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0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 I a /I e I e /I a EbN0 = 1.7 dB, altes Optimierungsverfahren EbN0 = − 2.3 dB, altes Optiemierungsverfahren EbN0 = 1.7 dB, neues Optimierungsverfahren EbN0 = −2.3 dB, neues Optimierungsverfahren (a) 6 6.5 7 7.5 8 8.5 9 9.5 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 E b /N 0 / dB BER ∆ SNR = 4 dB, method No. 2 ∆ SNR = 4 dB, method No. 1 ∆ SNR = 6 dB, method No. 2 ∆ SNR = 6 dB, method No. 1 (b) Figure 3.17: Performance analysis of Turbo Diversity with optimized LDPC codes for different code design methods a) EXIT functions, b) BER perfor- mance of TD with difference between diversity paths ∆SNR = 4 dB and ∆SNR = 6 dB Comparing the performance of these methods for the first and the second scenario (Fig. 3.17 b) ), considering BER=10 −3 it can be seen that for TD method No. 2 outperforms method No. 1. For LDPC codes with blocks of 9000 bits this gap is nearly 0.9 dB. Superiority of method No. 2 does not depend on the fading scenario but it should be mentioned that LDPC codes achieved by means of the method No. 2 turn to be worse for the system without TD (only one path) and on Additive White Gaussian Noise channel. 3.3.5 Summary In this contribution we investigated Turbo Diversity as an iterative decoding concept for diversity systems which outperforms MRC in single carrier and OFDM systems. Additional gains are achieved by using optimized LDPC codes as constituent codes. Two different criteria were proposed for the LDPC code design adapted to TD with OFDM. The method using the design goal to position the inverse EXIT function in the preferred area outperforms the classical criterion aimed at minimal area between EXIT functions. Despite of the fact that the area between EXIT characteristics does not have first priority in our new method, this area turns out to be less than in the case of the classical method, thus fulfilling both criteria in a better way and reducing the distance to channel capacity. The new method is better suited for different fading scenarios and block lengths of LDPC codes, what proves its robustness. For practical applications of TD the new method to design constituent LDPC codes delivers a robust approach for different fading scenarios and block lengths of LDPC codes. 60 3 Link-Level Aspects Bibliography [1] R. van Nee and R. Prassad, OFDM for Wireless Multimedia Communications, Artech House Publishers, Norwood, MA., USA, 2000. [2] M. Matuszak, W. Sauer-Greff and R. Urbansky, “Iterative Diversity Receiver Concept for Narrow-Band OFDM Systems,” in Proc. 13. International OFDM Workshop, pp. 251-255, Hamburg, Germany, 2008. [3] M. Matuszak, W. Sauer-Greff and R. Urbansky, “EXIT Chart Based LDPC Code Design for Iterative Diversity Receivers in OFDM Systems with Fading Channels,” in Proc. 14. International OFDM Workshop, pp. 20-24, Hamburg, Germany, 2009. [4] A. Dittrich, T. Schorr and R. Urbansky, “Diorama - A MATLAB Based Open Source Software Radio for Digital Radio Mondiale (DRM),” in Proc. 10. Inter- national OFDM-Workshop, pp. 391-395, Hamburg, Germany, 2005. [5] A. Paulraj, “Diversity Techniques,” in J.D. Gibson (Ed.) The Mobile Commu- nication Handbook, pp. 166-176, CRC Press, Boca Raton, FL., USA, 1996. [6] J. Hagenauer, “Das Turbo-Prinzip in Detektion und Decodierung,” in ITG- Fachberichte, Vol. 146, pp. 131-136, 1998. [7] T. Richardson, M. Shokrollahi and R. Urbanke, “Design of Capacity- Approaching Irregular Low-Density Parity-Check Codes,” IEEE Trans. on Inform. Theory, Vol. 47, No. 2, pp. 619-637, Febr. 2001. [8] L. Bahl, J. Cocke, F. Jelinek and J. Raviv, “Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate,” IEEE Trans. on Inform. Theory, Vol. 20, No. 2, pp. 284-287, March 1974. [9] S. ten Brink, “Convergence Behavior of Iteratively Decoded Parallel Con- catenated Codes,” IEEE Transactions on Communications, Vol. 49, No. 10, pp. 1727-1737, Oct. 2001. [10] European Telecommunications Standard Institute (ETSI), Digital Radio Mon- diale (DRM); System Specification, ETSI ES 201 980 V2.1.1, Sophia Antipolis Cedex, France, 2004. [11] C. Sgraja and J. Linder, “Estimation of Rapid Time-Variant Channels for OFDM using Wiener Filtering,” in Proc. IEEE International Conference on Communications (ICC), Vol. 4, pp. 2390-2395, AK., USA, May 2003. 