Luciano Izzo

The higher order theory of generalized almost-cyclostationary time series

In this paper, the class of generalized almost-cyclostationary (GACS) time series is introduced. Time series belonging to this class are characterized by multivariate statistical functions that are almost-periodic functions of time whose Fourier series expansions can exhibit coefficients and frequencies depending on the lag shifts of the time series. Moreover, the union over all the lag shifts of the lag-dependent frequency sets is not necessarily countable. Almost-cyclostationary (ACS) time series turn out to be the subclass of GACS time series for which the frequencies do not depend on the lag shifts and the union of the above-mentioned sets is countable. The higher order characterization of GACS time series in the strict and wide sense is provided. It is shown that the characterization in terms of cyclic moment and cumulant functions is inadequate for those GACS time series that are not ACS. Then, generalized cyclic moment and cumulant functions (in both the time and frequency domains) are introduced. Finally, the problem of estimating the introduced generalized cyclic statistics is addressed, and two examples of GACS time series are considered.

Signal interception in non-Gaussian noise

The interception of weak signals in nonGaussian noise is discussed. The spectral correlation property exhibited by all cyclostationary signals is exploited to synthesize multi-cycle and single-cycle detectors which assure a superior tolerance (as compared to radiometric techniques) to one of the most challenging problems in interception, namely accommodating unknown and changing noise level and interference activity. The proposed detectors perform a maximum likelihood estimate of the noise level and use the estimate to form the detection statistic. To obtain some analytical information about the performance of the multi-cycle and single-cycle detectors, the deflection, which is a useful measure of the output (signal-to-noise ratio), especially appropriate for weak-signal SNR interception, has been evaluated. The receiver operating characteristics, carried out via computer simulation, confirm the superiority of the proposed cycle detector with respect to the traditional radiometer. >

An interference-tolerant algorithm for localization of cyclostationary-signal sources

A method for detecting the number of cyclostationary signals radiated by remote sources and for estimating their directions of arrival by a linear and uniform array is presented. Whereas the traditional techniques exploit the spatial coherent properties, the new method locates the signal sources using the spectral coherence properties as well. This approach eliminates the need to know the characteristics of the noise and the interference, regardless of the extent of their spectral overlap. Moreover, the method applied equally well to environments containing more interferers than sensors. The conditions of applicability of the method are the existence and the knowledge of a cycle frequency at which all the signal sources exhibit spectral correlation but the noise and interference signals do not, and the existence and the knowledge of a value of the lag parameter such that the cyclic cross-correlation matrix of the desired signals has full rank. >

Higher-order cyclostationarity properties of sampled time-series

Abstract In this paper, the higher-order wide-sense stationarity or cyclostationarity properties of a continuous-time-series and those of the discrete-time-series of its samples are related in the fraction-of-time probability framework. In particular, for a cyclostationary continuous-time-series, it is shown how the ratio of the sampling period to the cyclostationarity period affects the cyclostationarity properties of the discrete-time-series. Moreover, it is shown that the higher-order wide-sense stationarity or cyclostationarity of a strictly band limited continuous-time-series can be analyzed by examining that exhibited by the discrete-time-series of its samples provided that the sampling rate is sufficiently high. Finally, the derived results are interpreted in the stochastic process framework.

Linear time-variant transformations of generalized almost-cyclostationary signals .I. Theory and method

The problem of linear time-variant filtering is addressed in the fraction-of-time (FOT) probability framework. The adopted approach, which is an alternative to the classical stochastic one, provides a statistical characterization of the system in terms of time averages of functions of time rather than ensemble averages of stochastic processes. Thus, it is particularly useful when stochastic systems transform ergodic input signals into nonergodic output signals, as it happens with several channel models encountered in practice. The analysis is carried out with reference to the wide class of the generalized almost-cyclostationary signals, which includes, as,a special case, the class of almost-cyclostationary signals. In this paper, systems are classified as deterministic or random in the FOT probability framework. Moreover, the new concept of expectation in the FOT probability framework of the impulse-response function of a system is introduced. For the linear time-variant systems, the higher order system characterization in the time domain is provided in terms of the system temporal moment function, which is the kernel of the operator that transforms the additive sinewave components contained in the input lag product into the additive sinewave components contained in the output lag product. Moreover, the higher order characterization in the frequency domain is also provided, and input/output relationships are derived in terms of temporal and spectral moment and cumulant functions. Developments and examples of application of the theory introduced here are presented in part II of this two-part paper.

