A Multi-levelled OFDM-CDMA Modem Using Complete Complementary Codes

Transcription

1 A Multi-levelled OFDM-CDMA Modem Using Complete Complementary Codes Alexander Merensky, Jaques van Wyk and ouis P. inde Department of Eletrial, Eletroni and Computer Engineering University of Pretoria, South Afria elephone: (8) 87 5, Fax: () alexmerensky@tuks.o.za ; {jaques.vanwyk, louis.linde}@up.a.za Abstrat In this paper, we introdue a novel multiple aess sheme based on a ombination of a multi-levelled modem and multi-arrier tehniques the use of omplete omplementary odes. his modulation tehnique ombines a multi-dimensional ode division multiple aess (CDMA) modem reent designs of perfetly omplete omplementary orthogonal odes. he rotational properties of the spreading odes are further exploited to improve the modulation tehnique, throughput, spetral effiieny, and apaity. Additionally, the system is extended by making use of multiple arrier frequenies as in OFDM, the additional benefits of being able to spread data in frequeny and/or in time. he modem offers multiple aess interferene MAI-free and multipath interferene MI-free operation in both asynhronous and synhronous ommuniation, due to perfet autoorrelation and zero ross-orrelation properties of the spreading odes. he unique multi-levelled multiple aess modulation tehnique together the integration of omplete omplementary odes, produes a spetrally effiient output signal high data throughput rates, better noise toleranes in harsh hannel onditions and an inreased user apaity. Index erms Code-division multiple aess (CDMA), orthogonal frequeny-division multiplexing (OFDM), multi-arrier modulation, omplete omplementary odes. I. INRODUCION HE need for a modulation tehnique that an reliably transmit at high data rates and high bandwidth effiieny has risen in the last deades, due to the enormous growth of wireless servies (wireless loal-area networks, ellular telephones, et.). Orthogonal frequeny division multiplexing (OFDM) has been applied extensively in many high speed wireline and wireless ommuniation standards, suh as in ADS, VDS, WiMAX, WAN radio interfaes (IEEE8.a,b,g,n) and in many other mobile broadband solutions, due to its effiient usage of the available frequeny bandwidth and robustness to frequeny seletive fading environments. However, it is limited by its spetral effiieny and the growing demand of digital audio/video broadasting, the availability of spetrum beomes a serious problem []. Meanwhile, ode division multiple aess (CDMA) has proven its spetral effiieny through flexible frequeny reuse and multiple aess tehniques [], []. he ombination of multiple aess tehniques like CDMA and OFDM, demonstrated inreased spetral effiieny, flexibility in radio resoure alloation and anti-multipath and antiinterferene features []. hus, these ombined systems have reeived signifiant attention as they apitalise on the benefit of both shemes and ombine high bandwidth effiieny and high data rates robustness against multipath distortion. he implementation of the fast Fourier transform (FF) allows for high spetral effiieny, due to the minimum frequeny spaing in arriers and for a low omplexity transmitter and reeiver design []. Various multi-arrier shemes whih use the ombination of CDMA and OFDM have been proposed, these an be mainly ategorised aording to the diretion of spreading. he spreading of the data is either done in the time domain or frequeny domain or even both [], []. An important fator in the overall performane of a CDMA multi-arrier type modulation sheme is the perfet autoorrelation and zero ross-orrelation property of the spreading odes. Due to non-ideal spreading odes used in urrent standardised CDMA systems, suh as those used in existing -G systems, problems of self-interferene are evident [5], [6]. hese existing problems in urrent systems suh as slow transmission rate, low apaity, and omplex system implementation are aused by the imperfet spreading odes implemented [7]. For example, aording to [8], the Walsh- Hadamard sequenes in the IS-95 standard and the OVSF odes in WCDMA standards made it impossible to ensure symmetri data throughput at the very beginning of the system design, beause of their imperfet orrelation harateristis in asynhronous and synhronous transmission modes. his artile presents an innovative modulation tehnique, by ombining the arhiteture of a multi-dimensional modem reent designs of perfetly orthogonal omplete omplementary odes. he shift or rotational properties of the spreading odes an further exploited in a novel way to improve the modulation tehnique, spetral effiieny and spreading ode usage. A periodi ross-orrelation method at the reeiver has been devised to optimally obtain the yli rotated omplete omplementary odes (CRCC). he arhiteture allows for a high proessing gain (PG) for interferene suppression out limiting the amount of users. Additionally, the system is extended by making use of multiple arrier frequenies (OFDM) and an thus spread the information in frequeny and/or in time. raditional CDMA-based systems (i.e., IS-95, dma, and W-CDMA), and even multi-arrier adaptations, have a spreading effiieny of / information

