ORTHOGONAL frequency division multiplexing (OFDM)

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1 144 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH 2005 Performance Analysis for OFDM-CDMA With Joint Frequency-Time Spreading Kan Zheng, Student Member, IEEE, Guoyan Zeng, and Wenbo Wang, Member, IEEE Abstract In this paper, a novel OFDM-CDMA system with joint time-frequency spreading methods is proposed. The average bit error probability of the proposed system using maximum-ratio combining (MRC) is derived for a frequency-selective fading channel and that of conventional MC-CDMA is also presented for comparison. Numerical analysis and simulation results indicate that the proposed system outperforms MC-CDMA system. Index Terms CDMA, maximum ratio combining, multiple access, OFDM. I. INTRODUCTION ORTHOGONAL frequency division multiplexing (OFDM) as a modulation technique is being applied extensively to high-speed wireless communication systems, such as digital audio broadcasting, digital TV broadcasting, and wireless LANs due to its efficient usage of the available frequency bandwidth and robustness to frequency selective fading environments [1] [3]. However, it has the limitation of spectral efficiency. With the rapid development of digital audio/video broadcasting, the availability of spectrum becomes one of the most serious problems when more applications are implemented. Meanwhile, code division multiple access (CDMA) has already shown quite a bit of promise in its spectral efficiency through the flexible frequency reuse and multiple access technique. So OFDM combined with code division multiple access (CDMA) has drawn a lot of interests in the research of new broadcasting schemes [4] [6]. The use of OFDM-CDMA provides a way to develop a new digital broadcasting scheme in areas with very limited spectral resource, where each user can be distinguished by its unique orthogonal code upon uplink transmission. OFDM-CDMA also can solve the power limitation problem in the uplink better than other schemes for broadcasting systems. Various OFDM-CDMA schemes have been proposed and can be mainly categorized into two groups according to code spreading direction [7] [10]. One is to spread the original data stream in the frequency domain; and the other is spread in the time domain, similar to a normal DS-CDMA scheme. Therefore, the frequency Rake receiver or time Rake receiver will be used, respectively. The former scheme, which is usually referred to as MC-CDMA, can obtain a good frequency Rake diversity effect through the despreading operation since the fading of each sub-carrier is different. Although the orthogonality will be degraded due to the frequency selective channel, a proper combining scheme can be selected to minimize such Manuscript received January 5, 2004; revised July 27, This work was supported by the Motorola Co. Ltd. (U.K.). The authors are with School of Telecommunication Engineering, Beijing University of Posts & Telecommunications, Beijing , China, ( Digital Object Identifier /TBC effect and improve the system performance. However, such scheme can t achieve the time diversity gain by itself. The latter scheme, which is usually called as MC-DS-CDMA, is a good scheme to introduce the OFDM technology into DS-CDMA systems, especially for the quasisynchronous mobile communication environment. However, the frequency diversity gain, which is the main advantage of using such technique, can t be achieved if good channel coding and interleaving in the frequency domain are not combined. In this paper, we will propose a novel joint time-frequency 2-dimensional (2D) spreading method in OFDM-CDMA systems, which can offer not only time diversity but also frequency diversity at the receiver efficiently. In time-frequency selective fading channel, the performance of the proposed system will be better than that of MC-CDMA systems, which is referenced as 1D spreading system for comparison. This paper is organized as follows. Section II gives the brief description of the OFDM-CDMA system with joint time-frequency spreading. Performance analysis for MRC receiver is carried out in Section III. Numerical and simulation results are presented and discussed in Section IV. Finally, Section V gives the conclusion. II. SYSTEM MODEL A synchronous 2D OFDM-CDMA with simultaneous users is considered. The original information bit stream of user, is modulated (e.g., BPSK) at first. As required in the joint time-frequency spreading method, modulated symbols are grouped together and one frame consists of OFDM symbols. represents the bandwidth expansion factor due to spreading. The spreading at the transmitter and the despreading at the receiver are all processed frame by frame. Fig. 1 describes the implementation of the th user s time-frequency spreading grid pattern when the number of available sub-carriers is equal to the length of orthogonal codes, where the horizontal axis represents time and vertical axis frequency. As shown in Fig. 1, when one group of symbols for the th frame is fed into the time-frequency model, the 0th modulated symbol of this group is duplicated into copies, then spread onto positions including the 0th sub-carrier in the 0th OFDM symbol by the 0th chip of the th orthogonal code, the 1st sub-carrier in the 1st OFDM symbol by the 1st chip of ; the 1st modulated symbol of this group is duplicated and spread onto positions including the 1st sub-carrier in the 0th OFDM symbol by the 0th chip of, the 2nd sub-carrier in the 1st OFDM symbol by the 1st chip of etc. By this method, each modulated symbol of one group can be spread onto the different sub-carriers in the different OFDM symbols by one orthogonal code. Each user will be allocated /$ IEEE

