Other than the conventional fast Fourier transform (FFT) for multicarrier modulation, a new approach for multicarrier modulation (MCM) has been known. Meanwhile, multicarrier modulation involves dividing the broadband channel into many orthogonal but overlapping narrowband carriers. In an OFDM modulation based multicarrier system using the FFT, a cyclic prefix (CP) is inserted after each symbol...

An Orthogonal Frequency Division Multiplexing (OFDM) scheme offers high spectral efficiency and better resistance to fading environments. In OFDM the data is modulated using multiple numbers of sub-carriers that are orthogonal to each other because of which the problems associated with other modulation schemes such as Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) are redu...

This paper presents a new approach based on multicarrier modulation (MCM) with OFDM, to accomplish the goals of 4G. MCM [1] is a form of multicarrier system and a derivative of frequency-division multiplexing. MCM is a baseband process that uses parallel equal bandwidth sub channels to transmit information. Normally implemented with Fast Fourier transform (FFT) techniques, MCM's advantages incl...

In this paper we will discuss the version of the Fourier analysis and pseudodifferential operators on the torus. Using the toroidal Fourier transform we will show several simplifications of the standard theory. We will also discuss the corresponding toroidal version of Fourier integral operators. To distinguish them from those defined using the Euclidean Fourier transform, we will call them Fou...

For the analysis of multi-grid methods applied to finite difference discretizations, two definitions of orders of intergrid transfer operators are being used. The order is either defined in terms of the symbol of the transfer operator, i.e., its Fourier transform, or as the order of polynomials being preserved. In [J. Comput. Appl. Math., 32(3) (1990), pp. 423–429], Hemker showed that the secon...

We propose a matrix approach to the computation of Battle-Lemari e's wavelets. Since the Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a b-spline of order m. The polynomial is the symbol of an bi-innnite matrix B associated with b-spline of order 2m. We approximate B 2m by its nit...

We address pilot-symbol aided channel estimation (PACE) for OFDM. To reduce the complexity of the optimum minimum mean squared error (MMSE) estimator, two sub-optimum estimators are investigated. First, an estimator utilizing an FIR filter of reduced length. The filter coefficients are determined according to a Wiener filter with model mismatch, i.e. the channel conditions which are assumed to ...

In this contribution we first derive the correlation coefficient of two subcarriers in multicarrier systems using cyclic-prefixing (CP) for inter-symbol interference (ISI) suppression and inverse fast Fourier transform (IFFT)/fast Fourier transform (FFT) for multicarrier modulation/demodulation. It can be shown that two subcarriers spaced far away may experience highly correlated fading. Then, ...