Far-Field Waveform Optimization for Multi-Beam Digital Arrays

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Solution Overview

Problem

Existing methods for simultaneously transmitting radar and communication signals using frequency-modulated waveforms are impractical due to the rapidly changing nature of the signals, requiring new waveforms for each pulse and lacking efficient real-world implementations.

Innovation Solution

A relaxed optimization problem is formulated to determine sets of waveforms suitable for simultaneous transmission of radar and communication signals, incorporating a constant amplitude constraint to minimize computational complexity and accommodate rapid signal changes, using a Lagrange dual problem for optimization.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If existing FFRED algorithms are used to determine waveforms for simultaneous radar and communication transmission, then the system can transmit multiple signals in different spatial directions, but the computational complexity increases significantly and the waveforms cannot be determined rapidly enough to accommodate pulse-to-pulse signal changes

Engineering Contradiction:

Improveability to transmit multiple signals simultaneously in different directionsVSAvoidcomputational complexity of waveform determination

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent transforms the complex waveform optimization problem into a simpler parameter estimation problem by changing the approach from direct waveform synthesis to parameter-based solution. The relaxed optimization problem reformulates the constraints and objective function to enable rapid computation while maintaining the essential capability of simultaneous multi-directional signal transmission.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent uses the Lagrange dual problem as a computational copy or representation of the original optimization problem. By solving the dual problem instead of the primal waveform optimization problem, the system obtains equivalent information about the optimal waveforms with significantly reduced computational complexity, enabling real-time pulse-to-pulse adaptations.

Inventive Principle:

Principle #26Copying

2Loss of energy

If the optimization problem is solved to find constant amplitude waveforms for simultaneous transmission, then power efficiency is improved, but the computational time required increases

Engineering Contradiction:

Improvepower efficiency of transmitted waveformsVSAvoidcomputational time for waveform determination

Core Design Contradiction:

Loss of energyVSLoss of time

Solution Approach 1:

The relaxed optimization problem incorporates feedback mechanisms through the Lagrange dual formulation, where the solution iteratively refines the waveform parameters based on the constraints and objective function. This feedback approach enables the system to converge to near-optimal constant amplitude waveforms that minimize energy loss while maintaining computational feasibility for real-time applications.

Inventive Principle:

Principle #23Feedback

3Adaptability or versatility

If new waveforms are determined for each pulse to accommodate signal changes, then the system adapts to pulse-to-pulse variations, but the computational burden increases and real-time implementation becomes impractical

Engineering Contradiction:

Improvepulse-to-pulse signal adaptation capabilityVSAvoidrate of waveform determination

Core Design Contradiction:

Adaptability or versatilityVSProductivity

Solution Approach 1:

The patent performs preliminary computational actions by pre-calculating and storing the Lagrange dual problem solution structure, which can then be rapidly applied to each pulse without re-solving the entire optimization problem from scratch. This preliminary preparation enables the system to quickly adapt waveforms for each pulse while maintaining low computational burden through efficient reuse of pre-computed information.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS20250341628A1Physical waveform optimization for multiple beam multifunction digital arrays

Publication Date: 2025.11.06 UNIVERSITY OF KANSAS

AI summary

Systems and methods provide an approach to implementing Far-Field Radiated Emission Design techniques suitable for simultaneous transmission of radar and communication signals. A set of signals for transmission and a transmission direction for each signal of the set of signals may be determined. The set of signals includes at least a first signal associated with a first transmission direction and a second signal associated with a second transmission direction that is different from the first direction. An optimization problem is configured based on characteristics of an antenna array and the set of signals and then solved to identify a set of waveforms suitable for transmitting the signals. The set of waveforms may include at least two waveforms, each of each of which is configured for transmission by a different antenna element of the antenna array. The determined waveforms may be coherent in the far-field and suitable for power efficient transmission.