Generalized DFT: extensions in communications

Discrete Fourier Transform (DFT) is a restricted version of Generalized DFT (GDFT) which offers a very limited number of sets to be used in a multicarrier communication system. In contrast, as an extension on Discrete Fourier Transform (DFT) from the linear phase to non-linear phase, the proposed GDFT provides many possible carrier sets of various lengths with comparable or better performance than DFT. The availability of the rich library of orthogonal constant amplitude transforms with good performance allows people to design adaptive systems where user code allocations are made dynamically to exploit the current channel conditions in order to deliver better performance. For MIMO Radar systems, the ideal case to detect a moving target is when all waveforms are orthogonal, which can provide an accurate estimation. But this is not practical in distributed MIMO radars, where sensors are at varying distances from a target. Orthogonal waveforms with low auto- and cross-correlations are of great interest for MIMO radar applications with distributed antennas. Finite length orthogonal codes are required in real-world applications where frequency selectivity and signal correlation features of the optimal subspace are compromised. In the first part of the dissertation, a method is addressed to design optimal waveforms which meets above requirements for various radar systems by designing the phase shaping function (PSF) of GDFT framework with non-linear phase. Multicarrier transmission such as orthogonal frequency-division multiplexing (OFDM) has seen a rise in popularity in wireless communication, as it offers a promising choice for high speed data rate transmission. Meanwhile, high peak-to-average power ratio (PAPR) is one of the well-known drawbacks of the OFDM system due to reduced power efficiency in non-linear modules. Such a situation leads to inefficient amplification and increases the cost of the system, or increases in interference and signal distortion. Therefore, PAPR reduction techniques play an essential role to improve power efficiency in the OFDM systems. There has been a variety of PAPR reduction methods emphasizing different aspects proposed in the literature. The trade-off for PAPR reduction in the existing methods is either increased average power and/or added computational complexity. A new PAPR reduction scheme is proposed that implements a pre-designed symbol alphabet modifier matrix (SAM) to jointly modify the amplitude and phase values of the original data symbol alphabets prior to the IFFT operation of an OFDM system at the transmitter. The method formulated with the GDFT offers a low-complexity framework in four proposed cases devised to be independent of original data symbols. Without degrading the bit error rate (BER) performance, it formulates PAPR reduction problem elegantly and outperforms partial transmit sequences (PTS), selected mapping technique (SLM) and Walsh Hadamard transform (WHT-OFDM) significantly for the communication scenarios considered in the dissertation

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

A Low-Complexity SLM PAPR Reduction Scheme for OFDMA

In orthogonal frequency division multiplexing (OFDM) systems, selected mapping (SLM) techniques are widely used to minimize the peak to average power ratio (PAPR). The candidate signals are generated in the time domain by linearly mixing the original time-domain transmitted signal with numerous cyclic shift equivalents to reduce the amount of Inverse Fast Fourier Transform (IFFT) operations in typical SLM systems. The weighting factors and number of cyclic shifts, on the other hand, should be carefully chosen to guarantee that the elements of the appropriate frequency domain phase rotation vectors are of equal magnitude. A low-complexity expression is chosen from among these options to create the proposed low-complexity scheme, which only requires one IFFT. In comparison to the existing SLM technique, the new SLM scheme achieves equivalent PAPR reduction performance with significantly less computing complexity. MATLAB tool is used for simulating the proposed work

A Low-Complexity SLM PAPR Reduction Scheme for OFDMA

In orthogonal frequency division multiplexing (OFDM) systems, selected mapping (SLM) techniques are widely used to minimize the peak to average power ratio (PAPR). The candidate signals are generated in the time domain by linearly mixing the original time-domain transmitted signal with numerous cyclic shift equivalents to reduce the amount of Inverse Fast Fourier Transform (IFFT) operations in typical SLM systems. The weighting factors and number of cyclic shifts, on the other hand, should be carefully chosen to guarantee that the elements of the appropriate frequency domain phase rotation vectors are of equal magnitude. A low-complexity expression is chosen from among these options to create the proposed low-complexity scheme, which only requires one IFFT. In comparison to the existing SLM technique, the new SLM scheme achieves equivalent PAPR reduction performance with significantly less computing complexity. MATLAB tool is used for simulating the proposed work

Digital signal processing techniques for peak-to-average power ratio mitigation in MIMO–OFDM systems

The focus of this thesis is to mitigate the very large peak-to-average transmit power ratios (PAPRs) inherent to conventional orthogonal frequency division multiplexing (OFDM) systems, particularly in the context of transmission over multi-input multi-output (MIMO) wireless broadband channels. This problem is important as a large PAPR generally needs an expensive radio frequency (RF) power amplifier at the transmitter due to the requirement for linear operation over a wide amplitude range and such a cost would be compounded when multiple transmit antennas are used. Advanced signal processing techniques which can reduce PAPR whilst retain the integrity of digital transmission therefore have considerable potential for application in emergent MIMO–OFDM wireless systems and form the technical contributions of this study. [Continues.

