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On the Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems (2404.05536v1)

Published 8 Apr 2024 in cs.IT, eess.SP, and math.IT

Abstract: This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory, the MMSE channel estimator has not been fully investigated in this context due to its general non-linearity and computational complexity. Instead, the typically suboptimal Bussgang linear MMSE (BLMMSE) estimator has been widely adopted. In this work, we develop a new framework to compute the MMSE channel estimator that hinges on computation of the orthant probability of the multivariate normal distribution. Based on this framework, we determine a necessary and sufficient condition for the BLMMSE channel estimator to be optimal and equivalent to the MMSE estimator. Under the assumption of specific channel correlation or pilot symbols, we further utilize the framework to derive analytical expressions for the MMSE channel estimator that are particularly convenient for computation when certain system dimensions become large, thereby enabling a comparison between the BLMMSE and MMSE channel estimators in these cases.

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References (33)
  1. E. Larsson, O. Edfors, F. Tufvesson, and T. Marzetta, “Massive MIMO for next generation wireless systems,” IEEE Commun. Mag., vol. 52, no. 2, pp. 186–195, 2014.
  2. E. Björnson, J. Hoydis, and L. Sanguinetti, “Massive MIMO networks: Spectral, energy, and hardware efficiency,” Found. and Trends Signal Process., vol. 11, no. 3–4, pp. 154–655, 2017.
  3. N. Rajatheva, I. Atzeni, E. Björnson et al., “White paper on broadband connectivity in 6G,” 2020. [Online]. Available: http://jultika.oulu.fi/files/isbn9789526226798.pdf
  4. R. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun., vol. 17, no. 4, pp. 539–550, 1999.
  5. J. Mo and R. Heath, Jr., “Capacity analysis of one-bit quantized MIMO systems with transmitter channel state information,” IEEE Trans. Signal Process., vol. 63, no. 20, pp. 5498–5512, 2015.
  6. Y. Li, C. Tao, G. Seco-Granados, A. Mezghani, A. L. Swindlehurst, and L. Liu, “Channel estimation and performance analysis of one-bit massive MIMO systems,” IEEE Trans. Signal Process., vol. 65, no. 15, pp. 4075–4089, 2017.
  7. I. Atzeni, A. Tölli, and G. Durisi, “Low-resolution massive MIMO under hardware power consumption constraints,” in Proc. Asilomar Conf. Signals, Syst., and Comput. (ASILOMAR), 2021.
  8. C. Mollén, J. Choi, E. G. Larsson, and R. W. Heath, “Uplink performance of wideband massive MIMO with one-bit ADCs,” IEEE Trans. Wireless Commun., vol. 16, no. 1, pp. 87–100, 2017.
  9. S. Jacobsson, G. Durisi, M. Coldrey, U. Gustavsson, and C. Studer, “Throughput analysis of massive MIMO uplink with low-resolution ADCs,” IEEE Trans. Wireless Commun., vol. 16, no. 6, pp. 4038–4051, 2017.
  10. J. Mo, P. Schniter, and R. W. Heath, Jr., “Channel estimation in broadband millimeter wave MIMO systems with few-bit ADCs,” IEEE Trans. Signal Process., vol. 66, no. 5, pp. 1141–1154, 2018.
  11. N. Bernardo, J. Zhu, Y. C. Eldar, and J. Evans, “Capacity bounds for one-bit MIMO Gaussian channels with analog combining,” IEEE Trans. Commun., vol. 70, no. 11, pp. 7224–7239, 2022.
  12. M. Shao and W.-K. Ma, “Divide and conquer: One-bit MIMO-OFDM detection by inexact expectation maximization,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. (ICASSP), 2021.
  13. J. Choi, J. Mo, and R. W. Heath Jr., “Near maximum-likelihood detector and channel estimator for uplink multiuser massive MIMO systems with one-bit ADCs,” IEEE Trans. Commun., vol. 64, no. 5, pp. 2005–2018, 2016.
