Generalizations of Cyclostationary Signal Processing: by Antonio Napolitano

By Antonio Napolitano

The relative movement among the transmitter and the receiver modifies the nonstationarity homes of the transmitted sign. particularly, the almost-cyclostationarity estate exhibited through just about all modulated indications followed in communications, radar, sonar, and telemetry will be reworked into extra basic sorts of nonstationarity. a formal statistical characterization of the got sign permits the layout of sign processing algorithms for detection, estimation, and class that considerably outperform algorithms in keeping with classical descriptions of signals.Generalizations of Cyclostationary sign Processing addresses those matters and contains the next key features: 

  • Presents the underlying theoretical framework, followed via info in their functional software, for the mathematical types of generalized almost-cyclostationary approaches and spectrally correlated techniques; periods of indications discovering becoming significance in components resembling cellular communications, radar and sonar.
  • Explains moment- and higher-order characterization of nonstationary stochastic tactics in time and frequency domains.
  • Discusses non-stop- and discrete-time estimators of statistical features of generalized almost-cyclostationary techniques and spectrally correlated processes.
  • Provides research of mean-square consistency and asymptotic Normality of statistical functionality estimators.
  • Offers large research of Doppler channels as a result of the relative movement among transmitter and receiver and/or surrounding scatterers.
  • Performs sign research utilizing either the classical stochastic-process method and the sensible strategy, the place statistical capabilities are outfitted ranging from a unmarried functionality of time.

Chapter 1 heritage (pages 1–43):
Chapter 2 Generalized Almost?Cyclostationary techniques (pages 45–121):
Chapter three enhances and Proofs on Generalized Almost?Cyclostationary techniques (pages 123–179):
Chapter four Spectrally Correlated approaches (pages 181–290):
Chapter five enhances and Proofs on Spectrally Correlated tactics (pages 291–354):
Chapter 6 useful method for sign research (pages 355–379):
Chapter 7 functions to cellular Communications and Radar/Sonar (pages 381–464):
Chapter eight Bibliographic Notes (pages 465–468):

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Extra resources for Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

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87) is the time-lag (conjugate) autocorrelation function of ACS processes. 87), one obtains the time-time (conjugate) autocorrelation function of ACS processes E{x(t1 ) x(∗) (t2 )} = α∈A Rαx (t1 − t2 ) ej2παt2 . 88) For a zero-mean process x(t) with finite or practically finite memory the result is that |Rαx (τ)| → 0 as |τ| → ∞. In contrast, if the process has non-zero almost-periodic expectation E{x(t)}, then some Rαx (τ) contain additive sinusoidal functions of τ which arise from products of finite-strength sinusoidal terms contained in E{x(t)} (Gardner and Spooner 1994).

144) c1,γ1 c2,γ2 R c1,γ1 c2,γ2 S − γ1 ). where, in the sums, only those values of γ1 and γ2 such that α − (γ1 + (−)γ2 ) ∈ Ax x(∗) give 1 2 nonzero contribution. 144), it follows that the set of the (conjugate) cyclefrequencies of the (conjugate) cross-correlation of y1 (t) and y2 (t) is {α} = α = γ1 + (−)γ2 + αx , αx ∈ Ax (∗) 1 x2 , γ1 ∈ G1 , γ2 ∈ G2 . 5 Cyclic Statistics of Communications Signals Cyclostationarity in man-made communications signals is due to signal processing operations used in the construction and/or subsequent processing of signals, such as modulation, sampling, scanning, multiplexing, and coding.

75) 1 with empty spectrum, that is ∀α ∈ R where zBap (t) is a Bp -AP function and z0 (t) ∈ Hap 1 T →∞ T lim T/2 −T/2 z0 (t) e−j2παt dt = 0. 75) can reduce to a uniformly AP function. Let us define the sets H0 R0 1 {z(t) ∈ Hap : z(t) has empty spectrum} {z(t) ∈ R1ap : z(t) has empty spectrum}. 78) Obviously R0 ⊂ H0 . 18 (Kahane 1962). Let be x(t) ∈ Lloc (R). Then, there exists z(t) ∈ R0 ∩ p Lloc (R) such that |z(t)| = |x(t)|. Let be x(t) ∈ C0 (R). Then, there exists z(t) ∈ R0 ∩ C0 (R) such that |z(t)| = |x(t)|.

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