Gaël Varoquaux

Russell A Poldrack

Predictive models avoid excessive reductionism in cognitive neuroimaging

Keywords: machine learning, cognitive models, psychology, brain imaging

Understanding the organization of complex behavior as it relates to the brain requires modeling the behavior, the relevant mental processes, and the corresponding neural activity. Experiments in cognitive neuroscience typically study a psychological process via controlled manipulations, reducing behavior to one of its component. Such reductionism can easily lead to paradigm-bound theories. Predictive models can generalize brain-mind associations to arbitrary new tasks and stimuli. We argue that they are needed to broaden theories beyond specific paradigms. Predicting behavior from neural activity can support robust reverse inference, isolating brain structures that support particular mental processes. The converse prediction enables modeling brain responses as a function of a complete description of the task, rather than building on oppositions.

Perception and action build upon an array of mental processes, which have been characterized in detail by the psychological sciences. However, unifying these psychological processes to model the relation between brain and mind in any given situation remains a great challenge [START_REF] Newell | You can't play 20 questions with nature and win: Projective comments on the papers of this symposium • Highlights the difficulty of giving an integrated picture on results on different mental processes involved in vision[END_REF]. The principal challenge lies in finding the appropriate representation of the components of cognition and behavior. Cognitive neuroscience builds upon controlled experiments to isolate these components and link them to brain activity. But quantifying the effects of any manipulation requires that the psychological or behavioral components of interest be clearly specified [START_REF] Poldrack | From brain maps to cognitive ontologies: Informatics and the search for mental structure[END_REF][START_REF] Krakauer | Neuroscience needs behavior: correcting a reductionist bias[END_REF]. Isolating components of mental processing leads to studying them only via oppositions, and this reductionism prevents the building of broad theories of the mind.

We believe that predictive modeling provides new tools to tackle this formidable task. The accumulation of a broad range of shared data in cognitive neuroimaging provides a widely varied set of observations of brain and behavior. Using these data, models can be built that accurately describe multiple experiments, going beyond the surface description of tasks to identify associations between brain systems and underlying mental processes that span across tasks. Whereas cognitive neuroscience has typically focused on particular theoretical oppositions, this approach instead builds models that generalize beyond specific tasks, based on the methodology of machine learning with a focus on out-of-sample prediction rather than the detection of specific experimental effects [START_REF] Yarkoni | Choosing prediction over explanation in psychology: Lessons from machine learning[END_REF].

Data-driven approaches are often distinguished from * Corresponding author hypothesis-driven research, with the implication that datadriven work is necessarily theory-free. However, we argue that data-intensive methods can actually provide the basis for building broader theories, which abstract away from the specifics of any particular experimental approach and thus have the potential to generalize to a much larger range of phenomena.

Prediction allows generalization to arbitrary new tasks and situations

Predictive models give a specific prediction, forecasting a target quantity numerical or categorical based on new data. In the framework of statistical machine learning, they contain tunable parameters that are adjusted to learn the association between data and target, usually with some penalty for model complexity [START_REF] James | An introduction to statistical learning[END_REF]. Performance can then be tested on unseen data. Predictive models provide powerful tools to learn brainmind associations from recordings of neural activity [START_REF] Varoquaux | How machine learning is shaping cognitive neuroimaging[END_REF][START_REF] Pereira | Machine learning classifiers and fMRI: a tutorial overview[END_REF][START_REF] Lebedev | Brain-machine interfaces: past, present and future[END_REF]. Compared to traditional computational neuroscience models, they allow generalization to new tasks and situations. Hence, they can provide conclusions that are not paradigm-bound, as cognitive neuroscience largely has been.

Broad generalizations can bridge very different situations. For instance [START_REF] Knops | Recruitment of an area involved in eye movements during mental arithmetic[END_REF] showed that learning brain-activity patterns that discriminate right from left saccades would classify mental additions as rightward saccades and subtractions as leftward. Whether or not brain-mind associations generalize can be tested across paradigms, and such tests highlight universal components of psychological processes. Studying memory encoding,

