A Unified Perspective of Different Multicarrier CDMA Schemes

26 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications A Unified Perspective of Different Multicarrier CDMA Schemes Yongfeng Chen Dept of ECE, University of Toronto Toronto, ON, Canada M5S 3G4 Email: yfchen@commutorontoca Elvino S Sousa Dept of ECE, University of Toronto Toronto, ON, Canada M5S 3G4 Email: essousa@utorontoca Abstract In the conventional multicarrier CDMA schemes, different users utilize different spreading codes to realize the multiple accessing (which is the CDMA technique) and the bits from the same user are transmitted on different frequency subcarriers to realize the multiplexing (which is the OFDM technique) However, the function of the set of subcarriers and the function of the set of spreading codes can be switched That is, the bits from the same user are spread with different accessing codes but they are transmitted on the same subcarrier Based on this idea, we introduce a new multicarrier scheme which is named as CDM-OFDMA e put the MC-DS-CDMA and CDM-OFDMA schemes into one unified formula format Their performances are evaluated and compared Under equal deterministic channel characteristic condition, it is found that the CDM-OFDMA scheme has a better performance than the MC-DS-CDMA scheme The main reason is that the MAI from the same subcarrier is much bigger than the MAI from other subcarriers and in the CDM-OFDMA scheme the MAI from the same subcarrier is avoided by employing the orthogonal spreading codes Keywords: Multicarrier CDMA, OFDM, correlated fading channels, equal gain combining, SINR I INTRODUCTION In the code-division multiple accessing (CDMA) technique, the signal bits are spread in the transmitter side and despread in the receiver side But the noise does not have the spreading operation So the despread of receive signal will reduce the noise variance by a factor of processing gain That is the main reason that CDMA technique is used in the wireless communication while with the price of bandwidth expansion However, the embedded multipath character of the wireless channel will destroy the orthogonality between the spreading codes and further cause the inter symbol interference (ISI) The multipath is not such an undesired character since path diversity can be utilized by the Rake receiving technique However the ISI still exists The orthogonal frequency-division multiplexing (OFDM) technique is introduced to extend the symbol duration, and by using the cyclic prefix which is longer than the channel length, the ISI can basically be eliminated The combination of OFDM and CDMA becomes the so call multicarrier CDMA system, which may be a key advance in the future wireless communication standards Many multicarrier schemes have been proposed so far, see for an early overview In 2-3 the MC-DS-CDMA scheme is presented, with different channel models or coding schemes It is so named because in each subcarrier a conventional DS-CDMA signal is transmitted The MC-CDMA scheme is introduced too, see 4-5 In the MC-CDMA the system bandwidth is further divided and the chips are passed through another serial to parallel conversion cently the OFCDM (orthogonal frequency and code division multiplexing) scheme is brought to the front and some work has been done on it, see 6-7 In the OFCDM scheme each user employs a set of spreading codes, which is sometime called as both time domain and frequency domain spreading There are also other schemes proposed In 8 a generalized multicarrier scheme is given, where different spread code is assigned to each bit The 9 uses the interferometry codes, where the phase shifts are introduced on all subcarriers in a controlled way so that the signal peak appears in different time spot which can be used to transmit the bit information In this paper, we stand a little back and try to view some of those schemes with one unified perspective A new scheme, CDM-OFDMA (code-division multiplexing and orthogonal frequency-division multiple accessing), is proposed in this work The performances of MC-DS-CDMA and CDM- OFDMA schemes are studied ith the equal deterministic channel characteristic condition, the CDM-OFDMA scheme