In-phase Channels Research Articles

Field-domain rapid-scan EPR at 240 GHz for studies of protein functional dynamics at room temperature

We present field-domain rapid-scan (RS) electron paramagnetic resonance (EPR) at 8.6T and 240GHz. To enable this technique, we upgraded a home-built EPR spectrometer with an FPGA-enabled digitizer and real-time processing software. The software leverages the Hilbert transform to recover the in-phase (I) and quadrature (Q) channels, and therefore the raw absorptive and dispersive signals, χ′ and χ′′, from their combined magnitude (I2+Q2). Averaging a magnitude is simpler than real-time coherent averaging and has the added benefit of permitting long-timescale signal averaging (up to at least 2.5×106 scans) because it eliminates the effects of source-receiver phase drift. Our rapid-scan (RS) EPR provides a signal-to-noise ratio that is approximately twice that of continuous wave (CW) EPR under the same experimental conditions, after scaling by the square root of acquisition time. We apply our RS EPR as an extension of the recently reported time-resolved Gd-Gd EPR (TiGGER) [Maity et al., 2023], which is able to monitor inter-residue distance changes during the photocycle of a photoresponsive protein through changes in the Gd-Gd dipolar couplings. RS, opposed to CW, returns field-swept spectra as a function of time with 10ms time resolution, and thus, adds a second dimension to the static field transients recorded by TiGGER. We were able to use RS TiGGER to track time-dependent and temperature-dependent kinetics of AsLOV2, a light-activated phototropin domain found in oats. The results presented here combine the benefits of RS EPR with the improved spectral resolution and sensitivity of Gd chelates at high magnetic fields. In the future, field-domain RS EPR at high magnetic fields may enable studies of other real-time kinetic processes with time resolutions that are otherwise difficult to access in the solution state.

Influence of quadrature transformation imbalance on the noise immunity of signal reception with amplitude-phase shift keying

Objectives. At the present time, amplitude-phase shift keyed (APSK) signals are actively used in satellite communication systems. In particular, they are applied in systems which operate in a limited radio frequency spectrum with increased data transmission quality requirements. Such systems use multi-channel type receivers with maximum likelihood decision on the received symbol (correlation receiver) or quadrature type receivers. The noise immunity of these receivers is directly dependent on the quality of the formation of reference oscillations. These oscillations are reference signals for correlation receivers and in-phase and quadrature components for quadrature receivers. The aim of the work is to analyze the influence of the amplitude and phase parameter spread of the in-phase and quadrature channels on the noise immunity of receiving APSK signals with a circular shape of the signal constellation.Methods. Methods of statistical radio engineering, theory of optimal signal reception, and computer simulation are used.Results. The study established the characteristics of noise immunity of the APSK signal reception depending on the spread of parameters of the quadrature converter. The theoretical calculations were confirmed by the results of modeling the transmission of APSK signals in a Gaussian communication channel. A comparison with systems using quadrature amplitude modulation (QAM) was carried out, in order to assess system stability in the presence of spread parameters among other similar systems.Conclusions. The studies enabled us to conclude that an imbalance of the quadrature reference oscillations can lead to a significant decrease in the noise immunity of radio systems using APSK signals. The minimum energy loss due to imbalance of quadrature reference oscillations is achieved when the imbalance value is less than 10% in amplitude and 2°–3° in phase. The amplitude imbalance of quadrature reference oscillations when receiving QAM signals is more pronounced than in the case of APSK signals. The phase imbalance affects approximately the same.

A novel capacitor voltage fluctuation suppression method for the low-frequency operating stage of MMC driven pumped storage system

The pumped storage power plant, which has the energy conversion and storage capacity, is an important solution for improving the power grid absorption ability to the unstable and fluctuating new energy from wind farms, as well as photovoltaic power stations. The modular multilevel converter (MMC) is a competitive topology for driving the pumped storage motor due to the advantages of high output power level and low output current harmonics. However, the voltages of the sub-module capacitors fluctuate largely when the MMC is operating at low-frequency stage, which would lead to an abnormal start-up process or an unstable low-speed running state of the variable speed pumped storage system. In order to suppress the low-frequency voltage fluctuation of the MMC sub-module capacitors, this paper proposes a charge channel topology including in-phase and inter-phase channel between the sub-modules for transferring the capacitor charge. Then, the reverse fluctuating fundamental component and third harmonic circulating component, as well as the synchronizing fluctuating second harmonic component, of the sub-module capacitor voltages could be counteracted, respectively. Eventually, the start-up operation performance, as well as the low-speed operation performance of the variable speed pumped storage system are enhanced greatly. The effectiveness of the proposed low-frequency capacitor voltage fluctuation suppression method is verified through simulation results.

