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C2Cdesignguidelines

WorkPackage9 Deliverable9.2

UNIVERSITYOFNOTTINGHAM

Gregor Tanner

24/10/18

Contributors: UoN, CNRS, ISAE, NXP, IMST, TUM

Abstract This report describes the formulation of guidelines for the design and implementation

of chip-level wireless interconnects as part of printed circuit board electronics.

Dissemination - Public

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Introduction

WP No: 9 Start/End Months: 31-36 Lead: TUM Part.: UoN(18) TUM(18) LPMC (7) ISAE(6) IMST(12) NXP(6)

WP Title: C2C design guidelines – formulation and validation

Objectives: Validation of C2C software tool and formulation of wireless C2C guidelines

Description of work: The combined expertise developed in WP8&9 will be put together; the software packages will be validated against measurement data on C2C devices and design decisions for the antenna and chip architecture will be verified. Guidelines for a future C2C technology will be formulated. Optimisation strategies will be developed for setting up C2C arrangements minimising unwanted interference; the basic features of the guidelines will be put together in a project workshop in months 34 (T9.1 all). Formulation of guidelines (T9.2 TUM). Deliverables: D9.1 Validation data set and numerical data; D9.2 C2C design guidelines.

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Task9.2–UoN

1. Introduction

This task concerns the formulation of guidelines for the design and implementation of chip-level wireless interconnects as part of printed circuit board electronics. All partners have worked together on defining step-by-step guidelines for the two different scenarios described in more detail in Sec.2 and 3 of this report as well as in the Final Report. These are the so-called 1) Generic scenarios (GS): The surrounding environment (PCB design, housing, etc) are not under the control of the wireless C2C design engineer and optimised C2C solutions need to be found with the constraints given. 2) Dedicated scenarios (DS): The surrounding environment are under full control of the wireless C2C design engineer and C2C solution can be constructed determining the constraints for the of the device.

Further sets of guidelines have been developed for measuring 2-point correlations in Sec. 4 and supporting hardware design through simulations in Sec. 5. A description of of the NEMF21 Simulation Toolbox is given in the Appendix.

While the guidelines and recommendations reported here result from both the modelling and the experimental work carried out from 2015 - 2018, their definition became clear only after a thorough study of the benchmarks tackled in WP7 and WP8 as described in the Deliverable Reports D7.1 and D8.1. We summarize the guidelines in this report D9.2, the interplay with the underpinning research is described in more detail in the Final Report.

2. Generic Scenario

The necessary steps for successful wireless C2C architecture will be described in the following sections, including the collection of the necessary information, the tools, a systematic description of the proposed workflow and different application examples.

Before getting started

I. Preliminary information needed: The questions that need to be answered when designing a C2C communication link are: what are the degrees of freedom for the design? Is it e.g. possible to change the routing and / or the stack-up of the PCB in order to add wired connections across the PCB? How much space may the functional blocks for the C2C communication occupy? Based on this information it can be decided whether a wired solution or one of the “general” or “dedicated” scenario wireless approaches is more suitable. In a second step, all necessary information about the geometry and material composition of the PCB and its environment needs to be collected. The reason for and importance of this is explained in more detail in the Final Report in the context of antenna types, position and orientation. Last, but not least, the application situation needs to be characterized with respect to noise. It needs to be clarified whether or not noise will have a significant impact on the signal-to-noise ratio, and therefore also on the channel capacity. If a significant noise level is expected, it is necessary to evaluate and characterise noise correlation by e.g. two-point measurements of the cross spectral-density (CSD) as described in separate guidelines in Sec.4 of this document. The resulting data can then be used to predict the noise signal power spectral-density at the antenna ports, by use of the C2C simulation toolbox that was developed in the context of WP8 and described in the Final Report.

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Figure 1: Application flow for the C2C simulation toolbox that uses inverse local imaging (ILI) to invert an evaluated vector field from a plane above the PCB onto an equivalent source distribution on the PCB.

II. The EMPIRE C2C simulation toolbox: The application flow of the numerical C2C simulation tool for EMPIRE XPU is depicted in Fig. 1. An inversion algorithm named Inverse Local imaging (ILI) is applied to evaluate vectorial field data from a plane parallel to and above the PCB. The ILI returns an equivalent source distribution on the surface of the PCB that produces the same field distribution. The source distribution is masked / windowed in an appropriate way to leave free areas, where the functional blocks of the wireless C2C communication can be designed.

