ITERATIVE CHANNEL ESTIMATION AND DECODING OF TURBO/CONVOLUTIONALLY CODED STBC-OFDM SYSTEMS Hakan Doğan 1, Hakan Ali Çırpan 1, Erdal Panayırcı 2 1 Istanbul University Electrical&Electronics Engineering Department 2 Kadir Has University Electrical&Electronics Engineering Department

Outline Introduction STBC-OFDM with outher channel coding Represantation of the Channel  KL Expansion MAP-EM Channel Estimation Performance Analysis Simulations Results Conclusion Acknowledgement

Space-time block coding (STBC) has been proposed by Alamouti, and later generalized by Tarokh et al. as a effective transmit diversity technique for mitigating the detrimental effects of channel fading. Unfortunately, their practical application can present a real challenge to channel estimation algorithms, especially when the signal suffers from frequency selective multipath channels. One of the solutions alleviating the frequency selectivity is the use of OFDM together with transmit diversity which combats long channel impulse response by transmitting parallel symbols over many orthogonal subcarriers yielding a unique reduced complexity physical layer capabilities. STBC are not designed to achieve an additional coding gain. Therefore, an outer channel code is applied in addition to transmit diversity to further improve the receiver performance. Introduction Why do we use STBC-OFDM systems with outher channel encoder

The goal of this study We propose Expectation Maximization (EM)-based Maximum A Posterior (MAP) channel estimation algorithm for space-time block coded orthogonal frequency division multiplexing (STBC-OFDM) systems with outer channel coding in unknown wireless dispersive channels. The proposed channel estimation approach employs a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve (KL) orthogonal expansion and finds MAP estimates of the uncorrelated KL series expansion coefficients. Based on such an expansion, no matrix inversion is required in the proposed MAP estimator. Moreover, optimal rank reduction is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the iterative estimation approach. Introduction

It is clear that good channel codes are more sensitive to the poorly estimated channel. With high correlation between the coded bits, a well designed channel code is more sensitive to channel estimation errors which might cause severe error propagation in the decoding process. To understand the behavior of different channel encoders, we therefore consider both turbo and convolutionally coded systems. The goal of this study Introduction

Tx1 STBC Encoder OFDMOFDM Channel Encoder  Tx2 OFDMOFDM Channel encoded and interleaved symbols yield an independent symbol stream Resorting subchannel grouping, X(n) is coded into two vectors Transmitter

Received Signal Model To simplify the problem, we assume that the complex channel gains remain constant across two consecutive STBC-OFDM blocks.

Channel Modelling (KL expansion) An orthonormal expansion of the H involves expressing the H as a linear combination of the orthonormal basis vectors The autocorrelation matrix can decomposed as Weights of the expansion Orthonormal basis vectors

Normalized discrete channel-correlations for different blocks and subcarriers of the channel model

Receiver structure Channel Estimation & STBC Decoder RxRx  -1 MAP Decoder  Nonlinear function OFDM Demodulator How it Works First iteration EM based channel estimator computes channel gains according to pilot symbols Output of channel estimator is used STBC demodulator Equalized symbol sequence is passed through a channel interleaver and MAP decoder module LLR of coded and uncoded bits are yielded Next iteration LLRs of coded bits are reinterleaved and passed through a nonlinearity (soft values calculated) MAP-EM channel estimator iteratively estimate channel by taking received signal and interleaved soft value of transmitted symbols which are computed bu outher channel decoder in the previous iteration.

Directly solving this equation is mathematically intractable. However, the solution can be obtained easily by means of the iterative EM algorithm. After long algebraic manipulations the expression of the reestimate of No matrix inversion Moreover, by selecting r orthonormal basis vectors among all basis vectors truncation property could be employed MAP channel estimation

Simulations Parameters

MSE performance of EM-MAP channel estimator for Turbo coded STBC-OFDM systems, (fd = 50,PIR = 1 : 8) Simulations

BER performance of Turbo coded STBC-OFDM Systems according to number of used KL coefficients, (fd =50,PIR = 1 : 8) Simulations

EM-MAP channel estimator BER performance of the Turbo/Convolutional coded STBC-OFDM systems as a function of PIRs for fd = 50 More sensitive to channel estimation errors Simulations

It is observed that the proposed EM-MAP outperforms the EM- ML as well as PSAM techniques. Based on such representation, we show that no matrix inversion is needed in the EM based MAP channel estimation algorithm. Moreover, a simplified approach (truncation property) with rank reduction is also proposed. Turbo coded receiver structure more sensitive to channel estimation errors than convolutional coded receiver structure was shown. It has been demonstrated that receiver with turbo codes perform outperforms convolutional coded receiver structures assuming channel estimation performance is sufficient. Conclusion

This research has been conducted within the NEWCOM Network of Excellence in Wireless Communications funded through the EC 6th Framework Programme. This work was also supported in part by the Turkish Scientific and Technical Research Institute (TUBITAK) under Grant 104E166. ACKNOWLEDGEMENT

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