Blind Estimation of GPS M-Code Signals under Noncooperative Conditions

In the process of Global Positioning System (GPS) modernization, M-code signals with better immunity to interference have been proposed and used in place of P(Y) signals as new authorization signals. A typical positioning, navigation, and timing (PNT) service is based on the local interrelation operation between the reference signal and the received signal. To obtain a PNT, the receiver should generate replicas of the pseudorandom code for acquisition and tracking. However, due to the use of an encryption algorithm, the receiver cannot use the M-code signal under noncooperative conditions. This paper presents an algorithm for estimating M-code sequences without prior knowledge. This algorithm adopts a waveform matching technique and a time domain filtering method to extract M-code from the in-phase channel and quadrature channel of the GPS L1 band. A high-gain antenna is used to receive GPS signals to keep the signal from being drowned out by noise. The experimental results show the feasibility of the method. Therefore, it is helpful for studying and evaluating the performance achieved without prior knowledge of the GPS signals.

Effect of Quadrature Control Mode on ZRO Drift of MEMS Gyroscope and Online Compensation Method.

The quadrature coupling error is an important factor that affects the detection output of microelectromechanical system (MEMS) gyroscopes. In this study, two quadrature error control methods, quadrature force-to-rebalance control (Mode I) and quadrature stiffness control (Mode II) were analyzed. We obtained the main factors affecting the zero-rate output (ZRO) under force-to-rebalance (FTR) closed-loop detection. The analysis results showed that the circuit phase delay in Mode I caused the quadrature channel to leak into the in-phase channel. However, in Mode II, the quadrature coupling stiffness was corrected in real time, which effectively improved the stability of the ZRO. The changes in the vibration displacement and Q-factor were the main factors for the ZRO drift in Mode II. Therefore, we propose an online compensation method for ZRO drift based on multiparameter fusion. The experimental results on a cobweb-like disk resonator gyroscope (CDRG) with a 340 k Q-factor showed that the bias instability (BI) of Mode II was significantly better than that of Mode I. After online compensation, the BI reached 0.23°/h, and the bias repeatability reached 3.15°/h at room temperature.

Differential RCS of Modulated Tag

Differential RCS characterizes the aptitude of a tag to modulate the backscattered power. This parameter is classically estimated based on the variation of the in-phase and quadrature (IQ) channels in the time domain. This communication introduces a generalization of the RCS backscattered by a tag and a new definition of the delta RCS in the frequency domain. The analytical model is based on stochastic processes and allows to estimate the delta RCS from the power spectral density of the modulated signal backscattered by the tag. The associated measurement is compared to the classical time-domain-based methods. Results show a good agreement with a difference between the different approaches less than 0.5 dB. Finally, the proposed method relies on simple synchronization between the emitter and the receiver to estimate the delta RCS while maintaining the accuracy.

Flow transition in periodically fully developed wavy channels

In the present study, numerical investigations have been performed to study the flow transition mechanism in wavy channels using finite volume-based open source field operation and manipulation. Two different wavy channel configurations are chosen, which represent two different flow destabilization mechanisms, viz., Kelvin–Helmholtz and centrifugal instabilities. Sinusoidal walls with out-of-phase and in-phase channel configurations have been considered in the present study. Steady to chaotic flow transition in two different channel configurations are investigated by varying Reynolds number. A detailed flow regime map is presented for the two different wavy channel configurations. Unsteady flow features have been illustrated with the help of instantaneous streamlines, velocity contours, vorticity contours, and iso-Q surfaces. For the out-of-phase configuration, the flow changes from two-dimensional steady to two-dimensional unsteady in the Re range of 175–185, and then three-dimensional unsteady flow is observed for the Re varying from 250 to 260. On the contrary, for the in-phase configuration, the transition happens directly from steady two-dimensional flow (Re < 101) to unsteady three-dimensional (Re > 102) in a very narrow range of Re. Transitions in the two different wavy channels have been examined in detail using Hilbert–Huang transformation, phase-space reconstruction, Poincaré section, recurrence plot, and dynamic mode decomposition. Frequency, growth rate, and vortex structures of the dominant modes are illustrated corresponding to each value of Re for the considered channel configurations.

