| Summary: | 碩士 === 國立臺灣大學 === 電信工程學研究所 === 105 === Generalized frequency division multiplexing (GFDM) is a promising modulation scheme featuring low out-of-band (OOB) radiation, which is achieved through the use of prototype filters. However, GFDM systems are usually non-orthogonal with prototype filters commonly used in the literature, incurring in-band performance degradation in receiver mean square error (MSE) and symbol error rate (SER) compared to that achieved through orthogonal frequency division multiplexing (OFDM).
In this thesis, a new matrix-based characterization of GFDM transmitter matrices is proposed, as opposed to traditional vector-based characterization with prototype filters. The new characterization facilitates deriving properties of GFDM (transmitter) matrices, including conditions for GFDM matrices being nonsingular and unitary, respectively.
Using the new characterization, the necessary and sufficient conditions for the existence of a form of low-complexity implementation for a minimum mean square error (MMSE) receiver are derived. Such an implementation exists under multipath channels if the GFDM transmitter matrix is selected to be unitary. For cases where this implementation does not exist, a low-complexity suboptimal MMSE receiver is proposed, with its performance approximating that of an MMSE receiver.
The new characterization also enables derivations of optimal prototype filters in terms of minimizing receiver MSE. They are found to correspond to the use of unitary GFDM matrices under many scenarios. The use of such optimal filters in GFDM systems does not cause the problem of noise enhancement, thereby demonstrating the same MSE performance as OFDM.
In addition, based on the proposed matrix characterization, a filter optimization algorithm that minimizes OOB radiation while maintaining good in-band performance is developed for GFDM. Through the characteristic matrix as the optimizing variable, the filter design problem is formulated as a nonconvex problem. After some transformations, an algorithm in which two convex problems are solved iteratively is proposed to tackle the original problem. Simulation results show that under the same spectral efficiency, optimized filters perform the best in terms of both OOB radiation and SER performance, compared to OFDM and prototype filters existing in the literature.
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