Non-circular Research Articles

Submaximal Cycling Power Using Noncircular Chainrings

During cycling, muscular power is produced during both leg extension and flexion, with minimal power production occurring during the transitions. Prolonged extension and flexion phases and reduced transition phases could increase cycling power by allowing muscles to generate power for a greater portion of the cycle. Noncircular (NC) chainrings could prolong the powerful leg extension phase by varying crank angular velocity (ω) within the pedal cycle. Mixed findings from previous comparisons of circular (C) and NC chainrings may be related to different approaches in quantifying cycling power. One approach common to power meters is to calculate power as the product of average ω and torque (T) for the pedal cycle. This assumption might overestimate power with NC chainrings. PURPOSE: To determine the extent to which the assumption of constant ω overestimates power values during submaximal cycling. METHODS: Eight healthy participants (age=35±8 yr, mass=75±7 kg, height=1.8±0.1 m) performed 5-min steady state cycling on an isokinetic cycle ergometer using a NC chainring. Following a 5-min warm-up, participants cycled at 90% of lactate threshold power (219±51 W) at 80 rpm and repeated the protocol with a C chainring after a 5-min rest. Participants were visually blinded to chainring conditions. Pedal forces were measured with a force sensing pedal and pedal and crank position were measured with optical encoders. T and ω were measured at 240Hz. Power was calculated as: Method 1: P1=[(ΣNn-1 Tn)/N]x[(ΣNn-1 ωn)/N] and Method 2: P2=[ΣNn-1 (Tn x ωn)]/N. A paired t-test was used to compare differences in power calculations between chainring conditions. RESULTS: Calculated power (P1: 110±22 W; P2: 110±22 W) did not differ for C chainring condition. P1 (117±21 W) was 4±1% higher than P2 (112±21 W) for NC chainring condition (p<0.01). CONCLUSIONS: Method 1 overestimated power with a NC chainring as it did not account for the generally sinusoidal ω produced by the NC chainring, where the largest instantaneous T values occurred when instantaneous ω values were below the average. These results suggest that the assumption of constant ω may overestimate power when using NC chainrings and may explain reports of increased cycling power.

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper, we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations.

Noncircular Chainrings Do Not Improve Maximum Cycling Power and Joint-Specific Power during Maximal Cycling

Net cycling power is mainly produced during leg extension and flexion actions with minimal power produced during the transition between extension and flexion. A possible strategy to maximize cycling power is to increase the time spent in extension and flexion, while decreasing the time spent in transition. Noncircular (NC) chainrings can be oriented to prolong the powerful leg extension phase by varying crank angular velocity (ω) within the pedal cycle. However, the degree to which instantaneous crank ω influence muscle and joint actions depends on the degrees of freedom (DOF) in the leg/crank/pedal system. Previous investigations on cycling power using NC chainrings have produced mixed findings. These mixed findings may be due to cyclists exploiting redundant DOF in the leg/crank/pedal system to manipulate joint ω independent of crank ω. PURPOSE: To evaluate the effects of NC chainrings on joint-specific kinematics and power production during maximal cycling. METHODS: Ten healthy trained cyclists (age=34±8yr, mass=72±9kg, height=1.8 ±0.1m) performed maximal cycling trials of 3 s at randomly assigned pedaling rates (60, 90, and 120 rpm), and chainring eccentricities (ratio of major-to-minor axis) of 1.0 (Cir), 1.13 (Rotor), and 1.24 (Osym), respectively. Participants were visually blinded to chainrings. Joint-specific powers were averaged over complete pedal revolutions and extension-flexion phases. Joint-specific kinematics were analyzed for the portion of the pedal cycle where NC chainrings imposed 80% of their eccentricities (ECC80) on crank ω. RESULTS: Joint-specific powers were unaffected by chainring eccentricity. Ankle extension ω was significantly reduced (-13±12% and -37±13% at 90 and 120 rpm, respectively; all p<0.05) with the Osym chainring, whereas knee and hip extension ω were unaffected. Crank ω, ankle, knee, and hip extension ω within ECC80 increased with increasing pedaling rates (all p<0.01). CONCLUSION: NC chainrings did not improve maximum cycling power or alter joint-specific power during maximal cycling. Knee and hip ω remained unaffected with only ankle ω affected by chainring eccentricity. These results suggest that the effects of the NC chainrings on crank ω were eliminated by the cyclists’ ankling action and thus did not alter the major power producing actions of the hip and knee.

DOA and Noncircular Phase Estimation of Noncircular Signal via an Improved Noncircular Rotational Invariance Propagator Method

We consider the computationally efficient direction-of-arrival (DOA) and noncircular (NC) phase estimation problem of noncircular signal for uniform linear array. The key idea is to apply the noncircular propagator method (NC-PM) which does not require eigenvalue decomposition (EVD) of the covariance matrix or singular value decomposition (SVD) of the received data. Noncircular rotational invariance propagator method (NC-RI-PM) avoids spectral peak searching in PM and can obtain the closed-form solution of DOA, so it has lower computational complexity. Animproved NC-RI-PMalgorithm of noncircular signal for uniform linear array is proposed to estimate the elevation angles and noncircular phases with automatic pairing. We reconstruct the extended array output by combining the array output and its conjugated counterpart. Our algorithm fully uses the extended array elements in the improved propagator matrix to estimate the elevation angles and noncircular phases by utilizing the rotational invariance property between subarrays. Compared with NC-RI-PM, the proposed algorithm has better angle estimation performance and much lower computational load. The computational complexity of the proposed algorithm is analyzed. We also derive the variance of estimation error and Cramer-Rao bound (CRB) of noncircular signal for uniform linear array. Finally, simulation results are presented to demonstrate the effectiveness of our algorithm.

Robust Spectrum Sensing for Noncircular Signal in Multiantenna Cognitive Receivers

Although noncircular (NC) signals are frequently encountered in wireless communications, their statistical property has not yet been utilized in state-of-the-art methods for spectrum sensing. In this paper, a variant of Hadamard (HDM) ratio test is devised to exploit the NC property of the primary signals for spectrum sensing, which is named the NC-HDM algorithm. As the NC-HDM approach is able to exploit full statistical property of the NC signals and handle deviations from independent and identically distributed (IID) noise, it is superior to the state-of-the-art algorithms in detection accuracy and/or robustness. Moreover, performance analysis is conducted for the NC-HDM approach, including the invariant property, false-alarm probability and detection probability. That is, employing the moment-matching Box's Chi-square approximation, the false-alarm probability can be determined. Since the exact moments of the NC-HDM test statistic under the signal-absence hypothesis can be determined and all moments have been matched, the derived false-alarm probability is very accurate, leading to simple and precise computation of the theoretical decision threshold. On the other hand, as the first two exact moments of the NC-HDM test statistic under the signal-presence hypothesis can be precisely calculated, the detection probability based on moment-matching Beta approximation is quite accurate. Numerical results are included to demonstrate the superiority of the NC-HDM approach and validate our theoretical calculations.

Reduced-Dimension Noncircular-Capon Algorithm for DOA Estimation of Noncircular Signals

The problem of the direction of arrival (DOA) estimation for the noncircular (NC) signals, which have been widely used in communications, is investigated. A reduced-dimension NC-Capon algorithm is proposed hereby for the DOA estimation of noncircular signals. The proposed algorithm, which only requires one-dimensional search, can avoid the high computational cost within the two-dimensional NC-Capon algorithm. The angle estimation performance of the proposed algorithm is much better than that of the conventional Capon algorithm and very close to that of the two-dimensional NC-Capon algorithm, which has a much higher complexity than the proposed algorithm. Furthermore, the proposed algorithm can be applied to arbitrary arrays and works well without estimating the noncircular phases. The simulation results verify the effectiveness and improvement of the proposed algorithm.

R-dimensional esprit-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) noncircular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R \mathchar"702DD NC Standard ESPRIT and the R \mathchar"702DD NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R \mathchar"702DD antenna arrays and do not require a centro-symmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R \mathchar"702DD NC ESPRIT-type algorithms is identical in the high-effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.

NON-CIRCULAR CHAIN RING ALLOWS A REDUCTION OF JOINT LOADING IN CYCLING

Non-circular (NC) chain rings were primarily designed to improve the mechanical effectiveness of cycling. Their use can be investigated for application in rehabilitation: they could provide a solution to design an effective exercise reducing joint loading. The aim of this study was to analyze the differences in kinematics, energy consumption, and joint moments between circular and NC chain rings, then to identify a profile that can reduce joint loads, maintaining equal mechanical and metabolic works. Five young participants performed two tests on a cycloergometer; one with a circular chain ring and the other with an NC one. The test consisted in 15 min of cycling; during which they were asked to cycle at three different speeds and at two different powers. Stereophotogrammetric and metabolic data were acquired. Statistical analysis was applied on metabolic data. Joint angular velocities were obtained from kinematic data. A two-dimensional (2D) model of cycling was designed to estimate joint moments with both chain rings. A different ring profile was suggested to further reduce joint flexion peak moment. NC chain ring allows a reduction of flexion joint moments with respect to the circular one without significant difference in metabolic and kinematic data. The new profile proposed further decreases maximum knee flexion moment maintaining equal mechanical work.

