### WP 2

## WP2: Stochastic modelling for channel and traffic (partners P1, P2, P3, INT1, INT2, INT3).

This WP deals with two random features met by any communication system: the wired or wireless transmission channel, and the traffic. Both subsystems are investigated in this WP as both can be characterized by stochastic space-time behaviors that directly impact the system performance. Regarding propagation, accurate models capturing all relevant effects are required in order to compensate and/or benefit from the variability of the channel, which can be observed in many dimensions (antenna, link, polarization, frequency, interference, etc). In particular, the introduction of high rate and cooperative multi-antenna schemes calls for a new framework of multi-dimensional channel modelling tools that capture all different propagation mechanisms, not only in a more accurate and a more comprehensive manner, but in an analytical and stochastic fashion. Another important recent trend is that antenna systems also become more and more complex, implying that their radiation characteristics must also be included in the complete channel model. Finally, the last years have also witnessed the convergence of methodologies used in wired and wireless channel modelling. Given the large bandwidth and the associated small wavelengths, random effects and crosstalk become increasingly important in wired links, whereas in complex wireless media, deterministic full-wave solutions that accurately solve the Maxwell equations are needed to grasp propagation effects when antennas are directly deployed on large and intricate supports. In terms of traffic, flexible and analytically tractable models must take into account the space-time variability of concurrent phenomena, i.e. the burstiness and the spatial characteristics of packets carried by a network during subsequent time intervals or between different nodes. Hence, modeling the space-time dynamics of traffic is essential to deliver the promised performance.

In this workpackage, on the one hand, more comprehensive channel models will be derived for multi-conductor, multi-link or multi-band systems and/or for systems operating in complex media. On the other hand, space-time traffic models will be developed taking into account the specific nature and characteristics of the communication environment. These models, after proper macro-modelling in WP1, will be applied in WP3 and WP4 to optimize transceiver designs as well as packet buffering and scheduling, for the performance metrics identified in WP1.

### SWP2.1: Stochastic full-wave modelling of multi-Gbit/s multiconductor wired links.

As explained in form C, we aim at further improving the backplane transceiver performance, beyond 10Gbit/s per lane and aspire to reach 100 Gbit/s per lane. To this end it is crucial to obtain very broadband models of the channel characteristics including crosstalk, such that signal coordination can be harnessed to fully exploit the channel. Channel behavior becomes extremely challenging for the following reasons: (i) most geometrical details are at least of the order of a tenth of the smallest wavelength of interest (say 1 mm). Hence, full-wave solutions of the Maxwell equations become necessary, as opposed to the classical quasi-TEM or quasi-TM ones; (ii) the electrical properties of the materials can no longer be regarded to be constant. Disregarding this frequency-dependent material behavior leads to non-causal waveforms, incorrect phase delays and incorrect signal losses; (iii) as at the highest frequencies, the roughness of the copper becomes at least of the order of the skin-depth, disregarding this roughness substantially underestimates the signal loss; (iv) geometry and material uncertainties become very important and channel models must be able to quantify these uncertainties and their impact. As full-wave Maxwell solvers are very expensive in terms of CPU-time, one must heavily rely on efficient multivariate macro-models.

#### Broadband channel models.

([Plaza2006][Demeester2008]) present the first multiconductor transmission line (MTL) RLGC-models for single and coupled lines in the presence of losses and semiconductor substrates based on an integral equation approach. Here, the approach of ([Demeester2008]) will be extended to the full-wave regime. A particular challenge is how to correctly account for the effect of copper roughness. A much used simplified model is that of Hammerstadt ([Hammerstad1975]) in which a single multiplicative coefficient, varying between 1 at low frequencies and 2 at high frequencies, is taken into account to increase the value of the elements of the resistance matrix. More recently, more complex models and modified coefficients have been proposed ([Hall2007], [Curran2010], [Tsang2010]). Here, the effect of stochastic roughness will be investigated using an integral equation approach. This approach builds on the ideas put forward in ([Tsang2010]) but will answer the very many questions that still remain open. Recent contributions to this discussion ([Demeester2009], [Demeester2010]) on the internal impedance and on current crowding near conductor corners pave the way for further advances.

#### Stochastic variability.

Of particular concern is the effect of stochastic variations of parameters and how to incorporate these into the models without running into insurmountable CPU-time demands. In the past the generalized stochastic polynomial chaos (gPC) methodology has been successfully used for stochastic computations ([Xiu2009]). Other recent applications of this approach can be found in ([Diouf2009], [Sumant2011]). From ([Xiu2009]) it follows that gPC has mainly been applied to differential equation formulations. In the past considerable experience in the sensitivity analysis (mean value, standard deviation) of backplane interconnections based on suitably modified integral equations ([Ureel1996], [Laermans1997]) was obtained. Here, we will extend these previous efforts to a general stochastic analysis based on the gPC methodology. This extension to integral equations is new and particularly challenging when stochastically changing boundary surfaces are considered.