Predictive models versus classic neuroimaging analyses

By predictive models we refer to mathematical models of the data that explicitly minimize prediction error, typically relying on methods from machine learning. They differ from standard neuroimaging statistical methods in several way. First, their validity is established by successful predictions from new data, and not by isolating significant differences across observations. This test is sound without the need for modeling assumption, such as Gaussian noise. As a consequence, predictive models often are more complex, departing from maximum-likelihood estimates and fitting more unknowns variables than available observations [START_REF] Wu | Complete functional characterization of sensory neurons by system identification[END_REF][START_REF] James | An introduction to statistical learning[END_REF]. For neuroimaging, this additional complexity opens the door to modeling more effects jointly, and therefore building models that describe more than an isolated dimension of cognition. Also, given that a model is validated by its predictions, rather than by its goodness of fit on the data used to fit the model, validation can be done using different constructs than those used to build the model, for instance using high-level descriptions of cognition instead of features of the experiments or brain signals. Testing for out-of-sample properties, as when measuring prediction, helps avoiding some pitfalls of in-sample model testing using p-values, such as circularity or trivial effects [START_REF] Wasserstein | The asas statement on pvalues: context, process, and purpose[END_REF]. [START_REF] Polyn | Category-specific cortical activity precedes retrieval during memory search[END_REF] used a classifier to generalize from perception to memory retrieval to show that both processes share a common neural substrate. In research on pain, neural evidence supports separating physical and emotional pain, as brain activity can robustly discriminate them across studies [START_REF] Wager | An fMRI-based neurologic signature of physical pain[END_REF].

Generalization to arbitrary tasks supports reverse inference

Associating neural activity in a brain structure or network to a predicted behavior that generalizes to arbitrary tasks provides a deeper understanding of the computations supported by the structure. Bound to a given paradigm, such characterization would be an invalid reverse inference, as in an experiment only neural activity is observed as a consequence of a psychological manipulation, rather than causing a mental state [START_REF] Poldrack | Can cognitive processes be inferred from neuroimaging data[END_REF]. Decoding studies, which predict behavior from observed activity, provide evidence for reverse inference. However, to characterize function beyond simple oppositions, decoding must be applied across a very broad sampling of behavior and cognition. Analyzing many different studies jointly provides a practical solution to sample such a variety of mental states [START_REF] Poldrack | Inferring mental states from neuroimaging data: from reverse inference to large-scale decoding[END_REF]. Generalization across experimental paradigms shows that identified brain structures are not a mere consequence of experimental details of the task [START_REF] Varoquaux | Atlases of cognition with large-scale human brain mapping[END_REF].

Causal questions are central to interpreting results of a neuroimaging experiment: what in the observed brain

Decoding

Extracting brain activity patterns that discriminate conditions and predict them from unseen neural activity.

Generalization

In a new paradigm, the brain-mind association carries over and predicts features of the behavior. activity is a consequence of the task, versus a cause of the behavior or the mental state? Comparing which brain structures are activated in a standard analysis to which ones support decoding can rule out structures that mediate a function but do not cause it. In stimuli-driven experiments, detecting a structure in both models suggests that it is a direct consequence of the stimulus, for instance activity in the fusiform face area for face recognition, rather than a non-specific side effect, such as activity in primary visual areas. Such side effect cannot support decoding [START_REF] Weichwald | Causal interpretation rules for encoding and decoding models in neuroimaging[END_REF].

Formal representations of tasks and behavior are important

Modeling brain activity beyond a specific paradigm needs robust and general descriptions of stimuli, tasks, and behavior [START_REF] Turner | The cognitive paradigm ontology: design and application[END_REF]Poldrack et al., 2011b). Building such descriptions faces two challenges: capturing all the relevant mental processes in a task, and formalizing their relationships. The psychological manipulations of a task provide information regarding the main mental processes it recruits. Yet, it is necessary to go beyond the primary effect of interest: a visual n-back experiment is not only a memory experiment, but also involves visual processing ,decision making, and many other functions [START_REF] Varoquaux | Atlases of cognition with large-scale human brain mapping[END_REF]. Relating mental processes across studies raises many subtle questions, for instance whether to distinguish between autobiographical and episodic memory. Taxonomies or ontologies give a formal framework to capture this knowledge [START_REF] Poldrack | From brain maps to cognitive ontologies: Informatics and the search for mental structure[END_REF].

However, using cognitive ontologies in brain mapping is a chicken-and-egg problem, given that neuroimaging should also inform these ontologies, via the links between mental processes that it reveals. Data-driven semantic techniques hold promise to build representations of cognitive neuroscience concepts informed by brain data [START_REF] Poldrack | Discovering relations between mind, brain, and mental disorders using topic mapping[END_REF][START_REF] Yeo | Functional specialization and flexibility in human association cortex[END_REF]Bolt et al., 2017). Used across the literature, they can overcome variations in terminology and link mental processes that elicit similar activity or build more open-ended encoding or decoding models [START_REF] Yarkoni | Large-scale automated synthesis of human functional neuroimaging data[END_REF][START_REF] Rubin | Decoding brain activity using a largescale probabilistic functional-anatomical atlas of human cognition[END_REF]Dockès et al., 2018).