III. When not to use C2C wireless communication: If the circumstances allow the use of wired connections e.g. strip lines instead of a wireless C2C communication link, this should usually be preferred. The advice “not to use wireless communication” within a design guideline for wireless C2C communication may seem odd at first, but in most cases this will be the reasonable decision with respect to costs, robustness and effort. Possible exceptions to this rule are applications with an excessive amount of on-PCB and between-PCB communication links with dynamic connections, e.g. in the context of a modular product concept. Another example would be extremely weight-critical devices, where all unnecessary wiring needs to be avoided.

Proposed work flow Sec. 4.2 in the Final Report contained various suggestions for approaching the design of a wireless C2C communication link. With this information in mind and the preliminary steps sketched above, the flow diagram shown in Fig. 2 has been devised to guide the work flow. This diagram can be used as a step-by-step guideline, starting with the upper left terminal labelled “Chip-to-chip communication required”. In the first steps, the user may decide to go for a wired solution or to proceed with a dedicated scenario approach, provided that this is indicated by the preconditions. If the general scenario approach is chosen, the user should analyse the environmental conditions of the problem and choose an appropriate antenna configuration. The workflow should then pass over to an iterative design process of creating a numerical model, possibly using the EMPIRE C2C simulation toolbox forming part of the NEMF21 Toolbox described in more detail in the Appendix. If a satisfying solution cannot be found with the current antenna configuration, the design process may go one step back and start over with a different antenna concept.

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Figure 2: Proposed workflow for designing a wireless C2C communication link.

Application examples The design guidelines for generic scenarios are discussed in the context of selected application examples.

I. Large distance between functional blocks: In case the distance between the functional blocks is very large, it shall be checked whether the blocks can be relocated to the edges of the PCB. If this is possible, a design with edge antennas should be considered, using guided EM waves around the PCB edges. This also applies if a between-PCB communication link is required.

II. Very noisy environment: If the environment of the wireless C2C communication link is very noisy, the power spectral density (PSD) of the noise should be investigated at the intended positions of the antennas. Thereby the noise correlation needs to be considered in a physical correct manner. Spatial and spectral minima of the PSD should be taken into account to decide optimal antenna positions and target frequencies.

III. Small enclosure (cavity modes): If the PCB is located in a small enclosure then special attention should be given to the cavity modes. The frequency of narrow-band dips is highly dependent on small geometric changes. Considering the unavoidable manufacturing tolerances for PCBs, the narrow band minima pose a serious risk to functionality, because in the final device they may coincide with the operation frequency of the antennas. Therefore suitable absorber concepts should be considered to increase the robustness of the design.

IV. Large/no enclosure: In case the PCB is intended to operate within a partly open enclosure or in free space, the challenge of the design is not limited to finding a suitable antenna for the in-plane communication on the PCB. Instead, the considerations regarding noise will become even more complex, because also external noise sources and electromagnetic interference (EMI) need to be taken into account.

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3. Dedicated Scenario

When wired solutions need to be avoided and wireless interconnects can form part of a new circuit design, multi-antenna type transmitter/receiver and their placement and configuration should be considered. In addition, accounting for system noise and environmental interference created by surrounding electronic components is important.

Before getting started

I. Preliminary information needed: The first question needs to be: is it possible to change the routing and/or the stack-up of the PCB at design-level stage? Arbitrary PCB layouts, for which all the information about geometry and materials of the PCB are available a priori and can be changed at will by the designer can be considered within the dedicated scenarios. Depending on the starting PCB layout – driven by the electronic design of components and depending on the specific functions to be implemented – the designer will face two scenarios where wireless interconnects may be designed, as shown in the initial work flow of Fig. 3.

Figure 3: Proposed workflow for designing a wireless C2C communication link.

If the chips and components to be interconnected wirelessly are close to each other and with no obstructions, an optimal decoupling and matching (DMN) can be designed from the known impedance matrix or scattering matrix of the antenna system as described in D8.1 and the Final Report in Sec. 4.3. This typically happens at distances shorter than a wavelength, and the design cycle should then be followed to maximize the channel capacity between adjacent chips where a wiring solution must be avoided. A flow chart for the design of near-field communication is sketched in Fig 4, the processes are explained in more detail in Sec 4.3 of the Final Report. In particular the interplay between antenna types, number and position of the antenna arrays and the distances between transmitting and receiving arrays needs to be optimized and the design of a Decoupling and Matching Network needs to be considered – see also remarks under point III below.

