarrer, x s the nteger part of x, and = /T c s the processng gan on any subcarrer equal for all k and. We also defne c k {±1} as the mth chp of user k s spreadng code, pt = 2snJπt/T c over the nterval t T c s the chp waveform wth nteger J {2, 3, } a selectable parameter, and f s the th subcarrer frequency. 1 Most of our results employ odd values of J. In addton, we use the same spreadng waveform for all subcarrers,.e., c k t = c k npt nt c s the same for all subcarrers of user k. The frequency separaton between adjacent subcarrers s selected such that any two subcarrers are orthogonal. Specfcally, when j ths requres Tb n= p 2 t nt c cos2πf t cos2πf j tdt = 2 As shown n Appendx I, 2 s satsfed when Δf,j = f f j = λ/ and Δf,j J where λ s an nteger. In ths work, we allow λ to vary from 1 to ; ths corresponds, by analogy, to confgurng the system to vary from MT-DS- CDMA to MC-DS-CDMA as n [11]. It s worth notng that when λ =1some subcarrers may no longer be orthogonal to each other. However, snce the dspersve channel destroys the orthogonalty between subcarrers n any case, we stll nvestgate the error performance of the λ = 1 case. The transmtted sgnal can also be expressed by a summaton of the LSB and USB of each subcarrer sgnal as s k t = V =1 [ ] s k, L t+sk, U t where each sdeband sgnal of subcarrer of user k can be expressed by s k, t = Eb d k n/ c k n 2 n= [ pt nt c cos2πf t ± ˆpt nt c sn2πf t ] 4 where ˆpt nt c s the Hlbert transform of the snusodal chp waveform pt = 2snJπt/T c, and = L or U represents the LSB or USB of the transmtted sgnal. Wth some algebrac smplfcaton, we can easly show that ˆpt = 2cosJπt/T c for t T c. Upon substtutng the chp waveform pt and ˆpt nto 4, we can wrte the sdeband sgnal of subcarrer as s k, t = Eb n= d k n/ c k n 3 E, t nt c, 5 In 5, E, t, ϕ s the passband chp waveform for subcarrer, whch s { [ ] sn E, t, ϕ = J T c f πt + ϕ t T c 6 otherwse In 6, ϕ s the phase of the passband chp waveform for subcarrer, the mnus sgn represents the passband chp 1 ote that the use of rectangular chp waveforms s dfferent from a smple upconverson of the baseband rectangular chp waveform subcarrer sgnal to some carrer frequency. Specfcally, when J s odd, phase dscontnutes are enforced at chp boundares where they otherwse would not be for an upconverson when two consecutve chp pulses c k m, c k m +1are equal.

4 1678 IEEE TRASACTIOS O WIRELESS COMMUICATIOS, VOL. 7, O. 5, MAY 28 5 USB LSB Up converson where = L or U agan represents LSB or USB. In 8 M s the number of resolvable channel paths gven by [6] M = BW/B c +1 9 PSDdB Frequency /R c Fg. 2. Example PSD of one subcarrer for proposed scheme wth J =5. waveform for the LSB sgnal, and the plus sgn represents the chp waveform for the USB sgnal. 2 It s worth notng that by expressng each subcarrer sgnal as a sum of LSB and USB component sgnals, the nature of each subcarrer sgnal s not changed, and thus orthogonalty between any two subcarrers s mantaned. B. Channel Model Each subcarrer of our proposed scheme s a DS-SS sgnal wth ts power spectral densty PSD determned by the Fourer transform of ts chp waveform [19]. For the snusodal chp waveform pt, the baseband PSD of one subcarrer s gven by ψf = E 2 b 2J 4πT c f 2 πj 2 [ 1 1 J cos2πt c f ] 7 An example PSD of one subcarrer usng the snusodal chp waveform wth J =5s shown n Fg The separaton between the peaks of the two sdelobes s approxmately J/T c, and the null-null bandwdth of each sdeband s 2/T c. Therefore, two sdeband sgnals ncur uncorrelated fadng when the chp waveform parameter s properly chosen,.e., the frequency separaton between the two manlobes of the LSB and USB s greater than the channel coherence bandwdth. We assume that the channel for ether LSB or USB, for the th subcarrer of user k, s a dspersve akagam-m channel wth mpulse response gven by, t = h k l= α k, exp jθ k, δ t τ k, 2 The representaton of 3 and 5 can be drectly obtaned by multplyng 2snJπt/Tc and cos2πf t. 3 As can be observed n ths fgure, the PSD of our proposed scheme for one subcarrer s dfferent from that of the subcarrer sgnal that s up-converted by the carrer waveform sn5πt/t c. Specfcally, despte the same manlobe shapes, the sdelobe levels of the two schemes-usng our chp waveform and conventonal up-converson-are dfferent. As prevously noted, ths s because when J s odd, phase dscontnutes are enforced at chp boundares where they otherwse would not be for an upconverson when two consecutve chp pulses c k m, c k m +1are equal. 8 where BW =2/T c s the baseband null-to-null bandwdth of ether sdeband. In 8, α k,, θ k,, and τ k, are respectvely the ampltude, phase shft, and delay of the lth tap for user k s LSB or USB sgnal on subcarrer. Under the assumpton of uncorrelated scatterng US and ndependent fadng for the LSB and USB sgnals, the phase shfts of dfferent user s dfferent paths of dfferent subcarrers are ndependent dentcally dstrbuted..d. random varables RVs unformly dstrbuted wthn [, 2π. Smlarly, the delays for dfferent, l, k and are..d. random varables unformly dstrbuted wthn the nterval [,. The tap ampltudes for dfferent sdebands, dfferent taps and dfferent users are assumed to be ndependent akagam-m RVs. We use the akagam model because of ts flexblty and ablty to model a wde range of fadng condtons [11]. The probablty densty functon pdf of a akagam-m RV s gven by p R r = 2 m m r 2m 1 e mr2 /Ω 1 Γm Ω where Γ s the gamma functon, Ω=E[r 2 ] s the average energy, and m>s the fadng parameter, whch characterzes the channel condtons. Specfcally, when m =1/2 the akagam-m dstrbuton becomes the one sded Gaussan dstrbuton; for m =1, t becomes the well known Raylegh dstrbuton, and when m, t becomes an mpulse, or a non-fadng dstrbuton. In ths paper, the power delay profle PDPof the channels between the transmtter and recever for both sdeband sgnals of all users subcarrers are assumed to be dentcal,.e.,ω k, = Ω l for = L, U, = 1, 2, V, and k = 1, 2, K. In addton, the PDP shape s assumed to be exponentally decayng [11],.e., the average power of the lth tap s gven by Ω l =Ω e ηl where η s the decay factor, and the total power of the channel s normalzed to be unty,.e., l= Ω l =1. C. Recever Model Assumng we have K asynchronous users wth dentcal system confguratons same number of subcarrers, processng gan and chp waveforms for each subcarrer, and ndependent channels for both the LSB and USB sgnals of all subcarrers of all users, the receved sgnal s rt = K V k=1 =1 [ r k, L t+rk, U t ] + nt 11 where nt s the AWG wth double sded PSD /2 W/Hz. The receved LSB or USB sgnal of the th subcarrer of user k, r k,, s gven by r k, = Eb l= n= α k, n/ c k n E, t nt c,φ k, d k 12

5 IOG and MATOLAK: SPECTRALLY SHAPED GEERALIZED MC-DS-CDMA WITH DUAL BAD COMBIIG FOR ICREASED DIVERSITY 1679 rt The 1 st subcarrer LSB RAKE The 1 st subcarrer USB RAKE The V th subcarrer LSB RAKE The V th subcarrer USB RAKE Z k 1, L Z k Z VL, k 1, U k Z VU,... Fg. 3. Recever block dagram for user k. DEC DEC where φ k, =2πf τ k, θ k, s the composte phase, also unformly dstrbuted wthn [, 2π. We assume that the recever s capable of estmatng the channel perfectly,.e., the recever can estmate the ampltude, delay, and phase of each multpath echo. Thus, smlar to the conventonal CDMA RAKE recever, wth each fnger locked to one path, two RAKEs are needed for one subcarrer. It s also worth notng that when the local reference sgnal of each RAKE fnger s c k ne, t nt c,φ k,, no addtonal sgnal processng component s needed before these RAKE recevers. The recever block dagram for user k s shown n Fg. 3, where two RAKEs, one for each sdeband, are used for each subcarrer. After maxmal rato combnng MRC the RAKE fngers, the outputs of the two RAKEs are combned to form the decson metrc for the gven subcarrer. Fnally, a hard decson s made va the sgn of the combned output, and these detected bts are parallel to seral converted to form the detected bt stream. The decson metrc for user k s jth subcarrer s Z k j = q= ˆ k 1 b ˆ k b V P/S ˆ k b Z k, j,q 13 where Z k, j,q s the correlator output of the qth RAKE fnger of the jth subcarrer of user k. III. PERFORMACE AALYSIS A. Corrrelator Output Wthout loss of generalty, we assume the phase and delay of the qth path of user k s subcarrer j are zero, and the delays and phases of other channel taps are relatve to those of path q. Thus, user k s qth RAKE fnger correlator output for subcarrer j can be separated nto four terms k, Z j, q = Tb k, rtα j, q n= c k ne j, t nt c dt = D + n + I 1 + I 2 + I 3 14 where D = E b d k j /2 s the desred sgnal term, n s the AWG sample wth zero mean and varance /4. The terms I 1 and I 2 are the nterferences from the same subcarrer both same and dfferent users due to the channel dsperson, and I 3 s the nterference from other subcarrers. The nterference from the same subcarrer of the same user, I 1, s gven by I 1 = M=1 Eb α k, j,q α k, β k,k j,j l=,l q M=1 Eb + α k, j,q α k,y j, l l= τ k,,φ k, ˆβ k,k j,j τ k,y,φ k,y 15 where we denote the correlaton functon between the same sdeband waveform from user v s subcarrer and that of the user k s subcarrer j by β v,k v,k,j, and smlarly ˆβ,j s defned for the correlaton functon between dfferent sdeband sgnals. ote that snce the LSB and USB sgnal undergo ndependent fadng, the nterference from the qth path of the other sdeband sgnal ndcated as Y s not excluded from the summaton of the second term of 15. Smlarly, the nterference from the same subcarrers of dfferent users, I 2, and the nterference from other subcarrers of all users, I 3, are respectvely gven by Eb K M=1 I 2 = α k, j,q α v, v=1,v k l= β v,k j,j τ v,,φ v, Eb K M=1 + α k, j,q α v,y I 3 = + Eb v=1,v k l= K ˆβ v,k j,j V v=1 =1, j l= β v,k,j Eb K V τ v,y,φ v,y j, l M=1 α k, j,q α v, τ v, M=1 v=1 =1, j l= ˆβ v,k,j ˆβ v,k,j where the β v,k,j, and as shown on the top of next page,φ v, α k, j,q α v,y τ v,y,φ v,y functons n are defned