Performance Degradation in Cross-Eye Jamming Due to Amplitude/Phase Instability between Jammer Antennas

Cross-eye gain in cross-eye jamming systems is highly dependent on amplitude ratio and the phase difference between jammer antennas. It is well known that cross-eye jamming is most effective for the amplitude ratio of unity and phase difference of 180 degrees. It is assumed that the instabilities in the amplitude ratio and phase difference can be modeled as zero-mean Gaussian random variables. In this paper, we not only quantitatively analyze the effect of amplitude ratio instability and phase difference instability on performance degradation in terms of reduction in cross-eye gain but also proceed with analytical performance analysis based on the first order and second-order Taylor expansion.

Entanglement and impropriety

The relationship between quantum entanglement and classical impropriety is considered in the context of multi-modal squeezed states of light. Replacing operators with complex Gaussian random variables in the Bogoliubov transformations for squeezed states, we find that the resulting transformed variables are not only correlated but also improper. A simple threshold exceedance model of photon detection is considered and used to demonstrate how the behavior of improper Gaussian random variables can mimic that of entangled photon pairs when coincidence post-selection is performed.

On the strong law of large numbers for ϕ-sub-Gaussian random variables

UDC 517.9 For let if and if . For a random variable ξ let denote ; is a norm in a space - subgaussian random variables. We prove that if for a sequence there exist positive constants and such that for every natural number the following inequality holds then converges almost surely to zero as . This result is a generalization of the strong law of large numbers for independent sub-Gaussian random variables [see R. L. Taylor, T.-C. Hu, <em>Sub-Gaussian techniques in proving strong laws of large numbers</em>, Amer. Math. Monthly, <strong>94</strong>, 295 – 299 (1987)] to the case of dependent -sub-Gaussian random variables.

Fisher Information and Uncertainty Principle for Skew-Gaussian Random Variables

Fisher information is a measure to quantify information and estimate system-defining parameters. The scaling and uncertainty properties of this measure, linked with Shannon entropy, are useful to characterize signals through the Fisher–Shannon plane. In addition, several non-gaussian distributions have been exemplified, given that assuming gaussianity in evolving systems is unrealistic, and the derivation of distributions that addressed asymmetry and heavy–tails is more suitable. The latter has motivated studying Fisher information and the uncertainty principle for skew-gaussian random variables for this paper. We describe the skew-gaussian distribution effect on uncertainty principle, from which the Fisher information, the Shannon entropy power, and the Fisher divergence are derived. Results indicate that flexibility of skew-gaussian distribution with a shape parameter allows deriving explicit expressions of these measures and define a new Fisher–Shannon information plane. Performance of the proposed methodology is illustrated by numerical results and applications to condition factor time series.

Digital Link—B

Chapter 7 explained the detection and hypothesis testing problems, Huffman codes and the situation where errors are independent and Gaussian. In this chapter, we prove the optimality of the Huffman code in Sect. 8.1 and the Neyman–Pearson Theorem in Sect. 8.2. Section 8.3 discusses the theory of jointly Gaussian random variables that is used to analyze the modulation schemes of Sect. 7.5 . Section 8.4 uses the results on jointly Gaussian random variables to explain hypothesis tests that arise when analyzing data. That section discusses the chi-squared test and the F-test. Section 8.5 is devoted to the LDPC codes that are widely used in high-speed communication links. These codes augment a group of bits to be transmitted over a noisy channel with additional bits computed from those in the group. When it receives the bits, when the augmented bits are not consistent, the receiver attempts to determine the bits that are most likely to have been corrupted by noise.