OFDM Code Division Multiplexing with Unequal Error Protection and Flexible Data Rate Adaptation

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1 OFDM Code Division Multiplexing with Unequal Error Protection and Flexible Data Rate Adaptation Stefan Kaiser German Aerospace Center (DLR) Institute of Communications and Navigation 834 Wessling, Germany Abstract In this paper, an OFDM-CDM (orthogonal frequency division multiplexing code division multiplexing) system with mapping is presented. This combination enables a robust transmission with flexible error protection and data rate adaptation for parallel data streams by exploiting additional diversity due to CDM. Performance results are presented for fading s where OFDM- CDM with mapping and soft interference cancellation is compared to conventional OFDM systems also taking into account coding with variable code rates. I. INTRODUCTION Future mobile communication systems have to offer a great variety of services from low-rate speech transmission to high-rate video transmission. This services have to be available in mobile outdoor and indoor scenarios. OFDM (orthogonal frequency division multiplexing) [] and OFDM-CDM (OFDM code division multiplexing) [] systems have proven to be robust in time-variant multipath fading s. In this paper, we investigate an OFDM-CDM system which can handle parallel data streams with different data rates and error protection by flexible adapting the mapping scheme individually to each data stream. This is of interest in systems like DVB-T [3], where data streams with different priorities are protected with different levels. The proposed scheme offers an additional degree of freedom besides coding with variable code rates as applied in DAB [4], DVB-T, HIPERLAN/ [5] or UMTS [6], e.g., realized by rate compatible punctured convolutional (RCPC) codes [7]. The principle of OFDM- CDM with mapping can also be applied in MC-CDMA systems [8] where the different data streams are mapped to different users. Since OFDM-CDM has to deal with self interference in fading s due to the loss of orthogonality between the parallel data streams, we apply a soft interference cancellation scheme [9], [0] to minimize the self interference. Simulation results are presented for fading s and are discussed with respect to bit error rate performance and bandwidth efficiency. Moreover, the performance of the presented OFDM-CDM system is compared to that of conventional OFDM systems with mapping, also taking into account coding with variable code rates. II. OFDM-CDM SYSTEM WITH ADAPTIVE SYMBOL MAPPING A. Transmitter The concept of mapping is shown in Fig. for an OFDM-CDM system. The total number of parallel data streams is K. The data of each stream are encoded by a encoder, where the code rate of the individual stream can be chosen according to the requirements by using RCPC codes. After outer interleaving,, the code bits are mapped and multiplexed by applying CDM as illustrated in Fig.. Adaptive CDM enables each data stream to apply a mapping scheme which is adapted to the data rate and robustness required by the individual stream and is independent of the other streams. As shown in Fig., data stream # applies QPSK, data stream #K applies 6-QAM and the rest e.g. 8-PSK. After mapping, a complex-valued data from each of the K data strames is spread with another streading code from a set of K orthogonal streading codes like Walsh Hadamard codes []. The importand property is that as long as linear mapping schemes are applied in the different data streams, the resulting spread s of the different data streams remain orthogonal, independent of the individually used mapping schemes. The spreading code length is L. To achieve a maximum throughput, we chose K = L. For K < L, the throughput would decrease while the system becomes more robust, i.e., CDM as inner coding would have a code rate of R<. After multiplexing

