Digital Receiver Signal Detection Using Cost Function Minimization
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Solution Overview
Problem
Existing digital communication systems face challenges in accurately determining the optimal threshold for signal detection, leading to poor performance due to uncertainties in signal and noise probability density, affecting both detection and frame start time estimation.
Innovation Solution
A method for controlling digital communication receivers that eliminates the need to set a threshold by calculating a first cost function as a linear combination of correlation and mean quadratic error between vectors, using the sign of the result to determine signal presence and estimate the frame beginning, specifically adapted for periodic preamble communications like 802.11.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If an empirical threshold is set for signal detection, then the receiver can operate with a simple detection mechanism, but the detection accuracy deteriorates due to uncertainty in signal and noise probability density
Solution Approach 1:
The patent changes the detection parameter from a fixed empirical threshold to a dynamic threshold derived from the cost function minimum. The threshold is no longer a static value K set empirically, but rather a dynamic value determined by minimizing the cost function J(θ) = E[|s(n) - e^jθ v(n-L)|^2], which adapts to the actual signal and noise conditions in the channel.
Solution Approach 2:
The system performs self-calibration by using the received signal itself to determine the optimal threshold through cost function minimization. The receiver automatically adjusts its detection threshold based on the statistical properties of the received signal, eliminating the need for external empirical threshold setting or prior knowledge of signal and noise distributions.
2Device complexity
If a fixed empirical threshold is used, then the detection mechanism is simple to implement, but the frame start time estimation becomes inaccurate due to false detections or missed detections
Solution Approach 1:
The patent changes the threshold parameter from a fixed empirical value to a dynamic value determined by cost function minimization. This dynamic threshold adapts to varying channel conditions, preventing false detections when noise is high and ensuring detection when signal is weak, thereby improving frame start time estimation accuracy.
Solution Approach 2:
The system implements feedback by using the cost function J(θ) to continuously evaluate detection performance and adjust the threshold accordingly. The minimum of the cost function provides feedback on the optimal threshold setting, which is then used to improve subsequent detections and frame start time estimations.
3Reliability
If the threshold is set too low to ensure signal detection, then detection sensitivity improves, but false alarm rate increases
Solution Approach 1:
The patent transforms the threshold from a static low value to a dynamic value determined by cost function minimization. The optimal threshold θ* = argmin_θ E[|s(n) - e^jθ v(n-L)|^2] automatically balances detection sensitivity and false alarm rate by finding the point that minimizes the expected squared error between the signal and the rotated reference vector.
Solution Approach 2:
The patent replaces the mechanical threshold setting process (manual or empirical selection of a fixed value) with an analytical optimization process based on cost function minimization. This substitution allows the system to automatically determine the optimal threshold that balances sensitivity and false alarm rate without manual intervention.
4Object-generated harmful factors
If the threshold is set too high to reduce false alarms, then false detection rate decreases, but signal miss detection rate increases
Solution Approach 1:
The patent changes the threshold from a static high value to a dynamic value derived from cost function minimization. The optimal threshold automatically adapts to channel conditions, ensuring high enough sensitivity to detect weak signals while maintaining low enough false alarm rates, thereby resolving the trade-off between these two opposing requirements.
Data Source
AI summary
Detection method and device for a receiver in a digital communication system designed to process a frame comprising a periodic sub-set of length n, said method comprising the following steps:—determining a first vector u having a length n;—determining a second shifted vector v;—calculating a correlation function between said first and second vectors;—calculating a quadratic error function between said first and second vectors;—calculating a first cost function that is a linear combination of both preceding functions and, according to the sign of the result,—calculating a second cost function of frame beginning estimate; and—starting the communication system receiver.