Additional Condition on CSCG Random Vectors for I/Q Channels: With Application to CIS in NOMA

Circularly-symmetric complex Gaussian (CSCG) random vectors (Rvecs) are often used to model practical in-phase and quadrature (I/Q) channels in communication systems. However, we know that CSCG Rvecs do not completely encompass practical I/Q channels. Thus, in this study, we propose an additional condition for CSCG Rvecs to be valid over I/Q channels, namely, a purely-real complex correlation coefficient (CCC). We then investigate the effects of an invalid CCC on the achievable data rate of non-orthogonal multiple access (NOMA) with correlated information sources. Results revealed that a purely-real CCC constraint should be imposed on CSCG Rvecs, when considering practical I/Q channels.

Chiral-induced spin selectivity in the formation and recombination of radical pairs: cryptochrome magnetoreception and EPR detection

That the rates and yields of reactions of organic radicals can be spin dependent is well known in the context of the radical pair mechanism (RPM). Less well known, but still well established, is the chiral-induced spin selectivity (CISS) effect in which chiral molecules act as spin filters that preferentially transmit electrons with spins polarized parallel or antiparallel to their direction of motion. Starting from the assumption that CISS can arise in electron transfer reactions of radical pairs, we propose a simple way to include CISS in conventional models of radical pair spin dynamics. We show that CISS can (a) increase the sensitivity of radical pairs to the direction of a weak external magnetic field, (b) change the dependence of the magnetic field effect on the reaction rate constants, and (c) destroy the field-inversion symmetry characteristic of the RPM. We argue that CISS polarization effects could be observable by EPR (electron paramagnetic resonance) of oriented samples either as differences in continuous wave, time-resolved spectra recorded with the spectrometer field parallel or perpendicular to the CISS quantization axis or as signals in the in-phase channel of an out-of-phase ESEEM (electron spin echo envelope modulation) experiment. Finally we assess whether CISS might be relevant to the hypothesis that the magnetic compass of migratory songbirds relies on photochemically-formed radical pairs in cryptochrome flavoproteins. Although CISS effects offer the possibility of evolving a more sensitive or precise compass, the associated lack of field-inversion symmetry has not hitherto been observed in behavioural experiments. In addition, it may no longer be safe to assume that the observation of a polar magnetic compass response in an animal can be used as evidence against a radical pair sensory mechanism.

A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.

I/Q Imbalance Aware Nonlinear Wireless-Powered Relaying of B5G Networks: Security and Reliability Analysis

Physical layer security is known as a promising paradigm to ensure secure performance for the future beyond 5G (B5G) networks. In light of this fact, this paper elaborates on a tractable analysis framework to evaluate the reliability and the security of wireless-powered decode-and-forward (DF) multi-relay networks. More practical, the nonlinear energy harvesters, in-phase and quadrature-phase imbalance (IQI) and channel estimation errors (CEEs) are taken into account. To further enhance the secure performance, two relay selection strategies are presented: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1) suboptimal relay selection (SRS); 2) optimal relay selection (ORS)</i> . Specifically, exact analytical expressions for the outage probability (OP) and the intercept probability (IP) are derived in closed-form. For the IP, we consider that the eavesdropper can wiretap the signal from the source or the relay. In order to obtain more deep insights, we carry out the asymptotic analysis as well as the diversity orders for the OP in the high signal-to-noise ratio (SNR) regimes. Numerical results show that: 1) Although the mismatches of amplitude/phase of transmitter (TX)/receiver (RX) limit the OP performance, it can enhance IP performance; 2) Large number of relays yields better OP performance; 3) There are error floors for the OP due to the CEEs; 4) There is a trade-off for the OP and IP to obtain the balance between reliability and security.