3.4 MMSE-based Turbo Equalization Principles 61 3.4 MMSE-based Turbo Equalization Principles for Frequency Selective Fading Channels M. Grossmann, R. Thomä, Ilmenau University of Technology, Germany 3.4.1 Introduction Turbo equalization [1–11] is one of the most promising techniques to implement powerful equalizers, without requiring high computational complexity, for coded communication systems with frequency-selective fading channels. The complexity advantage of turbo equalizers is due to the separation of channel equalization and decoding into two basic processors, while the high performance is achieved by ex- changing soft information between these two components in an iterative manner. The turbo equalization approach was originally proposed in [1], utilizing a maximum a posteriori probability (MAP) algorithm for iterative equalization in frequency- selective fading channels. However, because of its exponentially increasing complex- ity, the MAP-based equalizer is only practical for simple modulation formats, like binary phase shift keying (BPSK), and for channels with less multi-path components. In [2], the optimal MAP algorithm has been replaced by a low-cost alternative based on the soft cancellation (SC) and minimum mean-squared error (MMSE) principle. The SC-MMSE filtering approach in [2], originally proposed for detection of random coded code-division multiple-access (CDMA) signals, has been applied to channel equalization in [3], and to multiple-input multiple-output (MIMO) channel equaliza- tion in [4]. Recently, the SC-MMSE turbo concept has also been used to equalization of OFDM systems in time-varying channels [5]. In this contribution, we discuss three extensions of the basic SC-MMSE filter- ing concept for turbo equalization. In particular, we first propose a novel fre- quency domain (FD) turbo equalizer for MIMO-OFDM transmissions with insuf- ficient guard interval. The SC-MMSE-based equalizer exploits the banded structure of the FD channel matrices, allowing the implementation of the equalizer with a complexity which is only linear in the number of sub-carriers. We then present a hybrid turbo equalizer, suitable for multi-user OFDM transmissions with spatially- correlated channels, that combines SC-MMSE filtering and MAP-detection. Finally, we propose a nonlinear MMSE-based turbo equalizer for single-carrier spatially- multiplexed MIMO transmissions with high-rate codes. 3.4.2 System Model Consider the discrete-time baseband equivalent model of a cyclic-prefix (CP) as- sisted block transmission single-/multi-user system with M receive antennas, and U active users, each equipped with K transmit antennas in Fig. 3.18. The transmis- sion scheme of the u-th user is based on bit interleaved coded modulation, where the information bit sequence is independently encoded by a binary encoder, and mapped to complex symbols according to the applied mapping scheme. The encoded sym- bol sequence is then grouped into several blocks, OFDM modulated, and finally 62 3 Link-Level Aspects transmitted over the frequency-selective multiple-access MIMO fading channel. Encoder Interleaver Symbol Mapper DeInterleaver Decoder Interleaver Equalizer/ λ 1 (n) ζ 1 (n) b 1 (n) ˆb 1 (n) DeInterleaver Decoder Interleaver λ U (n) ζ U (n) ˆb U (n) Encoder Interleaver Symbol Mapper b U (n) Demapper Figure 3.18: Structure for a coded single-/multi-user MIMO system with turbo equalization. At the receiver side, iterative processing for joint equalization and decoding is performed. The receiver consists of an equalizer and several single-user channel decoders. Within the iterative processing, the extrinsic LLR sequences {λ u (n)} and {ζ u (n)} of the coded bits {b u (n)} are exchanged between the equalizer and both decoders, each separated by the interleaver and deinterleaver in their iteration loop, following the turbo principle [2]. 3.4.3 MMSE Turbo Equalization Principles MMSE Turbo Equalization for MIMO OFDM Transmission with Insufficient Cyclic Prefix In single-user MIMO-OFDM transmissions, the CP, located between neighboring OFDM symbols, should be longer than the expected length of the channel impulse response, to maintain orthogonality among sub-carriers. However, in channels with some far clusters, the maximum excess delay may exceed the length of the CP, resulting in a loss of sub-carriers’ orthogonality. The related inter-block and inter- carrier interference severely degrades the performance of the standard MIMO-OFDM receiver [12]. Several approaches have been proposed to cope with this problem [13], [14]. Among all these equalization schemes for OFDM and MIMO-OFDM, one of the the most promising approaches is the iterative (turbo) SC-MMSE equalizer of [6]. The equalizer utilizes the soft feedback from channel decoding for the separation of the spatially multiplexed streams jointly with the cancellation of inter-block and inter-carrier interference. However, for transmissions with a large number of sub- carriers, the receiver has still a high complexity. In [7], an MMSE turbo equalizer that exploits the banded structure of the FD channel matrices has been proposed. The equalizer in [7] uses a sliding window to enforce this banded structure, resulting in a complexity which is only linear in the number of sub-carriers. The performance of the proposed turbo receiver was evaluated using measurement data-based off-line simulations. The measurements were performed in a macro cell environment. The major specifications of the measurement campaign, the measure- ment device and setup are summarized in [15]. The main MIMO-OFDM simulation parameters follow the extended specification of the 5 GHz wireless LAN standard in [16]. A single-user MIMO-OFDM transmission (U = 1) with K = M = 2 an- tennas and 64 sub-carriers were assumed. Channel coding was performed with a |