66,286 research outputs found
Estimation of the modulation index of cpm signals using hos
Three simple methods are proposed for the estimation of the modulation index of continuous phase modulated signals in noise. These methods employ the estimated autocorrelation and fourth-order cumulant sequences of the received signal after sampling at the symbol rate. Analytic expressions are derived for the asymptotic mean and variance of the estimated parameters which are corroborated by means of Monte Carlo simulations. The performance of the methods is illustrated graphically and numerically. It is concluded that, under significant noise degradation, only the scheme based on the fourth-order cumulant sequence can be used to estimate consistently the modulation index h in the range 0(h(1.Peer ReviewedPostprint (published version
Blind multiuser deconvolution in fading and dispersive channels
An adaptive near-far resistant technique for the blind joint multiuser identification and detection in asynchronous CDMA systems is analyzed in fading and dispersive GSM channels.Peer ReviewedPostprint (published version
A relationship between the ideals of and the Fibonacci numbers
Let be the number of ideals of codimension of
, where is the
finite field with elements. Kassel and Reutenauer [KasselReutenauer2015A]
proved that is a polynomial in for any fixed value of .
For , this combinatorial interpretation of
is lost. Nevertheless, an unexpected connexion with Fibonacci numbers appears.
Let be the -th Fibonacci number (following the convention ,
). Define the series
We will prove that for each ,
where the integers are given by the following generating function
\prod_{m \geq 1} \left(1+F\left( t^m\right)\right) = 1 + \sum_{n \geq 1}
\lambda_n\,t^n. $
On prime numbers of the form
Consider the set of integers for which there are infinitely
many primes such that is a power of . The aim of this paper is to
show a relationship between and the limits points of some set
rational numbers related to a sequence of polynomials introduced by
Kassel and Reutenauer [KasselReutenauer]
On a function introduced by Erd\"{o}s and Nicolas
Erd\"os and Nicolas [erdos1976methodes] introduced an arithmetical function
related to divisors of in short intervals . The aim of this note is to prove that is the largest
coefficient of polynomial introduced by Kassel and Reutenauer
[kassel2015counting]. We deduce that has a coefficient larger than
if and only if is the perimeter of a Pythagorean triangle. We improve a
result due to Vatne [vatne2017sequence] concerning the coefficients of
Middle divisors and -palindromic Dyck words
Given a real number , we say that is a -middle
divisor of if We
will prove that there are integers having an arbitrarily large number of
-middle divisors. Consider the word given by where is the set of
divisors of , and are the elements of the symmetric difference written in increasing order. We will prove that the language contains Dyck words having an
arbitrarily large number of centered tunnels. We will show a connection between
both results
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