2 transmitter # receiver data streams #K IOFDM encoder encoder detector #k with demapping CDMA calc. calc. OFDM Fig.. OFDM-CDM transmitter/receiver with mapping/demapping the spread data s, the resulting sequence s is interleaved,, and modulated on several subcarriers by applying OFDM. Given the vector d =(d ;d ;:::;d K ) T consisting of K parallel complex-valued data s, each from a different data stream and generated with a possibly different mapping scheme, the sequence s obtained after CDM is given by s = C L d =(S ;S ;:::;S L ) T : () Variables which can be interpreted as values in the frequency domain like the s S l ;l =;:::;L, each modulating another subcarrier frequency, are written in capital letters. The Hadamard transformation [] with matrix C L = # #K data streams» CL C L ; 8L () C L C L and C 0 = is applied to perform CDM. The transposition is denoted by (:) T. The rows of C L represent the orthogonal spreading codes c (k) ;k =;:::;L. The interleaver with size I in performs frequency interleaving for I in» N c and time and frequency interleaving for I in >N c. The total number of subcarriers is given by N c. Moreover, L fi N c reduces the complexity of the receiver. Thus, several sequences s can be interleaved and modulated in parallel. OFDM comprises the blocks inverse fast Fourier transform (IFFT) and cyclic extension of an OFDM as guard interval. K data streams K mapper # (e.g. QPSK) mapper # K (e.g. 6-QAM) adapive CDM K spreading and multiplexing Fig.. CDM with mapping B. Receiver The orthogonality of the signals can get lost in a multipath fading, resulting in interference between different data streams. Thus, in the receiver we have to apply efficient detectors to separate the signals. After guard interval removal, fast Fourier transform (FFT) and inner deinterleaving, Π, the received sequence at the input of the data in detector is sequence s r = Hs+ n =(R ;R ;:::;R L ) T : (3) The L L diagonal matrix H represents the fading on the L subs where s has been transmitted on, assuming that the guard interval duration exceeds the delay spread of the multipath. The vector n gives the noise on the L subcarriers. B. Single Symbol Detection Single detection is realized by a bank of one-tap equalizers to combat the phase and amplitude distortions caused by the multipath propagation on the subs. The equalization coefficients are given by the L L diagonal matrix G. The detected data vector ^d is obtained by ^d = QfC Λ L Grg =(^d ; ^d ;:::; ^d L ) T ; (4) where the quantization operation Qf.g yields hard decisions according to the alphabets of d k ;k = ;:::;K. The conjugate complex is denoted by (:) Λ. Possible single detection techniques for OFDM-CDM are a) equal gain combining, where ony the phase distortion is corrected, b) zero forcing in order to avoid any interference between different data streams while tolerating noise amplification due to inversion and c) minimum mean square error (MMSE) equalization. As shown in [3], MMSE equalization is the most promising single detection technique and is used for the investigations in this paper.

3 MMSE equalization minimizes the mean square value of the error " l;l = S l;l G l;l R l;l (5) between the transmitted signal and the output of the equalizer. The mean square error J l;l = Efj" l;l j g (6) detection of interfering s (self-interference) { detector # g spreader incl. distortion demapper soft mapper calc. tanh(.) can be minimized by applying the orthogonality principle [], stating that the mean square error J l;l is minimum if the equalizer coefficient G l;l is selected such that the error " l;l is orthogonal to the received signal R Λ l;l, i.e., r detector # k demapper calc. data stream # k Ef" l;l Rl;l Λ g =0: (7) IOFDM When using MMSE equalization for single detection in OFDM-CDM systems, the diagonal elements of G result in ^H l;l Λ G l;l = j ^H l;l j + ff ; (8) where ^H l;l is the estimated state information () on the l-th subcarrier and ff is the variance of the noise. Thus, the computation of the MMSE equalization coefficients requires an estimation of the actual noise per subcarrier, which can be avoided by using suboptimal MMSE equalization [3]. When performing soft decision decoding, the calculation of the log-likelihood ratios (s) in CDM systems has to be performed in the same way as shown in [3], [4] for multi-carrier CDMA systems. B. Soft Interference Cancellation In this paper, we use soft interference cancellation where single detection with MMSE equalization is used in the individual detection stages. Fig. 3 shows the principle of soft interference cancellation. In the initial detection stage, the data s of all K data streams are soft detected in parallel by single detection. That is, v [0] = C Λ L G[0] r; (9) where G [0] denotes the equalization coefficients assigned to