Encoding models extract better representations of tasks

Encoding models, which predict brain data from the task [START_REF] Naselaris | Encoding and decoding in fMRI[END_REF], can go beyond describing a task with a small set of labels and capture details and interplay in its components. Because they allow for the use of much richer and less constrained descriptions of tasks [START_REF] Wu | Complete functional characterization of sensory neurons by system identification[END_REF], they can ground a model of brain function beyond specific experimental paradigms. To model psychological manipulations, encoding studies usually rely on machine-learning techniques that are well suited to complex and high-dimensional representations. Their testing procedure measures how well a representation of the stimuli or task can predict brain activity on unseen data, unlike standard analyses in brain imaging which use general linear models to detect significant effects of oppositions in brain activity (Poldrack et al., 2011a).

Encoding models replace crafting stimuli

Progress in visual neuroscience provides a striking example of the success of encoding models. Historically, our understanding of the human visual system has been driven by experiments crafting stimuli to reveal the selectivity of a hierarchy of brain modules (Grill-Spector and Malach, 2004), from spots and slab that revealed edge detectors in the visual area V1 [START_REF] Hubel | Receptive fields of single neurones in the cat's striate cortex[END_REF] to more complex shapes mapping mid-level regions [START_REF] Logothetis | Shape representation in the inferior temporal cortex of monkeys[END_REF], to semantic regions, studied via stimuli such as faces or scenes [START_REF] Haxby | Distributed and overlapping representations of faces and objects in ventral temporal cortex[END_REF][START_REF] Kanwisher | The fusiform face area: a module in human extrastriate cortex specialized for face perception[END_REF]. These experiments have been very successful in providing a conceptual model of the human visual system, but no one single experiment could ground this model of visual processing. Rather, it relied on combining interpretations across studies of disparate and non-ecological stimuli.

On more ecological stimuli, rich encoding models can reveal the properties of the primary visual cortex [START_REF] Kay | Identifying natural images from human brain activity[END_REF][START_REF] Miyawaki | Visual image reconstruction from human brain activity using a combination of multiscale local image decoders[END_REF], transforming them into a representation that provides the ability to accurately predict brain responses to complex stimuli [START_REF] Naselaris | Encoding and decoding in fMRI[END_REF]. To go beyond primary areas, rich statistical models of natural images are needed. Deep artificial

Fitting an encoding model

Given a model that builds complete representations of stimuli, rich tasks provide the information to predict brain responses as a function of stimuli.

Modeling new stimuli

The encoding model can be applied to stimuli with different properties. It yields brain responses that characterizes corresponding mental processes.

Figure 2: Encoding methodology and generalization: Encoding models capture the full details of brain responses given a rich description of the stimuli or tasks. This behavior-to-brain association can then be generalized to new stimuli or tasks, to characterize mental processes.

neural networks developed for computer vision build representations of the images used as stimuli that accurately predict brain responses, outperforming computationalneuroscience models of vision to explain the workings of mid-level areas (Khaligh-Razavi and Kriegeskorte, 2014; [START_REF] Yamins | Performance-optimized hierarchical models predict neural responses in higher visual cortex[END_REF]. They build a hierarchy of intermediate representations, from low-level edge detectors to more semantic information, that maps well to the full hierarchy of human visual processing [START_REF] Güçlü | Deep neural networks reveal a gradient in the complexity of neural representations across the ventral stream[END_REF]Eickenberg et al., 2017••). These results extend to high-level areas the hypothesis that V1 is tuned to Gabor filters because these form good statistical representations of natural images [START_REF] Olshausen | Emergence of simple-cell remainsceptive field properties by learning a sparse code for natural images[END_REF].

The latest studies do not require hand crafting stimuli to elicit controlled responses in a given region. They provide a full mapping of the computational steps of human vision from natural stimuli, and they jointly model all stimulus features important to brain responses, such that their model of brain response can generalize beyond the paradigm used in any given experiment. For example, Eickenberg et al. (2017)•• showed that a model learned from subjects watching natural images could generate both retinotopic maps and face versus scene contrasts.

The study of other sensory systems has demonstrated similar success. Encoding models have mapped the functional modules of the auditory cortex from spectrograms [START_REF] Santoro | Reconstructing the spectrotemporal modulations of real-life sounds from fMRI response patterns[END_REF], or using a hierarchy of represen-tations isolated by deep neural networks used to process sounds on computers [START_REF] Kell | A Task-Optimized neural network replicates human auditory behavior, predicts brain responses, and reveals a cortical processing hierarchy[END_REF]. Perceptual sciences lend themselves well to rich encoding models: as neuroimaging experiments can use rapid successions of trials with stimuli that are easily characterized across a broad set of features, providing large data accumulation.

