A lower bound on the error probability for signals in white Gaussian noise

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

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On the achievable rate of bandlimited continuous-time AWGN channels with 1-bit output quantization

EURASIP Journal on Wireless Communications and Networking ◽

10.1186/s13638-021-01892-9 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sandra Bender ◽

Meik Dörpinghaus ◽

Gerhard P. Fettweis

Keyword(s):

Lower Bound ◽

Mutual Information ◽

Gaussian Noise ◽

Continuous Time ◽

Additive White Gaussian Noise ◽

White Gaussian Noise ◽

Information Rate ◽

Achievable Rate ◽

Zero Crossing ◽

Lower Bounding

AbstractWe consider a real continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. We derive an approximate lower bound on the capacity by lower-bounding the mutual information rate for input signals with exponentially distributed zero-crossing distances, sine-shaped transition waveform, and an average power constraint. The focus is on the behavior in the mid-to-high signal-to-noise ratio (SNR) regime above 10 dB. For hard bandlimited channels, the lower bound on the mutual information rate saturates with the SNR growing to infinity. For a given SNR the loss with respect to the unquantized additive white Gaussian noise channel solely depends on the ratio of channel bandwidth and the rate parameter of the exponential distribution. We complement those findings with an approximate upper bound on the mutual information rate for the specific signaling scheme. We show that both bounds are close in the SNR domain of approximately 10–20 dB.

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Multi-position signal coherent reception error probability in a channel with generalized gamma or K fading and white noise

Information and Control Systems ◽

10.31799/1684-8853-2019-1-76-88 ◽

2019 ◽

pp. 76-88 ◽

Cited By ~ 1

Author(s):

N. V. Savischenko ◽

E. V. Lebeda

Keyword(s):

Gaussian Noise ◽

Error Probability ◽

Hypergeometric Functions ◽

Communication Channel ◽

Noise Immunity ◽

Special Function ◽

Additive White Gaussian Noise ◽

Algebraic Function ◽

White Gaussian Noise ◽

Position Signal

Introduction:One of the main problems in communication theory is giving definitions to such characteristics of an information transmission system as noise immunity (error probability) and transfer rate. Their knowledge allows you to determine the transmitted information quality and quantity, respectively. The calculation of the error probability for a communications channel (for example, with fading) allows you to estimate the loss or gain in noise immunity with modems of various signal designs.Purpose:Developing a technique for calculating the probability of a bit error with coherent reception of signals in a communication channel with additive white Gaussian noise and general (non-selective in terms of frequency) fading described by gamma distribution orKdistribution (called gamma fading andKfading respectively).Results:The obtained relations allow you to calculate the reception noise immunity in arbitrary twodimensional signaling designs for a communication channel with gamma orKfading and additive white Gaussian noise. Examples are given of bit error probability calculation for phase modulation and quadrature-amplitude modulation signals. The calculation of error probability in a channel with fading for two different distribution laws was reduced to a new special function which is an integral of the product of Tricomi function and an algebraic function. This allowed us to develop a universal mathematical approach valid for both variants of fading. To calculate the new special function introduced in the article and its representation through the known functions, we used both classical hypergeometric functions and a generalized hypergeometric functions of two variables which is Kampé de Fériet function.Practical relevance:When using multi-position signal structures in new telecommunication standards, this technique allows you to obtain an estimate of their potential noise immunity, objectively comparing signal constructions and correctly choosing the best options for new modem developer.

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