### SWP2.2: Stochastic antenna and multidimensional propagation modeling.

#### Multi-link analytical channel modeling.

One important multidimensional aspect of future cooperative networks lies in the joint signal processing of multiple links (e.g. transmitter-to-relay-to-receiver or network MIMO discussed in WP3). Even though very sophisticated radio channel models for single and multiple links, such as COST2100 ([Liu2010]) and WINNER II ([Kyosti2007]), already exist, they are often contradictory and still not fully validated. As an example, the intra- and inter-cell correlations of large-scale parameters (e.g. shadowing, delay-spread) can be 0, 0.5 or 1 depending on the model. While shadowing correlation has been studied extensively for non-distributed scenarios, the distributed (multi-cell) case is not well modeled at this stage. Also, only a few studies, such as COST 2100, take into account the impact of node mobility in a correct fashion. Recently, ([Agrawal2009]) modeled the shadowing between any two nodes as a weighted line integral of a spatial loss field, which, in turn, is modeled as a wide sense stationary Gaussian random field. Whereas the formulation allows calculating the shadowing correlation between the two links of any pair, the model always produces a positive shadowing correlation, although recent measurements ([Oestges2010]) also revealed negative correlations. Yet, it has been shown in ([Madan2008]) that some cooperative protocols are extremely sensitive not only to the value but also to the sign of the shadowing correlation. Further investigation is therefore required to address the issue of shadowing correlation in the network MIMO context ([Oestges2011]).

Furthermore, interference of other links is conventionally modeled on a system level by the signal to noise-and interference ratio (SINR), only. The shortcoming of this approach is that the correlation of different multi-antenna radio channels is not considered while this could likely impact the performance. Finally, most models totally ignore the impact of antenna patterns in network MIMO configurations, assuming large beamwidths for all antennas. Recently, the use of narrow-beam antennas was suggested to reduce the level of interference ([Marichenco2011]). This however raises other issues, which must be addressed globally. Research will therefore be oriented towards analytical stochastic models of multiple links (i.e. interference), by extending the recent work of ([Czink2011]) to less theoretical scenarios. Once models are developed and analytically expressed, they will be experimentally parameterized and/or validated in a number of representative scenarios, by means of a state-of-the-art MIMO channel sounder available within the BESTCOM network.

In all models, the main problem will be to keep the number of parameters limited (possibly a la carte, depending on the targeted performance metrics). This will enable a tractable abstraction in WP1, while still accounting for the relevant physical mechanisms, including the impact of antenna patterns.

#### Multi-band channel characterization.

Cognitive scenarios require efficient multiband or broadband antenna designs and channel models. Although multi-band communications could be seen as a particular case of multi-links, some challenges are very specific, and will be addressed in the SWP.

In the area of multi-band channel models, the variation of relevant channel parameters with frequency is still an open problem ([Porrat2010]). New models taking account of the possible cross-band correlations of such parameters would be beneficial in a view of future abstraction (as this strongly reduces the number of parameters) and will receive due attention.

A second challenge is to design multi-band antennas that exhibit stable radiation characteristics in terms of radiation pattern, antenna impedance and polarization when deployed with complex media in their reactive near-field, and/or when being subjected to bending ([Shaozhen2009]). ([Dierck2010], [Sani2010]) therefore proposed to design and fabricate active antennas that satisfy design criteria over a much wider band. In this project, this approach will be extended, relying on full-wave/circuit co-design combined with macro-model-based optimization. Relying on strategies such as ([Craeye2009]) can also be very helpful, where an accurate numerical modeling of the near-field coupling also accounts for important platform effects.

#### Hybrid deterministic/stochastic methods for complex transmission channels.

In order to model a complete transmission channel in complex propagation environments (such as indoor scenarios) including intricate antenna systems, deterministic (full-wave, ray-tracing, …) tools are often essential. However, they are computationally expensive, while their accuracy heavily depends on the accuracy of the geometric and material descriptions. Hence, in channel modeling, stochastic approaches are adopted, with channel statistics being fitted on experimental data, using various Gaussian distributions and their combinations ([Patzold2011], [Bandemer2009], [Cotton2009], [VanTorre2011], [Reusens2009]). Still, the quality of the channel model heavily depends on the particular conditions of the experimental setup. This makes it therefore difficult to build macro-models from measurements. Replacing measurements by deterministic models seems therefore a viable alternative, provided that these models are modified to account for the stochastic nature of the channel. A similar situation can be observed for antennas, where the recent interest in flexible antennas is one of the driving forces to include statistics in deterministic antenna models. Since antennas bend ([Hertleer2009]) or crumple ([Bai2011]), there is a need to ensure stable performance characteristics in a variety of operational conditions. Finally, in many configurations, it is very difficult to separate the antenna performance from the propagation mechanisms, as the antenna is directly located on, or integrated in a large object that influences both the radiowave propagation and the antenna characteristics ([Mecklenbräuker2011]). In even more critical cases, the large object is so close to the antenna that it must be included in the design phase of the antenna to obtain the correct radiation characteristics of the antenna.