has a better performance than the MC-DS-CDMA scheme Through the analysis we find that the same subcarrier MAI is much bigger than those from other subcarriers In the CDM- OFDMA schemes the same subcarrier MAI is avoided by utilizing the orthogonal codes and the orthogonality is kept due to the synchronization among bits from the same user The performance differences are later verified with the Monte Carlo simulationsto be rigorous, we compare four different channel models and choose the channel model 2 for analysis purpose and the channel model 4 for the simulation purpose The whole paper is organized as following In the system section we introduce the CDM-OFDMA scheme and express both the MC-DS-CDMA and CDM-OFDMA with one unified formula format In the channel section we consider four different channel models and point out which one is suitable In the performance section we provide the SINR formulas for both schemes, and the differences between them are examined In the simulation part we verify some claims made in the previous sections The conclusion is given at the end -783-978-/6/$2 26 IEEE 84

II SYSTEM DESCRIPTION Define the basis set T s = c (t),,c K (t), where c k (t) is the spreading waveform, and c k (t) = N c kn p(t nt c ), n= where N is the spreading factor, c kn is the nth chip, T c is the chip duration, p(t) is a square wave with support of,t c and amplitude of Define the basis set 2 s 2 = e j2π Tc t,,e j2π R t T Tc Using the vector direct product between s and s 2, we can have K R basis c (t)e j2π Tc t c K (t)e j2π Tc t S = s 2 s T = c (t)e j2π R Tc t c K (t)e j2π R Tc t If we assign the basis set s to different users to realize the multiple accessing, and the basis set s 2 to different bits from the same user to realize the multiplexing, we have the conventional MC-DS-CDMA scheme Let B denote the transmit bits matrix for all K users, B MCDS = b (I) b (I) K + j b (I) R b(i) KR b (Q) b (Q) K b(q) KR b (Q) R, where b (I) b(i) KR and b(q) b(q) KR are random data values (+ or ) with equal probabilities For reverse channel asynchronous users model, the signature matrix becomes S MCDS = c (t τ )e j2π Tc (t τ) c K (t τ K )e j2π Tc (t τk) c (t τ )e j2π R Tc (t τ) c K (t τ K )e j2π R Tc (t τk) where τ k is the delay of kth user due to the asynchronous transmitting Assume R is chosen large enough so that each subcarrier undergoes flat fading The channel characteristic for each subcarrier can be denoted as α kr, where α kr is a complex Gaussian distributed random variable The channel model for all users can be written as: H = α α K α R α KR Let a MCDS represent the transmit bits amplitude for K users 2P a MCDS =,, T 2P K, where Pk is the transmit bit power for the kth user In this paper, we assume the transmitter does not know the channel state information (CSI) and the bits on all subcarriers are transmitted with equal power The baseband equivalent receive signal at the base station is r MCDS (t) = T (B MCDS S MCDS H) a MCDS + n(t), () where denotes the Hadamard product and is the R dimensions all column vector, n(t) is the complex white Gaussian noise with two-sided power spectrum density of N /2 There exist other schemes of assigning the basis set S Ifwe assign s 2 to the different users to realize the multiple accessing and s to the different bits from the same user to realize the multiplexing, we have another scheme which is called as the code-division multiplexing orthogonal frequency-division multiple accessing scheme (CDM-OFDMA) The transmit bits matrix B CDM is the same as B MCDS However, the meanings of them are different In B MCDS, the bits in the same column belong to the same user In B CDM, the bits in the same row belong to the same user Also for CDM-OFDMA asynchronous users model, the signature matrix has some minor change from S MCDS,itcan be written as S CDM = c (t τ )e j2π Tc (t τ) c K (t τ )e j2π Tc (t τ) c (t τ R )e j2π R Tc (t τr) c K (t τ R )e j2π R Tc (t τr) Using the same channel model, the baseband equivalent receive signal for the CDM-OFDMA scheme is r CDM (t) = a T CDM (B CDM S CDM H) + n(t), (2) 2P where a CDM =,, T 2P R is the transmit bit amplitude vector and is the K dimensions all column vector III CHANNEL MODEL Assume an exponential multipath delay profile P (τ) =u e τu, (3) where u is the decaying parameter and is the system bandwidth From, we have u = 2πΔf c, where Δf c is the channel coherent bandwidth and Δf c = L p, L p is the number of taps in a tapped delay line channel model So, we have u = 2π L p Let P l denote the average power of the lth path, then P l = P (τ) τ= l = 2π L p e 2πl Lp, l =,,Lp ith the unit channel power constraint, ie, we get P l = P e 2πl Lp, where P = L p l= P l =, 2π e Lp (4) e 2π 85