Precise models of responses to stimuli capture high-level processes Data-intensive encoding models can also map more complex psychological functions. In particular, encoding models can accurately capture semantic representations of language in the brain at the level of words [START_REF] Mitchell | Predicting human brain activity associated with the meanings of nouns[END_REF], short texts [START_REF] Wehbe | Simultaneously uncovering the patterns of brain regions involved in different story reading subprocesses[END_REF], and stories [START_REF] Huth | Natural speech reveals the semantic maps that tile human cerebral cortex[END_REF]. Finely-tuned models of stimuli responses provide excellent windows to attentional (C ¸ukur et al., 2013;[START_REF] Hausfeld | Acoustic and higherlevel representations of naturalistic auditory scenes in human auditory and frontal cortex[END_REF] or perceptual decision [START_REF] Gwilliams | Performance-optimized hierarchical models only partially predict neural responses during perceptual decision making[END_REF] mechanisms. They relate better to experimental data than more conceptual models such as drift diffusion models [START_REF] Gwilliams | Performance-optimized hierarchical models only partially predict neural responses during perceptual decision making[END_REF]. Finally, using complex stimuli, such as a full movie, enables an ecological study of processes such as episodic memory (Baldassano et al., 2017•).

In all these settings, predictive modeling using encoding models enables the study of sensory and cognitive processes without reducing the experiment to one simple opposition or variation. As a result, predictions hold across paradigms and generalize to novel paradigms (Eickenberg et al., 2017••).

Prediction is a guiding principle to modeling stimuli

A key challenge for modeling in cognitive neuroscience is to generate rich representations of stimuli. Given data and a task to perform on it, artificial intelligence models extract representations that are optimal for information processing. These representations provide a good basis to study brain responses because they give a complete view of the task, but also because both artificial intelligence and human cognition capture the statistical regularities of our world. To model stimuli, minimizing prediction error is a guiding principle to extract relevant representations. For example, prediction of neighboring words is central to both cognitive and computational linguistic [START_REF] Willems | Prediction during natural language comprehension[END_REF]. Artificial neural networks optimized for object recognition form good representations to study object recognition in the ventral stream [START_REF] Yamins | Using goal-driven deep learning models to understand sensory cortex[END_REF]. Extending beyond prediction or recognition, recent progress in machine learning synthesizes rich data such as images guided by models that discriminate real from fake images [START_REF] Goodfellow | Generative adversarial nets[END_REF].

Generalization will ground broader theories

Scientific endeavors strive for conclusions that generalize, predicting features of new situations. While cognitive neuroscience has often focused on informal generalizations, machine-learning techniques will bring more precise predictions and more general models. Generalization across paradigms is key to achieving broader theories, in decoding to isolate the neural supports of mental states or in encoding to build complete descriptions of behavior.

Baldassano, C., Chen, J., Zadbood, A., Pillow, J.W., Hasson, U., Norman, K.A., 2017 •• This study shows that artificial neural networks used for computer vision can capture the neural responses to visual stimuli with a association that can then be used to distinguish functional modules in the full visual cortex, or to predict the neural responses to classic paradigms, such as retinotopy or face-scene oppositions.

Figure 1 :

 1 Figure1: An example of brain decoding and generalization: Brain decoding finds patterns in brain-activity data that discriminate given conditions on unseen data, here identifying perceptual stimuli. The corresponding brain-mind association can then be generalized to a new paradigm, or new stimuli, eg by applying the decoder in a visual memory task.

  . Discovering event structure in continuous narrative perception and memory. Neuron 95, 709-721.e5. • This work studies memory creation and consolidation via a datadriven segmentation of neural responses to movie watching into nested events. Bolt, T., Nomi, J.S., Yeo, B.T.T., Uddin, L.Q., 2017. Data-Driven extraction of a nested model of human brain function. J. Neurosci. 37, 7263-7277. C ¸ukur, T., Nishimoto, S., Huth, A.G., Gallant, J.L., 2013. Attention during natural vision warps semantic representation across the human brain. Nat. Neurosci. 16, 763-770. Dockès, J., Wassermann, D., Poldrack, R., Suchanek, F., Thirion, B., Varoquaux, G., 2018. Text to brain: predicting the spatial distribution of neuroimaging observations from text reports. MICCAI . Eickenberg, M., Gramfort, A., Varoquaux, G., Thirion, B., 2017. Seeing it all: Convolutional network layers map the function of the human visual system. NeuroImage 152, 184-194.


