Autocorrelation Minimization Research Articles

Revisiting the exomoon candidate signal around Kepler-1625 b

Context. Transit photometry of the Jupiter-sized exoplanet candidate Kepler-1625 b has recently been interpreted as showing hints of a moon. This exomoon, the first of its kind, would be as large as Neptune and unlike any moon we know from the solar system. Aims. We aim to clarify whether the exomoon-like signal is indeed caused by a large object in orbit around Kepler-1625 b, or whether it is caused by stellar or instrumental noise or by the data detrending procedure. Methods. To prepare the transit data for model fitting, we explore several detrending procedures using second-, third-, and fourth-order polynomials and an implementation of the Cosine Filtering with Autocorrelation Minimization (CoFiAM). We then supply a light curve simulator with the co-planar orbital dynamics of the system and fit the resulting planet–moon transit light curves to the Kepler data. We employ the Bayesian information criterion (BIC) to assess whether a single planet or a planet–moon system is a more likely interpretation of the light curve variations. We carry out a blind hare-and-hounds exercise using many noise realizations by injecting simulated transits into different out-of-transit parts of the original Kepler-1625 light curve: (1) 100 sequences with three synthetic transits of a Kepler-1625 b-like Jupiter-size planet and (2) 100 sequences with three synthetic transits of a Kepler-1625 b-like planet with a Neptune-sized moon. Results. The statistical significance and characteristics of the exomoon-like signal strongly depend on the detrending method (polynomials versus cosines), the data chosen for detrending, and the treatment of gaps in the light curve. Our injection-retrieval experiment shows evidence of moons in about 10% of those light curves that do not contain an injected moon. Strikingly, many of these false-positive moons resemble the exomoon candidate, that is, a Neptune-sized moon at about 20 Jupiter radii from the planet. We recover between about one third and one half of the injected moons, depending on the detrending method, with radii and orbital distances broadly corresponding to the injected values. Conclusions. A ΔBIC of − 4.9 for the CoFiAM-based detrending is indicative of an exomoon in the three transits of Kepler-1625 b. This solution, however, is only one out of many and we find very different solutions depending on the details of the detrending method. We find it concerning that the detrending is so clearly key to the exomoon interpretation of the available data of Kepler-1625 b. Further high-accuracy transit observations may overcome the effects of red noise but the required amount of additional data might be large.

LMMSE Channel Estimation Algorithm Based on Channel Autocorrelation Minimization for LTE-Advanced with Adaptive Guard Interval

In this paper, we propose an adaptive guard interval (GI) for LTE-advanced using channel impulse response (CIR) length estimation. The CIR length is estimated from the channel autocorrelation function. This estimate can be used to generate linear minimum mean square error filter coefficients for data subcarriers channel estimation and to adjust the GI length adaptively. The simulation results show that the improvement of mean square error for signal to noise ratio of 30 dB with CIR length estimation is about 10 dB when compared to conventional methods. Also, due to adaptive GI, the relative spectral efficiency can be increased by 0.11 compared to the conventional system with constant GI.

Lattice implementation of adaptive channel shortening in multicarrier transmission over IIR channels

Time-domain equalization is crucial in reducing channel dispersion and canceling interference in multicarrier systems. The equalizer is a finite impulse response (FIR) filter with the purpose that the delay spread of the combined channel-plus-equalizer IR is not longer than the cyclic prefix length. In this paper, a specific framework of long FIR channel-shortening problem is studied. In fact, approximated by a stable pole-zero model, we show that the channel transfer function poles introduce interference. Hence, to cancel bad poles, we propose the use of lattice structure to implement the channel shortener which places their zeros very close to critical channel poles and cancels them out. For low complexity implementation, we adopt adaptive algorithms to design the lattice channel shorteners. This paper analyzes the lattice structure performances of two blind adaptive channel shorteners: sum-squared autocorrelation minimization and multicarrier equalization by restoration of redundancy algorithms. The proposed implementation performances are given in terms of bit rate, and the simulation results are studied in the context of asymmetric digital subscriber line system.

Blind adaptive low-complexity time-domain equalizer algorithm for ADSL systems by adjacent lag autocorrelation minimization (ALAM)

This paper presents new algorithms that exploit uncorrelation between adjacent data samples produced by IFFT in ADSL systems. These algorithms update time-domain equalizer (TEQ) coefficients by adjacent lag autocorrelation minimization (ALAM) to shorten the channel. ALAM is an addition to the family of several existing autocorrelation-based algorithms that can achieve similar or better performance at lower complexity compared to other algorithms. The complexity reduction is achieved by designing a cost function without the sum-square, and further utilizing symmetrical TEQ property to reduce the complexity of the adaptation of TEQ to half of other existing algorithms. Furthermore, to avoid the limitations of lower bitrate after reaching the maximum bitrate and high complexity, an adaptive TEQ using equal-taps constraint (ETC) is introduced to maximize the bitrate along with achieving the lowest complexity. In addition, a simplified approach is used to calculate the expectation to reduce the computational complexity for ALAM and the other existing autocorrelation-based algorithms. Simulation results demonstrate that the proposed algorithms and modified existing algorithms achieve similar or better performance figures with reduced complexities.

Reduction of Average Path Length in Binary Decision Diagrams by Spectral Methods

This paper deals with analytic methods for the calculation and reduction of the average path lengths (APLs) in binary decision diagrams (BDDs). Usually, information-theoretic measures and information-theoretic techniques are used to construct BDDs of minimal APLs. Specifically, the mutual information between a Boolean function and its variables and the Shannon-Fano prefix coding are utilized. This paper deals with the problem of the APL reduction by using spectral techniques. Particularly, methods based on the properties of the Walsh spectrum of a Boolean function and its autocorrelation function are discussed. It is shown that the APL is a linear function of the autocorrelation values, that is, the APL depends on the Boolean function's properties in the time domain (autocorrelation) rather on the Boolean function's properties in the frequency domain (Walsh spectrum). In addition, it is shown that information-theoretic criteria like the mutual information or the conditional entropy are equivalent to frequency-domain criteria. Consequently, existing information-theoretic approaches for APL reduction that are based on mutual-information criterion or the Walsh transform coefficients may derive a suboptimal APL. The representation of the APL as a function of the autocorrelation values opens a way to determine the optimal ordering of the input variables analytically. Two procedures for APL reduction by ordering and by using linear combinations of the input variables are presented: (1) minimization by using the autocorrelation values and (2) minimization by using the mutual information between the Boolean function and a linear function of the input variables. The time-domain approach may derive a linearized BDD of a lower APL, whereas the information-theoretic approach has a lower computational complexity with comparable performance. Experimental results show the efficiency of the suggested techniques.

Blind, adaptive channel shortening by sum-squared auto-correlation minimization (sam)

We propose a new blind, adaptive channel shortening algorithm for updating the coefficients of a time-domain equalizer in a system employing multicarrier modulation. The technique attempts to minimize the auto-correlation terms of the effective channel impulse response outside a window of desired length. The proposed algorithm, known as sum-squared auto-correlation minimization (SAM), requires the source sequence to be zero-mean, white, and wide-sense stationary, and it is implemented as a stochastic gradient descent algorithm. Simulation results are provided, demonstrating the success of the SAM algorithm in an asymmetric digital subscriber loop (ADSL) system.