the initial detection stage and v [0] is the vector with the K soft decided values of the parallel data streams after initial detection. To apply soft interference cancellation it is important that the reliability of the interference which is fed back in the iterative process is given as log-likelihood ratios (s), so that the reliability information about decisions Fig. 3. OFDM-CDM receiver with soft interference cancellation from different data streams with different mapping schemes can be combined correctly. After soft-in/soft-out decoding, the log-likelihood values are mapped to soft bits w in the soft bit estimator and can take on values in the interval [ ; +], which is required to perform soft interference cancellation in the bit domain. The transformation of the soft bit estimator is given as follows [9], [0] w = tanh : (0) After interleaving, the soft bits are ly soft mapped such that the soft bits are mapped according to the individual mapping scheme assigned to the data stream they belong to and the reliability information included in the soft bits is not lost. It should be noted that the complexity of the receiver can be reduced by using hard decisions instead of s in the iterative process, resulting in slight performance degradations. The following detection stages work iteratively by using the soft decisions of the previous stage to reconstruct the interfering contribution in the received signal. The obtained interference v [j] is subtracted, i.e, cancelled from the received signal and the data detection is performed again with back reduced interference from the parallel data streams. Thus, the second and further detection stages apply 0 T B KX C v [j] = C Λ L H v (g)[j ] c (g) back A ; g= g6=k j = ;:::;J it ; ()

4 where except for the final stage the detection has to be applied for all K parallel data streams. The total numbers of iterations is given by J it. III. SYSTEM PARAMETERS The OFDM-CDM system under investigation uses a transmission bandwidth of B =MHz and the carrier frequency is located at GHz. The number of subcarriers is N c = 5, resulting in an OFDM duration of 56 μs. The guard interval duration is 0 μs. As codes, rate compatible punctured convolutional (RCPC) codes with memory 6 and variable code rates R of /3, /, /3 and 4/5 are used. The mapping scheme can vary between QPSK, 8- PSK and 6-QAM. Short Hadamard codes of length L =8 are applied for spreading, which is a good compromise between spreading and complexity [4]. The depth of the inner interleaver,, is for QPSK, 8-PSK and 6-QAM equal to 4, 6 and subsequent OFDM s, respectively, such that time and frequency interleaving is applied. The detector uses soft interference cancellation with iteration for data detection. In each detection stage, the single detector applies MMSE equalization. The achievable bit rates depend on the mapping scheme and the chosen code rate and are in the range from.4 Mbit/s with high error protection using code rate /3 and QPSK up to 5.94 Mbit/s using code rate 4/5 and 6-QAM. The performance of conventional OFDM, as e.g. applied in DVB-T and HIPERLAN/, with same parameters as used for OFDM- CDM except for the CDM component is shown as reference in the sequel. The mobile radio is modeled as time and frequency selective Rayleigh fading with perfect time and frequency interleaving. Moreover, perfect knowledge is assumed in the receiver. Thus, the presented results can serve as reproducible references. IV. SIMULATION RESULTS The bit error rate (BER) of an OFDM-CDM system and a conventional OFDM system versus the signal-to-noise ratio (SNR) in =N 0 are shown for code rate /3 in Fig. 4 and for code rate / in Fig. 5. The energy per bit is and the noise spectral density is N 0. Results are shown for QPSK, 8-PSK and 6-QAM mapping. As lower bound (LB) for OFDM-CDM, the performance with perfect interference cancellation, i.e. without interference, is shown. It can be observed, that OFDM-CDM with soft interference cancellation already after the first iteration outper- BER QPSK, OFDM QPSK, OFDM CDM QPSK, OFDM CDM LB 8 PSK, OFDM 8 PSK, OFDM CDM 8 PSK, OFDM CDM LB 6 QAM, OFDM 6 QAM, OFDM CDM 6 QAM. OFDM CDM LB Fig. 4. Performance of OFDM-CDM with mapping; rate /3 coding forms conventional OFDM especially when applying QPSK or 8-PSK. The bandwidth efficiency of OFDM-CDM with soft interference cancellation and for