Filter Bank Prototype Coefficient Calculation
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Solution Overview
Problem
Current methods for determining the coefficients of prototype filters in filter bank-based multicarrier modulation systems, particularly for oversampled OFDM and OFDM/OQAM, are computationally expensive and limited in scalability, especially when dealing with a large number of sub-carriers or subbands, and fail to provide efficient spectrum utilization and time-frequency localization.
Innovation Solution
A novel method using a compact polynomial representation to express the angle parameters of the prototype filter, allowing for efficient calculation of filter coefficients, which reduces optimization time and enables quick adaptation to changes in system parameters, such as the number of carriers or subbands, while ensuring perfect reconstruction conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current methods are used to determine filter coefficients, then perfect reconstruction conditions can be satisfied, but the computational complexity and optimization time become excessive
Solution Approach 1:
The patent transforms the optimization problem from directly determining filter coefficients to determining angle parameters that define the filter structure. This parameter transformation reduces the computational complexity while maintaining the perfect reconstruction property, as the angle parameters provide a more efficient degrees of freedom for optimization.
Solution Approach 2:
The patent segments the filter design into two parts: the structural framework defined by angle parameters and the specific coefficient values derived from these angles. This segmentation allows independent optimization of the angular parameters without requiring full coefficient optimization, significantly reducing computational burden.
2Quantity of substance
If the number of sub-carriers or subbands increases, then the system can handle more data, but the computational complexity and optimization time increase significantly
Solution Approach 1:
By changing the optimization variables from filter coefficients to angle parameters, the patent reduces the dimensionality of the optimization problem. This allows the system to scale to larger numbers of sub-carriers and subbands without proportionally increasing computational complexity, as the angle parameters provide a compressed representation of the filter design space.
3Ease of manufacture
If conventional OFDM modulation is used, then the system is simple to implement, but spectrum efficiency and time-frequency localization are poor
Solution Approach 1:
The patent introduces dynamic filter banks with adjustable angle parameters that can be optimized for specific time-frequency localization requirements. This allows the system to adapt between simplicity and performance based on the application needs, providing a flexible middle ground between conventional OFDM and highly complex optimized systems.
Data Source
AI summary
A method is provided for determining at least one filter of a filter bank in a transmission or coding system, on the basis of a prototype filter p. The method includes determining coefficients p[k] of the prototype filter p, of length L equal to N, from Δ angle parameters θi, for 0≦i≦Δ−1, expressed on the basis of a polynomial function ƒ(x), also referred to as a compact representation, such that:f(x)=π4+t∑k=0d-1βkT2k(t);t=2x-1.