B. Statstcs of Decson Metrc The statstcs of the desred sgnal term and AWG sample term were already gven, so here we derve the statstcs of the nterference terms. The nterference terms are assumed to be Gaussan random varables. Ths approxmaton s valdated va our smulatons shown n Secton IV. In ths secton, we nvestgate the statstcs of the cross correlaton functons β,j k, v and ˆβ,j k, v between the dfferent subcarrers and dfferent users. It s worth nothng that the cross correlaton functons between the same subcarrers of dfferent users can be obtaned by equatng the user ndces k and v; smlarly, the cross correlaton between the dfferent multpath echoes of the gven subcarrer from the same user can be found by lettng = j and v = k. Followng the method gven n [13], we represent the delay τ n 18 and 19 as τ = ST c + ε 2

6 168 IEEE TRASACTIOS O WIRELESS COMMUICATIOS, VOL. 7, O. 5, MAY 28 Tb β v,k,j τ,φ= Tb ˆβ v,k,j τ,φ= n= n= d v d v n/ c v n/ c v ne, t nt c τ,φ m= ne,y t nt c τ,φ m= c k j me j, t nt c, 18 c k j me j, t nt c dt 19 where S s an nteger gven by S = τ/t c and ε = τ ST c s the fractonal chp part of τ, unformly dstrbuted n [,T c. Ths representaton of the τ allows β,j k, v and ˆβ,j k, v to be expressed as β v,k, j τ,φ=d v ˆβ v,k,j τ,φ=d v 1R v,k,;j, τ,φ + d v v,k ˆR,; j, τ,φ 21 1R v,k,y ;j, τ,φ + d v v,k ˆR,Y ;j,τ,φ 22 where R v,k v,k,y ;j, and ˆR,Y ; j, are two partal correlaton functons wth defntons gven by R v,k,y ;j, τ,φ= ˆR v,k,y ;j, τ,φ= S m= ε + c k mc v m S 1 E,Y t ε, φe j, t, dt S 1 m= c k mc v m S Tc E,Y t ε, φe j, t, dt 23 ε m=s+1 ε + c k mc v m S 1 E,Y t ε, φe j, t, dt m=s c k mc v m S Tc E,Y t ε, φe j, t, dt 24 ε Snce we assume the data symbols and the spreadng codes are random and bnary, the two partal correlaton functons of 23 and 24 are zero mean, and ther varances are easy to evaluate, yeldng, [ ε ] var[β v,k,j τ,φ]=2var var[ v,k ˆβ,j τ,φ] = 2var [ ε E,t ε, φe j,t, dt E,Y t ε, φe j,t, dt ] The dervaton of the varances n 25 and 26 s gven n Appendx II. Wth the varance of 25 and 26, the varances of the nterference terms are var[i 1 ]= E b [ M 1 12M + 1 8J 2 π 2 ] α k, j, q 2 27 var[i 2 ]=K 1 E b var[i 3 ]= KE b [ ] 8J 2 π 2 α V j=1 j k, j, q var[i Δf, j T c ] +var[i Y Δf, j T c ] α q= k, j, q The defntons of I and I Y and ther varances are gven n Appendx II. The mean and varance of the correlator output of the decson metrc are thus E[Z v j ]= 1 Eb d [ ] 2 α k, j,q 3 2 { var[z v 1 [ j ]= K3 + 2J 2 24J 2 π 2 π 2 2J 2 π 2 /M ] + K V var[i Δf,j T c ] + var[i Y Δf,j T c ] =1 j + 4 } q= [ ] 2 α k, j,q 31 C. BER Performance The statstcs of the decson metrc of a gven subcarrer for all users are the same, snce each user has the same parameter set. The user superscrpt s henceforth removed. Wth BPSK modulaton, the bt error probablty of subcarrer j s thus E,j = Q 2 [Z j ] = Q 2γ j 32 var[z j ] whereqx = /2 x e t2 dt/ 2π, and γ j s the nstantaneous sgnal-to-nose-plus-nterference rato SIR of subcarrer j whch s defned as γ j = 2 γ j α j,q 33 q= whereγ j s the average SIR of the jth subcarrer s LSB or USB RAKE output, gven by { γ 1 [ j = K3 + 2J 2 3J 2 π 2 π 2 2J 2 π 2 /M ] 8K M =1 j [V Δf, j T c +V Y Δf, j T c ] + 2 } 1 34 E b

7 IOG and MATOLAK: SPECTRALLY SHAPED GEERALIZED MC-DS-CDMA WITH DUAL BAD COMBIIG FOR ICREASED DIVERSITY 1681 To obtan the average bt error probablty of subcarrer j, the nstantaneous bt error probablty gven by 31 should be averaged over the jont pdf of channel tap ampltudes; the jont pdf s the product of the margnal pdfs when the tap ampltudes are ndependent RVs under the uncorrelated scatterng US assumpton: p α,l,α 1,L, α,u α,l,α 1,L, α,u = p αq, α q, 35 q= The average bt error probablty of subcarrer j s thus gven by 2γj,j = Q p αq, α q, }{{} q= 2M fold dα,l, dα 1,L, dα,u 36 The drect evaluaton of 36 requres a 2M +1-fold ntegraton, whch s dffcult to obtan n closed form. To crcumvent ths dffculty, we use an alternatve form of the Q functon [2], Qx = 1 π/2 exp x2 π 2sn 2 dχ 37 χ The alternatve Q functon form allows us to concsely represent the average va the moment generatng functon MGF [2]: π/2,j = 1 π }{{} 2M fold q= exp q= γ j sn 2 χ α j,q 2 p αq, α q,dα,l, dα 1,L, dα,u = 1 π π/2 q= Gγ j,q χdχ 38 where γ j,q = γ j e ηq s the average SIR of the qth RAKE fnger output for the LSB or USB RAKE of the jth subcarrer, and Gx, y s the MGF of the akagam-m dstrbuton, [2] m sn 2 m χ Gγ, χ = m sn 2 39 χ+γ Fnally, wth the average bt error probablty of each subcarrer, the average bt error probablty of the proposed system can be obtaned va averagng the error probabltes V of all subcarrers as = =1, /V. IV. UMERICAL EAMPLES In ths secton the BER performance of our proposed scheme s compared wth that of the MC-DS-CDMA schemes whose average s gven by equaton 47 n [11]. Our comparson here s under the condtons n whch all schemes have the same number of subcarrers, the same data rate, the same overall bandwdth, and the same transmsson power. PSD db Proposed λ =1 Proposed λ = MC DS SS frequency/ R c Fg. 4. PSD of proposed scheme and conventonal MC-DS-SS wth V =5, MC =64, J =3,and =76for λ =1and =42for λ =. Recall that the bandwdth of one sdeband sgnal of our proposed scheme s 2/T c, and the frequency separaton of the peaks of two sdelobe sgnals s approxmately J/T c. Thus, the null-null bandwdth of our proposed scheme s BW =J +2/T c +V 1Δf 4 where Δf s the frequency separaton between the adjacent subcarrers,.e., Δf = λr b. The null-null bandwdth of the MC-DS-CDMA wth chp duraton of T c,mc and frequency separaton equal to the chp rate s BW =2/T c,mc +V 1/T c,mc 41 Thus under the equal bandwdth and data rate condton, the processng gan relaton between the MC-DS-CDMA scheme and our proposed scheme s J +2 + λv 1 MC = 42 V +1 The baseband PSD normalzed to ts maxmum value for the proposed scheme wth chp waveform parameter J =3 and frequency separatons of 1 and are compared wth that of MC-DS-CDMA n Fg. 4. The processng gan for a 5- subcarrer MC-DS-CDMA s set to be 64, and the processng gans for our proposed schemes are 76 and 42 respectvely for λ =1and λ =. It can be observed from ths fgure that λ =1and λ = are two extreme examples of spectrum shapng. Specfcally, when λ =1, the ntersubcarrer frequency separaton s the data rate on each subcarrer, and the PSD of our proposed scheme has spectral nulls around DC; conversely when λ =, the PSD of our proposed scheme reaches ts maxmum value around DC. Thus, the proposed scheme wth dfferent frequency separatons can be used to adaptvely compensate for channel fadng when the channel s known at the transmtter. Also worth notng s that the sdelobes of our scheme are more than 17 db down, whereas the conventonal MC-DS-SS sdelobes are down by approxmately 11 db, hence our scheme suppresses sdelobe levels by approxmately 6 db. Agan we note that throughout ths paper, the bandwdth to whch we refer s the null-to-null bandwdth. Ths bandwdth measure s used because t s relatvely easy to determne.

8 1682 IEEE TRASACTIOS O WIRELESS COMMUICATIOS, VOL. 7, O. 5, MAY Smulated λ=1 Analytcal λ=1 Smulated λ= Analytcal λ= Proposed scheme wth λ=1 Proposed scheme wth λ= MC DS CDMA E b / db E b / db Fg. 5. Analytcal and smulated vs. E b / for K =1users, V =5 subcarrers, =32for proposed scheme wth J =3, λ =1, λ = =32, n akagam-m dspersve channel wth m =1,η =2M =5channel taps. In Fg. 5 we show both smulaton and analytcal results for the systems wth K =1users, V =5subcarrers, chp waveform parameter J =3, and processng gan of =32 for both λ =1and λ =. The channel s a akagam-m dspersve channel wth m =1Raylegh fadng, PDP decay factor of η =2, and the number of resolvable paths for each sdeband s M =5, or a 5-tap channel. From ths fgure, we can observe that the smulaton results match the analytcal results, corroboratng our standard Gaussan assumpton for the nterference. The good agreement between the analytcal results and smulaton results hold for processng gan values greater than 8. Therefore, n the followng examples we use analytcal results to compare the BER performance of our proposed scheme wth that of MC-DS-CDMA, n whch we also consder 1 users, and 5 subcarrers, wth processng gan and the number of resolvable channel taps for each subcarrer set to be =64and M =5, respectvely. 4 The average of our proposed scheme wth J =3and dfferent frequency separatons λ s, and for MC-DS-CDMA wth parameters gven prevously are shown n Fg. 6. The processng gans of our proposed schemes are 76, and 42 respectvely for λ = 1 and λ =. In ths example, the channel s a dspersve akagam-m channel wth m = 1, η = 2, and the number of channel taps for our proposed scheme wth λ =1and λ = are respectvely 6, and 4. From ths example we can observe that the λ = ntersubcarrer frequency separaton case has better performance than that of the λ =1case because of the reduced spectral overlappng among subcarrers. In comparson to conventonal MC-DS, our proposed scheme wth λ =1has slghtly better performance at SRs less than 15 db, and approxmately the same performance for SRs greater than 15 db. The effect of the chp waveform parameter J on the BER 4 ote that n Fg. 5, we show that the analytcal results match the smulaton results for the proposed scheme wth two frequency separatons wthout settng the bandwdths of these two confguratons to be equal. For the examples n the rest of ths secton, we compare the BER performance of the proposed scheme wth that of the conventonal MC-DS-CDMA scheme that has the same number of users, the same number of subcarrers, the same total data rate, the same bandwdth, and the same transmsson power. Fg. 6. vs. E b / for 1 user MC-DS-CDMA system wth V =5 subcarrers and =64, and proposed scheme wth J =3, λ =1, =76, and J =3, λ = =42, n akagam-m dspersve channel wth m =1, η =2and M =5channel taps for MC-DS-CDMA, M =6, and 4 for proposed scheme wth λ = 1 and λ =, respectvely. at E b / =15dB Proposed Scheme λ=1 Proposed Scheme