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Figure 4: Near-field flowchart: DMN design.

For distances greater than the wavelength, obstructions may be present that enrich scattering between transmit and receive antenna arrays. The situation is further complicated by the presence of metallic casings/shields, necessary to protect the device circuitry from external electromagnetic interference (EMI) and reduce emission levels regulated by electromagnetic compatibility (EMC) standards. The enclosure confines the electromagnetic energy further enriching the scattered field components – beneficial for multi-path assisted MIMO systems. Here, wave front shaping is an additional option to increase signal throughput. Case loading will dissipate part of the energy: enclosure volume and electric material parameters are needed to characterize the loss level caused by the enclosure. As in the generic scenario, it is necessary to evaluate and characterise the noise correlation. Near-field scanning methods discussed in D7.1 and in the Final Report in Sec 4.4 are used to predict the noise correlation function at the antenna ports to feed DEA and CTLM+TWF methods, which are part of the NEMF21 C2C Simulation Toolbox, see the Appendix. Interestingly, besides reducing EMI/EMC effects – and as pointed out in the example of large enclosures in the generic scenario - propagating noisy fields is instrumental to understand frequency and bandwidth of operation within the enclosure. As opposed to mobile communications, no licensing problem is present in NEMF and the wireless interconnect designer is free to choose the least interfering frequency of operation.

II. Increasing or decreasing losses in enclosures: The absorption occurring within the enclosure hosting the PCB at the operation frequency is critical. In presence of an electrically large case/shield, the volume of the enclosure, permittivity and electric conductivity of both enclosure walls and loading materials needs to be used to calculate the average loss factor of the modes excited by the wireless interconnect. If the loss factor , the signal-to-noise ratio is reduced causing a degradation of the performance as shown in D8.1 and the Final Report. If the loss factor is , good reverberation supports multipath fading where MIMO links perform well. In the regime the loss factor does not constitute a penalty anymore as explained in the Final Report: the case/shield supports correlated multipath interference and antennas are highly mismatched due to low losses. While losses should be kept as low as possible to avoid multipath mitigation and power dissipation, narrowband behavior should be avoided to assist digital signal modulation. The right trade off is found by calculating the coherence bandwidth of the cavity and comparing it with the communication bandwidth, whence . Once losses are

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established and the starting antenna arrangement chosen, the design cycle in Fig. 5 can be operated to achieve the target channel capacity . This capacity can be achieved with appropriate modulation and coding that depends on the transceiver signal driving the antenna arrays.

Figure 5: Far-field flowchart: wireless C2C communication link in enclosures.

III. When to use DMNs: Once an EMI free operation frequency and bandwidth has been established

from near-field scanning, the electrical scale associated with the distance between interconnects is established. The outcome of NEMF 21 suggests that the use of DMNs is necessary when: a) the

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length of the wireless interconnect covers distances within the near field of the transmit array; b) when the shielding enclosure supports a low modal overlap at the EMI-free operation frequency. Importantly, the DMN network should be designed by optimizing a template topology using components available off-the-shelf as explained in the Final Report.

IV. Determining noisy fields: In the far-field scenario and for low model overlap estimates of the noise levels need to be performed as part of the workflow program shown in Fig. 5. The information is obtained in a separate step based on measurements as described in the guidelines Sec. 4 of this document.

V. Wave front shaping: An additional measure to increase the channel throughput in the far-field is

based on wave front shaping techniques as outlined in the flow-chart, Fig. 5. Multiple antennas are used to to increase the stability of the link (unlike the MIMO set-ups introduced for the near-field to increase the number of independent channels). To obtain a stable link against perturbations four possibilities are considered:

a. Stable transmission: The transmission matrix T is calculated between the different antennas, which shall give one communication channel. The most stable transport should be given by the eigenvector with the highest eigenvalue of the Wigner-Smith time delay operator !"#

"$%𝑇', where f is the frequency.

b. Focusing on transmitter antenna: The scattering matrix 𝑆$)* of all transmitter antennas is calculated for slightly different positions of the receiver antennas. The highest eigenvalue of the generalized Wigner Smith operator !"+,-.

