Cyclic Autocorrelation Function Research Articles

Experimental demonstration of localized Brillouin gratings with low off-peak reflectivity established by perfect Golomb codes

Dynamic Brillouin gratings (DBGs), inscribed by comodulating two writing pump waves with a perfect Golomb code, are demonstrated and characterized experimentally. Compared with pseudo-random bit sequence (PRBS) modulation of the pump waves, the Golomb code provides lower off-peak reflectivity due to the unique properties of its cyclic autocorrelation function. Golomb-coded DBGs allow the long variable delay of one-time probe waveforms with higher signal-to-noise ratios, and without averaging. As an example, the variable delay of return-to-zero, on-off keyed data at a 1 Gbit/s rate, by as much as 10 ns, is demonstrated successfully. The eye diagram of the reflected waveform remains open, whereas PRBS modulation of the pump waves results in a closed eye. The variable delay of data at 2.5 Gbit/s is reported as well, with a marginally open eye diagram. The experimental results are in good agreement with simulations.

Simple spectrum sensing techniques based on cyclostationarity detection in cognitive radio networks

A novel cyclostationarity-detection-based simple spectrum sensing technique of orthogonal frequency division multiplexing signals for cognitive radio networks is presented. The presented techniques do not require any reference tables to compute a cyclic autocorrelation function. The presented results are compared with the conventional results. Although these are found to be almost equal, the presented techniques have a lower hardware cost than the conventional techniques.

Signal Detection Based on Cyclic Autocorrelation under Noise Uncertainty

Signal detection is a key enabler of cognitive radio. This paper considers the detection signals in uncertain low SNR environments. We propose a feature detector based on cyclic autocorrelation function of signal. Compared with other feature detector based on cyclic spectral, the proposed detector need lower computational cost than computational cyclic spectrum. Similar radiometer detector,SNR wall also exists in noise power uncertainty model. Beyond this SNR wall robust detection is impossible.Detection performance including the SNR wall is proved.

Second-Order Cyclostationarity of BT-SCLD Signals: Theoretical Developments and Applications to Signal Classification and Blind Parameter Estimation

This paper investigates the second-order cyclostationarity of block transmitted-single carrier linearly digitally modulated (BT-SCLD) signals, and its applications to signal classification and blind (non-data aided) parameter estimation. Analytical closed-form expressions are derived for the cyclic autocorrelation function (CAF), cyclic spectrum (CS), complementary CAF (CCAF), complementary CS (CCS), and corresponding cycle frequencies (CFs). Furthermore, the conditions for avoiding aliasing in the cycle and spectral frequency domains are obtained. Based on these findings, we propose algorithms for classifying BT-SCLD, orthogonal frequency division multiplexing (OFDM), and SCLD signals, and for the blind estimation of the BT-SCLD block transmission parameters. Simulation and laboratory experiments demonstrate the effectiveness of the proposed algorithms under low signal-to-noise ratios (SNRs), short sensing times, and various channel conditions. Furthermore, these algorithms have the advantage of not requiring the recovery of carrier, waveform, and symbol timing information, or the estimation of signal and noise powers.

On Cyclostationarity Based Spectrum Sensing Under Uncertain Gaussian Noise

Detection of cyclostationary primary user (PU) signals in colored Gaussian noise for cognitive radio systems is considered based on looking for single or multiple cycle frequencies at single or multiple time lags in the cyclic autocorrelation function (CAF) of the noisy PU signal. We explicitly exploit the knowledge that under the null hypothesis of PU signal absent, the measurements originate from possible colored Gaussian noise with unknown correlation function. Our formulation allows us to simplify the spectrum sensing detector and obviates the need for estimating an unwieldy covariance matrix needed in some prior works. We consider both single and multiple antenna receivers, and both nonconjugate and conjugate CAFs. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided to demonstrate the efficacy of the proposed approaches and to compare them with some existing approaches. Our proposed approaches are computationally cheaper than the Dandawate-Giannakis and related approaches while having quite similar detection performance for a given false alarm rate.