2 Multi-layered modulation (MM) an be used to transmit s(t) = [d (t) r (t) + d (t) i (t)] os(w t) parallel data streams improved spetral effiieny ompared single-layer modulation, providing data throughput (t) r (t) + d (t) i (t)] sin(w t), () + [d rates proportional to the number of modulation layers at performanes equivalent to single-layer modulation. Alternatively, arrying data bits per hannel use. bitsmultiple per hiplayers per link an be (where used to is transmit the sequene oded information length) [5], to x (t) [9], ahieve whereas improved the novel performane modulationat tehnique throughput anrates transmit equivalent at information to a singlebits layer per system. hip per Anlink MMorfour-dimensional hannel user. (D) ode y (t) z (t) division multiple aess (CDMA) building blok employing x (t) os(w t) super-orthogonal omplex spreading sequenes (SO-CSS) is II. MUI-DIMENSIONA MODEM BUIDING BOCK used as MM platform [] for the evaluation of three lasses d(t) he of sparse novelgraph modulation odes. he tehnique ommuniation makes platform use of ainluding multidimensional modem to improve ode usage, S/P s(t) i(t) x (t) 9 the transmitter, reeiver and omplex spreading sequenes is o throughput disussedand in Setion overall performane II. he enoding of the and system. deoding hestrutures modem B. Four-Dimensional Reeiver y (t) z (t) is implemented of the blok-turbo-ode rotated andomplete details regarding omplementary the onstrution odes to offer themai-free onstituent and ode s MI-free trellis operation, struturedue and to deoding the perfet algorithm are onsidered and zero in setion ross-orrelation III. Setion IV properties briefly onsiders of the in Figure. he reeived signal is demodulated and de- he D reeiver is a orrelation-type x (t) demodulator as shown autoorrelation i(t) odes. DPC and RA odes and setion V provides details regardingspread to obtain approximations ˆd (t) to ˆd (t) of the original It thewas hannel shownsimulator by [], onfiguration. [] that a -dimensional Finally setion modem VI on-dattains error blok performane (out theresults newlyand implemented setion VIICRCC onludes odes) the Fig... AFour -Dimensional dimensional (CDMA) DSSS transmitter modem transmitter struturebuilding blok []. streams. he use of unique families of CSSs ontributes building to the signifiantly simplified MUI-free reeiver struture. haspaper. data throughput rates equivalent to that of a 6-ary quadrature amplitude modulated (6-QAM) WCDMA modulation s sheme, but the BER performane equivalent to that of v (t) w (t) BPSK/QPSK in both AWGN and fading multipath hannel senarios. s s X/7/$5. 7 IEEE. A. Desription of the -dimensional transmitter An example of a -dimensional modem transmitter building blok an be seen in Fig.. he input sequene is split up into four parallel data streams d (t) to d (t). he upper two streams are spread using orthogonal omplete omplementary odes to produe the inphase omponent and likewise, the lower two streams are spread to produe the quadrature omponent. he inphase and quadrature omponents are then modulated onto quadrature arriers and summed to produe a transmitted signal as given by s(t) = [d (t) r (t) + d (t) i (t)] os(ω t) his multi-dimensional building blok forms the foundation C. Complex Spreading Sequenes + [d (t) r (t) + d (t) i (t)] sin(ω t) () of the proposed modulation tehnique. Multiple transmitter hebloks performane are ombined of the and CDMA parallelised system topresented form a in highthis s = (d r + d i ) + j. (d r + d i ). () setion throughput depends modulation primarily tehnique, on the orrelation whih is spetrally harateristis effiientof Due to the orthogonality property of the arrier signals, the theand CSSs exploits used the (see diversity [] for ainthorough the radioorrelation hannel tostudy). improve he modulating signals an be independently deteted. his allows base performane. vetors ofhe the usage MD spae of theare rotated the CSSs omplete andomplemen- tary odes it is therefore the quadrature and inphase omponents to optionally use the important to enables employ the CSSs data from exellent multiple ombined ross orrelation multidimensional building bloks to be transmitted simultaneously same set of odes and thus save odes elements of the CRCC harateristis between the real and imaginary omponents. ode family. over one hannel, sine the odes allow the data to be One lass of CSSs fulfilling this ondition is Zero Cross he building blok depited in Fig. an be extended differentiated again at the reeiver as in CDMA tehniques. A Correlation to more dimensions by adding more D-bloks in parallel, olletion of (ZCC) these [] ombined Super-Orthogonal bloks an then (SO; be i.e. spread zero-ross onto orrelation eah using additional spreading odes from the family of different sub-arrier for all time frequenies shifts) Constant-Envelope using multiple aess (CE) OFDM CSSs CRCC odes. his an be ahieved while still maintaining the derived priniples. from Park-Park-Song-Suehiro (PS) [] CSSs using a respetive BER performane of one original building blok non-linear root-of-unity (RU) filtering tehnique [5]. he CE []. harateristi III. COMPEE of ZCC COMPEMENARY CSSs provides ORHOGONA the output signal CODESs(t) Fig. shows a typial low omplexity mathed filter of the hed performane modulatorof any CDMA near-onstant type system instantaneous depends onand orrelation-type reeiver for a -dimensional modem. he onstant the spreading average odes. output Anpower important by virtue fator in of the performane orthogonality reeiver is depited out the periodi ross orrelation reeiver struture needed when using the rotated odes (CRCC). effiieny orrelation is properties, the modulator s sine they ability determine to operate the robustness lose to the in of ofthe thebasis spreading funtions. ode he is based primary on itsadvantage ideal autoof and theross- power In [], [] it was shown that the data throughput rate dbharsh saturation hannelpoint onditions of the andpower the division amplifier amongst of thetransmitter different of one basi -dimensional building blok is twie that of a improving users. If the theorrelation ommuniation funtions range are not and/or ideal, handset every user battery or diret sequene spread spetrum (DSSS) QPSK modulation life. additional data stream an be viewed as another soure of system, yielding a spetral effiieny of / b/s/hz, i.e., noise. herefore, low ross-orrelation values between spreading odes allow the reeiver to separate user signals, whereas equal to that of M=6-QAM, but the BER performane of BPSK/QPSK assuming equal spreading sequene lengths, low autoorrelation III. BOCK values aid URBO in filteringcode out multiple reeived bandwidths and out the addition of rotating CRCC odes. signals, whih are delayed due to multipath propagation []. A. Enoding struture 9 o v (t) w (t) i(t) (t) i dt s s Sample Clok Fig. Fig... Four A -Dimensional dimensional (CDMA) DSSS reeiver modem orrelation-type struture reeiver building blok []. A D BC [6] (N, K) = (K, K) onstituent blok odes is used to form a (K, K ) enoder struture shown in Figure, by mapping the ode bloks to diretly to the D transmitter inputs d (t) to d (t) by removing the S/P onverter (see Figure ). A D data blok x is enoded by systemati row, olumn and depth enoders (, Fig. B. D C to a bit o amp ont sam n th the n [, softin F ~ ~ ~ ~ Fig.,, eah Λ han ree

3 If a CDMA system is not multiple aess interferene (MAI)-free and multipath interferene (MI)-free, due to nonideal ross-orrelation and autoorrelation properties respetively, then the apaity of the overall system an merely ahieve apaity equal to approximately one-third to a half of its proessing gain, whih is urrently seen in available CDMA-based -G wireless systems [8], []. he proposed system is based on omplete omplementary ode spreading, whih an ahieve interferene-free performane and high apaity due to their inherent ideal auto/rossorrelation properties. hese ideal spreading odes, as used in the proposed modulation sheme, suppress MAI and MI effets, hene the performane is limited only by noise. he main differene between traditional CDMA odes and omplete omplementary odes is that the orthogonality of omplete omplementary odes is based on a set of element odes alled a flok, instead of a single ode [9]. hese odes have a zero autoorrelation for all shifts exept the zero shift and zero ross-orrelation funtion for all possible shifts [5]. Orthogonality of the odes is maintained even for an asynhronous ase. he family size or number of floks is equal to the number of element odes in one flok and an be defined as M =. he proessing gain (PG) of the odes an then be defined by., where is the length of every element ode sequene [5], [9]. he autoorrelation and ross-orrelation of