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' gives a high

transmission and reasonably stable transport. The transport is less stable than (a.) but much more than (d.)

c. Least back reflection to transmitter: The scattering matrix 𝑆/01 for the transmitter antennas is calculated as in (b.) Now the lowest eigenvalue and its eigenvector of the scattering matrix is determined. If the main source of energy drain is done by the receiving antennas, i.e. strongly reverberating environment, the transmission between transmitter and receiver should be high but with especially small back reflection, which helps to adjust the DMNs.

d. Highest transmission: By variation of the excitation of the antennas the optimal transmission matrix T is calculated. This procedure ensures the highest transmission, but should also be very unstable against perturbations/variations of the environment.

From these eigenvectors, delay lines to each antenna need to be determined and the final maximization of the mutual information can be tested.

Proposed workflow The initial workflow diagram in Fig. 3 guides the user through the design cycle of the wireless interconnect. Near field: If the wireless interconnect is compact and its length is in the near-field of the transmit antenna array, a DMN should be designed to reach the target data-rate and the workflow in Fig. 4 should be used. Given the antenna positions and frequencies, one must choose the antenna-type, which depends on the available space. If at least a 2x2 monopole antenna setup is possible, then the theoretical prediction for the optimal ratio of sub-channel power gains can be fulfilled. If not, then a DMN has to be set up while taking the precise environment into account. The procedure for

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implementing the DMN on the given PCB might have to be repeated iteratively to obtain the wanted data rate. Far-field: If the wireless interconnect must reach the far-field, obstacles and multiple reflections can be exploited to route the energy efficiently. The design workflow to be followed is depicted in Fig. 5 for dedicated scenarios of PCBs with casing/shielding. In the first step, the user decides the antenna type and configuration, as well as case size and shape. The number of antennas and channels are dictated by the target data-rate. In the second step, the user calculates the loss factor in the form of mode overlapping parameter and decides whether to use a statistical or a deterministic channel model describing the wireless link between transmit and receive antenna array. In case of high modal overlapping, a statistical approach based on random matrix theory (RCM or EH) can be used to generate the interconnect channel model statistics renormalized by the loss factor of the dedicated environment. The generation process involves the following steps: 1. Measure/simulate (using the full-wave methods in the C2C Simulation Toolbox) the free-space

radiation impedance matrix for the RCM or the coupling matrix for the EH; 2. Generate zero-mean unit-width Gaussian Random Variables (GRV) for eigenfunction statistics; 3. Generate uniformly distributed eigenvalue statistics; 4. Add loss factor perturbation to eigenvalues; 5. Form impedance/scattering matrix element realizations by Monte Carlo using statistics in 2. to 4.; 6. Form dimensionless voltage-voltage or current-current channel transfer matrix realizations by

combining elements of the impedance/scattering matrix.

The distribution of the mutual information can then be calculated from the Gram matrix of the channel transfer matrix. In the case of moderate modal overlap and in the presence of Line of Sight (LoS) or short orbits between transmit and receive array, the transmission channels can be modeled by an overcoupled state. Based on the EH statistical model, the user will go through the following optimization steps:

1. Measure the distribution of transmissions of the shielded PCB; 2. Determine a maximum-likelihood parameter as described in the Final Report; 3. If is much larger than one, the environment is still more important than the direct

communication with this model. 4. Use and to generate the realizations of the channel transfer matrix.

In case the modal overlap is low, the user should design a DMN as done in the near-field workflow of Fig. 4 to increase the data-rate. For this, it will be necessary to have detailed information about the statistical properties of the fields surrounding the PCB for which Near Field Scanning (NFS) of the PCB under various modes of operation will need to be carried out. The NFS measurements are done in a separate step – the corresponding guidelines are described below in Sec 4.

After NFS is performed, the following steps should be followed to estimate the average mutual information carried by noise fields radiated within a case/shield:

1. Perform NFS of the antennas and surrounding circuitry to characterise sources of noise and of the communication channels themselves. Output of this step consists of two-point correlation functions characterising emissions from both noise sources and the transmitting antennas;

2. If the surrounding geometry is electrically small, use full-wave methods to propagate correlation functions to the proposed site of receiving antennas. FDTD as well as CTLM and CTWF methods have been used as part of the C2C Simulation Toolbox to achieve this;

3. If the surrounding geometry is electrically large, convert source correlation functions to Wigner distributions and use DEA to predict field intensities at the proposed site of receiving antennas;

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4. Estimate upper bounds for mutual information, either direct from the propagated correlation functions if step 2 has been undertaken, or following step 3 by using DEA output as outlined in section 4.4 of the Final Report.