wth λ= MC DS SS Chp Waveform Parameter J Fg. 7. vs. J for 1-user systems over akagam-m dspersve channel wth E b / =15dB, m =1,andη =2, V =5subcarrers, =64for MC-DS-CDMA, and λ =1and λ = for proposed scheme. performance of our proposed scheme s shown n Fg. 7. In the fgure, the average at E b / =15dB for our proposed scheme wth dfferent values of chp waveform parameter J, s compared wth that of the conventonal MC-DS-CDMA scheme. To ensure the same bandwdth, the processng gan of our proposed scheme wth dfferent frequency separatons s obtaned va equatng 4 and 41, and the number of resolvable channel taps s obtaned va 9. We can observe n ths example that as the value of J ncreases, the BER performance of our proposed scheme wth λ =1degrades whereas the λ = scheme nearly mantans ts performance. The reason for the performance degradaton s manly due to the fact that as the value of J ncreases, the processng gan of our proposed scheme must decrease n order to keep the bandwdth unchanged. For example, the processng gans for the two frequency separatons λ =1and λ = are reduced from 95 and 48, to 31 and 24, when the value of J ncreases from 2 to 1. For the λ =1confguraton, the spectra of all

9 IOG and MATOLAK: SPECTRALLY SHAPED GEERALIZED MC-DS-CDMA WITH DUAL BAD COMBIIG FOR ICREASED DIVERSITY Proposed Scheme λ=1 Proposed Scheme wth λ= MC DS SS 1 1 Proposed Scheme λ=1 Proposed Scheme wth λ= MC DS SS at E b / =15dB 1 2 at E b / =15 db decay factor η fadng factor m Fg. 8. vs. channel power decay factor for 1-user system wth E b / = 15 db, = 64, V = 5 subcarrers for MC-DS-CDMA, and for proposed scheme wth J = 3, λ = 1, = 76,andJ = 3,λ = = 42,n akagam-m dspersve channel wth m = 1,and M = 5 for MC-DS- CDMA, M = 6, and 4 for proposed scheme wth λ = 1 and λ =, respectvely. Fg. 9. vs. channel m for 1-user system wth E b / = 15 db, =64, V =5subcarrers for MC-DS-CDMA, and for proposed scheme wth J =3, λ =1, =76,andJ =3,λ = =42, n akagam-m dspersve channel wth η =2, and M =5for MC-DS-CDMA, M =6, and 4 for proposed scheme wth λ =1and λ =, respectvely. subcarrers overlap sgnfcantly, thus the loss n processng gan reduces ts capablty to suppress nterference from other subcarrers. On the other hand, only the spectra of adjacent subcarrers overlap for the λ = confguraton, yeldng less ntersubcarrer nterference. As a result, the reducton of processng gan for the λ = scheme does not as strongly affect the average. We next show the BER performance of our proposed scheme n dfferent channel condtons. The average ate b / =15dB wth K =1users for our proposed scheme wth J = 3 and for MC-DS-CDMA, wth dfferent decay factors, s shown n Fg. 8. The channel s a akagam-m fadng channel wth m =1, and the decay factor η vares from to 3. We assume the recever s capable of capturng all the channel taps,.e., we employ a 5-fnger RAKE for one subcarrer of MC-DS-CDMA, and 4-fnger and 6-fnger RAKEs for each sdeband of our proposed schemes wth λ =1and λ = respectvely. The results shown n Fg. 8 ndcate that as the decay factor ncreases, the average of all three system ncreases. Ths agrees wth the fact that RAKE has the best performance for a unform PDP. The proposed scheme wth λ = outperforms the reference system at any value of η and when η>1.8, the proposed scheme wth λ =1 has a better performance than that of MC-DS-CDMA. As the decay factor ncreases, the majorty of the energy s contaned wthn the frst few lower delay channel taps. Thus, when these lower-delay taps ncur deep fadng, the SIR output of the MRC s low even f the low-energy, hgher-delay channel taps are not faded. For our proposed scheme, however, the channels for LSB and USB are ndependent dentcal channels. Therefore, the probablty of both sdeband sgnals undergong a deep fade s greatly reduced. In Fg. 9 the average as a functon of the akagamm factor s shown for the three schemes. The parameters of conventonal MC-DS-CDMA and for our proposed schemes wth λ = 1 and λ = are the same as n the prevous example, and the channel s smlar to that of the prevous example except that nstead of varyng the decay factor η, here we fx the decay factor to be η =2and allow the fadng parameter m to vary from 1/2 to 1. As we know, m =1/2 s the so called one-sded Gaussan dstrbuton-a severe case of fadng. As m ncreases, the channel s less severely faded, and ths example shows the effect of the dversty va LSB and USB combnng n our proposed scheme. As can be observed from ths fgure, the average bt error probabltes of MC-DS-CDMA and those of our proposed schemes decrease as the value of m ncreases, as expected. Both our proposed schemes wth λ =1and λ = outperform MC-DS-CDMA at m =1/2. As the value of m ncreases, the performance of the λ =1scheme worsens relatve to that of conventonal MC-DS-CDMA, whereas the λ = scheme stll has better performance than that of the MC-DS-CDMA scheme. The reason s that when the channel fadng s mlder m ncreases, the domnant effect on performance