![]() ![]() On the ratio of two correlated complex Gaussian random variables. Principles of Digital Communication and Coding McGraw-Hill: New York, NY, USA, 1979. Statistical Distributions John Wiley & Sons: New York, NY, USA, 2000. Statistical Signal Processing Prentice-Hall: Upper Saddle River, NJ, USA, 1990. On the true and the modified Cramer-Rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters. The modified Cramer-Rao bound in vector parameter estimation. The modified Cramer-Rao bound and its application to synchronization problems. Probability, Random Variables, and Stochastic Processes McGraw-Hill: New York, NY, USA, 1991. Digital Communications McGraw-Hill: New York, NY, USA, 1989. Toeplitz and Circulant Matrices: A Review Now Publishers: Hanover, MA, USA, 2006. Fundamentals of Statistical Signal Processing: Estimation Theory Prentice Hall: Upper Saddle River, NJ, USA, 1993. Digital Signal Processing: Principles, Algorithms, and Applications Prentice Hall: Upper Saddle River, NJ, USA, 1996. A comparison of SNR estimation techniques for the AWGN channel. SNR mismatch and online estimation in turbo decoding. Degrees of freedom in adaptive modulation: A unified view. Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing Wiley: New York, NY, USA, 1998. Synchronization Techniques for Digital Receivers Plenum Press: New York, NY, USA, 1997. Emerging Optical Wireless Communications-Advances and Challenges. Survey on Free Space Optical Communication: A Communication Theory Perspective. Advanced Optical Wireless Communication Systems Cambridge University Press: New York, NY, USA, 2012. Wireless Optical Communication Systems Springer: New York, NY, USA, 2004. Minimum-bandwidth optical intensity Nyquist pulses. Bandlimited power-efficient signaling and pulse design for intensity modulation. In Proceedings of the IEEE 4th International Conference on Broadband Communications (CoBCom), Graz, Austria, 12–14 July 2022. Feedback solution for symbol timing recovery in bandlimited optical intensity channels. In Proceedings of the 12th IEEE/IET International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Porto, Portugal, 20–22 July 2020. Blind symbol timing estimation for bandlimited optical intensity channels. On parameter estimation for bandlimited optical intensity channels. These observations also hold true for modulation schemes and roll-off factors other than those used in Figure 3 especially, one can see that for L ≫ 1 and ρ s ≫ 1, the normalized variance is simply given by 2/ L. However, the diagram illustrates also that the MCRLB is more and more approximated by the jitter variance of the related estimator algorithm, when we increase the observation length in Figure 3, verified for 16-PAM, L = 100, and α ∈. We observe that the latter is fairly loose for such small observation windows, whereas the lower bound of the variance in (44) appears to be very tight as confirmed by simulation results, in particular at larger SNR values. For comparison purposes, the normalized MCRLB expressed by (22) is shown in dashed style. Using a 4-PAM scheme with L = 10 and the same roll-off factors as before, Figure 3 illustrates the evolution of the normalized variance as a function of the true SNR value in dB. Numerical results confirming the analytical work conclude the paper. Furthermore, we derive and analyze a maximum likelihood algorithm for SNR estimation, which turns out to be particularly simple for specific values of the excess bandwidth, among them the most attractive case of minimum bandwidth occupation. Focusing on this kind of scenario, the modified Cramer–Rao lower bound is derived, representing the theoretical limit of the error performance of the data-aided SNR estimator developed in this context. This requires a unipolar signal design regarding the symbol constellation, but also a non-negative pulse shape satisfying the Nyquist criterion is necessary. In the current paper, this topic is discussed for a bandlimited optical intensity link under the assumption that the data symbols are known to the receiver unit in form of pilot sequences. ![]() Not only for radio frequency but also for optical communication systems, knowledge of the signal-to-noise ratio (SNR) is essential, e.g., for an adaptive network, where modulation schemes and/or error correction methods should be selected according to the varying channel states. ![]()
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