arXiv subjects
Publications and source records attributed to Karl-Ludwig Besser.
In the first part of this two-part letter, we introduced methods to study the impact of dependency on the expected value of functions of two random variables. In this second part, we present tools to derive worst- and best-case bounds on the outage probability of multi-user communication systems, including multiple access channels, wiretap channels, and reconfigurable intelligent surface-assisted channels.
Statistically independent or positively correlated fading models are usually applied to compute the average performance of wireless communications. However, there exist scenarios with negative dependency and it is therefore of interest how different performance metrics behave for different general dependency structures of the channels. Especially best-case and worst-case bounds are practically relevant as a system design guideline. In this two-part letter, we present methods and tools from dependency modeling which can be applied to analyze and design multi-user communications systems exploiting and creating dependencies of the effective fading channels. The first part focuses on fast fading with average performance metrics, while the second part considers slow fading with outage performance metrics.
The amount of sensitive data, which is transmitted wirelessly will increase with future technologies. This raises many questions about secure data transmission. Besides cryptography, information-theoretic security gained increasing attention over the recent years. Among others, it deals with the problem of secure data transmission on the physical layer to a legitimate receiver (Bob) in the presence of an eavesdropper (Eve). In this work, we investigate upper and lower bounds on the secrecy outage probability for slowly-fading wiretap channels with an arbitrary dependency structure between the fading channels to Bob and Eve. Both cases of absence of channel-state information at the transmitter (CSI-T) and availability of CSI-T of only the main channel to the legitimate receiver are considered. Furthermore, we derive explicit expressions for the upper and lower bounds for Rayleigh fading and compare them to the case of independent channels. The joint distribution of the legitimate and eavesdropper channels has a tremendous impact on the achievable secrecy outage probability. The bounds enable developing guaranteed secrecy schemes by only measuring the marginal channel distributions.
Unreliable fading wireless channels are the main challenge for strict performance guarantees in mobile communications. Diversity schemes including massive number of antennas, huge spectrum bands and multi-connectivity links are applied to improve the outage performance. The success of these approaches relies heavily on the joint distribution of the underlying fading channels. In this work, we consider the $\varepsilon$-outage capacity of slowly fading wireless diversity channels and provide lower and upper bounds for fixed marginal distributions of the individual channels. This answers the question about the best and worst case outage probability achievable over $n$ fading channels with a given distribution, e.g., Rayleigh fading, but not necessarily statistically independent. Interestingly, the best-case joint distribution enables achieving a zero-outage capacity greater than zero without channel state information at the transmitter for $n \geq 2$. Furthermore, the results are applied to characterize the worst- and best-case joint distribution for zero-outage capacity with perfect channel state information everywhere. All results are specialized to Rayleigh fading and compared to the standard assumption of independent and identically distributed fading component channels. The results show a significant impact of the joint distribution and the gap between worst- and best-case can be arbitrarily large.