Democratic Representations

Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization, approximate nearest neighbor search, peak-to-average power ratio (or "crest factor") reduction in communication systems, and peak force minimization in robotics and control. This paper analyzes the fundamental properties of signal representations obtained by solving such a convex optimization problem. We develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, and study the efficacy of $\ell_{\infty}$-norm-based dynamic range reduction. Our analysis shows that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the computation of what we call democratic representations, whose entries all have small and similar magnitude, as well as low dynamic range. To compute democratic representations at low computational complexity, we present two new, efficient convex optimization algorithms. We finally demonstrate the efficacy of democratic representations for dynamic range reduction in a DVB-T2-based broadcast system.Comment: Submitted to a Journa

DFT-Spread Spectrally Overlapped Hybrid OFDM-Digital Filter Multiple Access IMDD PONs

A novel transmission technique—namely, a DFT-spread spectrally overlapped hybrid OFDM–digital filter multiple access (DFMA) PON based on intensity modulation and direct detection (IMDD)—is here proposed by employing the discrete Fourier transform (DFT)-spread technique in each optical network unit (ONU) and the optical line terminal (OLT). Detailed numerical simulations are carried out to identify optimal ONU transceiver parameters and explore their maximum achievable upstream transmission performances on the IMDD PON systems. The results show that the DFT-spread technique in the proposed PON is effective in enhancing the upstream transmission performance to its maximum potential, whilst still maintaining all of the salient features associated with previously reported PONs. Compared with previously reported PONs excluding DFT-spread, a significant peak-to-average power ratio (PAPR) reduction of over 2 dB is achieved, leading to a 1 dB reduction in the optimal signal clipping ratio (CR). As a direct consequence of the PAPR reduction, the proposed PON has excellent tolerance to reduced digital-to-analogue converter/analogue-to-digital converter (DAC/ADC) bit resolution, and can therefore ensure the utilization of a minimum DAC/ADC resolution of only 6 bits at the forward error correction (FEC) limit (1 × 10−3). In addition, the proposed PON can improve the upstream power budget by >1.4 dB and increase the aggregate upstream signal transmission rate by up to 10% without degrading nonlinearity tolerances

Optimization of Multi-Band DFT-Spread DMT System for Polymer Optical Fiber Communications

Abstract--Recently, polymer optical fiber (POF) became a popular solution for the indoor communications. In this paper, a multi-band discrete-Fourier-transform spread (MB-DFT-S) discrete multi-tone (DMT) system is proposed to study and optimize in terms of POF communications. A joint optimization of used subcarrier number, used bandwidth and multi-band number is investigated. The transmission of MB-DFT-S DMT over 50 m POF link is implemented. Both theoretical and experimental results demonstrate that optimized MB-DFT-S DMT system outperforms the original DMT and DFT-S DMT systems, which means that it is a promising technique for future POF transmission systems

IMPLEMENTATION AND PERFORMANCE ANALYSIS OF LONG TERM EVOLUTION USING SOFTWARE DEFINED RADIO

The overwhelming changes in the field of communication brought about need for high data rates, which led to the development of a system known as Long Term Evolution (LTE). LTE made good use of Orthogonal Frequency Division Multiplexing Access (OFDMA) in its downlink and Single Carrier Frequency Division Multiplexing Access (SCFDMA) in its uplink transmission because of their robust performance. These multiple access techniques are the major focus of study in this thesis, with their implementation in the LTE system. GNU Radio is a software Defined Radio (SDR) platform. It comprises of C++ signal processing libraries. For user simplicity, it has graphical user interface (GUI) known as GNU Radio Companion (GRC), to build a signal processing flow graph. GRC translates any specific task flow graph to a python program which calls inbuiltC++ signal processing blocks. By leveraging this feature and existing modules in GRC, OFDMA and SCFDMA is implemented. In this study we made use of existing OFDMA flow graph of GNU Radio to study the behavior of downlink and general performing SCFDMA system was implemented with some modifications of the existing GNU Radio blocks. With the GNU Radio implementation, we tested the working mechanism of both the systems. OFDMA is used in downlink for achieving high spectral efficiency and SCFDMA was introduced in uplink due to its low PAPR feature. These multiple access schemes have to meet the requirement of high throughput with low BER and PAPR, low delays and low complexity. In this thesis we are focused on evaluating these multiple access techniques in terms of BER and PAPR with modulation techniques like QPSK, 16-QAM and 64-QAM. Performance analysis part is performed in MATLAB

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

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

Numerical study of a hybrid optical DMT/DFT-S QAM modulation

A hybrid modulation offers the peak-to-average power ratio (PAPR) robustness of discrete Fourier transform spread (DFT-S) QAM (quadrature amplitude modulation) with the bit rate optimization of discrete multi-tone (DMT) modulation. We examine via simulation under what circumstances this hybrid can increase achievable bit rate. Hybrid PAPR reduction allows us to increase the peak-to-peak voltage at the modulator electrical input to increase the signal mean power at the modulator output. We propose a methodology to identify the optimal driving strategy. We optimize the bit rate for the available spectrum, i.e., the spectral efficiency, taking into account the bandwidth limited nature of the transmitter. The final optimization we propose is the partition of the available spectrum into a lower frequency band for DFT-S QAM and a higher frequency band for DMT. The modulation level of the DFT-S QAM is also optimized. We compare the optimal hybrid performance versus DMT performance for a range of bit rates for a given modulation bandwidth. Improved performance comes at the cost of greater DSP complexity for the hybrid solution. We compare the number of complex multipliers required to implement hybrid versus DMT for both dispersive and non-dispersive systems