On multi-carrier code division multiple access (MC-CDMA) modem by nsr11162


									        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
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 .
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
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
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
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

 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
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
CDMA code. (Note ta the CDMA code can have complex
valued coefficients.)

       F r simplicity we assume that the frequency of the smallest
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
                                                                       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
                      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
 tmnsfamed codes  {C} a also arthogonal. In classical
 CDMAspreadspectmmtransmiSsiontheoriginalcode {c} is

     The received signal spectrum is


     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



                                                                                    Figure 3: MC-SS   receiver for Doppler s p d
                                                                                           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
                                                                           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
                                                                           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
IFET at the receiver cascaded by optimum receiver for range                      it is well-known that t e RAKE receiver is the optimum
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
maximizing the S N R at the sampling time). These two                      larger t a the MC fkquency spacing 1/T the same RAKE
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

        For DS-SS signalhg over a channel with delay spread. t e
                                                               h           Fig.4 shows a block diagram o this MC-SS RAKE
received signal is given by t e convolution of the delay spread
                               h                                     receiver.
(            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
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
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
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
 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
                      Rm =           r,e
                              k=O                                    computation F, canbe extended as
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,
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]

            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
 Y a s                                                                     This leads to anew block diagram ofthe RAKE&ver                         as
                                                                     seen in Fig. 5. N t that F only needs to be computed for thcse
                            y = CHiFi

?his i done far every symbol.

                                                                                  Figure 5: Simplified RAI<E receiver

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
      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
which says ta the crosscomlation of two functions in time
             ht                                                       domain
( f a and fkquency @.GI is equal. allowing t apply known
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
                                                                      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,
                                                                            COM-30. p ~ 855-884. May 1 8 .
                                                                                         .             92
synchronized i symbol time. Hence, tbe energy per MC sub-
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
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

      On t e uplink the mobiles axe time-aligned to allow
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


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