Once the channel model has been established and mutual information statistics predicted given specific antenna configurations within a shielded PCB, the workflow should then pass over to an iterative process that achieves channel capacity and target data-rates. This is typically done by optimizing the input signals exciting the transmit antenna array. To determine the excitation parameters, the following procedure is suggested: 1. numerically determine the transmission by illuminating each antenna; 2. group antennas for communication channels; 3. calculate the eigenvalues and eigenvectors of the corresponding operator (transmission,

generalized Wigner-Smith operator, reduced scattering matrix) for a given channel; 4. obtain the optimal eigenvalue; 5. start from 1. by restructuring, if the eigenvalue is not adequate; 6. calculate complex excitation eigenvector and adjust delay lines and powers for the antennas; 7. repeat from 4. for all other communication channels.

If the predicted channel capacity after wave front shaping does not reach the target data-rate, antenna number and arrangement should be modified, as well as frequency of operation, leading to an improved PCB layout and casing, and the design cycle should be restarted by evaluating the overlap factor and decide a channel model to re-evaluate the wireless interconnect performances.

Application examples The design guidelines for dedicated scenarios are discussed in the context of selected application examples.

I. Typical C2C configurations in free-space and LoS: In case the distance between transmit and receive arrays is smaller than a wavelength and there is LoS, the minimal configuration proposed to improve data-rate is a 2x2 MIMO wireless interconnect. On-board dipoles can be used to achieve two strong channels. Performances scale with the number of antennas used, although increasing the MIMO array size would result in an overly complicated DMN topology and network.

II. Typical C2C configurations in an enclosure: Wireless interconnects with patch antennas that are separated by several wavelengths show a poor transmission and, consequently, a low data-rate. MIMO interconnects benefit from enclosure reflection and the presence of the shield increases the average transmission. Unfortunately, it also causes large transmission parameter fluctuations which cause digital transmission instability.

III. Typical C2C configurations in free-space and NLoS: The presence of a metallic plate close to the planar PCB increases the average transmission while it reduces its magnitude of fluctuation. This situation suggests that increasing losses results in a more stable digital transmission across wireless interconnects.

4. Near Field Scanning (NFS)

Before getting started

An important component for both the GS and the DS is an evaluation of the noise levels in wireless C2C set-ups which may be due to system and component noise (and thus part of the transmitted signal), unwanted radiation from nearby components or EMI. Often – in particular if far-field components play a role – detailed information of the noisy fields emanating from the PCB is needed as input for the

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NEMF21 C2C Simulation Toolbox (ILI, DEA, CTLM+TWF) and to give system specific channel models. Near-field scanning (NFS) measurements of the PCB (including antenna configurations) need to be carried out in free space then.

Proposed workflow

To perform an NFS measurement run, first an appropriate field probe should be chosen. The probe needs to provide sufficient sensitivity in the desired frequency range and yet also has to allow for the spatial resolution of sample points desired for the scanning plane. Usually a trade-off exists between those requirements. The required spatial step for the sampling grid is determined by the wavelength and proximity to the radiation sources as

where h is the distance of the observation plane from the planar source.

The measurement set-up is shown in Fig. 6, where is the distance between the two red dots in the observation plane at the right.

Figure 6: Near-field scanning (NFS) of noisy wireless fields with two loop probes, connected to a multi–channel digital oscilloscope: scanning plane (left) and propagation of field-correlations to a further

observation plane (right).

A low noise amplifier (LNA) will enhance signal strength obtained from the probe before sampling and digitizing the signal. In general, characterization by either magnetic or electric tangential field components is sufficient. However, higher accuracy in characterization could by achieved by sampling both, magnetic and electric field components. While magnetic and electric field are coupled to each other, this coupling decreases at low frequencies and vanishes for the dc case.