becomes the MAI; n ths case, snce dversty s used to combat fadng nstead of suppressng MAI, the dversty ntroduced by combnng LSB and USB sgnals n our scheme s less effectve. As a result, the performance of the λ = scheme approaches that of MC-DS-CDMA. Ths example and the prevous one show that the proposed scheme can be used n envronments where the wreless channel s severely faded,.e., a large PDP decay factor η and a small m value. The average of our proposed scheme at E b / =15 db wth λ =1and λ = and that of conventonal MC- DS-CDMA are shown n Fg. 1. The parameters of all three schemes are the same as n the prevous examples, except that we vary the number of subcarrers from 3 to 2, and adjust each subcarrer s processng gan of our proposed scheme to make sure that our proposed schemes and the conventonal MC-DS-CDMA wth a processng gan of = 64 have the same bandwdth. The channel s a akagam-m fadng channel wth m =1, η =2and the number of resolvable channel taps for conventonal MC-DS-CDMA s M = 5,

10 1684 IEEE TRASACTIOS O WIRELESS COMMUICATIOS, VOL. 7, O. 5, MAY Proposed wth λ=1 Proposed wth λ= MC DS CDMA 1 Proposed scheme wth λ=1 Proposed scheme wth λ= MC DS CDMA wth Rectangular chpwaveform MC DS CDMA wth half sne chpwave form MC DS CDMA wth rase cosne chp waveform at E b / =15 db umber of subcarrers E b / db Fg. 1. vs. number of subcarrers for 1-user system wth E b / =15 db, =64for MC-DS-CDMA, and proposed scheme wth J =3, λ = 1,and J =3,λ= =42, n akagam-m dspersve channel wth m =1 η =2,and M =5for MC-DS-CDMA. Fg. 12. vs. E b / for 1 user MC-DS-CDMA system wth V =5 subcarrers =64, 43 and 32 respectvely for rectangular, half-sne and rased-cosne chp waveforms, proposed scheme wth J =3, λ =1, =76, and J =3, λ = =42, n akagam-m dspersve channel wth m = 1,η =2and M =5channel taps for MC-DS-CDMA, M =6,and4for proposed scheme wth λ = 1 and λ =, respectvely. 1 1 at E b / =15 db Proposed wth λ=1 Proposed wth λ= MC DS CDMA umber of users Fg. 11. vs. number of users wth E b / =15dB, =64, V =5 subcarrers for MC-DS-CDMA and proposed scheme wth J =3, λ =1, =76,andJ =3, λ = =42, n akagam-m dspersve channel wth m =1η =2,andM =5for MC-DS-CDMA, M =6, and 4 for proposed schemes wth λ =1and λ =, respectvely. and the number of resolvable channel taps for our proposed schemes are gven by 9. As demonstrated n ths fgure, the error performance of all three schemes s nsenstve to the number of subcarrers, V, when V s greater than some value. Specfcally for the parameters n the fgure, when V s greater than 6, the curves are flat as the number of subcarrers ncreases. In addton, the error performance of our proposed scheme wth λ =1s smlar to that of conventonal MC- DS-CDMA when the number of subcarrers s large because of the ncreased nterference caused by strongly overlapped subcarrers; conversely, snce the adjacent subcarrers overlap at ther spectral nulls n our proposed scheme wth λ =,ths scheme has lower bt error probabltes despte the ncrease n the number of subcarrers. The nfluence of dfferent system load number of users on the average s shown n Fg. 11. The parameters of conventonal MC-DS-CDMA and for our proposed schemes wth λ =1and λ = and the channel are the same as n the example shown n Fg. 6. We show the average of three systems wth dfferent numbers of actve users. As expected, wth more users added to the system, the error performance of all three schemes degrades, and the performance of our proposed schemes wth λ =1and λ = approaches that of conventonal MC-DS-CDMA as the number of users ncreases. Ths s due to reasons smlar to those of the example n Fg. 1. Specfcally, as the number of user ncreases, MAI becomes the domnant factor n performance loss, and the dversty ntroduced by combnng the LSB and USB sgnals n our scheme s less effectve. We also compare the error performance of our scheme wth the conventonal MC-DS-CDMA wth the half sne and rased cosne chp waveforms of [17] n Fg. 12. The parameters of conventonal MC-DS-CDMA wth the rectangular chp waveform, our proposed schemes, and the channel are the same n prevous example. The processng gans of MC- DS-CDMA wth chp waveforms other than rectangular are adjusted to ensure the same bandwdth for all schemes. Specfcally, wth the spectral expanson of the half sne and rased cosne chp waveforms [17] consdered, the processng gans of MC-DS-CDMA wth these two chp waveforms are respectvely 43 and 32. The performance rankng shown n ths fgure our proposed scheme wth λ = followed by the proposed scheme wth λ =1, conventonal MC-DS-CDMA wth rectangular chp waveform, MC-DS-CDMA wth the half sne chp waveform, and MC-DS-CDMA wth the rased cosne chp waveform 5 suggests that our proposed scheme wth λ = yelds the maxmum dversty gan. 5 The authors of [17] reached the concluson that the MC-DS-CDMA wth rectangular, half sne, and rased cosne chp waveform have smlar error performances wthout equatng the bandwdth of MC-DS-CDMA wth these chp waveforms.

