In this article, the computational complexity reduction of zero forcing (ZF) and minimum mean square error (MMSE) detection is presented for the uplink multiple input multiple output (MIMO) single carrier frequency division multiple access (SC-FDMA) systems. MIMO SC-FDMA structure with detection of user’s data by the well-known multiuser linear detection approaches such as MMSE and ZF often use single input single output detection systems due to its simple detection and significant performance. Although, these approaches involve inversion of a matrix computation whose matrix dimension depend on number of subcarriers used in the system, mainly, it can be few thousands. In practical detection, the computational complexity of matrix inversion becomes very high. Also, the complexity of the receiver is raised because of the superposition of all the transmitted signals at each antenna received in the systems. The proposed conjugate gradient approach reduces the higher computational overhead of linear detectors, which updates iteratively the ZF and MMSE solution and avoids the direct computation of matrix inverse operation. The analysis of the proposed algorithm reveals the superior performance and the low complexity detection in spatial multiplexing SC-FDMA system. Simulations have investigated that the computational complexity of the proposed method has been greatly reduced and bit-error-rate performance is closer to matched filter bound.
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Alamouti, S. M. (1998). A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications,16(8), 1451–1458.
Lee, S.-R., Ueng, F.-B., Wang, H.-F., & Chang, Y.-K. (2016). Iterative multiuser detection for LDPC MIMO SC-FDMA communication systems’. Transactions on Emerging Telecommunications,27(1), 6–16.
Judson, D., Bhaskar, V., & Selvaraj, K. (2018). Pre-equalization schemes for MIMO CC–CDMA systems over frequency-selective fading channels. Wireless Personal Communication,98(1), 1587–1603.
Al-kamali, F. S., Dessouky, M. I., Sallam, B. M., & Abd El-Samie, F. E. (2012). Regularized MIMO equalization for SC-FDMA systems. Circuits, System and Signal Processing.,31(4), 1423–1441.
Dhivagar, B., Kuchi, K., & Giridhar, K. (2014). An iterative DFE receiver for MIMO SC-FDMA uplink. IEEE Communication Letters,18(12), 2141–2144.
Noh, H., Kim, M., Ham, J., & Lee, C. (2009). A practical MMSE-ML detector for a MIMO SC-FDMA system. IEEE Communications Letters,13(12), 902–904.
Jeong, D., & Kim, J. (2016). Signal detection for MIMO SC-FDMA systems exploiting block circulant channel structure. IEEE Transactions on Vehicular Technology,65(16), 7774–7779.
Okuyama, S., Takeda, K., & Adachi, F. (2011). Iterative MMSE detection and interference cancellation for uplink SC-FDMA MIMO using HARQ. In Proceedings of the IEEE communication conference (pp. 1–5).
Lin, Z., Xiao, P., Vucetic, B., & Sellathurai, M. (2010). Analysis of receiver algorithms for LTE SC-FDMA based uplink MIMO systems. IEEE Transactions on Wireless Communications,9(1), 60–65.
Al-Kamali, F. S., Dessouky, M. I., Sallam, B. M., Shawki, F., Al-Hanafy, W., & Abd El-Samie, F. E. (2012). Joint low-complexity equalization and carrier frequency offsets compensation scheme for MIMO SC-FDMA systems. IEEE Transactions on Wireless Communication,11(3), 60–65.
Matthe, M., & Zhang, D. (2018). Low-complexity iterative MMSE-PIC detection for MIMO-GFDM. IEEE Transactions on Communication,66(4), 1467–1480.
Duel-Hallen, A. (1992). Equalizers for multiple input multiple output channels and PAM systems with cyclostationary input sequences. IEEE Journal on Selected Areas in Communications,10, 630–639.
Benesty, J., Huang, Y., & Chen, J. (2003). A fast recursive algorithm for optimum sequential signal detection in a BLAST system. IEEE Transactions on Signal Processing,51, 1722–1730.
Shang, Y., & Xia, X.-G. (2008). An improved fast recursive algorithm for VBLAST with optimal ordered detections. In Proceedings of 2008 IEEE ICC (pp. 756–760).
Al-Dhahir, N., & Sayed, A. H. (2000). The finite-length multi-input multi-output MMSE-DFE. IEEE Transactions on Signal Processing,48(10), 2921–2936.
Ganeshkumar, P., Selvaraj, K., Anandaraj, M., & Vijayakumar, K. P. (2016). Iterative nonlinear detection for SFBC SC–FDMA uplink MIMO transmission systems. International Journal of Communication Systems,29(9), 1568–1581.