Blind CFO Estimators for OFDM/OQAM Systems With Null Subcarriers

This paper deals with the problem of blind carrier-frequency offset (CFO) estimation in OFDM systems based on offset quadrature amplitude modulation (OFDM/OQAM) with null subcarriers. Specifically, by assuming that the number of subcarriers is sufficiently large, the received signal is modeled as a complex Gaussian random vector (CGRV). Since the OFDM/OQAM signal results to be a noncircular (NC) process, by exploiting the generalized probability density function for NC-CGRVs, the unconditional maximum likelihood (ML) algorithm for CFO estimation in non dispersive channel is proposed. Moreover, a modified version of the unconditional ML CFO estimator is considered. The performance of the derived algorithms, assessed via computer simulation, is compared with that of recently proposed estimators exploiting the second-order cyclostationarity and with the Gaussian Cramer-Rao bound.

Blind Frequency-Offset Estimation for OFDM/OQAM Systems

This paper deals with the problem of blind carrier-frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems based on offset quadrature amplitude modulation (OFDM/OQAM). Specifically, by assuming that the number of subcarriers is sufficiently large, the received signal is modeled as a complex Gaussian random vector (CGRV). Since the OFDM/OQAM signal results to be a noncircular (NC) process (i.e., its relation function is different from zero), by exploiting the generalized probability density function for NC-CGRVs, the unconditional maximum-likelihood algorithm for CFO estimation in nondispersive channel is derived. Moreover, due to its computational complexity, a more feasible estimator is considered. The performance of the proposed estimators, assessed via computer simulation, is compared with that of recently proposed CFO estimators exploiting second-order cyclostationarity and with the Gaussian Crameacuter-Rao bound

ML-based symbol timing and frequency offset estimation for OFDM systems with noncircular transmissions

This paper deals with the problem of joint symbol timing and carrier-frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems with noncircular (NC) transmissions. Maximum-likelihood (ML) estimators of symbol timing and CFO have been derived under the assumption of nondispersive channel and by modeling the OFDM signal vector as a circular complex Gaussian random vector (C-CGRV). The Gaussian assumption is reasonable when the number of subcarriers is sufficiently large. However, if the data symbols belong to an NC constellation, the received signal vector becomes an NC-CGRV, i.e., a CGRV whose relation matrix (defined as the statistical expectation of the product between the vector and its transpose) is not identically zero. Hence, in this case, previously mentioned estimators, termed MLC estimators, are not ML estimators. In this paper, by exploiting the joint probability density function for NC-CGRVs, ML estimators are derived. Moreover, since their implementation complexity is high, feasible computational algorithms are considered. Finally, refined symbol timing estimators, apt to counteract the degrading effects of intersymbol interference (ISI) in dispersive channels, are suggested. The performance of the derived estimators is assessed via computer simulation and compared with that of MLC estimators and that of modified MLC (MMLC) estimators exploiting only ISI-free samples of the cyclic prefix

Kinematic optimization of ball-screw transmission mechanisms

Abstract The paper proposes a method for the kinematic optimization of transmission mechanisms, where non-circular (NC) gears are used to perform a mechanical control on the output motion. The investigation presented here deals with the motion control of a ball-screw transmission mechanism. The objective is lowering the peak acceleration value of the screw, by designing a pair of variable radius gears as a driving mechanism. The kinematic characteristics of the ball-screw mechanism are analyzed by means of non-dimensional motion equations in order to formulate the optimization problem. A genetic algorithm (GA) is then implemented to optimize the objective function, and a penalty method is used to fulfil the design rules. The kinematic analysis of the optimal mechanism revealed a 37% reduction of the peak acceleration of the screw in comparison with a constant pitch screw, operated at a constant speed. A kinematic simulation is used to validate the method.

A Data-Aided Symbol Timing and Frequency Offset Estimation Algorithm for OFDM Systems

In this paper the problem of data-aided symbol timing and frequency offset estimation in OFDM systems is considered. A synchronization scheme based on a pilot symbol containing two identical parts obtained by transmitting BPSK data symbols on the even subcarriers and setting zero on the remaining subcarriers is proposed. In this case, if the number of subcarriers is sufficiently large, the pilot symbol can be modeled as a noncircular (NC) complex Gaussian random vector (CGRV). By exploiting the joint probability density function of NC-CGRVs, the joint maximum likelihood estimator for the parameters of interest is derived. Since its implementation complexity is high, a simpler synchronization scheme is obtained. Moreover, refined symbol timing and frequency offset estimators, that assure relevant performance in multipath channels, are proposed.