Non-Data-Aided SNR Estimation for Bandlimited Optical Intensity Channels

Abstract

Powerful and reliable estimation of transmission parameters is an indispensable task in each receiver unit—not only for radio frequency, but also for optical wireless communication systems. In this context, the signal-to-noise ratio (SNR) plays an eminent role, especially for adaptive scenarios. Assuming a bandlimited optical intensity channel, which requires a unipolar waveform design, an algorithm for SNR estimation is developed in this paper, which requires no knowledge of the transmitted data. This non-data-aided approach benefits to a great extent from the fact that very long observation windows of payload symbols might be used for the estimation process to increase the accuracy of the result; this is in striking contrast to a data-aided approach based on pilot symbols reducing the spectral efficiency of a communication link. Since maximum likelihood, moment-based or decision-directed algorithms are not considered for complexity and performance reasons, an expectation-maximization solution is introduced whose error performance is close to the Cramer-Rao lower bound as the theoretical limit, which has been derived as well.

Novel Results on SNR Estimation for Bandlimited Optical Intensity Channels

“…Using again a 4-PAM constellation applied to α = 0 and 1, Figure 4 visualizes the normalized error performance for NDA estimation of the SNR, but now for larger observation lengths, i.e., L = 100 and 1000, as is typical for an NDA situation. For comparison purposes, the diagram includes the evolution of NMCRLB-DF given by (27), in the diagram shown by solid lines, but also that of the normalized true CRLB for NDA estimation of the SNR assuming a single filter receiver (NTRCLB-SF), illustrated in dashed-dotted style, which has been derived in [ 10 ]. For , we see that the single-filter limit is again twice as large as NMCRLB-DF, irrespective of the chosen excess bandwidth.…”

“…The signal and channel model for the current paper are more or less the same as those in [ 10 , 11 ] for NDA as well as DA estimation of the SNR, respectively. Nevertheless, for convenience, the model is briefly recapitulated in the sequel.…”

“…If we adopt a pulse shape expressed by h ( t ), the signal at the output of the opto-electrical receiver module develops as [ 10 , 11 ] where A > 0 is the channel gain, T and τ specify the symbol period as well as the propagation delay between transmitter and receiver, respectively. Of course, the signal part in (2) is impaired by w ( t ), representing a zero-mean white Gaussian noise component with variance .…”

“…In this context, some knowledge about the signal-to-noise ratio (SNR) is indispensable for a lot of scenarios; e.g., many adaptive systems [ 8 ] or powerful error correction schemes [ 9 ] necessitate this sort of information so that the link can be operated close to the Shannon bound. In this context, a non-data-aided (NDA) algorithm for SNR estimation has been discussed by the author in a recently published paper [ 10 ], i.e., no a priori knowledge about data is needed in the receiver unit for this purpose, or, in other words, payload data might be used so that the spectral efficiency does not depend on the observation length required for the estimation process. This is in striking contrast to a data-aided (DA) approach, where part of the data frame is occupied by pilot sequences [ 11 ].…”

A simple baseline for signal detection and extraction

“…Signal-to-noise ratio estimation 13,14 is part of channel parameter estimation. Signal-to-noise ratio (SNR) is a key parameter of the communication signal since it refers to the ratio of the power of the signal to the power of background noise and it determines the strength and clarity of a communication signal..…”