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On Multi-Carrier Code Division Multiple Access (MC-CDMA) Modem Design Gerhard Fettweis, Ahmad Shaikh Bahai, and Kiomars Anvari Teknekron Communications Systems. Inc. 2121 &ton Way, Berkeley, CA 94704, USA fax +I (510) 848-8851,fettweis / ahmad@tcs.com Abstruct: Standard spread-spectrum techniques the difficulty in achieving low complexity code acquisition encounter a severe performance loss under channels with implementations. large doppler spread. It i shown that the novel spread- s the inability to cope with significant doppler spread. spectrum technique, called multi-canier (MC) CDMA, is hs dual to direct-sequence CDMA. T i enables to derive that Since these SS systems use code division multiple access MC-CDMA is a signalling technique w i h a l w optimum hc los (CDMA) for allocating bandwidth to diffemt users. all systems detection under severe doppler spread. The receiver for this nta have to deal with the problem that at i i i l start-up. the receiver is a RAKE receiver in the frequency domain. has to detect theconectcode phase ofthe transmitter and has to acquire synchronization. This code acquisition is one of the most challenging design problems of SS system design. I. INTRODUCTION Another interesting approach f a coping with the delay Major reasons for the use of spread spectrum ( S S ) spmd of wireless channels is the use of multicarrier modulation Cammunications are the ability to combat jamming, have low (MCM. also called orthogonal frequency division m d l t o . ouain probability of intercept. and be able to design code division OFDM) [21. In this case the symbol frequency is lowed to be multiple access (CDMA) systems. The l w case allows multiple a D much below the source symbol frequency I .d t i n g in the users to share a commonfrequency band by using orthogonal (or T fact that the delay spread is a fraction of the symbol duration N . close to dogonal) access codes. This allows for detecting the t k n away the need for combatting the delay spread 133. In aig different user^ Oe-by-OE. addition it is more robust against bwsty e m in Rayleigh fading channels. However. to date MCM does not allow for sharing t e h The recent emergence of using SS signall@ for fresuency band in a CDMA manner. commercial mobile communication has been supported by two key factors. the robustness against interference and channel In this paper wediscuss anew SS sigdiugmethod. based impairments (fading), as well as the ability to easily implement ~n the combination d MCM and DS-SS,hm called MC-SS e the baseband processing of SS modems with current VLSI (multicarrier spread-spectrum). The basic idea of DS-SS is to technology. subdivide one symbol duration in time into multiple chips which are then multiplied with the spreadq code. 'Ihe basic idea of Two main characteristics of mobile fading channels are MC-SS is to use the same spreading code. however not by delay spread and doppler spread. Due to multipath propagation dividing the symbol in tm but dividing it in me~ by ie un y the channel is composed of multiple scatterers with different MCM, and then multiplying the spreading code over the different delays, w i h results in the delay spread. In case the multipath hc rm carriers. The intentiond this paper is to introduce MC-SS f o a ChaMel is createdby scattering on multiple moving objects, a d n systems understanding point of view, motivating its application or a moving transmitterkeiver. not one doppler shift occurs but areas, problems. and p i t n out advantages and disadvantages onig the signal can experience a doppler spread (fast fading). O V DS-SS. ~ Current spread-spectrum (SS) systems range f o TH-SS rm II. MC-SPREAD SPECTRUM PRINCIPLE (time hopping). FH-SS (frequency hopping). to DS-SS (direct sequence) [I]. While TH-SS has purely military applications, We d e n e the symbol period T. Assume a data bit is FH-SSand DS-SSare prime candidatesfor commercial