In the first type of channel model, we assume the tap gains are uncorrelated L p independent rvs are generated with complex Gaussian distribution and the variances of real and imaginary parts are 2 P l respectively Taking the Fourier transform of equation (3), we get φ c (Δf) = P (τ)e j2πδfτ u dτ = u + j2πδf (5) e can view the frequency domain channel model as dividing the whole system bandwidth into R parts, (R is the total number of subcarriers or the size of FFT), so Δf = R, and Φ= φ c ( Δf) φ c ( Δf) φ c ((R )Δf) φ c ( Δf) φ c ( Δf), φ c (( R)Δf) φ c ( Δf) where Φ is the R R channel correlation matrix Since Φ is a Hermitian positive-definite matrix, we can perform Cholesky factorization on Φ Let Φ=L L H, where L is a lower triangular matrix and ( ) H denotes the conjugate transpose In the second type of channel model, R independent complex Gaussian rvs were generated with variances of 2R for the real and imaginary parts respectively The rvs are then multiplied with the L matrix to form the specific correlation The third type of channel model is widely used in current literatures, which assumes that the fading characteristics on each subcarrier are iid complex Gaussian random variables That is, each subcarrier undergoes flat and uncorrelated fading The correlated tap gain model is introduced as the fourth type of channel model In a slow fading scenario, we can write the correlation between the mth and nth tap gains as 2 ( ) ( ) ψ mn = P (τ)sinc (τ mt c ) sinc (τ nt c ) dτ Let Ψ denote the L p L p tap gain correlation matrix which takes ψ mn as its elements, m, n = L p Ψ is a real symmetric positive-definite matrix and can be decomposed as Ψ= L L T Similar to the second type of channel model, we generate L p complex Gaussian rvs with unit variance and pass them through the L matrix To normalize the power, the rvs are further divided with tr(ψ) The reason is that we have the unshaped rv vector g N(, I Lp L p ) The shaped rv vector h = L g and the covariance matrix of h is Ψ The power of each tap is simply the diagonal element of Ψ The first and the fourth types of channel use time domain model, the second and third types use the frequency domain models For frequency domain channel model, the system does not require an IFFT at the transmitter side nor a FFT at the receiver side All signals are processed in frequency domain directly Obviously the fourth model is more rigorous than the first one, and the second model is more rigorous than the third one In this paper, we use channel model 2 for analysis and channel model 4 for simulation, since they are close to each other (see the simulation part for further explanation) Please note that it is not good to use channel model 2 for simulation since in real world signal is finally transmitted in time domain IV PERFORMANCE COMPARISON In both the MC-DS-CDMA and CDM-OFDMA schemes, we have three system parameters: K, R and N In the MC- DS-CDMA scheme, K represents the number of users and R represents the number of bits transmitted together for one user In the CDM-OFDMA scheme, the meanings of symbols K and R are swapped N stands for the spreading factor For a full load system, N = K Given the system bandwidth Hz, the spacing between subcarriers is /R Hz So the chip duration T c = R/ second and the bit duration is NR second Since there are KR bits transmitted together, the bit rate is K N bps for the whole system For MC-DS-CDMA scheme, the user bit rate is K N bps For CDM-OFDMA scheme, the user bit rate is RN bps For a full load system, the CDM-OFDMA scheme has user bit rate as R bps e now investigate the performance difference between the two schemes Assume self synchronization