34 research outputs found
Optimization Methods for Designing Sequences with Low Autocorrelation Sidelobes
Unimodular sequences with low autocorrelations are desired in many
applications, especially in the area of radar and code-division multiple access
(CDMA). In this paper, we propose a new algorithm to design unimodular
sequences with low integrated sidelobe level (ISL), which is a widely used
measure of the goodness of a sequence's correlation property. The algorithm
falls into the general framework of majorization-minimization (MM) algorithms
and thus shares the monotonic property of such algorithms. In addition, the
algorithm can be implemented via fast Fourier transform (FFT) operations and
thus is computationally efficient. Furthermore, after some modifications the
algorithm can be adapted to incorporate spectral constraints, which makes the
design more flexible. Numerical experiments show that the proposed algorithms
outperform existing algorithms in terms of both the quality of designed
sequences and the computational complexity
Generalization and Improvement of the Levenshtein Lower Bound for Aperiodic Correlation
This paper deals with lower bounds on aperiodic correlation of sequences. It intends to solve two open questions. The first one is on the validity of the Levenshtein bound for a set of sequences other than binary sequences or those over the roots of unity. Although this result could be a priori extended to polyphase sequences, a formal demonstration is presented here, proving that it does actually hold for these sequences. The second open question is on the possibility to find a bound tighter than Welch’s, in the case of a set consisting of two sequences M = 2. By including the specific structure of correlation sequences, a tighter lower bound is introduced for this case. Besides, this method also provides in the cases M = 3 and M = 4 a tighter bound than the up-to-now tightest bound provided by Liu et al
The theory of linear prediction
Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vector linear prediction is explained in considerable detail and so is the theory of line spectral processes. This focus and its small size make the book different from many excellent texts which cover the topic, including a few that are actually dedicated to linear prediction. There are several examples and computer-based demonstrations of the theory. Applications are mentioned wherever appropriate, but the focus is not on the detailed development of these applications.
The writing style is meant to be suitable for self-study as well as for classroom use at the senior and first-year graduate levels. The text is self-contained for readers with introductory exposure to signal processing, random processes, and the theory of matrices, and a historical perspective and detailed outline are given in the first chapter