Sultan Aldirmaz

Adaptive fractional Fourier domain filtering

A novel adaptive filtering scheme based on fractional Fourier transform (FrFT) is introduced and characterized. As a generalization of the ordinary Fourier transform, FrFT is a powerful analysis tool to describe signals with chirp-type components. We show that in case of linear frequency modulated (LFM) signals fractional Fourier domain adaptive filtering schemes provide less error and faster convergence. The adaptation algorithm is employed in an active noise control system application with various LFM signals and a real multi-component signal. Simulation results present that the adaptation performance in FrFT-domain adaptive filtering is superior compared to time-domain adaptation.

BROADBAND INTERFERENCE EXCISION IN SPREAD SPECTRUM COMMUNICATION SYSTEMS BASED ON SHORT-TIME FOURIER TRANSFORMATION

An interference excision algorithm in direct-sequence spread spectrum (DS-SS) communication systems is introduced. The proposed excision algorithm is developed for linear frequency modu- lated (LFM) signals that have broadband frequency characteristics. It is based on the time-frequency analysis of received signals employing short-time Fourier transformation (STFT). To analyze the interfer- ence, STFT of the received signal block is evaluated and thresholded. The interference detection is followed by an inverse-STFT computation to estimate the high-power jamming signal. The estimated jammer is then mitigated before demodulation. Simulations present adequate interference estimation results with mean estimation errors less than 0.01%. Various scenarios with different jammer-to-signal ratios (JSRs) and signal-to-noise ratios (SNRs) vs. bit error rates (BERs) are pre- sented for single and multi-component LFM signals. Interference exci- sion algorithms improve the system performance more than an order of magnitude.

Spectrally efficient OFDMA lattice structure via toroidal waveforms on the time-frequency plane

We investigate the performance of frequency division multiplexed (FDM) signals, where multiple orthogonal Hermite-Gaussian carriers are used to increase the bandwidth efficiency. Multiple Hermite-Gaussian functions are modulated by a data set as a multicarrier modulation scheme in a single time-frequency region constituting toroidal waveform in a rectangular OFDMA system. The proposed work outperforms in the sense of bandwidth efficiency compared to the transmission scheme where only single Gaussian pulses are used as the transmission base. We investigate theoretical and simulation results of the proposed methods.

An Investigation on Number of Effective Taps for Multicarrier Schemes

In a wireless communication medium, the transmitted signal reaches to the receiver antenna after passing through multipath channel. The difference in path delays and mobility cause the transmitted signal spread both in time and frequency, resulting in inter-symbol (or adjacent block) and inter-carrier (or adjacent channel) interference, respectively. The pulse shaping and matching filters used in the transceivers also impact the level of dispersion in both time and frequency. In this study, the composite effects of wireless medium and the used filters are investigated on the equalization of multicarrier systems. For this purpose, considering a symbol-spaced tap model for the equalization, the number of effective taps in both time and frequency domains is obtained via Akaike information criterion (AIC) for different signal-to-noise ratios (SNRs). Subsequently, a method which characterizes the equalization complexity of the receiver as a function of the transmit pulse shape, communication medium, the receive filter response, and SNR is proposed.

Compressive Sensing of Linear Frequency Modulated Signals in Fractional Fourier Domains

Compressive sensing is a new technique that allows sampling at very low rates compared to the Nyquist sampling rate, if the signal is sparse. Thus the signal should either be sparse in time domain or we should be able to determine any domain in which the signal is represented sparsely. In the reconstruction process, the signal is reconstructed by using linear projections of itself in an iterative way rather than using all samples of the signal. In this paper, multi-component linear frequency modulated (LFM) signals that are highly dense in time and frequency domains, are transformed into fractional Fourier domains in order to form sparse representations. Then, it is shown that by using compressive sensing in fractional Fourier domains, LFM signals can be represented almost by half of their lengths with high accuracy.

