Reduced Complexity of QRD-M Detection Scheme in MIMO-OFDM Systems

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1 Advanced Science and echnology Letters Vol. (ASP 06), pp.4- Reduced Complexity of QRD-M Detection Scheme in MIMO-OFDM Systems Jong-Kwang Kim, Jae-yun Ro and young-kyu Song u Communication Research Institute, Sejong University, Seoul, Korea jongkwang9@naver.com, ilovebisu@nate.com, songhk@sejong.ac.kr Abstract. In multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems, several detection schemes have been developed for high error performance and low complexity. In several detection schemes, maximum likelihood (ML) and QRD-M have optimal error performance. owever, these detection schemes have very high complexity. hus, this paper proposes reduced complexity of QRD-M detection scheme in MIMO-OFDM systems. he proposed detection scheme has two stages, i.e. partial zero-forcing () and conventional QRD-M. he proposed detection scheme has higher error performance and lower complexity than the decision feedback equalizer (DFE). Keywords: MIMO-OFDM, partial, QRD-M Introduction In wireless communication systems, multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system offers high data rate without additional bandwidth. owever, because all transmission signals are simultaneously sent to the receiver, the received signals are combination of multiple distorted transmission signals. So, MIMO-OFDM system has always difficulty in accurate detection of each transmission signal. For accurate detection in MIMO-OFDM systems, several detection schemes have been developed. Maximum likelihood (ML) detection has optimal error performance. owever, the complexity of ML detection increases exponentially when the number of transmission antennas and modulation set increase. And QR decomposition-m algorithm (QRD-M) has optimal error performance with lower complexity than the ML detection []. owever, the complexity of the QRD-M also increases exponentially when the number of candidates M, transmission antennas and modulation set increase due to tree structure. Also, zero-forcing () is attractive for simple linear implementation. owever, the error performance of the is often not acceptable for other systems []. he performance indicators of detection schemes in MIMO-OFDM systems are error performance and complexity. owever, in general, these two indicators have trade-off relationship. hus, for seeking a compromise between the error performance and the complexity, this paper proposes very low complex QRD-M detection scheme which is inferior to conventional QRD-M in terms of the error performance. ISSN: ASL Copyright 06 SERSC Corresponding Author

2 Advanced Science and echnology Letters Vol. (ASP 06) System Model he MIMO-OFDM system model which has M L transmission antennas and receive antennas is considered where L is integer which is larger than. As shown in Fig., input data is demultiplexed into N data substreams [3]. So, M OFDM symbols which have cyclic prefix (CP) are denoted as X X X X M where means transpose operator. For simple notation, subcarrier index k is dropped. And all OFDM symbols from M transmission antennas are sent through rich scattering complex Rayleigh fading channel as follows, M M M M MM where, i, j,,, M means channel coefficient from the j -th transmission ij antenna to the i -th receive antenna. hen, at the receiver, M received symbols M after the process of fast Fourier transform (FF) are denoted as where N N N N M vector which has zero mean and covariance matrix means transpose operator and I is identity matrix., () X N, () is a complex additive white Gaussian noise (AWGN) E NN I where Fig.. he block diagram of MIMO-OFDM system. Copyright 06 SERSC 5

3 Advanced Science and echnology Letters Vol. (ASP 06) 3 Conventional Detection Schemes 3. he nulls other transmission signals perfectly regarding as interference by simply multiplying the pseudo-inverse of channel matrix G by received signals in (). G. (3) So, the transmission symbol ˆX is estimated as follows, where N X ˆ G X N, (4) G N is a new noise component vector. he may have low error performance due to the amplified noise component N. owever, the has low complexity because the only has to multiply the pseudoinverse matrix by received signals. 3. QRD-M In the QRD-M, the channel matrix is decomposed as QR where Q is M M unitary quadrature matrix which is satisfied with Q Q I and R is M M upper triangle matrix by using QR decomposition for low complexity. QR q q q M R R R 0 R R 0 0 R M M where q i, i,,, M is the i -th column of Q. o remove the influence of Q, the left side of the is multiplied by resultant vector W W W W M is denoted as MM, (5) Q and W Q RX N, (6) where N Q N is a new noise vector which has same statistical property with existing noise vector N. After the QR decomposition, squared Euclidean distances are calculated in (6) with tree structure. At the first stage, the l -th squared Euclidean distance between the received signal and all modulated symbols at the bottom layer in (7) is calculated as follows, 6 Copyright 06 SERSC

4 Advanced Science and echnology Letters Vol. (ASP 06) M MM l, e l W R C (7) where C C C C S is modulated candidates vector in constellation S and l is index number of C. hen, M candidates with the smallest squared Euclidean distances are retained and transferred to next layer as survival paths. At the second stage, MS squared Euclidean distances between the received symbol and modulated symbol are calculated like first stage. owever, from the second stage to final stage, accumulated squared Euclidean distance at previous layers has to be calculated as follows, where C ˆ e d l W R R X d E d, M M M l M M M X d is the d d M -th survival candidate and E ˆ N (8) d is accumulated squared Euclidean distance at the first layer. his process is repeated until the last layer. And at the last layer, a path with the minimum accumulated squared Euclidean distance is selected as transmission symbol. Fig. shows the tree structure of QRD-M in 4 4 MIMO-OFDM system. In Fig., ˆX is estimated transmission symbol which has minimum accumulated Euclidean distance. Fig.. he tree structure of QRD-M in 4 4 MIMO-OFDM system. 4 Proposed Detection Scheme he proposed detection scheme has two stages. At first, partial (slightly different to conventional ) stage is used to divide large matrix into multiple small matrix for low complexity. hen, conventional QRD-M (full M) is used to each small matrix for Copyright 06 SERSC 7