Joel Ortiz Sosa

Olivier Sentieys
email: olivier.sentieys@inria.fr

Christian Roland
email: christian.roland@univ-ubs.fr

A Diversity Scheme to Enhance the Reliability of Wireless NoC in Multipath Channel Environment

Keywords: Wireless Network-on-Chip, Channel Effects, Multi-Path Propagation, Communication Reliability, Digital Transceiver Architecture

Wireless Network-on-Chip (WiNoC) is one of the most promising solutions to overcome multi-hop latency and high power consumption of modern many/multi core System-on-Chip (SoC). However, the design of efficient wireless links faces challenges to overcome multi-path propagation present in realistic WiNoC channels. In order to alleviate such channel effect, this paper presents a Time-Diversity Scheme (TDS) to enhance the reliability of on-chip wireless links using a semi-realistic channel model. First, we study the significant performance degradation of state-of-the-art wireless transceivers subject to different levels of multi-path propagation. Then we investigate the impact of using some channel correction techniques adopting standard performance metrics. Experimental results show that the proposed Time-Diversity Scheme significantly improves Bit Error Rate (BER) compared to other techniques. Moreover, our TDS allows for wireless communication links to be established in conditions where this would be impossible for standard transceiver architectures. Results on the proposed complete transceiver, designed using a 28-nm FDSOI technology, show a power consumption of 0.63mW at 1.0V and an area of 317 µm 2 . Full channel correction is performed in one single clock cycle.

I. INTRODUCTION

The emerging manycore architecture era comes up with critical issues in communication latency and power consumption. Network-on-Chip (NoC) was a very promising solution to solve these challenges. However, with the scaling of advanced CMOS technologies, the number of cores is continuously growing. As a consequence, the number of hops needed to communicate between cores creates a critical bottleneck in the communication backbone by increasing latency and power consumption due to large volume data transmission. To deal with the surge of high performance computing systems and to overcome this communication bottleneck, new interconnect technologies, such as 3D-NoC [START_REF] Das | Energy-efficient and reliable 3D Network-on-Chip (NoC): Architectures and optimization algorithms[END_REF], Radio-Frequency Interconnects (RF-I) based on waveguides [START_REF] Valadbeigi | An Energy-Efficient Reconfigurable NoC Architecture with RF-Interconnects[END_REF], Optical NoC [START_REF] Guo | Designs of 3D mesh and torus optical Network-on-Chips: Topology, optical router and routing module[END_REF] [START_REF] Chen | A Power Efficient and Compact Optical Interconnect for Network-on-Chip[END_REF] and Wireless NoC [START_REF] Mineo | Runtime Tunable Transmitting Power Technique in mm-Wave WiNoC Architectures[END_REF], have emerged.

Although it is true that Wireless Network-on-Chip (WiNoC) is one of the most promising solutions for the communication infrastructure of chip multiprocessors (CMP) and multiprocessor System-on-Chip (MPSoC), the reliability of on-chip wireless links is still an important and unsolved issue [START_REF] Karkar | A survey of emerging interconnects for onchip efficient multicast and broadcast in many-cores[END_REF]. Indeed, most of the approaches from the literature estimate performance using a very simplistic wireless channel model, which only considers path loss through free space and Additive White Gaussian Noise (AWGN). However, a realistic wireless channel model should consider some of the most important parasitic phenomena introduced by the physical structures of the chip (e.g. multi-path propagation), especially, when communication data rate is aiming at several tens of gigabits per second.

The main contributions of this paper are as follows:

• We demonstrate, by simulation, the significant degradation of wireless communications facing multi-path propagation for current Wireless NoC architectures. Simulation is performed by adopting a proposed semi-realistic wireless channel models, based on the wireless intra-chip communication literature. • We study traditional channel cancellation techniques to improve communication reliability and adapt them to the on-chip wireless communication context. • We propose a digital transceiver architecture for each of the adopted techniques and evaluate their performance, power consumption and area for a 28 nm FDSOI technology and show that this overhead is very small compared to the gain in communication reliability. This paper is organized as follows. Section II highlights the main limitations in the state-of-the-art of current WiNoC architectures. In Section III, we present a semi-realistic channel model, while in Section IV, we study the traditional wireless interfaces used in WiNoC and show their weaknesses. After introducing some techniques to improve communication reliability, we propose a new transceiver architecture in Section V. Finally, in Section VI, we show some performance and synthesis results of the proposed architecture before to conclude in Section VII.