Choi, J. H., Yu, H. Y., & Lee, Y. H. (2005). Adaptive MIMO decision feedback equalization for receivers with time-varying channels. IEEE Transactions on Signal Processing,53(11), 4295–4303.
Iqbal, N., Al-Dhahir, N., Zerguine, A., & Zidouri, A. (2015). Adaptive frequency-domain RLS DFE for uplink MIMO SC-FDMA. IEEE Transactions on Vehicular Technology,64(7), 2819–2833.
Myung, H. G., Lim, J., & Goodman, D. J. (2006). single carrier FDMA for uplink wireless transmission. IEEE Vehicular Technology Magazine,1(3), 30–38.
Zhang, J., Yang, L.-L., Hanzo, L., & Gharavi, H. (2015). Advances in cooperative single-carrier FDMA communications: Beyond LTE-advanced. IEEE Communication Surveys and Tutorials,17(2), 730–756.
Lin, C.-H., Fang, R., Lin, C.-T., Wei, C.-C., & Chi, S. (2018). 43.63-Gbit/s multiple-user SC-FDMA PON with sub-Nyquist receiver and PAPR reduction. IEEE Photonics Technology Letters,30(19), 1663–1666.
Ng, B. K., Choi, T., & Lam, C. T. (2017). Performance of SC-FDMA-based multiuser massive MIMO system in the presence of phase noise. In 2017 IEEE 17th international conference on communication technology (ICCT), October 2017. https://doi.org/10.1109/icct.2017.8359716.
Selvaraj, K., Ganeshkumar, P., & Anandaraj, M. (2016). Iterative MMSE equalization and CFO compensation for the uplink SC-FDMA transmission. International Journal of Communication Systems, Wiley,29(7), 1323–1337.
Huang, M., Chen, X., Zhou, S., & Wang, J. (2005). Iterative ICI cancellation algorithm for uplink OFDMA system with carrier-frequency offset. In Proceedings of IEEE 62nd Vehicle Technology Confererence (Vol. 3, pp. 1613–1617), Fall.
Yin, B., Wu, M., Studer, C., Cavallaro, J. R., & Dick, C. (2013). Implementation trade-offs for linear detection in large-scale MIMO systems. In Proceedings of IEEE ICASSP (pp. 2679–2683).
Mandloi, M., & Bhatia, V. (2017). Low-complexity near-optimal iterative sequential detection for uplink massive MIMO systems. IEEE Communications Letters,21(3), 568–571.
Proakis, J. G. (2001). Digital communications (4th ed.). New York: McGraw-Hill.
Lee, K., Lee, S. R., Moon, S. H., & Lee, I. (2012). MMSE- based CFO compensation for uplink OFDMA systems with conjugate gradient. IEEE Transactions on Wireless Communications,11(8), 2267–2275.
Farhang, A., Marchetti, N., Doyle, L. E., & Farhang-Boroujeny, B. (2015). Low complexity CFO compensation in uplink OFDMA systems with receiver windowing. IEEE Transactions on Signal Processing,63(10), 2546–2558.
Myung, H. G., & Goodman, D. J. (2008). Single carrier FDMA: A new air interface for long term evolution. New York: Wiley.
Judson, D., & Bhaskar, V. (2018). Error rate analysis of SIMO-CDMA with complementary codes under multipath fading channels. Wireless Personal Communication,98(2), 1663–1677.
Chen, G., Zhu, Y., & Letaief, K. B. (2010). Combined MMSE-FDE and interference cancellation for uplink SC-FDMA with carrier frequency offsets. In Proceedings of the IEEE communication conference (pp. 1–5).
Van der Vorst, H. A., & Dekker, K. (1988). Conjugate gradient type methods and preconditioning. Journal of Computational and Applied Mathematics,24, 73–87.
Axelsson, O. (2003). Iteration number for the conjugate gradient method. Mathematics and Computers in Simulation,61, 421–435.
Spatial channel model for multiple input multiple output (MIMO) simulations, 3GPP, vol. TR 25.996, v. 10.0.0, Apr. 2011.
“Evolved universal terrestrial radio access (LTE); User equipment (UE) radio transmission and reception,” Sophia-Antipolis Cedex, France, 3GPP TS 36.101, Jul. 2013.
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Selvaraj, K., Judson, D., Ganeshkumar, P. et al. Low Complexity Linear Detection for Uplink Multiuser MIMO SC-FDMA Systems. Wireless Pers Commun (2020). https://doi.org/10.1007/s11277-020-07065-z
- Spatial multiplexing
- Conjugate gradient