Noise immunity of autocorrelation demodulator of signals with differential phase shift keying in the presence of rayleigh fading and harmonic interference

The wide spread of various radio systems with phase shift keying, including multi-position (MPSK), is due to their high noise immunity and ease of construction of the transmitting and receiving parts of the equipment. In real equipment, additional differential (relative) encoding is used when implementing transmitter and receiver circuits and, accordingly, DMPSK signals are used. One of the ways to receive such signals is to use an autocorrelation demodulator built on a quadrature scheme. The paper studies the noise immunity of an autocorrelation demodulator of signals with differential phase shift keying in the presence of Gaussian noise, Rayleigh fades and harmonic interference in the radio channel. The statistical parameters of signals and interference in the inphase and quadrature channels of the autocorrelation demodulator are determined. For M = 2 and 4, analytical formulas are obtained for the probability of a symbolic error, conditional on the random phase of harmonic. It is verified that the formula at M = 2 without harmonic interference reduces to an expression known from the literature. The values of the unconditional probabilities of symbolic errors are obtained by numerical averaging. It is shown that at a low level of harmonic interference, Rayleigh fading has a dominant effect. With a large level of interference, the additional energy loss can be several decibels, and at M = 4 these losses are significantly greater than at M = 2.

High Data Rate Discrete-Cosine-Spreading Aided M-Ary Differential Chaos Shift Keying Scheme With Low PAPR

Traditional differential chaos shift keying (DCSK) systems have low spectrum efficiency since half of time slots are used to transmit the reference chaotic signals. Our objective is to utilize the orthogonality of chaotic vectors and orthogonal cosine functions to construct a high data rate M-ary modulation scheme while providing improved reliability over wireless channels. In this brief, we propose a discrete-cosine-spreading (DCS) aided M-ary DCSK scheme. In our design, we first utilize the Gram-Schmidt algorithm to generate orthogonal chaotic basis vectors, then the linear combination of these vectors is used for M-ary modulations to improve the data rate. In order to suppress the interferences between modulated signals and reduce the peak to average power ratio (PAPR) induced by the overlapping of linear combinations, subsequently we apply discrete cosine codes to spread the modulated symbols. The resultant symbols are respectively transmitted over the quadrature and inphase channels. Furthermore, we derive the theoretical bit error rate (BER) expression over additive white Gaussian noise (AWGN) channel and multipath Rayleigh channels, then we analyze the computational complexity. Simulation results validate the theoretical derivations, and demonstrate that compared with the benchmark schemes, the proposed scheme could achieve higher data rate with the improved bandwidth efficiency, better BER performances over multipath fading channels, and lower PAPR.

Identical Code Cyclic Shift Multiple Access—A Bridge Between CDMA and NOMA

A traditional direct sequence CDMA (DS-CDMA) system works based on spreading codes, which should have good auto-correlation and cross-correlation properties to eliminate multiple access interference (MAI) and multipath interference (MI). However, to find a large number of good spreading codes is extremely difficult, and thus the capacity of a DS-CDMA system is limited strictly by the number of available spreading codes. This work proposes a downlink DS-CDMA design to enable multiple access using only one spreading code, namely identical code cyclic shift (ICCS) code, where in-phase and quadrature channels are used to transmit data and pilot, respectively. In particular, the ICCS code is used at a transmitter to perform DS modulation for user data, which is then sent to the in-phase channel. At the same time, the pilots are sent over the quadrature channel in a time-division multiplex (TDM) mode to construct a correlation matrix of ICCS code. At a receiver, MAI is removed by so-designed pilots plus a matched filter-bank. Simulation results show that the proposed ICCS multiple access (ICCSMA) can achieve a better performance than a traditional DS-CDMA system in a high signal to noise ratio region. ICCSMA serves as a bridge to turn CDMA to NOMA to enable massive connectivity in 5 G and beyond communications.

