OFDM systems design using harmonic wavelets

Orthogonal frequency-division multiplexing (OFDM) is a popular multi-carrier technique used in many digital communication systems such as wireless fidelity (Wi-Fi), long term evolution (LTE) and power line communication systems. It can be designed using fast Fourier transform (FFT) or wavelet transform (WT). The major drawback in using WT is that it is computationally inefficient. In this study, we introduce a simple and computationally efficient WT, harmonic wavelet transform, for OFDM signal processing. The new WT uses the orthogonal basis functions of conventional FFT-OFDM except that it involves translation and dilation of the input signal; the new wavelets is referred to as harmonic wavelets (HW). When compared with pilot-assisted OFDM system in terms of reduction in the peak-to-average power ratio, the results show that HW-OFDM outperforms FFT-OFDM by 3 dB at 10−4 CCDF (complementary cumulative distribution function). Over Rayleigh fading channel with additive white Gaussian noise (AWGN), the bit error ratio of both FFT-OFDM and HW-OFDM perfectly matched, showing that the proposed HW-OFDM is better in terms of peak-to-average power ratio reduction

Compactly Supported Wavelets Derived From Legendre Polynomials: Spherical Harmonic Wavelets

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated with Legendre multiresolution analysis is a linear phase finite impulse response filter (FIR).Comment: 6 pages, 6 figures, 1 table In: Computational Methods in Circuits and Systems Applications, WSEAS press, pp.211-215, 2003. ISBN: 960-8052-88-

Grassmannian Frames with Applications to Coding and Communication

For a given class ${\cal F}$ of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation $|< f_k,f_l >|$ among all frames $\{f_k\}_{k \in {\cal I}} \in {\cal F}$. We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These bounds yield a simple condition under which Grassmannian frames coincide with uniform tight frames. We exploit connections to graph theory, equiangular line sets, and coding theory in order to derive explicit constructions of Grassmannian frames. Our findings extend recent results on uniform tight frames. We then introduce infinite-dimensional Grassmannian frames and analyze their connection to uniform tight frames for frames which are generated by group-like unitary systems. We derive an example of a Grassmannian Gabor frame by using connections to sphere packing theory. Finally we discuss the application of Grassmannian frames to wireless communication and to multiple description coding.Comment: Submitted in June 2002 to Appl. Comp. Harm. Ana

A Unique Wavelet-based Multicarrier System with and without MIMO over Multipath Channels with AWGN

yesRecent studies suggest that multicarrier systems using wavelets outperform conventional OFDM systems using the FFT, in that they have well-contained side lobes, improved spectral efficiency and BER performance, and they do not require a cyclic prefix. Here we study the wavelet packet and discrete wavelet transforms, comparing the BER performance of wavelet transform-based multicarrier systems and Fourier based OFDM systems, for multipath Rayleigh channels with AWGN. In the proposed system zero-forcing channel estimation in the frequency domain has been used. Results confirm that discrete wavelet-based systems using Daubechies wavelets outperform both wavelet packet transform- based systems and FFT-OFDM systems in terms of BER. Finally, Alamouti coding and maximal ratio combining schemes were employed in MIMO environments, where results show that the effects of multipath fading were greatly reduced by the antenna diversity

Pseudodifferential operators and Banach algebras in mobile communications

AbstractWe study linear time-varying operators arising in mobile communication using methods from time–frequency analysis. We show that a wireless transmission channel can be modeled as pseudodifferential operator Hσ with symbol σ in FLw1 or in the modulation space Mw∞,1 (also known as weighted Sjöstrand class). It is then demonstrated that Gabor Riesz bases {φm,n} for subspaces of L2(R) approximately diagonalize such pseudodifferential operators in the sense that the associated matrix [〈Hσφm′,n′,φm,n〉]m,n,m′,n′ belongs to a Wiener-type Banach algebra with exponentially fast off-diagonal decay. We indicate how our results can be utilized to construct numerically efficient equalizers for multicarrier communication systems in a mobile environment

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

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

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior