Zak-Space Signal Sequence Construction for Low-Interference MIMO Radar
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Solution Overview
Problem
Existing methods for generating signals struggle to create large families of signals with optimal auto- and cross-correlation properties, limiting their application in MIMO radar and wireless communications systems, where interference and bandwidth efficiency are critical.
Innovation Solution
The use of the finite Zak transform to generate sequences with perfect or suboptimal auto- and cross-correlation properties, allowing for the design of large families of signals with minimal cross-talk and optimal bandwidth allocation by applying constraints in the Zak space and determining permutations of these sequences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If multiple signals are simultaneously generated and transmitted through a shared medium, then the system can achieve higher productivity and information capacity, but the signals interfere with each other causing loss of information
Solution Approach 1:
The patent segments the signal space by introducing orthogonal codes that divide the transmission medium into non-interfering channels. Each signal is assigned a unique orthogonal code, effectively segmenting the shared medium into multiple independent communication paths that do not interfere with each other.
Solution Approach 2:
The patent changes the correlation parameters of the signals by designing specific orthogonal code sequences with predetermined auto-correlation and cross-correlation properties. By adjusting these parameters, the system maintains high signal capacity while minimizing interference through optimized correlation characteristics.
2Reliability
If a limited number of waveforms are designed for specific applications using existing techniques, then the waveforms can be optimized for particular uses, but the system lacks adaptability to different conditions and applications
Solution Approach 1:
The patent creates a universal waveform generation system based on orthogonal codes that can be applied across multiple applications including radar, sonar, and wireless communications. The orthogonal code framework provides a multi-functional foundation that adapts to different conditions while maintaining optimized performance through its mathematical properties.
Solution Approach 2:
The patent introduces dynamic adaptability by allowing the selection and permutation of orthogonal codes based on specific application requirements. The system can dynamically adjust which orthogonal codes are used and how they are permuted to optimize performance for different conditions while maintaining the underlying orthogonal structure.
3Productivity
If signals are designed to maximize bandwidth utilization, then the system achieves higher productivity, but the cross-correlation between signals increases causing interference
Solution Approach 1:
The patent converts the potentially harmful cross-correlation between signals into a beneficial property by designing orthogonal codes with controlled cross-correlation properties. The cross-correlation, which could cause interference, is transformed into a predictable mathematical property that can be exploited for signal detection and separation, turning what was previously harmful into useful information.
Data Source
AI summary
A computer-implemented method and system for generating large families of sequences with desirable properties for many applications, including communications and radar applications, applies constraints to a sequence in the Zak space, modulates the constrained sequence in the Zak space, and determines permutations of the modulated sequence in the Zak space. The constraints are associated with predetermined properties, including predetermined autocorrelation and cross-correlation properties. Other embodiments of the computer-implemented method and system transform an input sequence into a transformed sequence using the finite Zak transform and determine at least one other different sequence based on the transformed sequence. The at least one other different sequence can be determined by collecting a plurality of sequences that are finitely supported on an algebraic line in the Zak space and modulating and/or determining permutations of some or all of the sequences.