wire1e.s~ modulated with e.g. BPSK.The same bit is transmitted in parallel multiple access systems. One of the key advantages of DS-SS is at N carriers which are spaced in fresuency by ID, quivalent to t e ability to efficiently implement a RAKE receiver which acts h anNdimemidMCMBPSKsignal. whereeachdimensionhas as a matched lilter for multipath combining at the receiver for the same input data. Since the carrier fquencia m locked in channels with delay spread. However, some of the problems are phase to each other. a coherent diversity combining can be achieved by adding the N different carrier signals. In case the 1670 0-7803--1927-3/94/$4.00 @ 1994 IEEE channel impairments do not allow for coherent detection, transmitted in time. w e e s it here is transmitted in frequency. It hra diffwential detection can be canied out on t e individual MCM h is clear that mathematically both achieve the same spreading and carriers. coding gain. One spreadingcodeisused tomodulate over the Werent sub-caniers f i .Therefore. at tbe receive side, the N individual subcarriers o the MCM signal are combined according to the f CDMA code. (Note ta the CDMA code can have complex ht valued coefficients.) F r simplicity we assume that the frequency of the smallest o MQM subcarrier is f+O. The time discrete formulation of te h transmitter signal s(i) for ore symbol al, of duration T, with N sample values, and with being the modulator impulse respcmse. is as follows Figure 1: Transmitter model n=O m.DUALITY i E {O, ...,N - 1 } A proper model for slowly varying Rayleigh fading channel for wide band signals such as CDMA is a tapped delay where f,, = n / T and ti = i T / N . line model in which each tap correspcmds to a slowly varying scatterer. This model is called input tapped delay line 13 4. Since the^ is no time variant term in the sum, it can be However. as d i & before we can consider the multicarrier writtenas modulaticn as a Fourier transform by which data at chip level is spread among different subcarriers l/T apart. Therefm, if the s,(i) = a#(i) channel is the dual of a tapped delay l n we can use t e dual of ie h h t e optimum receiver for a range spread channel. In a Doppler where ie{O,l, ...,N-1) , and with the generalized s p ~ a dchannel the delay unit is replaced by a frequency modulatmfunction g ( i ) as converter and tap gains are replaced by filters so the transmitted signal is frequency shifted and convolved with the transfer N- 1 -jzXk! functions dtd to the channel impulse Rsponse as in equations ae g(i) = C cnhie N (2) and (3). The canditions for their independence and their auto- n=O correlation are discussed later. It is clear that the dual d Gaussian white noise is Gaussian white noise of identical spectral Thiscan belefomlulated t o amplitude. Now it can be seen that the summation is equivalent to the Fouriertransformof {c,} .with C, bemgthei-thsample oftheFauier~ausfomof { c n } . NoticethatthesignaltransmittedonthechannP.1is C ( r ) .and g ( i ) = hiCI e ak Rm r Since {c} is onecode Out o f a set of orthogonalcodes which BI~used by the different userS/ChannelS. and the Fourier trm- form is an orthogonal transfa ta preserves orthogonality, the ht tmnsfamed codes {C} a also arthogonal. In classical m CDMAspreadspectmmtransmiSsiontheoriginalcode {c} is 1671 The received signal spectrum is AWGN where H (f, U) is the input Doppler-spread function and is related to the channel impulse respcnse by: Figure 2 MC-SS receiver for Doppler spreaa channelusing a receiver for a delay spread channel inthedualdomain AWGN -- Define I Figure 3: MC-SS receiver for Doppler s p d h channel using t e dual and IV. MODEMRECEIVER In te previous section it was shown that MC-SS ( n h i “n~y) is dual to DS-SS (in time) [a]. and that doppler spread is dual to delay spread. In addition.it is clear that AWGN in t m ie ey is dual to AWGN i n f r e q m y . The k ofthe duality harem is t a given a receiver which is optimum for a channel, the