Enhancement of Selective Mapping Technique for Peak-To-Average Power Ratio Reduction in OFDM using Normalized Hilbert Matrix

Orthogonal Frequency Division Multiplexing (OFDM) is good multicarrier transmission system used for broadband wireless communication systems owing to it is numerous benefits such as high bandwidth efficiency, high transmission rate, and robustness against multi path problem. However, one of the hitches of OFDM high Peak-to-Average Power Ratio (PAPR) of the transmitted signal, which results in signal distortion and reduced power amplifier efficiency. Selective Mapping (SLM) is attractive distortion less method for PAPR reduction. The performance of this technique in reducing the PAPR is largely affected by the magnitude of phase rotation vectors. It also requires to  transmit the selected phase rotation vectors that produce the signal with the lowest PAPR to the receiver end for the recovery of the original data. In this paper, two normalization procedures in conjunction with the Hilbert matrix are used to obtain phase rotation vectors for the SLM technique to further reduce the PAPR value. The reduction of PAPR is desirable in order to have a better power efficiency of the amplifier. The simulation results demonstrated that the enhanced SLM technique using normalized Hilbert matrix achieved a better PAPR reduction compared to SLM using Hilbert matrix without normalization with 14.0%, and 14.0%  percentage improvement. Another benefit of this method is that the matrix can be generated at the receiver end to obtain the data signal, thus eliminating the transmission of side information with the original data

OFDM System with g-CPFSK Mapper: Properties and Performance

Orthogonal Frequency Division Multiplexing (OFDM) system with a generalized Continuous Phase Frequency Shift Keying (g-CPFSK) mapper is considered which is used to introduce systematic correlation among the transmitted OFDM symbols. The correlation thus introduced is exploited at the receiver to enhance the physical layer performance of the system by using multiple-symbol observation detector. Three subclasses of g- CPFSK mapper, single-h CPFSK, multi-h CPFSK, and asymmetric multi-h CPFSK mappers, are considered; although the class of g-CPFSK mapper comprises of a large class of mappers. The resulting OFDM signals and their properties are examined. The Peak-to-Average Power Ratio (PAPR) characteristics of these signals in conjunction with three PAPR reduction techniques, namely, Selective Mapping (SLM), Partial Transmit Sequence (PTS), and Clipping and Filtering (CF) are also investigated. Maximum Likelihood (ML) multiple-symbol detection of OFDM signals in AWGN is addressed and the structure of the optimum detector/demapper is derived using the criterion of minimum probability of Bit Error Rate (BER). Closed-form expression for BER of this detector is derived in terms of high-SNR upper and lower bounds. It is noted that BER is a function of: i) Eb=No, Signal-to-Noise Ratio (SNR); ii) parameters of the g-CPFSK mapper; iii) n, observation length of the receiver; and iv) M, number of levels used in the mapper. Finally, the performance of OFDM system with g-CPFSK mapper is evaluated over nonfrequency selective Rayleigh and Nakagami-m fading channels. It is shown that OFDM system with single-h and multi-h CPFSK mappers in conjunction with PTS technique can be designed to achieve PAPR reductions of 6.1 dB and 3.5 dB, respectively, relative to corresponding OFDM system with conventional BPSK mapper. However, when SLM technique is used, PAPR reductions of 1.6 dB and 1 dB, respectively, can be achieved. Asymmetric multi-h and multi-h CPFSK mappers in conjunction with CF technique can be designed to realize PAPR reductions of 4.1 dB and 2.5 dB, respectively, with 25% clipping. Optimum sets of mapper parameters for single-h, multi-h and asymmetric multi-h CPFSK mappers are determined that minimize BER of the system. It is observed that the optimum asymmetric multi-h and multi-h CPFSK mappers outperform BPSK mapper by nearly 2.2 dB and 1.4 dB, respectively, when 4- symbol observation length detector is used. However, it is noted that the complexity of the detector increases as a function of observation length and the type of mapper used. Closed-form expressions for BER performance of OFDM system with g-CPFSK mapper are derived over Rayleigh and Nakagami-m frequency-non selective slowly fading channels and the penalty in SNR that must be paid as a consequence of the fading is assessed and illustrated