2 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH where is the th path gain of the th user, which is independently complex Gaussian random process with zero mean and variance for different and ; is the propagation delay for the th path of the th user. If the cyclic prefix is longer than the impulse of the channel, then it is assumed that the narrowband signal that is transmitted through each subcarrier experiences a nonselective Rayleigh fading channel. Furthermore, each amplitude and phase of the channel for a narrowband signal keeps constant in each subcarrier. The frequency response of the fading channel assumed for the th user at the th subcarrier can be expressed as (3) Fig. 1. Time-frequency spreading grid pattern of the kth user. For the sake of analysis, it also can be rewritten as (4) with one orthogonal code and spread its information data over the frequency and time domain uniformly. When the time-frequency spreading grid patterns are designed, the common principle is to spread the information of the same modulation symbol onto the different sub-carriers and different OFDM symbols in order to obtain both time diversity gain and frequency diversity gain simultaneously. Furthermore, in order to achieve time diversity gain well, the duration of one frame should be close or larger than the channel coherent time. So the length of frame must be designed carefully according to the typical mobile communication environment. On the other hand, the frequency diversity gain can be obtained more easily since the bandwidth occupied by several sub-carriers, on which the same modulated symbol is spread, is much larger than the channel coherent bandwidth. The transmitted signal for the th user may be expressed as (1) where is the transmitted power, is the th user s th data symbol of the th frame at the th subcarrier and is the th chip of the th user s orthogonal spreading code. is the th subcarrier frequency. is the rectangular pulse response defined on the interval. Here is the residue of modulo. The channel of the th user is modeled as a wide sense stationary, uncorrelated scattering (WSSUS), Rayleigh fading channel with paths in the complex equivalent low-pass time-variant impulse response (2) where the random amplitudes of each individual user are assumed to be correlated Rayleigh random variables for different subcarriers; the random phases of each individual user are assumed to be uniform random variables on the interval for different subcarriers. The received signal can be written as (5), shown at the bottom of the page, where is the number of active users, is the complex envelope of additive white Gaussian noise (AWGN) with zero mean and double-sided power spectral density. At the receiver, the despreading and combining procedure with the time-frequency spreading grid pattern corresponding to the transmitter can t be processed until all the symbols within one frame are received. Without the loss of generality, the signal from the 0th user is regarded as the desired signal and the signals from all other users as interference signals. With coherent demodulation, the decision variable for the 0th data symbol of the th frame is given by (6) (9), shown at the top of the next page. The desired signal component, multiple access interference (MAI) and the noise component are,,, respectively. III. BIT ERROR RATE ANALYSIS FOR MRC Maximum-ratio combining (MRC) is considered in this section. Frame index is omitted for simplification in the rest of the paper. Ideal channel frequency response for the 0th user is assumed to be available at the receiver, and its sampled value at the th symbol in the th OFDM symbol during one frame can be expressed as (10) Then, the MRC gain corresponding to the 0th data symbol is given by (11) (5)

3 146 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH 2005 (6) and (7) (8) (9) Then Characteristic function of can be written as (12) (13) (14) where. Since are uniformly distributed over, the probability density function of can be easily obtained and. Assuming that the number of subcarriers is large and the input data symbols are random, MAI can be approximated by a Gaussian random variable with zero mean and variance where,. And (15) (16) The conditional signal to noise and interference (SNIR) of the 0th user conditioned on can be expressed as (17) Since and are mutually independent, the probability of error conditioned on can be simply given by To compute its distribution, as follows: can be expressed by where. (18) (19) (20) And the covariance matrix of can be expressed as [10] (21) Furthermore, (20) can be simplified by mean of the unitary decomposition of the matrix. The simplified form of characteristic function [11] is given by (22) where are eigenvalues of and denotes matrix determinant. By the inverse transfer of (22), the probability density function of can be calculated by (23) Then, the integral of (23) can be simply calculated by the sum of residues. There are two resulted pdfs from the eigenvalues of as follows: all all are equal are not equal. (24) Finally, to compute the average BER, we must statistically average (18) over the probability density function of, i.e., (25) It is assumed that any bit sent via any of the data in one frame with equal error probability and the BER of each user is equal. Therefore, the system average BER is given by (26)