High‐data‐rate PO‐CDSK: a high effective chaotic communication scheme

To eliminate the intrasignal interference (ISI), phase-orthogonality correlation-delay-shift-keying (PO-CDSK) alternately chooses quadrature sinusoidal wavelets to modulate the reference signals in different symbol durations and keeps the reference and information-bearing signals orthogonal in one symbol duration. Unfortunately, in PO-CDSK, one data-modulated signal can carry only 1-bit information, resulting in a relatively low data rate. In this brief, the authors design a high-data-rate PO-CDSK system, in which 2-bits information share one time slot but transmitted over the inphase and quadrature channels, respectively. Theoretical BER expression of the proposed system is studied analytically, and simulations are performed over additive white Gaussian noise and Rayleigh multipath fading channels for verification. Results show that, without ISI components, the authors' new system performs much better than differential-chaos-shift-keying (DCSK), CDSK and high-efficiency DCSK systems in BER performance. Besides, the proposed system also achieves doubled spectral and energy efficiencies in comparison with PO-CDSK.

Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis

This paper studies optimum detectors and error rate analysis for wireless systems with low-resolution quantizers in the presence of fading and noise. A universal lower bound on the average symbol error probability ( $\mathsf {SEP}$ ), correct for all $M$ -ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve $M$ signal points. In the special case of $M$ -ary phase shift keying ( $M$ -PSK), the maximum likelihood detector is derived. Utilizing the structure of the derived detector, a general average $\mathsf {SEP}$ expression for $M$ -PSK modulation with $n$ -bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. For the Nakagami- $m$ fading, it is shown that a transceiver architecture with $n$ -bit quantization is asymptotically optimum in terms of communication reliability if $n \geq \log _{2}M +1$ . That is, the decay exponent for the average $\mathsf {SEP}$ is the same and equal to $m$ with infinite-bit and $n$ -bit quantizers for $n\geq \log _{2}M+1$ . On the other hand, it is only equal to $\frac {1}2$ and 0 for $n = \log _{2}M$ and $n , respectively. An extensive simulation study is performed to illustrate the accuracy of the derived results, energy efficiency gains obtained by means of low-resolution quantizers, performance comparison of phase modulated systems with independent in-phase and quadrature channel quantization and robustness of the derived results under channel estimation errors.

Frequency Interleaving IF Transmitter and Receiver for 240-GHz Communication in SiGe:C BiCMOS

This article presents a fully integrated modular wideband frequency interleaving (FI) transmitter and receiver for high data rate communication applications. At the transmitter side, three independent in-phase and quadrature-phase (IQ) baseband channels are upconverted to different intermediate frequencies (IFs) and then interleaved. At the receiver side, the interleaved signals are downconverted and separated back to each independent channel. Single-ended inputs and outputs are utilized to reduce the pin count, for a more practical realization and higher potential toward future system scaling. Special design techniques are followed to minimize crosstalk and intermodulation products between the channels. All circuits are manufactured and measured in a 130-nm SiGe:C BiCMOS technology with $f_{\textbf {T}}/f_{\textbf {max}}$ =300/500 GHz. The FI transmitter achieves a channel bandwidth of 2.5 GHz with less than 3-dB difference across different channels until 15-GHz IF. It consumes 560 mW from 2.5 and 3.3 V supplies and occupies a silicon area of 1.9 mm2. The FI receiver achieves a baseband channel bandwidth of 2.5 GHz with a 1-dB difference between the channels until the same IF. It consumes 860 mW from 2.5 and 3.3 V supplies and has a chip area of 1.55 mm2. The circuits are deployed in a communication experiment; first, in a back-to-back test with a direct cable connection, demonstrating a data rate of 15.6 Gb/s across the three IQ channels with a 16-QAM modulation scheme and a worst case transmitter-to-receiver error vector magnitude (EVM) of −18.6 dB. Then, a wireless experiment is performed with a 240-GHz front end with on-chip antenna, demonstrating a data rate of 7.8 Gb/s with QPSK modulation and a worst case EVM of −8.3 dB, across a wireless link of 15 cm. To the best of our knowledge, this is the first article that demonstrates a wireless transmission at sub-terahertz (sub-THz) carrier frequencies utilizing FI architectures.