the ode an be expressed as follows [5]: φ xx (j) = φ xy (j) = n= i= n= i= a (x) n,i a(x) n+j,i = {, j =, j () a (x) n,i a(y) n+j,i = () where φ xx is the autoorrelation funtion () of set x, φ xy is the ross-orrelation funtion () of sets x and y, j is the number of shifts between the sequenes, and n is the nth element of eah ode sequene [5]. A. Complete Complementary Code generation here are various ways in onstruting omplete omplementary odes. In [8], [6] an algebrai method is used to generate super omplementary ode sets alled the real environment adapted linearisation (REA) approah. he REA approah generates interferene-free CDMA ode sets perfet auto- and ross-orrelation properties, however, the approah requires a great omputational load [7]. Below, a more pratial approah to generating the odes is shown aording to the algorithm outlined in [6]. A matrix approah is taken in generating the ode sets using a -dimensional orthogonal matrix, where is the length of the ode generated [6]. Define an N N dimensional orthogonal matrix A suh that a ij = and N a ij a ki =, where j k. (5) i= hen let B be another N N orthogonal matrix from whih N sequenes of length N an be onstruted as follows: E = (b A, b A,..., b N A N ) = (e, e,..., e N ) E = (b A, b A,..., b N A N ) = (e, e,..., e N ). E N = (b N A, b N A,..., b NN A N ) = (e N, e N,..., e NN ). (6) where A i is the ith row of the A matrix [7]. Eah E i ( i N) has an autoorrelation of zero for any shift exept the zero shift and the ross-orrelation of any two sequenes is zero for all shifts. Again let D be another N-dimensional orthogonal matrix from whih the final spreading sequenes an be onstruted by C ij =(e i d j, e i d j,..., e in d jn, e i(n+) d j, e i(n+) d j,..., e i(n) d jn,..., e i(n N+)d j,..., e i(n )d jn ) (7) =(C ij, C ij,..., C ijn ), for i, j =,,..., N (8) where C ij is the jth sequene in the ith flok [7], [6]. Conventional omplete omplementary odes support only a limited number of users. herefore, a yli rotation tehnique is used to extend the original ode family size, whih allows for more odes/users and inreases the system apaity and spetral effiieny out loosing performane. IV. SYSEM MODE he signal of the novel system is generated using a ombination of CDMA and OFDM tehniques. Multiple transmitter bloks are ombined and parallelised by the omplete omplementary odes to form a high throughput modulation tehnique, whih is spetrally effiient and exploits the diversity in the radio hannel to improve performane and still keep the original bit error rate performane. A total of M data symbols are spread and summed together, similar to offset staked spreading modulation (OSM), whih enables parallel transmission and thus improves spetral effiieny. his shows that a large number of data symbols an be proessed in one instane. he spetral effiieny (SE) is not equal to /P G as in traditional CDMA systems, instead, it is equal to /M. his system does not use the spreading odes as in a onventional spreading system. he bit stream is not aligned in time bit after the other, but rather a new bit be staked onto the other. When assuming a BPSK modulation and onsidering the multi-dimensionality of the novel transmission sheme, a spetral effiieny of bits/s/hz an be ahieved for one user s building blok if the set size equals the flok size. he simplified transmitter struture of the proposed system is portrayed in Fig. (detail omitted tehnique used an not be explained further - patent pending). It desribes the implementation of the Uth user s transmitter and the generated signal S U. Multiple aess is then ahieved by assigning the users to different sub-arriers, as in orthogonal frequenydivision multiple aess (OFDMA), to provide multi-user and frequeny diversity. he proposed system uses CDMA not to

4 distinguish between users, whih the OFDMA tehnique does, but rather it improves the multi-dimensional modem design and spetral effiieny when spreading the data. A. Multiple aess implementation he generated signal of the U th user is fed through an inverse fast Fourier transform (IFF) to produe a multi-user system by assigning subsets of sub-arriers to individual users. he multiple aess implementation of the system an be seen as an OFDMA modulation tehnique. he use of the simple IFF/FF operations in the generation of the signal results in a low omplexity transmitter and reeiver struture. A blok diagram of the multiple aess implementation is shown in Fig.. It depits how the signal S U from Fig. is transmitted further via OFDM tehniques to produe a multiuser or multiple aess system. Multiple aess is ahieved by assigning different OFDM sub-hannels to different users, using various subarrier alloation strategies. For example, a group of adjaent subarriers or subbands an be assigned to eah user in both frequeny and time, or users an be assigned to interleaved or randomly hosen subarriers. In the design of the novel modulation tehnique, various alloation strategies of the IEEE standards an be diretly implemented before the IFF. he multi-arrier aspet an be designed in many ways to adapt to the requirements of the system and hannel onditions. After the subarriers and subhannels are assigned and sent through the IFF, a guard interval or yli prefix an be inserted into the signal to eliminate intersymbol interferene from the previous symbols. he yli prefix allows for simple frequeny domain proessing, suh as hannel estimation and equalisation, due to the irular onvolutional properties of the repeated endpart of the symbols when taking its disrete Fourier transform (DF). Pilot symbols an additionally be inserted to aid in the measurement of the hannel onditions and an also be used to avoid time and frequeny synhronisation problems, whih an ause intersymbol interferene (ISI) and interarrier interferene (ICI) respetively [7]. he pilot and guard subarriers plaement parameters an be found in the various subarrier usage strategies as defined in the IEEE standards [7]. he implemented multiple aess sheme allows different users to transmit over different portions of the broadband spetrum. When a broadband signal experienes frequeny seletive fading, different users pereive different hannel qualities (multi-user diversity). For example, a deep faded hannel for one user an still be favourable to another user. he use of the OFDMA tehnique allows for effiient use of the spetrum simple FF proessing and produes a better performing system in fading environments. V. DISCUSSION he integration of a multi-dimensional modem the multi-arrier funtionality of OFDMA, produes a novel system that is not only appliable to ellular tehnology and wireless broadband solutions, but also in wired digital data ommuniations tehnologies suh as in digital subsriber lines,, -Dimensional transmitter and 9 its, rotations,, 9,,,,, M, Data bits S/P,, -Dimensional 9 9 transmitter and 9 its rotations 9 Fig.. Fig..,,,,,,,,, he transmitter struture of the proposed system. IFF Multi-arrier transmission via IFF/FF for multiple aess. (DS). By making use of orthogonal omplete omplementary ode families a multi-levelled modulation tehnique, a method is devised whih greatly improves throughput and spetrum effiieny of the basi transmission sheme. he system is apable of supporting IFF multiple users making use of OFDMA tehniques. he different users all experiene the same noise effets in AWGN and thus the system performane does not degrade an inrease in the number of users, beause perfet odes were used. he system an dynamially assign users to different subarriers and ontrol the amount of hannels available to eah user. hus, the throughput for a speifi user ould be inreased or dereased depending on the hannel onditions and required throughput or quality of servie needed by a user. Similar performane advantages are expeted in multipath fading hannels, but results fall out of the sope of this paper. he system an be adapted to any required design riteria and shows an improvement of the basi modulation and transmission tehnique used in various urrently available IFF IFF

5 standards. Although no omplex hannel oding is applied, the design holds high appliation potential in future generation ommuniation systems and shows to be a promising tehnique whih an improve urrently implemented systems. VI. CONCUSION he primary objetives of next-generation wireless networks for mobile and broadband servies, is to make use of the limited radio spetrum in order to ahieve higher data rates and throughput higher bandwidth effiieny and user-apaity. By ombining OFDMA and a modified multi-dimensional modulation method in a novel manner the use of omplete omplementary odes and a yli rotation sheme, a unique digital broadasting tehnique, whih supports high data rates and apaities over hostile radio hannels, was developed. he proposed ommuniations system shows improvements to the fundamental modulation tehnique out the aid of omplex forward error orreting (FEC) odes. he system lays a powerful foundation whih an outperform previous designs where the basis laks in effiieny, performane and throughput. herefore, the proposed system would show greater improvements and would reah the Shannon Bound more easily the addition of hannel oding, interleaving and equalisation, ompared to previously designed systems