conventional OFDM in a Rayleigh fading is presented in Fig. 6. Results are shown for the BER of 0 4. OFDM-CDM outperforms conventional OFDM with QPSK and 8-PSK mapping. When the mapping scheme has also information in the amplitude, as in the case of 6-QAM, the performance gains of OFDM-CDM decrease. Nevertheless, an OFDM- CDM system can handle mapping schemes with 6- QAM to increase the data rate with acceptable performance so that the multiplexing scheme has not to be changed to guarantee optimum performance. It can be summarized that the bandwidth efficiency of an OFDM system can be increased up to 50% when using additionally CDM. To achieve this performance gains, OFDM-CDM needs additional complexity due to spreading and detection. For the investigated OFDM-CDM system with mapping and flexible coding a system can transmit data in Rayleigh fading s with about 4 db =N 0 at a BER of 0 4 and with more favorable transmission conditions can increase the bandwidth efficiency by a factor of greater than 4. This figures illustrate the bandwidth of error protection and data rate levels on different data streams available in OFDM-CDM systems with mapping. The presented performance improvements can also be ap-

5 BER QPSK, OFDM QPSK, OFDM CDM QPSK, OFDM CDM LB 8 PSK, OFDM 8 PSK, OFDM CDM 8 PSK, OFDM CDM LB 6 QAM, OFDM 6 QAM, OFDM CDM 6 QAM, OFDM CDM LB bandwidth efficiency.5.5 OFDM, QPSK OFDM, 8 PDSK OFDM, 6 QAM OFDM CDM, QPSK OFDM CDM, 8 PSK OFDM CDM, 6 QAM Fig. 5. Performance of OFDM-CDM with mapping; rate / coding Fig. 6. Bandwidth efficiency of OFDM-CDM in a Rayleigh fading at a BER of 0 4 plied in systems which have only one data stream by inserting a serial-to-parallel converter before the CDM block in the transmitter and a parallel-to-serial converter after detection and demapping in the receiver. V. CONCLUSIONS It has been shown in this paper that OFDM-CDM with mapping offers an adjustable error protection and flexible data rate adaptation to parallel data streams. Soft interference cancellation has been applied in the receiver to separate the different data streams. The OFDM- CDM scheme has been compared to conventional OFDM schemes. It has been shown that OFDM-CDM outperforms conventional OFDM by enabling an =N 0 reduction of db - 3 db or increase in bandwidth efficiency of up to 50%, respectively, in fading s. REFERENCES [] S. Weinstein and P. M. Ebert, Data transmission by frequencydivision multiplexing using the discrete Fourier transform, IEEE Trans. Comm. Tech., vol. 9, pp , Oct. 97. [] S. Kaiser, Performance of multi-carrier CDM and COFDM in fading s, in Proc. IEEE Global Telecommun. Conf. (GLOBE- COM 99), pp , Dec [3] ETSI ETS , Digital video broadcasting (DVB); frame structure, coding and modulation for digital terrestrial television (DVB-T), tech. rep., ETSI, Mar [4] ETSI ETS , Radio broadcasting systems; digital audio broadcasting (DAB) to mobile, portable and fixed receivers, tech. rep., ETSI, Feb [5] ETSI TS 0 475, Broadband radio access networks (BRAN); HIPERLAN type ; physical (PHY) layer, tech. rep., ETSI, Feb. 00. [6] ETSI, The ETSI UMTS terrestrial radio access (UTRA) ITU-R RTT candidate submission, tech. rep., ETSI SMG, June 998. [7] J. Hagenauer, Rate-compatible punctured convolutional codes (RCPC codes) and their applications, IEEE Trans. Comm., vol. 36, pp , April 988. [8] K. Fazel and S. Kaiser (Eds.), Multi-Carrier Spread-Spectrum & Related Topics. Boston: Kluwer Academic Publishers, 000. [9] J. Hagenauer, Forward error correcting for CDMA systems, in Proc. IEEE Fourth Int. Symp. on Spread Spectrum Techniques & Applications (ISSSTA 96), pp , Sept [0] S. Kaiser and J. Hagenauer, Multi-carrier CDMA with iterative decoding and soft-interference cancellation, in Proc. IEEE Global Telecommun. Conf. (GLOBECOM 97), pp. 6 0, Nov [] J. G. Proakis, Digital Communications. New York: McGraw-Hill, 995. [] S. Haykin, Adaptive Filter Theory. Upper Saddle River, NJ: Prentice Hall, third ed., 996. [3] S. Kaiser, Multi-Carrier CDMA Mobile Radio Systems Analysis and Optimization of Detection, Decoding, and Channel Estimation. Dusseldorf: VDI-Verlag, Fortschrittberichte VDI, series 0, no. 53, 998, Ph.D. thesis. [4] S. Kaiser, Trade-off between coding and spreading in multicarrier CDMA systems, in Proc. IEEE Fourth Int. Symp. on Spread Spectrum Techniques & Applications (ISSSTA 96), pp , Sept. 996.