A Novel Equalizer for 112 Gb/s CAP-Based Data Transmission Over 150 m MMF Links

In this paper a novel feedforward and decision feedback equalizer is proposed for the first time for use in short-reach high-speed communication links based on carrierless amplitude and phase (CAP) modulation. The proposed new equalizer mitigates crosstalk between the in-phase (I-) and quadrature (Q-) channels resulting from the non-linear phase response of the link enabling significant improvement in the link performance when operating at high data rates. The structure of this novel equalizer is introduced, its operation is described, and simulation and experimental studies on short-reach high-speed MMF links using 850 nm multimode VCSELs are presented. Data transmission tests are carried out over 150 m of OM4 MMF at 112 Gb/s using CAP modulation and the proposed CAP equalizer, and a bit-error-rate (BER) within the hard-decision forward error-correction (HD-FEC) threshold of 3.8 × 10−3 is achieved. The link is also tested when a conventional equalizer is used instead of the CAP equalizer and when adaptive discrete multitone (DMT) modulation is applied. The performance of the link is compared for these different transmission schemes and it is shown that the use of the novel equalizer and CAP modulation outperforms the other two schemes. The proposed equalizer can be implemented with low additional complexity, providing a potential cost-effective solution enabling >100 Gb/s single-lane data transmission in short-reach MMF-based links.

Coherent ePIC Receiver for 64 GBaud QPSK in 0.25 μm Photonic BiCMOS Technology

In this paper, we present a monolithically integrated coherent receiver with on-chip grating couplers, 90° hybrid, photodiodes and transimpedance amplifiers. A transimpedance gain of 7.7 kΩ was achieved by the amplifiers. An opto-electrical 3 dB bandwidth of 34 GHz for in-phase and quadrature channel was measured. A real-time data transmission of 64 GBd-QPSK (128 Gb/s) for a single polarization was performed.

Secondary flow in spanwise-periodic in-phase sinusoidal channels

Direct numerical simulations (DNSs) are performed to analyse the secondary flow of Prandtl’s second kind in fully developed spanwise-periodic channels with in-plane sinusoidal walls. The secondary flow is characterized for different combinations of wave parameters defining the wall geometry at $Re_{h}=2500$ and 5000, where $h$ is the half-height of the channel. The total cross-flow rate in the channel $Q_{yz}$ is defined along with a theoretical model to predict its behaviour. Interaction between the secondary flows from opposite walls is observed if $\unicode[STIX]{x1D706}\simeq h\simeq A$, where $A$ and $\unicode[STIX]{x1D706}$ are the amplitude and wavelength of the sinusoidal function defining the wall geometry. As the outer-scaled wavelength ($\unicode[STIX]{x1D706}/h$) is reduced, the secondary vortices become smaller and faster, increasing the total cross-flow rate per wall. However, if the inner-scaled wavelength ($\unicode[STIX]{x1D706}^{+}$) is below 130 viscous units, the cross-flow decays for smaller wavelengths. By analysing cases in which the wavelength of the wall is much smaller than the half-height of the channel $\unicode[STIX]{x1D706}\ll h$, we show that the cross-flow distribution depends almost entirely on the separation between the scales of the instantaneous vortices, where the upper and lower bounds are determined by $\unicode[STIX]{x1D706}/h$ and $\unicode[STIX]{x1D706}^{+}$, respectively. Therefore, the distribution of the secondary flow relative to the size of the wave at a given $Re_{h}$ can be replicated at higher $Re_{h}$ by decreasing $\unicode[STIX]{x1D706}/h$ and keeping $\unicode[STIX]{x1D706}^{+}$ constant. The mechanisms that contribute to the mean cross-flow are analysed in terms of the Reynolds stresses and using quadrant analysis to evaluate the probability density function of the bursting events. These events are further classified with respect to the sign of their instantaneous spanwise velocities. Sweeping events and ejections are preferentially located in the valleys and peaks of the wall, respectively. The sweeps direct the instantaneous cross-flow from the core of the channel towards the wall, turning in the wall-tangent direction towards the peaks. The ejections drive the instantaneous cross-flow from the near-wall region towards the core. This preferential behaviour is identified as one of the main contributors to the secondary flow.