Understanding Autocorrelation and Cross-Correlation in Communication Systems

In the context of wireless communication systems, the terms "average achievable rate" and "mismatch rate" are used to measure an algorithm’s ability to resist errors caused by noise. However, these metrics are insufficient for assessing the impact of deterministic errors, which arise when an algorithm cannot cover all spaces.
To address this limitation, the authors propose using performance indicators that distinguish between random and deterministic errors. They argue that relying solely on average achievable rate and mismatch rate can interfere with the practical use of algorithms in near-field problems, as they do not account for the codebook’s ability to cover the user’s area.
The authors then delve into a detailed explanation of the autocorrelation and cross-correlation functions, which are essential in assessing the performance of wireless communication systems. They clarify that these functions are related but distinct concepts, with the former measuring the amplitude of a signal as it is reflected back to the transmitter, while the latter measures the phase shift between the original and delayed signals.
The authors also explore the relationship between these functions and the modulus of the autocorrelation function, which provides a more comprehensive understanding of an algorithm’s performance. They note that this formula can be transformed into a discrete form for practical applications, allowing for easy implementation in wireless communication systems.
Throughout the article, the authors aim to demystify complex concepts by using everyday language and engaging metaphors or analogies. For instance, they compare the autocorrelation function to a mirror reflecting light, while the cross-correlation function is likened to a ruler measuring the distance between two points.
In summary, the article provides a detailed analysis of the limitations of average achievable rate and mismatch rate in assessing an algorithm’s performance in wireless communication systems. The authors propose using performance indicators that distinguish between random and deterministic errors, and they offer a thorough explanation of the autocorrelation and cross-correlation functions, which are critical in evaluating an algorithm’s ability to resist errors caused by noise and other factors. By leveraging relatable analogies and clear explanations, the authors aim to make this complex subject matter more accessible to readers.