  14. S. Rao, A. Mezghani, and A. L. Swindlehurst, “Channel estimation in one-bit massive MIMO systems: Angular versus unstructured models,” IEEE J. Sel. Topics Signal Process., vol. 13, no. 5, pp. 1017–1031, 2019.
  15. M. S. Stein, S. Bar, J. A. Nossek, and J. Tabrikian, “Performance analysis for channel estimation with 1-bit ADC and unknown quantization threshold,” IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2557–2571, 2018.
  16. I. Atzeni and A. Tölli, “Channel estimation and data detection analysis of massive MIMO with 1-bit ADCs,” IEEE Trans. Wireless Commun., vol. 21, no. 6, pp. 3850–3867, 2022.
  17. I. Atzeni and A. Tölli, “Uplink data detection analysis of 1-bit quantized massive MIMO,” in Proc. IEEE Int. Workshop Signal Process. Adv. in Wireless Commun. (SPAWC), 2021.
  18. B. Fesl, M. Koller, and W. Utschick, “On the mean square error optimal estimator in one-bit quantized systems,” IEEE Trans. Signal Process., vol. 71, pp. 1968–1980, 2023.
  19. J. J. Bussgang, “Crosscorrelation functions of amplitude-distorted Gaussian signals,” Res. Lab. Electron., MIT, Cambridge, MA, U.S.A., 1952.
  20. G. Jacovitti and A. Neri, “Estimation of the autocorrelation function of complex Gaussian stationary processes by amplitude clipped signals,” IEEE Trans. Inf. Theory, vol. 40, no. 1, pp. 239–245, 1994.
  21. A. K. Saxena, I. Fijalkow, and A. L. Swindlehurst, “Analysis of one-bit quantized precoding for the multiuser massive MIMO downlink,” IEEE Trans. Signal Process., vol. 65, no. 17, pp. 4624–4634, 2017.
  22. S. Jacobsson, G. Durisi, M. Coldrey, and C. Studer, “Linear precoding with low-resolution DACs for massive MU-MIMO-OFDM downlink,” IEEE Trans. Wireless Commun., vol. 18, no. 3, pp. 1595–1609, 2019.
  23. I. G. Abrahamson, “Orthant probabilities of the quadrivariate normal distribution,” Ann. Math. Statist., vol. 35, no. 4, pp. 1685–1703, 1964.
  24. D. R. Childs, “Reduction of the multivariate normal integral to characteristic form,” Biometrika, vol. 54, no. 1–2, pp. 293–300, 1967.
  25. R. L. Plackett, “A reduction formula for normal multivariate integrals,” Biometrika, vol. 41, no. 3–4, pp. 351–360, 1954.
  26. H.-J. Sun, “A general reduction method for n𝑛nitalic_n-variate normal orthant probability,” Comm. Statist. Theory Methods, vol. 17, no. 11, pp. 3913–3921, 1988.
  27. A. Genz, “Numerical computation of multivariate normal probabilities,” J. Comput. Graphical Statist., vol. 1, no. 2, pp. 141–149, 1992.
  28. D. M. Keenan, “A time series analysis of binary data,” J. Amer. Statist. Assoc., vol. 77, no. 380, pp. 816–821, 1982.
  29. M. Sinn and K. Keller, “Covariances of zero crossings in Gaussian processes,” Theory Probab. Appl., vol. 55, no. 3, pp. 485–504, 2011.
  30. V. Aalo, “Performance of maximal-ratio diversity systems in a correlated Nakagami-fading environment,” IEEE Trans. Commun., vol. 43, no. 8, pp. 2360–2369, 1995.
  31. M. Chiani, M. Z. Win, and A. Zanella, “On the capacity of spatially correlated MIMO Rayleigh-fading channels,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2363–2371, 2003.
  32. A. Abdi and M. Kaveh, “A space-time correlation model for multielement antenna systems in mobile fading channels,” IEEE J. Sel. Areas Commun., vol. 20, no. 3, pp. 550–560, 2002.
  33. R. M. Gray, “Toeplitz and Circulant Matrices: A Review,” Found. and Trends Commun. and Inf. Theory, vol. 2, no. 3, pp. 155–239, 2006.
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