5 Advanced Science and echnology Letters Vol. (ASP 06) high error performance. For easy understanding, the proposed detection scheme is described in 44MIMO-OFDM system without noise components. So, the received signals in 44MIMO-OFDM system can be denoted as follows, 3 4 X 3 4 X (9) X R44 X4 4. Partial Unlike the conventional, partial nulls not all interference signals. So, the partial does not have to calculate the pseudo-inverse of channel matrix. he purpose of the partial is to simply divide the 4 4 MIMO-OFDM system into two MIMO-OFDM system for low complexity. So, one matrix contains X and X. And another matrix contains X 3 and X 4. For the partial, cancelling is used as follows, k k where k k equation as follows,, c 3,, c K 4 (0) 3 4 K is a weight matrix for cancelling which is satisfied with k3 k k4 k So, after the cancelling, the received signals c, c, c in (0) are as follows, c, c X, X, c where ij, i, j, is a new channel component. For clarity, the new channel components are denoted as follows, 3 3. K 4 4 In the result of (), the modified received signals contain only X and X. Likewise, the same cancelling process is applied to the and existing () () (3) 8 Copyright 06 SERSC

6 Advanced Science and echnology Letters Vol. (ASP 06) MIMO-OFDM system is divided into two MIMO-OFDM systems. Another MIMO-OFDM system c 3, c 4, c c 3, c X X 4, c is as follows, (4) 4. QRD-M in MIMO-OFDM After the partial, two MIMO-OFDM systems are generated in () and (4). And then, all transmission symbols Xˆ, Xˆ ˆ,, X 4 are estimated by applying conventional QRD-M with M S to the () and (4). he complexity of the proposed detection scheme is very lower than the conventional QRD-M which is applied to original MIMO-OFDM system in () because the QRD-M in the proposed detection scheme is applied to only MIMO-OFDM system. In able, the complexity of the proposed detection scheme is explained. In the calculation of the complexity, only complex multiplication is considered assuming the multiplication of two complex numbers require four multiplications. able. he complexity of the proposed detection scheme. Scheme Required complex multiplications Partial with LU decomposition M 3M M M log M Conventional QRD-M in system S 8 S 48 he whole proposed detection scheme able. he used simulation parameters M S 8 S 48 3 M 3M M M log M + Parameter Value or scheme he number of subcarriers 56 CP length 64 Modulation scheme (BER) Modulation scheme (Complexity) BPSK, BPSK, QPSK and 6-QAM Channel 7-path Rayleigh fading 5 Simulation Results In this section, the simulation results for bit error rate (BER) performance and required complexity are shown. he used simulation parameters are explained in Copyright 06 SERSC 9

7 Advanced Science and echnology Letters Vol. (ASP 06) able. Fig. 3 shows the BER performance of the proposed detection scheme and -DFE for comparison. At low signal-to-noise ratio (SNR), the BER performance of the proposed detection scheme is lower than the -DFE because the partial stage in the proposed detection scheme amplifies the noise components. So, due to these amplified noise components, the conventional QRD-M stage in the proposed detection scheme may detect wrong transmission symbol no matter how it has great error performance. owever, at high SNR, the error performance of the proposed detection scheme is higher than the -DFE because the partial stage amplifies the noise components with lower scale than that of low SNR. So, the conventional QRD-M stage detects the transmission symbol well. Fig. 4 shows the required complexity of the proposed detection scheme and - DFE for comparison like Fig. 3 according to the number of the transmission antennas and the used modulation scheme. he used modulation scheme is binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and 6-quadrature amplitude modulation (QAM). When the modulation scheme is BPSK and QPSK, the required complexity of the proposed detection scheme is lower than the -DFE because the conventional QRD-M does not require many complex multiplications. owever, when the modulation scheme is 6-QAM, the required complexity of the proposed detection scheme is higher than the -DFE at low antenna number because the conventional QRD-M requires many complex multiplications due to highly increased modulation set. owever, when the number of the transmission antennas is high, the required complexity of the proposed detection scheme is lower than the -DFE. Fig. 3. he BER performance of the proposed detection scheme in 4 4 MIMO-OFDM system. 0 Copyright 06 SERSC

8 Advanced Science and echnology Letters Vol. (ASP 06) Fig. 4. he required complex multiplications of the proposed detection scheme in 4 4 MIMO-OFDM system. 6 Conclusion his paper proposes the low complex QRD-M detection scheme in MIMO-OFDM systems. he proposed detection scheme has higher error performance than the - DFE at high SNR. And, the required number of the complex multiplications is lower than the -DFE when the modulation order is not large. hus, the second stage in the proposed detection scheme needs low complex QRD-M detection scheme not to require many complex multiplications regardless of modulation order. Acknowledgments his research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, IC and future Planning (No. 03RAAA ) and was supported by IC R&D program of MSIP/IIP. [R , Development of the next generation convergence broadcasting and monitoring systems combined with the networks]. References. Choi,.J., Song,.K.: Advanced QRD-M Detection with Iterative Scheme in the MIMO- OFDM System. IEICE rans. Inf. & Syst., vol. E97-D, no., pp (04). Ahn, J.K, Jang,.W., Song,.K.: An Improved Low Complexity Detection Scheme in MIMO-OFDM Systems. IEICE rans. Inf. & Syst., vol. E97-D, no. 5, pp (04) 3. u, S.J., Ahn, J.K., Song,.K.: Channel-Adaptive Detection Scheme Based on hreshold in MIMO-OFDM Systems. IEICE rans. Inf. & Syst., vol. E97-D, no. 6, pp (04) Copyright 06 SERSC