has been realized The decision variable for the rth bit of the kth user in MC- DS-CDMA scheme is: Tb r MCDS (t)c k (t τ k )e j2π r Tc (t τk) dt (6) ˆb(I) kr = = 2P k b (I) kr α kr + I kr + J kr + n kr, where = NT c is the bit duration, α kr is the channel characteristic defined in H The correlations among α kr s for the same k and different r(r =,,R) are given in Φ (see channel model 2, equation (5)) denotes the real part I kr is the MAI from the same subcarrier and K I kr = Tb 2Pk (b (I) k r + r jb(q) k r )ej2π Tc (τ k τ k ) α k r c k (t τ k )c k (t τ k )dt (7) J kr is the MAI from other subcarriers and K J kr = Tb 2Pk (b (I) k r + jb (Q) k r )e j 2π Tc (rτ k r τ k ) α k r c k (t τ k )c k (t τ k )e j 2π Tc (r r)t dt n kr is the noise variable and Tb n kr = n(t)c k (t τ k )e j2π r Tc (t τk) dt The variances of I kr,j kr,n kr can be obtained as 4P k α k var(i kr ) = r 2, (8) 86

I 2 Fig I I 3 var(j kr ) = Interference patterns of two schemes I 5 I 6 2P k α k r 2 Nπ 2 (r r) 2, var(n kr ) = N 2 The SINR for the rth bit of kth user in MC-DS-CDMA scheme is found to be SINR MCDS (k, r) = 4P k α k r 2 + K 2P k α kr 2 (9) 2P k α k r 2 Nπ 2 (r r) + N 2 2 For CDM-OFDMA scheme, there will be no self user interference on the same subcarrier if the orthogonal codes are used In the analysis of MC-DS-CDMA scheme, we use the random codes since the asynchronization between users will destroy the orthogonality The interference patterns on the first bit of the first user can be generalized as in Figure In the MC-DS-CDMA scheme, I is the MAI from same subcarrier (equivalent to I kr in equation (7)), I 2 is the self user other subcarriers interference which is zero due to the self synchronization and orthogonality among subcarriers I 3 is the other subcarriers MAI (equivalent to J kr in equation (8)) In the CDM-OFDMA scheme, I 4 is the self user same subcarrier interference which is zero due to the orthogonal codes employed I 5 together with I 6 are the other subcarriers MAI Using the same analysis as before, it is found the SINR of CDM-OFDMA scheme is SINR CDM (k, r) = 2P r α kr 2 () 2P r α k r 2 Nπ 2 (r r) + N 2 2 One may argues that the CDM-OFDMA is not a fair scheme since one subcarrier may suffer deep fading and all the bits from one user will be lost The problem is easy to solve by either frequency hopping or subcarrier rotating among users Comparing the SINR in MC-DS-CDMA scheme with that in the CDM-OFDMA scheme, it is easy to see the main difference is that in the denominator of SINR MCDS,wehavethe I 4 term K 4P k α k r 2 of SINR CDM,we have the term The term K (ie, var(i )), while in the denominator 2P k α k r 2 Nπ 2 (r r) 2 R 2P r α kr 2 Nπ 2 (r r) 2 (ie, var(i 5 )) (var(i 3 )orvar(i 6 )) appears in both SINR MCDS and SINR CDM as the common term e now compare the variance of I with the variance of I 5 In general, α k r 2 is a chi-square distributed random variable with 2 degrees of freedom Var(I ) and var(i 5 ) become random variables and it is difficult to do a comparison between them However, by considering a simplified case it can give us a sense how they behave differently Assume α k r 2 =and P k = P r = P for all K and R, and ignore the noise, then var(i ) = var(i 5 ) = 4P k 4P (K ) =, () 2P Nπ 2 (r r) 2 < P (2) In equation (2), we set r =and use the identity that i = π2 2 6 e see that var(i ) >> var(i 5 ), especially for i= the large value of K So we claim that under equal deterministic channel condition, the CDM-OFDMA scheme will have a better performance than the MC-DS-CDMA scheme V SIMULATIONS First we illustrate the reason that channel model 2 is used for analysis and channel model 4 is used for Monte Carlo simulation Figure 2 gives a comparison of different channel models The simulation setups are L p = 5 and R = 64 The calculated correlation curve is obtained from equation (5) The first simulated correlation curve is obtained by using the channel model 4, where the channel taps are generated and then Fourier transformed to the frequency domain to compute the correlation Similarly, the second simulated correlation curve is obtained with channel model It is seen that the channel model 4 performs very close to the channel