PAPR reduction in OFDM communications with generalized discrete Fourier transform

The main advantage of Generalized Discrete Fourier Transform (GDFT) is its ability to design a wide selection of constant modulus orthogonal code sets, based on the desired performance metrics mimicking the engineering specs of interest. One of the main drawbacks of Orthogonal Frequency Division Multiplexing (OFDM) systems is the high Peak to Average Power Ratio (PAPR) value which is directly related to power consumption of the system. Discrete Fourier Transform (DFT) spread OFDM technology, also known as Single Carrier Frequency Division Multiple Access (SCFDMA), which has a lower PAPR value, is used for uplink channel. In this thesis, the PAPR of DFT spread OFDM was further decreased by using a GDFT concept. The performance improvements of GDFT based PAPR reduction for various SCFDMA communications scenarios were evaluated by simulations. Performance simulation results showed that PAPR efficiency of SCFDMA systems for Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK) and 16 Quadrature Amplitude Modulation (16-QAM), digital modulation techniques are increased

Generalized discrete fourier transform based minimization of PAPR in OFDM systems

Orthogonal frequency division multiplexing OFDM is a preferred technique in digital communication systems due to its benefits of achieving high bit rates and its ability to resist multipath effect over fading channels. However, high peak to average power PAPR ratio of the OFDM transmitted signal is a main drawback in OFDM systems. In this paper, the nonlinear phase from the theory of generalized discrete Fourier transform (GDFT) is used to improve the performance of the partial transmit sequence (PTS) scheme which is one of the techniques used to reduce PAPR. This technique divides the input OFDM block into a number of sub-blocks. IFFT is taken for each sub-block, then the output phase is rotated by coefficients to produces minimum PAPR. Simulation results show that modifying the phase of the OFDM before applying the technique reduces the number of the sub-blocks for the same amount of PAPR reduction

Generalized discrete Fourier transform with non-linear phase : theory and design

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in various engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. Among these popular transforms, DFT is a linear phase transform and widely used in multicarrier communications due to its performance and fast algorithms. In this thesis, a theoretical framework for Generalized DFT (GDFT) with nonlinear phase exploiting the phase space is developed. It is shown that GDFT offers sizable correlation improvements over DFT, Walsh, and Gold codes. Brute force search algorithm is employed to obtain orthogonal GDFT code sets with improved correlations. Design examples and simulation results on several channel types presented in the thesis show that the proposed GDFT codes, with better auto and cross-correlation properties than DFT, lead to better bit-error-rate performance in all multi-carrier and multi-user communications scenarios investigated. It is also highlighted how known constant modulus code families such as Walsh, Walsh-like and other codes are special solutions of the GDFT framework. In addition to theoretical framework, practical design methods with computationally efficient implementations of GDFT as enhancements to DFT are presented in the thesis. The main advantage of the proposed method is its ability to design a wide selection of constant modulus orthogonal code sets based on the desired performance metrics mimicking the engineering .specs of interest. Orthogonal Frequency Division Multiplexing (OFDM) is a leading candidate to be adopted for high speed 4G wireless communications standards due to its high spectral efficiency, strong resistance to multipath fading and ease of implementation with Fast Fourier Transform (FFT) algorithms. However, the main disadvantage of an OFDM based communications technique is of its high PAPR at the RF stage of a transmitter. PAPR dominates the power (battery) efficiency of the radio transceiver. Among the PAPR reduction methods proposed in the literature, Selected Mapping (SLM) method has been successfully used in OFDM communications. In this thesis, an SLM method employing GDFT with closed form phase functions rather than fixed DFT for PAPR reduction is introduced. The performance improvements of GDFT based SLM PAPR reduction for various OFDM communications scenarios including the WiMAX standard based system are evaluated by simulations. Moreover, an efficient implementation of GDFT based SLM method reducing computational cost of multiple transform operations is forwarded. Performance simulation results show that power efficiency of non-linear RF amplifier in an OFDM system employing proposed method significantly improved

On quasi-twisted codes over finite fields

AbstractIn coding theory, quasi-twisted (QT) codes form an important class of codes which has been extensively studied. We decompose a QT code to a direct sum of component codes – linear codes over rings. Furthermore, given the decomposition of a QT code, we can describe the decomposition of its dual code. We also use the generalized discrete Fourier transform to give the inverse formula for both the nonrepeated-root and repeated-root cases. Then we produce a formula which can be used to construct a QT code given the component codes

A new algorithm for fast generalized DFTs

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here $\omega$ is the exponent of matrix multiplication, so the exponent $\omega/2$ is optimal if $\omega = 2$. Previously, "exponent one" algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known (even under the assumption $\omega = 2$) for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for $SL_2(F_q)$ had exponent $4/3$ despite being the focus of significant effort. We unconditionally achieve exponent at most $1.19$ for this group, and exponent one if $\omega = 2$. Our algorithm also yields an improved exponent for computing the generalized DFT over general finite groups $G$, which beats the longstanding previous best upper bound, for any $\omega$. In particular, assuming $\omega = 2$, we achieve exponent $\sqrt{2}$, while the previous best was $3/2$

Generalized discrete Fourier transform on the base of Lagrange and Hermite interpolation formulas

The article offers several generalizations of Discrete Fourier Transfor

Fast Matrix Multiplication via Group Actions

Recent work has shown that fast matrix multiplication algorithms can be constructed by embedding the two input matrices into a group algebra, applying a generalized discrete Fourier transform, and performing the multiplication in the Fourier basis. Developing an embedding that yields a matrix multiplication algorithm with running time faster than naive matrix multiplication leads to interesting combinatorial problems in group theory. The crux of such an embedding, after a group G has been chosen, lies in finding a triple of subsets of G that satisfy a certain algebraic relation. I show how the process of finding such subsets can in some cases be greatly simplified by considering the action of the group G on an appropriate set X. In particular, I focus on groups acting on regularly branching trees

Subnanometer Translation of Microelectromechanical Systems Measured by Discrete Fourier Analysis of CCD Images

Abstract—In-plane linear displacements of microelectromechanical systems are measured with subnanometer accuracy by observing the periodic micropatterns with a charge-coupled device camera attached to an optical microscope. The translation of the microstructure is retrieved from the video by phase-shift computation using discrete Fourier transform analysis. This approach is validated through measurements on silicon devices featuring steep-sided periodic microstructures. The results are consistent with the electrical readout of a bulk micromachined capacitive sensor, demonstrating the suitability of this technique for both calibration and sensing. Using a vibration isolation table, a standard deviation of σ = 0.13 nm could be achieved, enabling a measurement resolution of 0.5 nm (4σ) and a subpixel resolution better than 1/100 pixel. [2010-0170