dual ht receiver is optimum for the dual chanuel. If P ( A ~ , A U ) O E ( H ( ~ , U ) H * ~ , V ’ varies little for )) A. Receiver for Channels with Doppler Spread changes i AV of t e order of input time constaut, then the n h different Hk0 - s are h d e p b t . For a delay spread T,,,larger than the chip duration T, . So optimum receiver for a Doppler spread channel, with its input being Fourier transform of the input for range spread channel can be w r e out using duality principle. We can use an okd IFET at the receiver cascaded by optimum receiver for range it is well-known that t e RAKE receiver is the optimum h spread channel. w i h is hown to be a RAKE receiver [51. or hc receiver for DS-SS detection. Fram the duality theorem now dual of a RAKE receiver can be used as an optimum receiver immediately follows that for the dual charmel a d dual (optimality here ~ssumes Symbol-by-symbol dewtion and transmission (MC-SS). for a chanuel wt a doppler spread 2fd ih maximizing the S N R at the sampling time). These two larger t a the MC fkquency spacing 1/T the same RAKE hn approaches are shown in Figures 2 and 3. receiver is optimum in the dual domain, i.e. a RAKE d v e r aperating in the frequency domain 1672 For DS-SS signalhg over a channel with delay spread. t e h Fig.4 shows a block diagram o this MC-SS RAKE f received signal is given by t e convolution of the delay spread h receiver. 1 - ( hlpdse respome) and the channel input signal. Incase of MC-SS and a doppler spxead the same holds in the dual dnmain Le. the received spectnun is given by the ccglvolution of ih the transmit spectrwn w t the d o p p k spread,as in equation (1). ?his holds f a all cases where the doppler spread is fquency indepepet over the! transmit bandwidth NE, i.e. N/T has to be -t mall c u n p d to the caniex frequency. which is justified by equation(3)mcaseHk(f) a n d H p r ) areindependent.Hence, it ht is clear t a the doppkr spread wideas the spectrum of the transnit signal by 2 f d . The RAKE receiver in the dud domain I Y faMC-SS detection thedare cmsists of a pipeline of 3 basic D uis see FQ. A first 811 I m is carried out (to get to the dual nt. 4. t domain) over one symbol interval ofthe received signal r, .The Figure 4 Discrete tm MC-SSRAKE ie IDFI'has to be wide enough to include the transmit bandwidth N/ receiver in frequency T plus the doppler spread 2 f d . Thus, in addition to the N frequency m w ~O~IUS due to MC-SS - p , XdT B. Practical Considerations a d d i t i d frequency sampling points must be cunputed by the IDFT t iocludethe spectral widemng due to doppler spread. The o DT The I l computes N+2fdT fkquency samples. Now let outputoftheL-pohtIDFI'is Rm.where L 2 2 f d T + N us assume it produces all possible output f q u e n c y samples for t e set of L input samples, w e e L > 2 f d T + N . Since the h hr L-1 jZnfm spreadq code c,can be extended to L samples by adding zero L values, noted as Cm ,the summation bounds o the RAKE finger f Rm = r,e k=O computation F, canbe extended as L-1 kllowing the IDFT is the d e s p d e r w i h canies out the hc F, = Z.,*_,Rm i € (0,..., 2fdT] carelatianofthe!fresuency samples with t e spreadingcode c. h m =O Due to the Qppler s p ~ ~ ah s must be carried out 2fdT times, tdi once for each possible d q ~ ~ l shift, i.e. for each finger F, o er f hc w i h equals the RAKE m i v . This is in analogy to DS-SS. where t e h canelationmust be carried out TflC times. L- 1 j& F; = C,rke i E { 0 , ..., 2fdT] i+N-1 k=O Fi= c,,,fiRm i E (0,..., 2fdT} m=i Where L- 1 j*%!!! The results Fi of this correlation are given to the RAI<E C, = ?,,,e L combiner. which is the channel matched filter (in frequency). ma0 Assuming that the Doppler spread frequency function is noted Hi, the RAKE combiner compltes t e final decision variable h Y a s This leads to anew block diagram ofthe RAKE&ver as i seen in Fig. 5. N t that F only needs to be computed for thcse oe 2fJ y = CHiFi c, i=O ?his i done far every symbol. s Figure 5: Simplified RAI<E receiver 1673 fingers of t e RAKE which have a sisnificant gain (delay spread h , time periods of misalipnmt of length T and only Bccept Compaoent) H . At I l u i 2 f d T h e C S need to be Computed. i ll r" reception of the q"ued parts of duration T T . 