Factored Multiplicative Mismatched Filters for Compound Barker Codes

2007 ◽  
Author(s):  
Indranil Sarkar ◽  
Adly T. Fam
Keyword(s):  
Mismatched Filters ◽  
Barker Codes

Nested code sequences of Barker — Mersenne — Raghavarao

2019 ◽  
pp. 71-81
Author(s):  
M. B. Sergeev ◽  
V. A. Nenashev ◽  
A. M. Sergeev
Keyword(s):  
Data Transfer ◽  
Radio Channel ◽  
Main Peak ◽  
Synthesis Methods ◽  
Orthogonal Matrices ◽  
Useful Signal ◽  
New Codes ◽  
Increase In Accuracy ◽  
Application Fields ◽  
Barker Codes

Introduction: The problem of noise-free encoding for an open radio channel is of great importance for data transfer. The results presented in this paper are aimed at stimulating scientific interest in new codes and bases derived from quasi-orthogonal matrices, as a basis for the revision of signal processing algorithms.Purpose: Search for new code sequences as combinations of codes formed from the rows of Mersenne and Raghavarao quasi-orthogonal matrices, as well as complex and more efficient Barker — Mersenne — Raghavarao codes.Results: We studied nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard, providing estimates for the characteristics of the autocorrelation function of nested Barker, Mersenne and Raghavarao codes, and their combinations: in particular, the ratio between the main peak and the maximum positive and negative “side lobes”. We have synthesized new codes, including nested ones, formed on the basis of quasi-orthogonal matrices with better characteristics than the known Barker codes and their nested constructions. The results are significant, as this research influences the establishment and development of methods for isolation, detection and processing of useful information. The results of the work have a long aftermath because new original code synthesis methods need to be studied, modified, generalized and expanded for new application fields.Practical relevance: The practical application of the obtained results guarantees an increase in accuracy of location systems, and detection of a useful signal in noisy background. In particular, these results can be used in radar systems with high distance resolution, when detecting physical objects, including hidden ones.

scholarly journals Code Optimisation Framework for Multicode Sonar Systems

2021 ◽  
Author(s):  
◽  
Muhammad Rashed
Keyword(s):  
Transmission Loss ◽  
Matched Filter ◽  
Signal To Noise Ratio ◽  
Welch Bound ◽  
Optimisation Algorithm ◽  
Sonar System ◽  
Channel Effects ◽  
Sonar Systems ◽  
Mismatched Filters ◽  
Quadratically Constrained

<p>The ocean is a temporally and spatially varying environment, the characteristics of which pose significant challenges to the development of effective underwater wireless communications and sensing systems.  An underwater sensing system such as a sonar detects the presence of a known signal through correlation. It is advantageous to use multiple transducers to increase surveying area with reduced surveying costs and time. Each transducers is assigned a dedicated code. When using multiple codes, the sidelobes of auto- and crosscorrelations are restricted to theoretical limits known as bounds. Sets of codes must be optimised in order to achieve optimal correlation properties, and, achieve Sidelobe Level (SLL)s as low as possible.  In this thesis, we present a novel code-optimisation method to optimise code-sets with any number of codes and up to any length of each code. We optimise code-sets for a matched filter for application in a multi-code sonar system. We first present our gradient-descent based algorithm to optimise sets of codes for flat and low crosscorrelations and autocorrelation sidelobes, including conformance of the magnitude of the samples of the codes to a target power profile. We incorporate the transducer frequency response and the channel effects into the optimisation algorithm. We compare the correlations of our optimised codes with the well-known Welch bound. We then present a method to widen the autocorrelation mainlobe and impose monotonicity. In many cases, we are able to achieve SLLs beyond the Welch bound.  We study the Signal to Noise Ratio (SNR) improvement of the optimised codes for an Underwater Acoustic (UWA) channel. During its propagation, the acoustic wave suffers non-constant transmission loss which is compensated by the application of an appropriate Time Variable Gain (TVG). The effect of the TVG modifies the noise received with the signal. We show that in most cases, the matched filter is still the optimum filter. We also show that the accuracy in timing is very important in the application of the TVG to the received signal.  We then incorporate Doppler tolerance into the existing optimisation algorithm. Our proposed method is able to optimise sets of codes for multiple Doppler scaling factors and non-integer delays in the arrival of the reflection, while still conforming to other constraints.  We suggest designing mismatched filters to further reduce the SLLs, firstly using an existing Quadratically Constrained Qaudratic Program (QCQP) formulation and secondly, as a local optimisation problem, modifying our basic optimisation algorithm.</p>

scholarly journals A NOTE ON BARKER POLYNOMIALS

2013 ◽  
Vol 09 (03) ◽  
pp. 759-767 ◽  
Author(s):  
PETER BORWEIN ◽  
TAMÁS ERDÉLYI
Keyword(s):  
Newton’S Identities ◽  
Polynomial Formula ◽  
Barker Codes ◽  
Elegant Proof

We call the polynomial [Formula: see text] a Barker polynomial of degree n-1 if each aj ∈{-1, 1} and [Formula: see text] Properties of Barker polynomials were studied by Turyn and Storer thoroughly in the early sixties, and by Saffari in the late eighties. In the last few years P. Borwein and his collaborators revived interest in the study of Barker polynomials (Barker codes, Barker sequences). In this paper we give a new proof of the fact that there is no Barker polynomial of even degree greater than 12, and hence Barker sequences of odd length greater than 13 do not exist. This is intimately tied to irreducibility questions and proved as a consequence of the following new result. Theorem.Ifn ≔ 2m + 1 > 13and[Formula: see text]where eachbj ∈{-1, 0, 1}for even values of j, each bj is an integer divisible by 4 for odd values of j, then there is no polynomial[Formula: see text]such that[Formula: see text], where[Formula: see text]and[Formula: see text]denotes the collection of all polynomials of degree 2m with each of their coefficients in {-1, 1}. A clever usage of Newton's identities plays a central role in our elegant proof.

Systematic search for optical Barker codes with minimum length

1974 ◽  
Vol 10 (12) ◽  
pp. 245 ◽  
Author(s):  
P.S. Moharir ◽  
A. Selvarajan
Keyword(s):  
Systematic Search ◽  
Minimum Length ◽  
Barker Codes
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