Hence, in this SWP we shall develop analytical stochastic tools that combine full-wave or asymptotic deterministic models, such as multi-level Fast Multipole Algorithms (MLFMA) or ray-tracing ([Mani2011]), with stochastic methods that account for the uncertainties about the actual environment, with respect to geometry, materials parameters, location and orientation of the different objects affecting the propagated signals. In recent literature, stochastic full-wave techniques have appeared, e.g. combining finite element techniques with polynomial chaos theory ([Sumant2011]). We will expand on these approaches and perform research on applying them within the context of fast boundary integral equation techniques. Again, experimental validations will rely on a channel sounder available inside the BESTCOM network. Alternatively, recent efforts ([Sibille2008]) also point towards the directions of stochastic antenna modeling, together with reduced pattern representations based for instance on spherical or cylindrical-wave expansions with stochastic representations of the modal coefficients.

### SWP2.3: Space-time traffic models.

There has been a considerable volume of research on traffic modeling during the past decades, e.g. for file exchange, voice, streaming video, video conferencing or surveillance, etc, mainly for (fixed) IP backbone or access networks, leading to the investigation of models such as Markov-modulated arrivals, on/off-sources, train arrivals and batch-renewal arrivals. This points the way towards the development and evaluation of powerful, realistic, flexible and analytical models for traffic streams carried by wired and wireless digital communication links. Because of the time-dependence between the numbers of packets carried by a link during subsequent time intervals, such traffic is often referred to as being “bursty” (see e.g., ([Jia2005]), where the property that internet traffic exhibits burstiness and correlation over a wide span of time scales is discussed). This dependence or burstiness has different origins, which can be catalogued and modeled as follows:

- Some sources, such as streaming video, are inherently bursty. A popular approach has been to model such sources by means of a Discrete-Batch Markovian Arrival Process (D-BMAP; for more details, see ([Blo1993], [Ste2011]), which is an arrival model whereby a traffic source can find itself in a finite number of possible states (which correspond e.g. to the speed at which the data in the subsequent video frames is generated, depending on the type of codec, coding rate, type of frame, etc), and transitions between source states are Markovian. On some occasions, autoregressive models have been adopted as well to model such sources. Some topics of special interest on this behalf are the impact of the heterogeneous nature of the sources that are carried by the links on the specifics of the model that is being adopted (i.e., which model to select for a specific type of source, or aggregation of sources), and the parameter fitting procedure/algorithm for realistic sources (i.e., once a specific model has been selected, how to determine the specific numerical values of the respective parameters: a genetic algorithm e.g. could be a good approach).
- A very specific type of dependence is incurred when multiple traffic streams - say two, typically of the same type - have different end-to-end destinations (they may or may not share the same channel between two nodes or relays). This invokes the concept of class-based blocking: if the arriving packets are accommodated by a common resource that takes care of their processing and transmission to the proper destination, then data packets with a given destination A may be hindered or blocked by packets destined to B that arrived earlier, even when the link to destination A is free. This dependence between traffic streams, which is of a very specific nature, has not yet been examined in a very detailed way; one recent study that examines this mechanism in a packet switch can be found in ([Bee2009]).
- On a higher level, traffic burstiness also originates from session-based user behavior: in a session-based source model (see e.g. [Hof2010]), data packets are generated by some (possibly heterogeneous) set of sources, whereby each source is capable of starting and ending finite-length sessions during which they are active and generate traffic. For instance, in a web server on the internet, a session could correspond to a file download by a user. Session-based arrival models take into account that packets are typically generated by the sources in bursts that may last over a relatively long period of time. We should emphasize that such type of session-based behavior can also be a consequence of the network or channel conditions: it is, for instance, well known that the fading state of a wireless link is of a bursty nature (i.e., if the link is in a fading state, it is likely to remain there for a while), which basically gives rise to a behavior that is of a similar nature as session-based, albeit that it is now network/channel-induced instead of user-induced.

Eventually, modelling the combination of the above phenomena in a viable stochastic traffic model, taking into account the specific nature and characteristics of the communication network, will be investigated, as no model exists at this stage.

In addition to temporal characteristics, a growing number of applications and protocols now adapt their spatial traffic pattern in response to congestion inside the network. A first example is that most networks have the ability to load balance flows over multiple paths by using equal cost multipath. This is a rather static technique that depends on the flow identifiers, but one can expect that in the future this will become more dynamic. Content Distribution Networks (CDNs) are another example. These CDNs are key players in the delivery of a large fraction of the internet traffic. When considering their spatial distribution, they rely on efficient load-balancers that enable them to move huge aggregated flows between servers based on various metrics. Other applications are able to dynamically change the destination of the flows depending on the network conditions ([Xu2011]). While CDNs are often centralized (or at least managed by a single organization), peer-to-peer applications are completely distributed. Another example is the work on multipath transport protocols, such as Multipath TCP that is currently being standardized ([Ford2011]) and implemented ([Barre2011]). Once deployed, this TCP extension could have a major impact on all applications by enabling them to transparently use multiple paths between a given source-destination pair. Despite the impact that the spatial distribution of the traffic has on the network performance and the network resources, most of the work in this area has not considered how the paths taken by traffic flows change over time. We will address this challenging problem by first developing models of the spatial distribution of specific applications based on measurements. These models will then be generalised in a second step. Finally, we will study the interactions between the temporal and the spatial models.