'Ibis -, i.e. 2fdT DET computations need to be carried out. This is a windowing of the received s@ i r(t) by the windowing functian signiticant reductionin implementation complexity. noted w(t) results in a spread ofthe firequency spectnrm ofthe received signal, as can be seenby V. CDMA AND FUTURE WORK m r (r) w ( t ) e-jZzfffldr R U = , * sinc ( 2 l r f ~ , ) This section is aimed at pointing out some general -m properties of MC-CDMA, and the direction of fume work. Hence. besides r d i g the SNR the whdowhg wi& the e wn A. CDMA received spectrum just like an additiaaal doppler spnad for which tbe RAKE in -y derived above is the optimum receiver. The basis for CDMA is tohave different users sharing the same spectrum by having them use diffmnt codes which have a small crossccarelariondative t the autocorrelation peak. The o VI. CONCLUSIONS best performance (and capcity) is achieved if orthogonal codes can be used.having zero ~OsSCorrelation. Multi& M ( a CDMA is dual to direct-sequuUn CDMA. The RAKE receiver is optimum fur DS-CDMAfur a chnnnd with delay .qnead. The duslity principle allows fur the derivationofthe RAKEin the dual -for h t e dual channel using MC-CDMA. Hence. MC-CDMA is a s i p a l k g technique which allows o p t i " detection under WeIe Dqqlcr spread. The receiver for this is a RAKE receiver in t e f"cy h which says ta the crosscomlation of two functions in time ht domain ( f a and fkquency @.GI is equal. allowing t apply known o CDMA codes for MC-CDMA. A CDMA m s s code in of MC-CDMA a robustness against Dcrppler f"y is a CDMA axess code in time. s p d . and ease of sydmmkation. lkthe". receiver is the simple and of low implemeatatian complexity. B. Synchronization in the Down-Link VII. R E F E F S N W The only timing synchronization which must be estimated in MC-SS is the symbol sync€" with lfl. On the down- R. L Pickholtz.D. L Schilling, and L B. Mhtcin, "Ibeay Otspred- l n it can be ~ssumedthat the base statim transmits all users ik - speanun cunmunicatiom A tutarid." IEEETI~M. Commamidons, on COM-30. p ~ 855-884. May 1 8 . . 92 synchronized i symbol time. Hence, tbe energy per MC sub- n carrier is at least multiplied by the number of users. Therefore,in Burton R. Saltzbag. ''PPcrfamaaa of an efficient pwdld data the likely case that each MC s u b 4 e r is a linearly modulated t " k i a n system," IEEE T a a (ICanmunicatiau COM-IS. 6 rn I no. . signal, bit synchronization can be carried out by traditional e pp. 801811,D& 1967. square-law detection an one sub-carrier. For better acquisition Len Cimini, "Analysis and s'nnuttion of a digitd mob& chanx1 using and tracking performance (e.g. in fading). multiple subcarrim a t h o g a d m c divisioo multipkxin.g." IEEE T d o m an wy canbetrackedsimultaaeously. Communications, COM-33. No. 7 pp. 665-675. July 1985. . The synchronization problem of MC-CDMA is the same as Philip F Bcllo, - ! " . 'an of nndomly time-vuying linear channels," IEEE Trans. an Commun., CS 11. pp. 360.393. Dec. 1963. that of any classical MC system, having a traditid S w e characteristic. allowing =-type syachronization. This is in R. Wcq and F E. Green. "A camnuniation technique far multipath ! contrast to DS-SS. a channels." Proc. IRE, VOL46,pp. 555-570, M & 1958. John Rolkis, "Digital ~ a n m d c l t i a ~ qMdhw-HiIl, 2 d edition, " C. Synchronization in the Up-Link 1989. On t e uplink the mobiles axe time-aligned to allow h overall networsr syochraaizati<w. This time alrr"ent cannot result in perfect synchronization of all mobile transmit signals at the base. If. howevex, time alignment can be achieved within a fractionT, of the symbol durationT. the mxiver can null a t t e h 1674