Analysis of Alternative Metrics for the PAPR Problem in OFDM Transmission

The effective PAPR of the transmit signal is the standard metric to capture the effect of nonlinear distortion in OFDM transmission. A common rule of thumb is the log$(N)$ barrier where $N$ is the number of subcarriers which has been theoretically analyzed by many authors. Recently, new alternative metrics have been proposed in practice leading potentially to different system design rules which are theoretically analyzed in this paper. One of the main findings is that, most surprisingly, the log$(N)$ barrier turns out to be much too conservative: e.g. for the so-called amplifier-oriented metric the scaling is rather $\log[ \log(N)]$. To prove this result, new upper bounds on the PAPR distribution for coded systems are presented as well as a theorem relating PAPR results to these alternative metrics.Comment: 5 pages, IEEE International Symposium on Information Theory (ISIT), 2011, accepted for publicatio

Expected Supremum of a Random Linear Combination of Shifted Kernels

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order \sqrt{\log n}, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order \log\log n. This is a noteworthy difference to orthonormal functions on the unit interval, where the expected supremum is of order \sqrt{n\log n} for all reasonable coefficient statistics.Comment: To appear in the Journal of Fourier Analysis and Application

Peak-to-average power ratio of good codes for Gaussian channel

Consider a problem of forward error-correction for the additive white Gaussian noise (AWGN) channel. For finite blocklength codes the backoff from the channel capacity is inversely proportional to the square root of the blocklength. In this paper it is shown that codes achieving this tradeoff must necessarily have peak-to-average power ratio (PAPR) proportional to logarithm of the blocklength. This is extended to codes approaching capacity slower, and to PAPR measured at the output of an OFDM modulator. As a by-product the convergence of (Smith's) amplitude-constrained AWGN capacity to Shannon's classical formula is characterized in the regime of large amplitudes. This converse-type result builds upon recent contributions in the study of empirical output distributions of good channel codes

Peak Power Reduction of OFDM Signals with Sign Adjustment

It has recently been shown that significant reduction in the peak to mean envelope power (PMEPR) can be obtained by altering the sign of each subcarrier in a multicarrier system with n subcarriers. However, finding the best sign not only requires a search over 2n possible signs but also may lead to a substantial rate loss for small size constellations. In this paper, we first propose a greedy algorithm to choose the signs based on p-norm minimization and prove that the resulting PMEPR is guaranteed to be less than c log n where c is a constant independent of n for any n. This approach has lower complexity in each iteration compared to the derandomization approach of while achieving similar PMEPR reduction. We further improve the performance of the proposed algorithm by enlarging the search space using pruning. Simulation results show that PMEPR of a multicarrier signal with 128 subcarriers can be reduced to within 1.6 dB of the PMEPR of a single carrier system. In the second part of the paper, we address the rate loss by proposing a block coding scheme in which only one sign vector is chosen for K different modulating vectors. The sign vector can be computed using the greedy algorithm in n iterations. We show that the multi-symbol encoding approach can reduce the rate loss by a factor of K while achieving the PMEPR of c logKn, i.e., only logarithmic growth in K. Simulation results show that the rate loss can be made smaller than %10 at the cost of only 1 db increase in the resulting PMEPR for a system with 128 subcarriers

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

Cyclic-Coded Integer-Forcing Equalization

A discrete-time intersymbol interference channel with additive Gaussian noise is considered, where only the receiver has knowledge of the channel impulse response. An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of intersymbol interference. This is accomplished by combining the recently proposed integer-forcing equalization approach with cyclic block codes. The channel impulse response is linearly equalized to an integer-valued response. This is then utilized by leveraging the property that a cyclic code is closed under (cyclic) integer-valued convolution. Explicit bounds on the performance of the proposed scheme are also derived