Signal Representation: Wireless Applications in a Statistical Spectrum Domain

In this article, a new concept of data transmission over the statistical spectrum domain is presented and discussed its corresponding multiple access schemes based on signal cyclostationarity. The extra data transmitted over the statistical spectrum domain can be separated independently from the signals sent via the conventional time-frequency-space domain. Numerical results showed that the performance of the statistical spectrum domain signal transmission depended largely on the length of observation period. Moreover, new multiple access schemes can be designed over the statistical spectrum domain via the detection of cyclic autocorrelation function of communication signals.

A new method of micro-motion parameters estimation based on cyclic autocorrelation function

Signals with sinusoidal frequency modulation (FM) are the general form of micro-Doppler signals in radar echoes from targets with micro-motions. This paper derives the cyclic autocorrelation function of a sinusoidal FM signal using its cyclostationary characteristics, and estimates the parameters of amplitude, modulation index, micro-motion period and noise power based on cyclic autocorrelation function. The estimation method is robust in noise environment when compared with conventional time-frequency analysis methods. Finally, the performances of estimation by utilizing the simulation data and darkroom measurement are shown in tables. The Monte-Carlo simulation results show that the estimator is asymptotically optimal at SNR above −6 dB.

A Novel Method Based on Cyclic Spectral Analysis about Carrier Frequency Estimation in the UAV Data Chain

When UAV works on the end of the task path, or affected by waves transmission environment and the influence of the electromagnetic interference, the signal of receiver will be made low signal-to-noise ratio (SNR) signal and the phase lock loop (PLL) using for carrier extraction will performance serious decline or loss locks. Therefore, in order to ensure UAV completed a predefined task successfully, low SNR carrier recovery has become one of the key technologies in the UAV data chain. In this paper, based on the basic concept of cyclic spectral analysis, we research and give the cyclic autocorrelation function and the cyclic spectral density function of the BPSK modulation signal. We emphasis a computer simulation method based on the time-smoothing FFT accumulation method and use this method to verify cyclic spectral analysis is still effective to estimate the carrier frequency when the SNR is -10 dB.

Second-Order Cyclostationarity of Mobile WiMAX and LTE OFDM Signals and Application to Spectrum Awareness in Cognitive Radio Systems

Spectrum sensing and awareness are challenging requirements in cognitive radio (CR). To adequately adapt to the changing radio environment, it is necessary for the CR to detect the presence and classify the on-the-air signals. The wireless industry has shown great interest in orthogonal frequency division multiplexing (OFDM) technology. Hence, classification of OFDM signals has been intensively researched recently. Generic signals have been mainly considered, and there is a need to investigate OFDM standard signals, and their specific discriminating features for classification. In this paper, realistic and comprehensive mathematical models of the OFDM-based mobile Worldwide Interoperability for Microwave Access (WiMAX) and third-Generation Partnership Project Long Term Evolution (3GPP LTE) signals are developed, and their second-order cyclostationarity is studied. Closed-from expressions for the cyclic autocorrelation function (CAF) and cycle frequencies (CFs) of both signal types are derived, based on which an algorithm is proposed for their classification. The proposed algorithm does not require carrier, waveform, and symbol timing recovery, and is immune to phase, frequency, and timing offsets. The classification performance of the algorithm is investigated versus signal-to-noise ratio (SNR), for diverse observation intervals and channel conditions. In addition, the computational complexity is explored versus the signal type. Simulation results show the efficiency of the algorithm is terms of classification performance, and the complexity study proves the real time applicability of the algorithm.