implementing the same improvement tehniques. he system possesses several advantages over urrently available G and G mobile ellular systems. It an, firstly, ahieve a muh higher bandwidth effiieny than onventional CDMA systems by onveying as muh as two bits of information in eah hip width, yielding a spreading effiieny equal to two, using the same proessing gain. Seondly, the system offers MAI-free and MI-free operation in both synhronous and asynhronous hannels. his attributes to ohannel interferene redution and apaity inrease and in addition, the system has an improved throughput. he benefits of both OFDM and a CDMA type modulation sheme are ombined and further improved by the multidimensionality and spreading of ylially rotated orthogonal omplete omplementary odes. his novel ombination forms an attrative modulation tehnique for next-generation ommuniation systems that require high data rates, high spetral effiieny, diversity and robustness in harsh hannel onditions. ACKNOWEDGMEN he researh was made possible the support from our industry partners elkom, Unisys, ellumat, EMC and Alvarion; and the ehnology and Human Resoures for Industry Program (HRIP) managed by the National Researh Foundation (NRF), finaned by the Department of rade and Industry (DI), South Afria. [].-. Yang and. Hanzo, Multiarrier ds-dma: a multiple aess sheme for ubiquitous broadband wireless ommuniations, IEEE Commun. Mag., vol., no., pp. 6, Ot.. [] R. Prasad and S. Hara, An overview of multi-arrier CDMA, in 8th IEEE Int. Symp. on Spread Spetrum ehniques and Appliations, vol.. IEEE, Sep. 996, pp. 7. [] F. Adahi, D. Garg, S. akaoka, and K. akeda, Broadband CDMA tehniques, IEEE Wireless Communiations, vol., no., pp. 8 8, Apr. 5. [5] H.-H. Chen, J.-F. Yeh, and N. Suehiro, A Multiarrier CDMA arhiteture based on orthogonal omplementary odes for new generations of wideband wireless ommuniations, IEEE Commun. Mag., vol. 9, no., pp. 6 5, Ot.. [6] C. Han, N. Suehiro, and. Hashimoto, N-Shift Cross-Orthogonal Sequenes and Complete Complementary Codes, in IEEE Int. Symp. on Information heory ISI 7. IEEE, Jun. 7, pp [7] H.-H. Chen, D. Hank, M. E. Magaña, and M. Guizani, Design of nextgeneration CDMA using orthogonal omplementary odes and offset staked spreading, IEEE Wireless Communiations, vol., no., pp. 6 69, Jun. 7. [8] H.-H. Chen, S.-W. Chu, N. Kuroyanagi, and A. J. Han Vink, An algebrai approah to generate super-set of perfet omplementary odes for interferene-free CDMA, Wirel. Commun. Mob. Comput., vol. 7, no. 5, pp. 65 6, Jun. 7. [9] M. E. Magaña,. Rajatasereekul, D. Hank, and H.-H. Chen, Design of an MC-CDMA System hat Uses Complete Complementary Orthogonal Spreading Codes, IEEE rans. Veh. ehnol., vol. 56, no. 5, pp , Sep. 7. []. inde and. Staphorst, Performane of a quasi-synhronous fourdimensional super-orthogonal WCDMA modulator for next generation wireless appliations, South Afrian Journal of Siene, vol., no. -, pp. 59 6, De. 7. []. inde, A Multi-dimensional super-orthogonal modulation alternative to M-QAM WCDMA for next generation wireless appliations, in Pro. IEEE AFRICON 7, 7. [] J. D. Vlok and. inde, Performane of sparse graph odes on a four-dimensional CDMA system in AWGN and multipath fading, Pro. IEEE AFRICON 7, pp. 7, Sep. 7. [] M. E. Magaña and. Rajatasereekul, Complete Complementary Orthogonal (CCO) Code-Based CDMA Using Natural Mapping QAM Constellations, Wireless Personal Communiations, vol. 8, no., pp. 5, Jun. 6. [] H.-H. Chen, he REA Approah to Generate Orthogonal Complementary Codes for Next Generation CDMA Systems, Interdisiplinary Information Sienes, vol., no., pp. 7 6, 6. [5]. u and V. K. Dubey, Performane of a Complete Complementary Code-Based Spread-ime CDMA System in a Fading Channel, IEEE rans. Veh. ehnol., vol. 57, no., pp. 5 59, Jan. 8. [6] H.-H. Chen, S.-W. Chu, and M. Guizani, On Next Generation CDMA ehnologies: he REA Approah for Perfet Orthogonal Code Generation, IEEE rans. Veh. ehnol., vol. 57, no. 5, pp. 8 8, Sep. 8. [7] Air Interfae for Fixed and Mobile Broadband Wireless Aess Systems, IEEE Std P8.6 (Amendment and Corrigendum to IEEE Std 8.6-), 5. Alexander Merensky holds a B.Eng(9) and an Honours-B.Eng() (um laude) degree from the University of Pretoria and is presently working on his Master of Siene dissertation in Eletroni Engineering at the same institution. His researh interests inlude digital ommuniations, OFDM, CDMA, estimation, equalization, oding and signal proessing for mobile ommuniation systems. REFERENCES [] K. Zheng, G. Zeng, and W. Wang, Performane Analysis for OFDM- CDMA With Joint Frequeny-ime Spreading, IEEE rans. Broadast., vol. 5, no., pp. 8, Mar. 5.