11 IOG and MATOLAK: SPECTRALLY SHAPED GEERALIZED MC-DS-CDMA WITH DUAL BAD COMBIIG FOR ICREASED DIVERSITY 1685 V. COCLUSIO A new modulaton scheme that shapes the spectrum of an MC-DS-SS sgnal va snusodal chp waveforms was proposed. Ths snusodal chp shapng enables generaton of dstnct upper and lower sdeband component sgnals for each subcarrer, whch can be exploted for frequency dversty. The BER of ths spectrally shaped MC-DS-CDMA wth dual sdeband combnng was consdered over akagam-m dspersve fadng channels. We nvestgated the effects of chp waveform ndex, PDP shape, and the channel fadng condtons on the performance of the proposed scheme. Wth properly selected parameters, the BER performance of the proposed scheme s better than that of an equvalent MC-DS-SS sgnal wth rectangular, half sne, and rased cosne chp waveforms. Future work ncludes nvestgatng the performance of our proposed scheme when the two sdebands ncur correlated fadng, and the effects of Doppler. APPEDI I By substtutng the chp waveform and dscardng the double frequency term, 4 can be wrtten as Tb n= n+1tc p 2 t nt c cos2πf t cos2πf j tdt = sn 2 nt c n= Jπ t cos 2πΔf,j t dt 43 T c where Δf,j = f f j. Wth some straght forward algebra, t can be shown that when Δf,j J 43 can be expressed as J 2 snπδf,j T c 2πΔf,j T [J 2 Δf,j T 2 cos[πδf,j T c 2n + 1] ] n= 44 Followng the dentty [21] m= cosmy + x = 44 reduces to cos{x +[ 1/2]y} sny/2 sny/2 45 J 2 cosπδf,j T c snπδf,j T c 2πΔf,j T [J 2 Δf,j T 2 46 ] whch equals zero when Δf,j = λ/t c =λr b. Followng the same method, t can be shown that when Δf,j = J, 43 reduces to /4, not zero. Thus, n order to make sure that subcarrer and subcarrer j are orthogonal, we requre Δf,j = f f j = λ/ and Δf,j J. APPEDI II We derve the varance of the ntegrals n 25 and 26. Denote the ntegral n 25 as I Δf,j T c. ε I Δf,j T c = E, t ε, E j, t, dt 47 Wth the defnton of E,, t s easy to show that 47 can be expressed as I Δf,j T c = 1 ε cos 2πΔf,j t + Jπ ε + θ dt 48 2 T c where θ = φ +2πf ε Jπε/T c s the aggregate phase due to the delay and the channel, unformly dstrbuted n [, 2π. ote that n 48 we have dscarded the term contanng the hgh frequency component at frequency f + f j. Upon averagng the varable gven by 48 over the aggregate phase θ and the fractonal chp part of delay, ɛ the varance of I x s var[i Δf,j T c ] = T c 2 2πΔf,j T c sn2πδf,j T c πδf,j T c When Δf,j =, representng the same-subcarrer samesdeband nterference, the varance of I Δf,j T c s var[i Δf,j T c ] = T c Followng the same method, the ntegral n the cross correlaton functon between dfferent sdeband sgnals n 19 s denoted by I Y Δf,j T c, and when Δf,j T c J ts varance s var[i Y Δf,j T c ] = T c 2 2 sn where = πδf,j T c J. When Δf,j T c = J, ts varance s var[i Y Δf,j T c ]= T c REFERECES [1] R. L. Pckholtz, D. L. Schllng, and L. B. Mlsten, Theory of spread-spectrum communcatons a tutoral, IEEE Trans. Commun., vol. COM-3, no. 5, pp , May [2] S. Hara and R. Prasad, Overvew of multcarrer CDMA, IEEE Commun. Mag., vol. 35, no. 12, pp , Dec [3], Desgn and performance of multcarrer CDMA system n frequency-selectve raylegh fadng channels, IEEE Trans. Veh. Technol., vol. 48, no. 5, pp , Sept [4]. Gu and T. g, Performance of asynchronous orthogonal multcarrer CDMA systems n frequency selectve fadng channel, IEEE Trans. Commun., vol. 47, no. 7, pp , July [5] E. A. Sourour and M. akagawa, Performance of orthogonal multcarrer CDMA n a multpath fadng channel, IEEE Trans. Commun., vol. 44, pp , Mar [6] S. Kondo and L. B. Mlsten, Performance of multcarrer DS-CDMA system, IEEE Trans. Commun., vol. 44, no. 2, pp , Feb [7] L. Vandendorpe, Multtone spread spectrum multple access communcatons system n a multpath rcan fadng channel, IEEE Trans. Veh. Technol., vol. 44, no. 2, pp , May [8] K. Yp,. Zhang, T. S. g, and J.Wang, On the multple-access capacty of Multtone-CDMA communcatons, IEEE Commun. Lett., vol. 4, no. 2, pp. 4 42, Feb. 2. [9] I. Sen and D. W. Matolak, Reduced-complexty bandwdth effcent multtone drect sequence spread spectrum, n Proc.24 IEEE Sarnoff Symp. on Advances n Wred and Wreless Comm., Prnceton, J, Apr. 24, pp [1] H. L and D. W. Matolak, Phase nose and fadng effects on system performance n MT-DS-SS, IEEE Trans. Veh. Technol., vol. 54, no. 2, pp , 26. [11] L.