On the Use of the Sparse Property of the Cyclic Autocorrelation Function to Blindly Estimate the Cyclostationarity

AbstractBased on the sparse property of the Cyclic Autocorrelation Function (CAF) in the cyclic frequency domain, we propose in this paper a new blind estimator using compressed sensing, which better estimates the Cyclic Autocorrelation Function at a given delay compared to the classical non blind estimator when using the same number of samples. Two metrics are used to evaluate this estimation: the Mean Square Error of type one and that of type two (

Spectral Correlation of Multicarrier Modulated Signals and Its Application for Signal Detection

Spectral correlation theory for cyclostationary time-series signals has been studied for decades. Explicit formulas of spectral correlation function for various types of analog-modulated and digital-modulated signals are already derived. In this paper, we investigate and exploit the cyclostationarity characteristics for two kinds of multicarrier modulated (MCM) signals: conventional OFDM and filter bank based multicarrier (FBMC) signals. The spectral correlation characterization of MCM signal can be described by a special linear periodic time-variant (LPTV) system. Using this LPTV description, we have derived the explicit theoretical formulas of nonconjugate and conjugate cyclic autocorrelation function (CAF) and spectral correlation function (SCF) for OFDM and FBMC signals. According to theoretical spectral analysis, Cyclostationary Signatures (CS) are artificially embedded into MCM signal and a low-complexity signature detector is, therefore, presented for detecting MCM signal. Theoretical analysis and simulation results demonstrate the efficiency and robustness of this CS detector compared to traditionary energy detector.

Application of Cyclic Correlation Analysis to Gear Damage Detection

The cyclic autocorrelation function is used with regard to the cyclostationarity of gear vibrations in order to extract the modulation features of gearbox vibration signals, and to detect localized gear damage. The properties of the amplitude and frequency modulated signals in the cyclic frequency domain are summarized in order to investigate the differences between the modulation features of normal and faulty gearbox vibration signals. Gear tooth spalling is detected by the presence of many sidebands in a zero-lag time-slice of the cyclic autocorrelation function, thereby indicating an increase in the degree of modulation effect. The damage source is located by the spacing of the sidebands.

A Robust Spectrum Sensing Method Based on Maximum Cyclic Autocorrelation Selection for Dynamic Spectrum Access

Spectrum sensing is an important function for dynamic spectrum access (DSA) type cognitive radio systems to detect opportunities for sharing the spectrum with a primary system. The key requirements for spectrum sensing are stability in controlling the probability of false alarm as well as detection performance of the primary signals. However, false alarms can be triggered by noise uncertainty at the secondary devices or unknown interference signals from other secondary systems in realistic radio environments. This paper proposes a robust spectrum sensing method against such uncertainties; it is a kind of cyclostationary feature detection (CFD) approaches. Our proposed method, referred to as maximum cyclic autocorrelation selection (MCAS), compares the peak and non-peak values of the cyclic autocorrelation function (CAF) to detect primary signals, where the non-peak value is the CAF value calculated at cyclic frequencies between the peaks. In MCAS, the desired probability of false alarm can be obtained by setting the number of the non-peak values. In addition, the multiple peak values are combined in MCAS to obtain noise reduction effect and coherent combining gain. Through computer simulations, we show that MCAS can control the probability of false alarm under the condition of noise uncertainty and interference. Furthermore, our method achieves better performance with much less computational complexity in comparison to conventional CFD methods.

A Blind OFDM Detection and Identification Method Based on Cyclostationarity for Cognitive Radio Application

The key issue in cognitive radio is to design a reliable spectrum sensing method that is able to detect the signal in the target channel as well as to recognize its type. In this paper, focusing on classifying different orthogonal frequency-division multiplexing (OFDM) signals, we propose a two-step detection and identification approach based on the analysis of the cyclic autocorrelation function. The key parameters to separate different OFDM signals are the subcarrier spacing and symbol duration. A symmetric peak detection method is adopted in the first step, while a pulse detection method is used to determine the symbol duration. Simulations validate the proposed method.

