Convolutional compressed sensing using deterministic sequences

This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain

On the Peak-to-Mean Envelope Power Ratio of Phase-Shifted Binary Codes

The peak-to-mean envelope power ratio (PMEPR) of a code employed in orthogonal frequency-division multiplexing (OFDM) systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift. Motivated by some previous designs of phase shifts using suboptimal methods, the following question is considered in this paper. For a given binary code, how much PMEPR reduction can be achieved when the phase shifts are taken from a 2^h-ary phase-shift keying (2^h-PSK) constellation? A lower bound on the achievable PMEPR is established, which is related to the covering radius of the binary code. Generally speaking, the achievable region of the PMEPR shrinks as the covering radius of the binary code decreases. The bound is then applied to some well understood codes, including nonredundant BPSK signaling, BCH codes and their duals, Reed-Muller codes, and convolutional codes. It is demonstrated that most (presumably not optimal) phase-shift designs from the literature attain or approach our bound.Comment: minor revisions, accepted for IEEE Trans. Commun

Near Shannon Limit and Reduced Peak to Average Power Ratio Channel Coded OFDM

Solutions to the problem of large peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems are proposed. Although the design of PAPR reduction codewords has been extensively studied and the existence of asymptotically good codes with low PAPR has been proved, still no reduced PAPR capacity achieving code has been constructed. This is the topic of the current thesis.This goal is achieved by implementing a time-frequency turbo block coded OFDM. In this scheme, we design the frequency domain component code to have a PAPR bounded by a small number. The time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity. Through comparative numerical evaluation we show that our method achieves considerable improvement in terms of PAPR with slight performance degradation compared to capacity achieving codes with similar block lengths. For the frequency domain component code, we used the realization of Golay sequences as cosets of the fi rst order Reed-Muller code and the modi cation of dual BCH code. A simple MAP decoding algorithm for the modi ed dual BCH code is also provided. Finally, we provide a flexible and practical scheme based on probabilistic approach to a PAPR problem. This approach decreases the PAPR without any signi cant performance loss and without any adverse impact or required change to the system.Engineering and Applied Science

A Direct Construction of 2D-CCC with Arbitrary Array Size and Flexible Set Size Using Multivariable Function

Recently, two-dimensional (2D) array codes have been found to have applications in wireless communication.In this paper, we propose direct construction of 2D complete complementary codes (2D-CCCs) with arbitrary array size and flexible set size using multivariable functions (MVF). The Peak-to-mean envelope power ratio (PMEPR) properties of row and column sequences of the constructed 2D-CCC arrays are investigated. The proposed construction generalizes many of the existing state-of-the-art such as Golay complementary pair (GCP), one-dimensional (1D)-CCC, 2D Golay complementary array set (2D-GCAS), and 2D-CCC with better parameters compared to the existing work

Structured Compressed Sensing Using Deterministic Sequences

The problem of estimating sparse signals based on incomplete set of noiseless or noisy measurements has been investigated for a long time from different perspec- tives. In this dissertation, after the review of the theory of compressed sensing (CS) and existing structured sensing matrices, a new class of convolutional sensing matri- ces based on deterministic sequences are developed in the first part. The proposed matrices can achieve a near optimal bound with O(K log(N)) measurements for non-uniform recovery. Not only are they able to approximate compressible signals in the time domain, but they can also recover sparse signals in the frequency and discrete cosine transform domain. The candidates of the deterministic sequences include maximum length sequence (or called m-sequence), Golay's complementary sequence and Legendre sequence etc., which will be investigated respectively. In the second part, Golay-paired Hadamard matrices are introduced as structured sensing matrices, which are constructed from the Hadamard matrix, followed by diagonal Golay sequences. The properties and performances are analyzed in the following. Their strong structures ensure special isometry properties, and make them be easier applicable to hardware potentially. Finally, we exploit novel CS principles successfully in a few real applications, including radar imaging and dis- tributed source coding. The performance and the effectiveness of each scenario are verified in both theory and simulations

Peak to average power ratio reduction and error control in MIMO-OFDM HARQ System

Currently, multiple-input multiple-output orthogonal frequency division multiplexing (MIMOOFDM) systems underlie crucial wireless communication systems such as commercial 4G and 5G networks, tactical communication, and interoperable Public Safety communications. However, one drawback arising from OFDM modulation is its resulting high peak-to-average power ratio (PAPR). This problem increases with an increase in the number of transmit antennas. In this work, a new hybrid PAPR reduction technique is proposed for space-time block coding (STBC) MIMO-OFDM systems that combine the coding capabilities to PAPR reduction methods, while leveraging the new degree of freedom provided by the presence of multiple transmit chairs (MIMO). In the first part, we presented an extensive literature review of PAPR reduction techniques for OFDM and MIMO-OFDM systems. The work developed a PAPR reduction technique taxonomy, and analyzed the motivations for reducing the PAPR in current communication systems, emphasizing two important motivations such as power savings and coverage gain. In the tax onomy presented here, we include a new category, namely, hybrid techniques. Additionally, we drew a conclusion regarding the importance of hybrid PAPR reduction techniques. In the second part, we studied the effect of forward error correction (FEC) codes on the PAPR for the coded OFDM (COFDM) system. We simulated and compared the CCDF of the PAPR and its relationship with the autocorrelation of the COFDM signal before the inverse fast Fourier transform (IFFT) block. This allows to conclude on the main characteristics of the codes that generate high peaks in the COFDM signal, and therefore, the optimal parameters in order to reduce PAPR. We emphasize our study in FEC codes as linear block codes, and convolutional codes. Finally, we proposed a new hybrid PAPR reduction technique for an STBC MIMO-OFDM system, in which the convolutional code is optimized to avoid PAPR degradation, which also combines successive suboptimal cross-antenna rotation and inversion (SS-CARI) and iterative modified companding and filtering schemes. The new method permits to obtain a significant net gain for the system, i.e., considerable PAPR reduction, bit error rate (BER) gain as compared to the basic MIMO-OFDM system, low complexity, and reduced spectral splatter. The new hybrid technique was extensively evaluated by simulation, and the complementary cumulative distribution function (CCDF), the BER, and the power spectral density (PSD) were compared to the original STBC MIMO-OFDM signal