Upon selection of preferably two identical field probes, probe compensation should be considered. The relation of the response of the output voltage level, delivered by the probe, to the magnetic or electric field impinging on the probe has to be quantified by magnitude and phase. Probe calibration is usually performed in frequency domain. After alignment of the DUT in its fixture and calibration of the automated two-probe scanning unit, a preliminary single-probe scan is executed to identify radiation hot-spots and thus to determine or adjust the scanning area for the subsequent two-probe scan. For a full characterization, both x- and y-components of the magnetic or electric field have to be captured for determining the field correlations. Hence, probes have to be oriented accordingly and multiple runs

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over all sample point pairs have to be executed. Cross-polarization correlation has to be considered as well. In some scenarios, with a known preferred polarization of the radiated emission, this requirement can be relaxed. For cyclo-stationary processes, the periodicity of the processes involved has to be taken into account. It is recommendable to test for the periodicity and analyze it first, in order to perform appropriate averaging in the post-processing step for the collected measurement data. In order to speed up the measurement process, the sequence of the sampling point pairs that have to be probed can be optimized in order to minimize the overall distance which probes have to be moved along by the automated positioner over the entire measurement run. Free-space propagation to different observation planes or estimates for correlated field distributions in enclosures can be done using the C2C NEMF21 software Toolbox.

5. Combining full-wave EM simulations and measurements for complex circuits and systems for C2C configurations

In designing fully integrated hardware components, advanced simulation tools have been developed and used in the context of Sec. 5 of the Final Report. The complexity of the task lead to the necessity to develop efficient partitioning methodologies in order to bring full-wave EM simulation accuracy at system-level, see schematically in Fig. 7. Efficient partitioning methods have been developed and applied to practical scenarios. The objective of partitioning strategies is to segment a complex circuit into sub-partitions to analyze separately and then combine, later on, with active parts/sources for global performances analysis/optimization.

Figure7:CircuitsandSystemspartitioningmethodologyaccountingforconductedand

radiatedcouplings.

The following Partitioning Rules and guidelines have been applied for properly dividing complex circuits and systems into sub-partitions for bringing EM accuracy at system-level:

1) No (or very little) EM coupling between the dividing planes. 2) The current at the location of the divider should be traveling perpendicular to the plane of the divider. This includes the ground return current. 3) The port should be well away from the DUT. If not, reference planes should be used. This rule is needed because a single mode of propagation should be on the line connected to the port. Otherwise, circuit theory does not work. 4) Any ports that are close to each other need to be calibrated together (i.e., co-calibrated/de-embedded). 5) At each divider, the ground reference for the ports needs to be clearly defined. When connecting the pieces back together with circuit theory, the circuit theory program will assume that the grounds are perfectly connected together with no discontinuity between them.

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6) Incorporation of measurement results in modeling can be achieved by using Field-Field correlation information as obtained through the guidelines in Sec. 4.

Appendix: The NEMF21 C2C Simulation Toolbox

In order to cover the vast range of topics necessary in a C2C design process multiple tools have been used and developed. The set of methods are combined in the NEMF21 Simulation Toolbox defined and described in more detail here and in the Final report in Sec. 3.1. In particular, the following tools are part of the toolbox:

The list of tools – see Sec. 3.1. in the Final Report:

- Direct field simulation using IMST's EMPIRE FDTD solver. This includes the Inverse Local Imaging (ILI) for analysing the optimal local placements of antennas on PCBs.

- Transmission Line Model (TLM & CTLM): The software contributed by UoN and TUM is equivalent to FDTD and allows to compute time-dependent field components and correlation functions.

- Transverse Wave Formulation (TWF&CTWF): An integral method developed by ISAE reducing the EM field to their component transversal to the PCB normal. It is the integral counter part of the above TLM description.

- Wigner functions and Dynamical Energy Analysis: Approximate methods developed by UoN to describe energy flow of radiation in the mid-frequency regime where finite-difference solvers (FDTD, TLM) become unmanageable due to small mesh sizes necessary for convergence. This versatile set of tools is held together by the guidelines describing use cases for each of the methods. Secondly, the tools are linked either by direct integration (e.g. ILI into Empire) or by allowing to reuse existing descriptions across methods; for example, meshes used in Empire can be used in DEA calculations and thereby extend the range of frequencies. TLM and TWF are linked via a conceptional similarity. Their difference, i.e. being an either integral or differential method, therefore allows to incorporate other aspects of the problem solution, for example, propagating correlations or cyclo-stationary noise.