Experimental study of the propagation of noise-like acoustic signals in aqueous and air media

The propagation of acoustic signals of special form, having a phase modulated by noise-like phasecoded sequences with a single-level cyclic autocorrelation function, in aqueous and air media has been experimentally investigated. The data transfer by noise-like signals at subkilometer distances is reported.

On the Spectral Correlation of UWB Impulse Radio Signals

Cyclostationarity is an inherent characteristic of many communication signals, which can be exploited for performing various signal processing tasks. Determining the cyclic statistics of a signal of interest is often necessary in the design of signal processing systems exploiting this cyclostationary behaviour. This work investigates the second order cyclic statistics of various signalling schemes employed in ultra wideband impulse radio systems. Analytical expressions are derived for the cyclic autocorrelation and spectral correlation density functions.

Cyclostationarity-Inducing Transmission Methods for Recognition among OFDM-Based Systems

This paper proposes two cyclostationarity-inducing transmission methods that enable the receiver to distinguish among different systems that use a common orthogonal frequency division multiplexing- (OFDM-) based air interface. Specifically, the OFDM signal is configured before transmission such that its cyclic autocorrelation function (CAF) has peaks at certain preselected cycle frequencies. The first proposed method inserts a specific preamble where only a selected subset of subcarriers is used for transmission. The second proposed method dedicates a few subcarriers in the OFDM frame to transmit specific signals that are designed so that the whole frame exhibits cyclostationarity at preselected cycle frequencies. The detection probabilities for the proposed cyclostationarity-inducing transmission methods are evaluated based on computer simulation when optimum and suboptimum detectors are used at the receiver.

On the cyclostationary statistics of ultra-wideband signals in the presence of timing and frequency jitter

Cyclostationarity is an inherent characteristic of many man-made communication signals, which, if properly recognized, can be exploited for performing various signal-processing tasks. Determining the cyclostationary characteristics of a signal of interest is the first step in the design of signal processing systems exploiting this cyclostationary behaviour. This paper investigates the cyclostationary statistics of various signalling schemes employed in ultra-wideband (UWB) communication systems. Analytical expressions are derived for the cyclic autocorrelation and spectral correlation density functions in the presence of random timing and frequency jitter, which are characterized by discrete-time stationary random processes with known distribution functions.

Frequency-Demodulated Analysis Based on Cyclostationarity for Local Fault Detection in Gears

The demodulation analysis has been extensively used for gear diagnosis. However these techniques mainly deal with the amplitude-modulated signal instead of the frequency-modulated signal. Due to the symmetrical phase relationship of the sidebands, the amplitude-demodulated methods are not suitable for the frequency-modulated signal. This paper introduces the theory of cyclostationary processes as a powerful frequency-demodulation tool for the diagnosis of gears. The Cyclic Autocorrelation Function (CAF) is an important second-order cyclic statistics and acts as an efficient parameter to the frequency-demodulated analysis. In this paper, the CAF of frequency-modulated signal is deduced carefully. Through the discussion of frequency feature of the CAF slice at different cyclic frequency, two useful conclusions have been arrived about the frequency-demodulation. Firstly, the CAF slice at even multiples of the modulator-frequency can demodulate the frequency-modulated signal directly. Secondly, the amplitude-demodulated methods are suitable for the CAF slice of frequency-modulated signal at some special cyclic frequencies, which are equal to odd multiples of the modulator-frequency or close to the double carrier-frequency. These features of the CAF slice mentioned above overcome the invalidation of amplitude-demodulated methods for the frequency-modulated signal and increase it’s application range in engineering. Application in simulated and experimental data from a gear rig verifies the effectiveness of the frequency-demodulated method based on cyclostationarity.

Algebraic solution of the synthesis problem for coded sequences

The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations for a given code dimension is solved. It is pointed out that the problem of synthesis of PC sequences is related to the fundamental problems of discrete mathematics and, first of all, to a number of combinatorial problems, which can be solved, as the number factorisation problem, by algebraic methods by using the theory of Galois fields and groups.