On suitability of PSD method for opportunity detection in OFDM(A) based cognitive radio systems

In this study, orthogonal frequency division multiple access (OFDMA) based primary and secondary usage in a cognitive radio system is considered and conventional power spectral density (PSD) based technique is used to detect the opportunities in the spectrum. Primary user employs block-based or scattered subcarrier allocation scheme and the overlay system aims to utilize the spectral gaps. Comparison of the allocation schemes and effect of windowing are presented in terms of true detection and false alarm rates. It is observed that when block-based allocation is employed, the unlicensed user will be able to detect more opportunities in the spectrum compared to the case in which the scattered allocation is employed. Simulation results show that threshold selection is crucial since it is the main factor in determining the false alarm and true detection rates. It has been shown that, for either of the schemes all possible spectral gaps cannot be found when PSD is used. Questioning the suitability of PSD method results in that a new definition of opportunity is needed, forming a basis for the second part of this study.

Eigenfunctions of the linear canonical transform

The linear canonical transform (LCT) is a powerful tool for signal processing applications and is also the generalized form of the well-known transforms such as Fourier, fractional Fourier and Fresnel transforms, and some operators such as scaling, chirp multiplication and chirp convolution. The LCT is characterized by a 2 × 2 unit-determinant matrix of parameters {a, b, c, d}. When studying linear operators, one of the crucial steps in order to understand what the operators do, is to find their eigenfunctions. Eigenfunctions of the LCT may be useful for applications such as self-imaging and resonance problems. In this paper, we derive eigenfunctions of the LCT for different cases. In order to expose eigenfunctions of the LCT, we split our investigation into three parts: (a + d) >; 2, (a + d) <; -2, and |a+d| <; 2. The complete set of eigenfunctions is known to be chirp functions modulated by scaled harmonic oscillator (also known as Hermite-Gaussian) functions for the case |a+d| <; 2. However, we propose that when |a + d| >; 2, the eigenfunction set of the LCT are chirp functions modulated with imaginary-width Hermite polynomials.

Channel estimation for a wireless communication systems with chirp carriers

In this paper, a new communication system that inherently enables the estimation of channel parameters by employing the fractional Fourier transform is proposed. The system uses chirp bases as carriers and two of these carriers are also employed as pilot signals without decreasing the capacity of the system. We make use of two important properties of the fractional Fourier transform which are related to time and frequency shifts to determine the time-delay and doppler frequency parameters. Moreover data is transmitted in a circular time-frequency area rather than a rectangular one.

A new OFDM lattice structure: Toroidal-lattice on the time-frequency plane

We introduce a new frequency division multiplexed (FDM) system where multiple orthogonal Hermite-Gaussian carriers are used as a transmission basis and investigate the performance of the proposed system. The toroidal waveform in a rectangular OFDMA system is constituted by using multiple Hermite — Gaussian functions. The proposed work outperforms the transmission scheme where only single Gaussian pulses are used as the transmission base in the sense of bandwidth efficiency. We investigate both theoretical and simulation results of the proposed method.

Cognitive OFDMA: Exploring a new FFT based detection technique for opportunistic usage

In this paper, a new opportunity search technique is introduced for OFDMA based Cognitive Radio systems. In, which forms a basis for this study, the conventional opportunity search method was utilized for various subcarrier allocations where power spectral density calculations were used. Since all possible spectral gaps could not be found using the conventional technique, in order to increase the detection rate, a new technique is presented in this paper, which involves more than just determining the power in a frequency band. In the proposed technique, the opportunity search is done at the receiver part with synchronization stage and utilizing FFT calculations after removing cyclic prefix. Also it has been shown that by using the proposed technique all opportunities can be found when AWGN channel is considered without any impairments such as frequency offset and delay. Performance of the proposed technique is presented in comparison with the the conventional PSD method, and effects of OFDM impairments are studied individually. Simulation results show the superiority of the new technique in terms of true detection rates.