Sampling of generalized almost-cyclostationary signals

In this paper, the problem of sampling a continuous-time generalized almost-cyclostationary (GACS) signal is addressed. The class of such nonstationary signals includes, as a special case, the almost-cyclostationary (ACS) signals. ACS signals filtered by some linear time-variant channels are further examples. It is shown that the discrete-time signal constituted by the samples of a GACS signal is a discrete-time ACS signal. Thus, the nonstationarity kind of a continuous-time GACS signal cannot be deducted from that of the discrete-time signal of its samples. However, in the paper it is shown how, starting from the sampled signal, the GACS or ACS nature of the continuous-time signal can be conjectured, provided that analysis parameters such as sampling period, padding factor, and data-record length are properly chosen.

Linear time-variant transformations of generalized almost-cyclostationary signals.II. Development and applications

For pt. I see ibid., vol.50, no.12, p.2947-61 (2000). In Part I, the problem of the linear time-variant (LTV) filtering is addressed in the fraction-of-time (FOT) probability framework. The adopted approach, which is an alternative to the classical stochastic one, provides a statistical characterization of the systems in terms of functions that can be estimated by a single time-series. The analysis is carried out with reference to the wide class of the generalized almost-cyclostationary (GACS) signals, which includes, as a special case, the class of the almost-cyclostationary (ACS) signals. Examples of applications and developments of the theory introduced in Part I are presented here in Part II. Specifically, the countability of the set of the output cycle frequencies is studied with reference to linear time-variant systems for both ACS and GACS not containing any ACS component input signals. Thus, the linear almost-periodically time-variant filtering and the product modulation are considered in detail. Moreover, several Doppler channel models are analyzed. In all these examples, it is shown that the FOT probability approach allows one to characterize the system and its output in terms of statistical functions that can be measured by a single time-series. Furthermore, the usefulness of considering the linear filtering problem within the class of the GACS signals is clarified, and several pitfalls arising from continuing to adopt for the observed time-series the ACS model when an increase in the data-record length makes the GACS model more appropriate are pointed out.

Error Rates for Fading NCFSK Signals in an Additive Mixture of Impulsive and Gaussian Noise

The effects of slow and nonselective signal fading on the performance of multilevel noucoherent FSK (NCFSK) systems in an additive mixture of Gaussian and highly impulsive noise are analyzed. For binary systems the bit error rate is derived; for M -ary NCFSK systems upper and lower bounds of the character error probability are obtained. The analysis is performed considering the maximum likelihood receiver for additive white Gaussian noise.

Minimum-redundancy linear arrays for cyclostationarity-based source location

The problem of designing minimum-redundancy linear arrays (MRLAs) and appropriate augmentation techniques to be utilized with cyclostationarity-exploiting (cyclic) methods for source location is addressed. The MRLA geometries proposed in the literature for the conventional case, which apply equally well when the signals of interest exhibit cyclostationarity are not appropriate when they exhibit conjugate cyclostationarity. In this case, the problem of finding optimal MRLAs is restated as the problem of number theory that is commonly referred to as the postage stamp problem. Results of computer simulations show that in densely crowded environments, the use of cyclic methods with MRLA geometries and appropriate matrix augmentation techniques can offer a significant performance improvement on cyclic methods that do not resort to matrix augmentation techniques.

Asymptotically Optimum Space-Diversity Detection in Non-Gaussian Noise

The theory of asympoticalllly optimum detection in nonGaussian noise is considered to synthesize a space-diversity structure for the noncoherent detection of a bandpass signal subject to amplitude fluctuations. An asymptotic sufficient statistic is obtained for arbitrary fading laws on the diversity branches and, then, for Rayleigh-distributed amplitude fluctuations, the asymptotically optimum detector is synthesized. The performance of the proposed detection structure is obtained and numerical results and comments are presented. Moreover, a comparison between the asymptotically optimum detector and a simple suboptimum structure is made.