4 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH On the other hand, in 1D MC-CDMA systems, the conditional signal to noise and interference (SNIR) of the 0th user conditioned on, which is only related to one OFDM symbol so that time index for is omitted, can be expressed as (27) Similar to, can be also expressed by (28) where. And the covariance matrix of can be expressed as (29) which is only dependent on the frequency spacing between different subcarriers. Then, the probability density function of can be calculated by using the similar method that was described above for 2D OFDM-CDMA system. And the average BER of 1D MC-CDMA can be obtained by statistically averaging its conditioned BER over the probability density function of. Fig. 2. Probability density function (pdf) of and (1) Solid lines calculated (2) Dot lines simulated. IV. NUMERICAL AND SIMULATION RESULTS In order to compare the performances of our proposed 2D OFDM-CDMA system and 1D MC-CDMA system, the fading channel and the system parameters are kept same. Both computer simulation and numerical analysis are carried out to investigate the performance gain of the system with joint frequency-time spreading. The channel is a multipath channel modeled as a finite tapped delay line with Rayleigh fading paths and the multipath intensity profile of the channel is exponential with. Each path of the channel is modeled by a classical Doppler spectrum. The bandwidth used is MHz at a carrier frequency band GHz. The period of one OFDM symbol including effective symbol period, 32, and cyclic prefix, 8, is40. Walsh-Hadamard (WH) codes are utilized for spreading. Different codes are allocated to different users. The spacing of subcarrier is 31.3 khz and the number of subcarrier 64, which equal to the length of the orthogonal spreading code. To calculate the BER, it is assumed that the mean power of each interfering user is equal to the mean power of the desired signal. Fig. 2 shows the probability density function of and respectively, which are generated by simulation using Monte-Carlo method or by calculation from (21), (24) and (29). The probability of the event that is large value is a little bigger than that of, which means that the average SNIR of proposed system will be more likely to be higher than that of the MC-CDMA system. So the better BER performance of 2D OFDM-CDMA system is expected. In Fig. 3, the performances of MC-CDMA with 1D spreading and OFDM-CDMA with 2D spreading in term of BER with different mobile speeds are compared. The Doppler frequency is up to 83, 139, or 555 Hz when mobile speed up to 18, 30, or 120 km/h, respectively, which is much less than Fig. 3. BER comparison between 2D OFDM-CDMA and 1D MC-CDMA Systems with different mobile speed (single user, N =64) (1) Dash dot lines 1D MC-CDMA (2) Solid lines 2D OFDM-CDMA. the spacing of subcarrier. Therefore, the inter-carrier-interference caused by Doppler frequency can be omitted. Then, the BER performance of 1D MC-CDMA system won t be affected by the mobile speed as shown in Fig. 3. On the other hand, with the increase of the mobile speed, the channel coherence time becomes close or even smaller than the duration of one processing frame of 2D OFDM-CDMA. So that the time diversity gain can be more easily achieved by joint frequency-time spreading method and the BER performance of 2D OFDM-CDMA system becomes better. Higher mobile speed, the gain between 2D and 1D system becomes larger. If the target BER is assumed to be, it is clear the gain with 2D OFDM-CDMA compared with 1D MC-CDMA is about 2 db or 4 db when the mobile speed is 30 km/h or 120 km/h, respectively. Fig. 4 shows the BER performance of 1D MC-CDMA and 2D OFDM-CDMA systems versus the average with different number of active users when the mobile speed is 30 km/h. As shown in Fig. 4, the BER performance become worse in both systems with the increase of the number of active users due to multiple access interference. Moreover, the performances

5 148 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH 2005 Fig. 4. BER comparison between 2D OFDM-CDMA and 1D MC-CDMA systems with multiple users, N =64and mobile speed =30km=h (1) Solid lines 2D OFDM-CDMA (2) Dash dot lines 1D MC-CDMA. of 2D OFDM-CDMA still keep little better than those of 1D MC-CDMA. V. CONCLUSION In this paper we propose a novel OFDM-CDMA system with joint time-frequency spreading method. The performance of the joint time-frequency spreading OFDM-CDMA systems is analyzed over time-frequency selective fading channel. Numerical analysis and simulation results show that the proposed system performs better than the traditional MC-CDMA system, especially in the fast fading channel, by making full use of both time and frequency diversity. REFERENCES [1] Radio Broadcasting Systems: Digital Audio Broadcasting (DAB) to Mobile, Portable and Fixed Receivers, ETSI, ETSI ETS , Feb [2] Digital Video Broadcasting (DVB): Frame Structure, Channel Coding and Modulation for Gigital Terrestrial Television (DVB-T), ETSI, ETSI ETS , Mar [3] A. Doufexi et al., IEEE Commun. Mag., vol. 40, no. 5, pp , May [4] M. Chrysochoos and J. Kim, Performance analysis of an MC-CDMA broadcasting system under high power amplifier nonlinearities.i. System proposal, IEEE Trans. Broadcast., vol. 46, pp , Dec [5] A. S. Madhukumar and F. Chin, Residue number system-based multicarrier CDMA system for high-speed broadband wireless access, IEEE Trans. Broadcast., vol. 48, pp , Mar [6] Y.-H. You, W.-G. Jeon, J.-H. Paik, and H.-K. Song, A simple construction of OFDM-CDMA signals with low peak-to-average power ratio, IEEE Trans. Broadcast., vol. 49, pp , Dec [7] R. Prasad and S. Hara, An overview of multi-carrier CDMA, in Proc. IEEE 4th Int. Symp. Spread Spectrum Techniques and Applications, Mainz, Sep , 1996, pp [8] S. Kaiser and K. Fazel, A flexible spread-spectrum multi-carrier multiple-access system for multi-media applications, in Proc Int. Symp. Personal, Indoor and Mobile Radio Communications, Helsinki, Finland, Sep. 1 4, 1997, pp [9] S. Kaiser, OFDM code-division multiplexing in fading channels, IEEE Trans. Commun., vol. 50, pp , Aug [10] P. K. Frenger, N. Arne, and B. Svensson, Decision-directed coherent detection in multicarrier systems on Rayleigh fading channel, IEEE Trans. Veh. Technol., vol. 48, pp , Mar [11] J. N. Pierce and S. Stein, Multiple diversity with nonindependent fading, Proc. IRE, pp , Jan

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