II. RELATED WORK

Wireless Network-on-Chip (WiNoC) was proposed as a more feasible and promising solution that can scale with transistor technology and the ever-increasing number of cores in a NoC [START_REF] Ganguly | Performance evaluation of wireless networks on chip architectures[END_REF]. Most of the contributions in the literature attempt to demonstrate that the WiNoC paradigm can overcome the limitations of conventional multi-hop NoC architectures for core-to-core [START_REF] Pande | Hybrid wireless network on chip: A new paradigm in multi-core design[END_REF], [START_REF] Ditomaso | A-WiNoC: Adaptive Wireless Networkon-Chip Architecture for Chip Multiprocessors[END_REF], and core-to-memory (e.g. cache coherency) [START_REF] Kayi | Adaptive Cache Coherence Mechanisms with Producer-Consumer Sharing Optimization for Chip Multiprocessors[END_REF], [START_REF] Asaduzzaman | An Energy-Efficient Directory Based Multicore Architecture with Wireless Routers to Minimize the Communication Latency[END_REF] communications. Many works have also investigated different network topologies to take advantage of long distance links [START_REF] Kim | Wireless NoC for VFI-Enabled Multicore Chip Design: Performance Evaluation and Design Trade-Offs[END_REF], [START_REF] Pande | Hybrid wireless network on chip: A new paradigm in multi-core design[END_REF]. WiNoC can thus allow for the reduction of energy consumption involved by transporting information packets through the network routers. The topology also impacts the total latency and throughput of the network [START_REF] Ganguly | Performance evaluation of wireless networks on chip architectures[END_REF].

Despite all these efforts to propose efficient WiNoC architectures, the considered wireless channel model is very simple (i.e., using an additive white Gaussian noise) and therefore not representative of actual on-chip wireless channels. In particular, this basic model does not consider the frequency and time behavior of WiNoC for isotropic antennas, such as multi-path propagation and bandwidth limitation.

However, few prior works have introduced some interesting channel features that could be considered for WiNoC simulations. As an example, the authors of [START_REF] Matolak | Channel modeling for wireless networkson-chips[END_REF] give a general overview of the main WiNoC characteristics considering a two-ray channel model. Besides, their analysis concludes that on-chip wireless channel resembles to familiar terrestrial settings. An analytical channel model is proposed in [START_REF] Agyeman | An Analytical Channel Model for Emerging Wireless Networks-on-Chip[END_REF]. This model introduces the concept of molecular absorption attenuation (MAA), which makes the wireless communication through the air unsustainable. In any case, both analyses consider multi-path propagation as an unavoidable phenomenon for intra-chip wireless communications. However, to the best of our knowledge, there is no work that considers during performance simulations the significant impact of multi-path propagation on the reliability of WiNoC communications. In contrast, the use of highly directive antennas based on carbon nanotube (CNT) is proposed in [START_REF] Ganguly | A Unified Error Control Coding Scheme to Enhance the Reliability of a Hybrid Wireless Network-on-Chip[END_REF], which could avoid multipath propagation. Nevertheless, CNT antennas are still facing many challenges to be fully integrated in current chip fabrication process. Moreover, with such solution, broadcasting wireless signals will be hardly achievable without a dense antenna array. Other research studies around antennas designed for on-chip communications (e.g., [START_REF] Lin | Communication Using Antennas Fabricated in Silicon Integrated Circuits[END_REF], [START_REF] Zhang | Propagation Mechanisms of Radio Waves Over Intra-Chip Channels With Integrated Antennas: Frequency-Domain Measurements and Time-Domain Analysis[END_REF], [START_REF] Kim | A plane wave model approach to understanding propagation in an intra-chip communication system[END_REF]) also provide relevant information to build more realistic WiNoC channel models. However, the experimental setup only considers simple scenarios such as point-to-point communications without effects of chip package and real multicore context as it should exist in WiNoC. Effects of wave propagation caused by using monopole or dipole antennas fabricated on silicon wafer as well as channel analysis for this simple type of communication are also proposed [START_REF] Zhang | Performance of integrated antennas on silicon substrates of high and low resistivities up to 110 GHz for wireless interconnects[END_REF], [START_REF] Hajimiri | mm-Wave Silicon ICs: Challenges and Opportunities[END_REF], [START_REF] Babakhani | A 77-GHz Phased-Array Transceiver With On-Chip Antennas in Silicon: Receiver and Antennas[END_REF], [START_REF] Kim | On-chip wireless interconnection with integrated antennas[END_REF].

III. CHANNEL MODELING

In any wireless communication system, it is very important to estimate the channel characteristics. Depending on the channel, the design of the transceiver needs to ensure a certain degree of wireless link reliability, as well as to reach a trade-off in design complexity. WiNoC, as a specific scheme of intrachip wireless communication, also requires a precise estimation of the channel. The channel must be modeled considering the parasitic phenomena introduced by the physical structure and electrical properties of all the components inside the chip, as well as the chip-package [START_REF] Agyeman | An Analytical Channel Model for Emerging Wireless Networks-on-Chip[END_REF]. As a result, building an accurate model of a WiNoC channel is important but it is also a complex task.

