Iterative Design Methods for Filter Banks and Transceivers

Multirate filter banks have recently drawn a lot of attention. Filter banks can decompose signals into separate frequency subbands. Separate operations can be applied to those subband signals to obtain very good results. The theory and design methods of uniform filter bank have been well studied and developed. In many applications, however, uniform filter banks do not provide appropriate frequency decomposition, and it is sometimes more desirable to decompose a signal into nonuniform frequency subbands. System which are closely related to filter banks are filter bank transceivers. It is well known that when transmission channels are one tap channels, we can obtain transceivers that achieve ISI-free by interchanging the analysis with the synthesis parts of perfect reconstruction (PR) maximally decimated filter banks, even in the case of nonuniform subbands. For multipath channels, however, these transceivers are no longer ISI-free. In the first part of this thesis, we propose a direct and simple design method suitable for designing any filter bank (uniform or nonuniform) with a set of sampling factors that can achieve PR. Also, we show that we can easily incorporate the method with some constraints, such as linear phase, frequency constraints, paraunitariness, the IFIR structure, and low delay condition. In addition, we generalize some necessary or sufficient conditions developed in the past for the case of integer decimation factors to the case of rational sampling factors. In many applications, some statistical information of the input signals may be known. If the information is incorporated into the design of filter banks, we can often obtain better results such as smaller reconstruction error or better frequency response. We modify the proposed filter bank design method to take into consideration the input statistics as well as the quatization noise effect. In the second part of this thesis, we consider generalized design methods for filter bank transceivers, which can be either uniform or nonuniform, to combat against multipath channels. Furthermore, the proposed methods can be modified by adding frequency constraints to improve the frequency characteristics of the filters.1 Introduction 1 2 2-Channel Nonuniform Filter Banks 7 2.1 Traditional 2-Channel Nonunifrom Filter Bank Scheme 8 2.2 New 2-Channel Nonuniform Filter Bank Scheme 10 2.3 Time Domain Design Method for 2-Channel Nonuniform PR Filter Banks 13 2.3.1 Time Domain Representation of LPTV Systems 13 2.3.2 PR Condition for 2-Channel Nonuniform Filter Banks 15 2.3.3 Design Procedure 17 2.4 Design with Constraints 20 2.4.1 Frequency Constraints 20 2.4.2 Linear Phase 22 2.4.3 Low Delay 25 2.5 Quadrature Mirror Filter Banks 26 2.6 Design with the IFIR Structure 27 2.7 Design Examples 32 3 M-Channel Filter Banks 51 3.1 M-Channel Nonuniform Filter Banks 52 3.1.1 Conditions for PR Nonuniform Filter Banks 53 3.1.2 Generalized Time Domain Design Method 57 3.2 M-Channel Cosine Modulated Filter Banks 61 3.3 Paraunitary Filter Banks 62 3.4 Design Examples 63 4 Designing Filter Banks Based on Statistics 73 4.1 Nonuniform Filter Banks 74 4.1.1 Time Domain Formulation 74 4.1.2 Iterative Design Algorithm and Discussion 82 4.2 Uniform Filter Banks 82 4.3 Design Examples 90 5 Filter Bank Transceivers 103 5.1 Nonuniform Filter Bank Transceivers with Integer Decimation Factors 104 5.1.1 Introduction to Nonuniform Filter Bank Transceivers 104 5.1.2 ISI-Free Conditions 105 5.1.3 SIR Optimized for Known Channels 108 5.1.4 SIR Optimized for Multipath Fading Channels 111 5.1.5 Iterative Design Algorithm 113 5.1.6 Design with Frequency Constraints 114 5.2 Nonuniform Filter Bank Transceivers with Rational Sampling Factors 116 5.2.1 Direct Method 116 5.2.2 Indirect Method 122 5.2.3 Comparison between the Direct and Indirect Methods 125 5.3 DFT Modulated Filter Bank Transceivers 125 5.3.1 Introduction to DFT Modulation Filter Bank Transceivers 125 5.3.2 SIR Optimized for Known Channels 130 5.3.3 SIR Optimized Transceivers for Multipath Fading Channels 131 5.3.4 Iterative Design Algorithm 133 5.3.5 Design with Frequency Constraints 133 5.4 Design Examples 134 6 Conclusion 143 A Examples of the Matrices 145 Bibliography 14