Concerning the power complementary limitation due to the time-reversed assumption of prototype filter in the design of traditional DFT (Discrete Fourier Transform) modulated filter banks, a time domain modified method was introduced to design the DFT filter banks from the time domain perfect reconstruction perspectives in this paper. Moreover, the designed filter banks were applied to the filter banks based multi-carrier transceivers. The time domain modified method relaxed the time-reversed assumption of prototype filter, that is, the filter banks at the receiver were conjugate transpose form of the filter banks at the transmitter. Moreover, it adopted the time domain formula of the perfect reconstruction property as the solution to design the filter banks at the receiver, which would ensure the perfect reconstruction of filter banks and avoid the power complementary limitation in the design of prototype filter at the same time. Compared to the traditional design method, the time domain modified method improves the design freedom of prototype in the filter banks, so suitable prototype filters could be obtained according to the various application environments without considering power complementary restrictions. Moreover, the time domain modified DFT filter banks based multi-carrier transceivers has a better SER (Symbol Error Ratio) performance in QPSK (Quadrature Reference Phase Shift Keying) modulation, ideal and the 3GPP TS 25.104 pedestrian multipath channel and one-tap frequency-domain equalization.

As a new intelligent spectrum sharing technology, Cognitive Radio (CR) technology could effectively improve the spectrum utilization. It allows the cognitive user to use the idle spectrum of licensed user under the premise of free interference. Because of the high sidelobe attenuation, the traditional physical layer transmission technology in cognitive radio system, that is Orthogonal Frequency Division Multiplexing (OFDM) multi-carrier modulation technology, suffers from the the interference between the adjacent subbands and the interference among licensed users and cognitive users, an alternative multi-carrier modulation technology, filter bank based multi-carrer technology, was introduced in this paper to eliminate the interferences. An indirect design method for designing the prototype filter in filter bank was proposed while formulating the filter bank as an unconstrained linear optimization problem of prototype filter.Firstly,two low-order and linear lowpass filters were designed by using the Parks-McClellan algorithm, and then the prototype filter was optimally designed through the interpolation and cascade operation. Compared to the conventional direct method, the simulation results show that the modulated filter banks designed by the proposed method in this paper present better performance in the length of filter coefficients and the alias errors.

In order to improve the poor frequency selectivity and spectral leakage of traditional Orthogonal Frequency Division Multiplexing (OFDM) multi-carrier transceiver, multi-carrier transceiver based on modified Discrete Fourier Transform (DFT) filter bank was introduced. The design problem of it was formulated as nonconstrained minimized optimization of perfect reconstruction error of modulated filter banks, and the modified window method was taken to design the prototype filter in the modulated filter banks and linear optimization was used to optimize the objective function. Compared to the traditional window method, a spline function was exploited in the transition band of ideal filter of the modified window to eliminate the Gibbs effect. The simulation results show that the designed filter bank with the proposed method gives a better performance in terms of stopband attenuation, and reconstruction error, and the resulted multicarrier transceiver a better Symbol Error Rate (SER) performance in Quadrature Phase Shift Keying (QPSK) modulation and the 3GPP TS 25.104 vehicular multipath and one-tap frequency-domain equalization.