-L. Yang and L. Hanzo, Performance of generalzed multcarrer DS-CDMA over akagam-m fadng channels, IEEE Trans. Commun., vol. 5, no. 6, pp , June 22. [12] C. W. You and H. D.S., Multcarrer CDMA systems usng tme-doman and frequency-doman spreadng codes, IEEE Trans. Commun., vol. 51, no. 1, pp , Jan. 23. [13] D. W. 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12 1686 IEEE TRASACTIOS O WIRELESS COMMUICATIOS, VOL. 7, O. 5, MAY 28 [16] H. H. guyen, An mproved desgn of chp waveforms for band-lmted DS-CDMA systems, IEEE Trans. Veh. Technol., vol. 53, no. 5, pp , 24. [17] L. Yang and L. Hanzo, An mproved desgn of chp waveforms for band-lmted DS-CDMA systems, IEEE Trans. Veh. Technol., vol. 51, no. 5, pp , May 23. [18] H. H. guyen, Effect of chp waveform shapng on the performance of multcarrer CDMA systems, IEEE Trans. Veh. Technol., vol. 54, no. 3, pp , May 25. [19] J. G. Proaks, Dgtal Communcatons, 4th ed. ew York: McGraw- Hll, 2. [2] M.-S. Aloun and A. J. Goldsmth, A unfed approach for calculatng error rates of lnearly modulated sgnals over generalzed fadng channels, IEEE Trans. Commun., vol. 47, pp , [21] R. L. Peterson, R. E. Zemer, and D. E. Borth, Introducton to Spread Spectrum Communcatons. Upper Saddle Rver, J: Prentce-Hall, Wenhu ong SM 3 was born n Chengdu, Chna, and receved hs B.S. and M.S. degrees from the Unversty of Electronc Scence and Technology of Chna, Chengdu, Chna, n 1999 and 22, and the Ph.D Degree from Oho Unversty, Athens, OH, n 27 all n electrcal engneerng. He s currently workng as a senor engneer at corporate R&D group, Qualcomm nc., where he s workng on moble postonng for CDMA network. Davd W. Matolak M 83-SM was born n Johnstown, PA, and receved the B.S. degree from The Pennsylvana State Unversty, Unversty Park, PA, n 1983, the M.S. degree from The Unversty of Massachusetts, Amherst, MA, n 1987, and the Ph.D. degree from The Unversty of Vrgna, Charlottesvlle, VA, n 1995, all n electrcal engneerng. He was wth the Rural Electrfcaton Admnstraton, Washngton, D.C., from 1983 to 1985, and worked on upgradng specalzed rural telecommuncaton systems. From 1985 to 1986, he was wth the UMass LAMMDA Laboratory, where he worked on the full-wave analyss, desgn, fabrcaton, and testng of planar mcrowave transmsson lnes and antennas. From 1986 to 1989 he was wth AT&T Bell Laboratores, n the Mcrowave Rado Systems Development Department, where he worked on analytcal and emprcal characterzaton of nonlneartes and ther effect on QAM transmsson. In 199, he joned the Unversty of Vrgna s Communcaton Systems Laboratory, where he researched trells codng and equalzaton for TDMA moble rado systems. From 1994 to 1996, he was wth Lockheed Martn Tactcal Communcaton Systems, where he was Lead System Engneer on the development of a wreless local loop synchronous CDMA communcaton system. From 1996 to 1998, he was wth the MITRE Corporaton, where he worked on the analyss and modelng of varous dgtal rado communcaton systems. He was wth Lockheed Martn Global Telecommuncatons from 1998 to 1999, and worked on moble satellte communcaton system analyss and desgn. In September 1999, he joned the School of Electrcal Engneerng and Computer Scence at Oho Unversty, Athens, Oho. Hs research nterests are communcaton over fadng channels, rado channel modelng, multcarrer transmsson, and CDMA. Prof. Matolak s a member of Eta Kappa u, and Sgma. He has served on served on multple IEEE conference techncal program commttees, and was also char of the Geo Moble Rado Standards group n the Telecommuncatons Industres Assocaton s TIA s Satellte Communcatons Dvson.