A wave propagated through a channel can suffer reflection, refraction and diffraction. Accordingly, waves can be propagated using different media at the same time. This approach was modeled and validated in [START_REF] Kim | A plane wave model approach to understanding propagation in an intra-chip communication system[END_REF], creating different ray paths through the silicon wafer. Besides, Zhang et al. [START_REF] Zhang | Propagation Mechanisms of Radio Waves Over Intra-Chip Channels With Integrated Antennas: Frequency-Domain Measurements and Time-Domain Analysis[END_REF] demonstrated that at least three types of waves on which the signal is propagated over intra-chip channel must be considered: space wave (air), surface wave (air-wafer interface), and guided wave (through silicon substrate). Likewise, their study concludes that the dominant path is not transmitted by space wave, but mainly by surface wave.

Furthermore, the resistivity of the silicon substrate is a very important parameter for intra-chip wireless communication. Propagating waves through a low-resistivity (ρ = 10 -20 Ω • cm) or a high-resistivity (ρ ≥ 5 kΩ • cm) material, can significantly affect signal attenuation. Moreover, as demonstrated in [START_REF] Zhang | Performance of integrated antennas on silicon substrates of high and low resistivities up to 110 GHz for wireless interconnects[END_REF], the influence of multi-path fading effects is more important for low-resistivity silicon substrate and for shorter distances.

Also, a delay spread was measured for different antennas (zigzag, meander, and linear) in [START_REF] Zhang | Propagation Mechanisms of Radio Waves Over Intra-Chip Channels With Integrated Antennas: Frequency-Domain Measurements and Time-Domain Analysis[END_REF]. It was observed that the delay spread generally increases with the transmitting and receiving antennas (T-R) separation, although delay spread for a specific channel impulse response (CIR) depends on the surrounding of the T-R pair. For instance, a delay spread for a distance of 10 mm, using zigzag monopole-pair with some interference structures, is 120 ps.

In this paper, to estimate and analyze the impact of a semi-realistic channel, the provided simulations are based on the previously discussed models defined for intra-chip wave propagation. We consider that a channel impulse response should include at least two propagation paths for realistic WiNoC simulations together with Additive White Gaussian Noise (AWGN). Obviously, the number of paths is dependent on the symbol duration. For instance, considering a data rate up to 32 Gbit/s for WiNoCs, the symbol duration will be as small as 32.25ps, which is four time smaller than the delay spread for a distance of 10 mm. This indicates that the number of significant paths could be up to three, each one separated by a symbol duration.

On the other hand, due to the low complexity of its implementation, the classical modulation scheme considered for WiNoCs is On-Off Keying (OOK) with a maximum data rate of 16 Gbit/s. However, other modulation schemes (BPSK, QPSK, 16-QAM, etc.) can provide better spectral efficiency and higher resilience to multi-path propagation, although consuming more power and area than OOK.

In order to test the reliability of current WiNoCs facing multi-path propagation, Fig. 2 represents the Bit-Error Rate (BER) of an OOK transceiver as a function of the Signalto-Noise Ratio (SNR) per bit in various multi-path conditions. Our simulations consider a two-ray model, and a time-invariant frequency-selective channel impulse response (CIR) composed of only two paths (the direct and the reflected paths), separated by a symbol duration, as shown in Fig. 1. Also, the gain of the reflected path, defined as a percentage of the direct one, varies from α = 0% to α = 60%. As observed in Fig. 2, the communication starts to degrade rapidly as soon as the reflected-path gain increases, even with small values of α. The degradation becomes significant even if the amplitude of second path is only 30% of the main path. For this reason, multi-path cancellation techniques and their respective architectures are required to increase reliability of WiNoC communications.

IV. OPTIMIZING THE WINOC COMMUNICATION SCHEME

In this section, we first detail the basic communication scheme for WiNoCs and then introduce our modifications to increase communication reliability. Moreover, to overcome the CIR presented in the above section, we introduce some techniques used in traditional wireless communication systems to decrease channel effects.