model 2 In channel model, due to the uncorrelated tap gains assumption, the correlation in frequency domain is also much lower than that in channel model 2 So we claim that channel model is unsuitable either for analysis or for simulation purpose Figure 3 is given for further explaining the reasonableness of using channel model 2 in the analysis Here we look at the channel characteristic of one subcarrier (say, subcarrier ) First we generate the time domain channel characteristic by using channel model 4 A Fourier transform is performed to obtain the frequency domain channel characteristic The pdf of channel characteristic in frequency domain is given e see that it does obey the Gaussian distribution when 87

9 calculated correlation (channel model 2) simulated correlation (channel model 4) simulated correlation (channel model ) simulated MC DS CDMA BER simulated CDM OFDMA BER 8 7 2 correlation 6 5 BER 3 4 3 2 4 2 3 4 5 6 subcarrier index Fig 2 Correlation of channel characteristic in frequency domain 2 4 6 8 2 4 6 8 2 SNR (db) Fig 4 BER curves for the two schemes with deterministic channel pdf 45 4 35 3 25 2 5 5 simulated pdf theorectical guassian pdf 4 3 2 2 3 4 channel characteristic in first subcarrier Fig 3 Pdf of channel characteristic in first subcarrier we use the Rayleigh channel model in the time domain So it is reasonable to use channel model 2 where we assume the channel characteristic on each subcarrier is a complex Gaussian distributed random variable It is easy to explain too Since Fourier transform is a linear transform, if the channel characteristic in time domain is Gaussian, it will be kept in the frequency domain Figure 4 verifies the claim made in the performance section It plots the simulated BER curves for the two schemes with single nonfading path channel model The simulation setups are N = 28, K =2and R =8 e see the CDM-OFDMA scheme does have a better BER performance VI CONCLUSION e have proposed a new multicarrier scheme CDM- OFDMA and put both CDM-OFDMA and MC-DS-CDMA into one unify formula format Also we consider four types of channel model e explain why the channel model 2 is close to channel model 4, while the previous one is used for analysis and the later one is used for simulation The SINR formulas for the two multicarrier schemes are given By comparing the formulas we make the claim that, with single path deterministic channel the CDM-OFDMA scheme has a better BER performance than the MC-DS-CDMA scheme REFERENCES S Hara and R Prasad, Overview of multicarrier CDMA, IEEE Communications Magazine, vol 35, no 2, pp 26-33, Dec 997 2 S Kondo and L B Milstein, Performance of multicarrier DS CDMA systems, IEEE Trans on Comm, vol 44, no 2, pp 238-246, Feb 996 3 Q Chen, E S Sousa and S Pasupathy, Multicarrier CDMA with adaptive frequency hopping for mobile radio systems, IEEE J Select Areas Commun, vol 4, no 9, pp 852-858, Dec 996 4 X Gui and T S Ng, Performance of asynchronous orthogonal multicarrier CDMA system in frequency selective fading channel, IEEE Trans on Comm, vol 47, no 7, pp 84-9, July 999 5 J P M G Linnartz, Performance analysis of synchronous MC-CDMA in mobile Rayleigh channel with both delay and Doppler spreads, IEEE Trans Veh Technol, vol 5, no 6, pp 375-387, Nov 2 6 C You and D S Hong, Multi-carrier CDMA systems using time-domain and frequency-domain spreading codes, IEEE Trans on Comm, vol 5, no, pp 7-2, Jan 23 7 Y Zhou and J ang, Downlink transmission of broadband OFCDM systems-part I: hybrid detection, IEEE Trans on Comm, vol 53, no 4, pp 78-729, April 25 8 G B Giannakis, Z ang, A Scaglione and S Barbarossa, AMOUR- Generalized multicarrier transceivers for blind CDMA regardless of multipath, IEEE Trans on Comm, vol 48, no 2, pp 264-276, Dec 2 9 B Natarajan, C Nassar, S Shattil, M Michelini and Z u, Highperformance MC-CDMA via carrier interferometry codes, IEEE Trans Veh Technol, vol 5, no 6, pp 344-353, Nov 2 C Y Lee, Mobile Communications Engineering, New York: Mc- Graw-Hill, 982 J Proakis, Digital communications, 4th Edition, pp 85, McGraw-Hill, 2 2 K Yip and T Ng, Efficient simulation of digital transmission over SSUS channels, IEEE Trans on Comm, vol 43, no 2, pp 297-293, Dec 995 88