Approximation of dual Gabor frames, window decay, and wireless communications

We consider three problems for Gabor frames that have recently received much attention. The first problem concerns the approximation of dual Gabor frames in $L_2(R)$ by finite-dimensional methods. Utilizing Wexler-Raz type duality relations we derive a method to approximate the dual Gabor frame, that is much simpler than previously proposed techniques. Furthermore it enables us to give estimates for the approximation rate when the dimension of the finite model approaches infinity. The second problem concerns the relation between the decay of the window function $g$ and its dual $\gamma$. Based on results on commutative Banach algebras and Laurent operators we derive a general condition under which the dual $\gamma$ inherits the decay properties of $g$. The third problem concerns the design of pulse shapes for orthogonal frequency division multiplex (OFDM) systems for time- and frequency dispersive channels. In particular, we provide a theoretical foundation for a recently proposed algorithm to construct orthogonal transmission functions that are well localized in the time-frequency plane

Unified Theory for Biorthogonal Modulated Filter Banks

Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

Adaptive 2×2 MIMO employed Wavelet-OFDM-Radio over Fibre Transmission

Due to high peak-to-average-power ratio (PAPR) and low spectral-efficiency, the conventional Fast Fourier Transform based orthogonal frequency division multiplexing (OFDM) is losing its place to the other multicarrier modulation schemes. Alternatively, the wavelet treated multiple-input multiple-output (MIMO)-OFDM is gaining its popularity in realization of futuristic 5G networks due to proffering high spectral-efficiency, low-cost and low phase-noise. Subsequently, this work demonstrates a RF transmission system in S-band employing \times 2$MIMO-OFDM using orthogonal- and biorthogonal-wavelets with diverse phase shift keying modulation (PSK) schemes. Among the available MIMO configurations, the authors implement spatial diversity as it promises good reliability in noisy links [11]. However, the distribution of Wavelet-OFDM (W-OFDM) signals over a radio over fibre (RoF) link is critically affected by the optical sub-system non-linearity. So, the simplest \times 2$ Alamouti's space-time block code (STBC) is implemented in this work to overcome this non-linearity and to realize a less-complex detection. The work is further extended to realize an adaptive MIMO-RoF system employing W-OFDM scheme to adjust itself to a suitable available phase shift keying strategy as per the link-situation to retain an optimal balance of link-quality and spectral-efficiency

A family of spread-sequences for CDMA system in a multipath fading channel

A new class of orthogonal code-division multiple access (CDMA) system is developed. The key characteristic of the system is that the data symbols are spreaded by a spread-sequence that is longer than the period of the symbol and hence overlapped with the neighboring symbols. Using this approach, temporal diversity is incorporated with other diversities. Due to the temporal diversity, the proposed CDMA system performs well in a fading environment. In this paper, a method for designing such a spread-sequence using filter bank theory is presented. The length of the spread-sequence could be varied according to the requirement. Simulation results show that the proposed spread-sequence based system yields lower BER than the conventional Gold codes based DS/CDMA system.published_or_final_versio

“Multicarrier Modulation for Wireless Communication using Wavelet Packets

Success of OFDM has proved that Multi carrier modulation is an efficient solution for wireless communications. Wavelet Packet Modulation (WPM) is a new type of modulation for transmission of multicarrier signal on wireless channel that uses orthogonal wavelet bases other than sine functions. Though this modulation is over all similar to that of OFDM, it provides interesting additional features. In this thesis, a detailed study is given on Wavelets and WPM and the BER performance comparison between the OFDM systems and WPM systems and equalization techniques are analysed. The analysis is done for different types of wavelet generating families, various number of modulations QAM constellation points (16 to 64), and simulated over AWGN channel, and other Multipath fading channels

A Novel Method for Designing M-Band Linear-Phase Perfrect-Reconstruction filter Banks

This paper studies the design of M-channel perfect-reconstruction (PR) linear-phase (LP) filter banks (FBs) with M=2k using a tree-structured FB. It is based on a observation of Fliege(1995) that the length of the analysis filters is decreased by a factor of two when the depth of the tree is increased by one, while its transition bandwidth is increased by the same factor. A lattice-based 2-channel LP FB is chosen because the frequency responses of the lowpass and highpass analysis (synthesis) filters can be designed to be closely symmetric to the other around π/2. By properly selecting the filter length, transition bandwidth. and stopband attenuation of the 2-channel PR LP FBs at each level of the tree structure, it is possible to design uniform PR LP FB with excellent frequency characteristic and much lower system delay.published_or_final_versio