A. Traditional Wireless Interface

A traditional Wireless Interface (WI) connects a conventional router/switch with the wireless medium. The WI can be divided into three main parts: antenna, analog and digital blocks, as shown in Fig. 3. The digital domain mainly incorporates the channel access token controller and a Serializer/Deserializer. The analog domain includes an On-Off Keying (OOK) transceiver module, which has a very low complexity compared to other modulation schemes. There exist several architectures proposed in literature for the OOK transceiver, considering coherent or non-coherent detection [START_REF] Yu | A 1.2-pJ/bit 16-Gb/s 60-GHz OOK Transmitter in 65nm CMOS for Wireless Network-On-Chip[END_REF], [START_REF] Yu | An 18.7-Gb/s 60-GHz OOK Demodulator in 65-nm CMOS for Wireless Network-on-Chip[END_REF], [START_REF] Yu | Architecture and design of multichannel millimeter-wave wireless noc[END_REF]. Moreover, power consumption reduction mechanisms can be applied [START_REF] Mineo | Runtime Tunable Transmitting Power Technique in mm-Wave WiNoC Architectures[END_REF], which would allow to optimize the power according to the distance. The communication between the router/switch and the WI begins with the source core setting the corresponding message into the Network Interface (NI) module. The NI packetizes the message by breaking it into several flits (such as header, payload, tailer). The router/switch is then used to forward the data flits into the wired interconnection network or towards the WI, whether the token flow controller (TFC) authorizes the use of the wireless medium. The data flits will be converted into a serial data stream using the serializer (SER) block. Then the OOK modulator adapts the baseband frequency signal into a high frequency one (carrier frequency). The signal obtained is transmitted to the power amplifier (PA), which delivers the required transmitting power. Finally, this amplified signal is spread through the wireless medium using a dedicated or shared antenna. In case of a shared antenna, a nonmagnetic nonreciprocal passive CMOS circulator [START_REF] Reiskarimian | A CMOS Passive LPTV Nonmagnetic Circulator and Its Application in a Full-Duplex Receiver[END_REF] allows for full-duplex (frequency-division duplexing) or halfduplex communication.

At the receiver side, once the signal reaches the antenna, it is intensified by a low noise amplifier (LNA). Then, a demodulator shifts the high frequency signal into a baseband one. The next step is to amplify and filter the serial baseband signal, which is converted into a parallel data stream of flits using the deserializer (DESER) block. Finally, considering that the destination core is connected directly to the router/switch, the received flits will be conducted towards the NI to retrieve the message forwarded by the source core.

B. Improving Communication Reliability

To the best of our knowledge, current transceiver solutions from WiNoC literature do not consider some channel effect cancellation mechanisms, even during performance simulations. In this paper, we therefore study, simulate and synthesize traditional channel cancellation techniques adapted to onchip wireless communications. One reasonable hypothesis of this work is that the WiNoC channel is time invariant. This characteristic prevents the use of complex adaptive filtering algorithms for WiNoC communications. Finally, the theoretical and mathematical approaches of each considered technique is obtained from [27].

1) Equalization Techniques: are widely studied in conventional wireless communication to compensate for Inter Symbol Interference (ISI) created by multi-path propagation. Equalization can be linear (e.g., Zero Forcing, Minimum Mean Square Error) and non-linear (e.g. Decision Feedback Equalizer). The effectiveness of multi-path cancellation varies widely in practice, according to the type of equalizer applied. Furthermore, hardware cost and computation complexity are important issues when equalization is adopted.

In this section we analyze the impact of Zero-Forcing (ZF) linear equalization, which is less complex than other equalization techniques. ZF restores the received signal applying the inverse of the channel frequency response computed off-line or on-line. Normally, a linear transverse filter is used when this technique is adopted. The coefficients b i of the filter can be calculated in the time domain from the CIR, by resolving the following matrix system

            h 0 0 0 0 0 h 1 h 0 0 • • • 0 h 2 h 1 • • • • • • • • • • • • • • • • • • h 0 0 h k-1 • • • h 2 h 1 h 0                         b 0 b 1 b 2 • • • b k-1             =             0 • • • 1 • • • 0             (1)
where h i are the multi-path components of the CIR and k the total number of ZF filter coefficients is an odd integer value. As an example following Fig. 1,h

0 = 1, h 1 = α and h i = 0, ∀ i = 2 . . . k -1.
The impact of using the ZF technique is simulated with different number of coefficients (i.e., taps) k using the CIR with α = 60% as defined in Section III. As shown in Fig. 4, the multi-path cancellation efficiency improves with the number of coefficients. However, a large number of taps occupies significant area and consumes a relatively high amount of power, especially when computed at high frequency. Furthermore, even with a large number of coefficients, the simulated BER will never match the theoretical OOK BER. This phenomenon occurs because the zero-forcing equalizer amplifies the noise power during the signal filtering process.

2) Direct Sequence Spread-Spectrum (DSSS): is a transmission technique used in wireless network communications where a data signal at the sending node is combined with a code sequence (e.g. Gold sequence, M-sequence, Hadamard codes) running at high frequency, the chip rate. DSSS combines users' data based on a spreading factor (SF) defined as the chip rate divided by the symbol (data) rate. The main advantages of DSSS are a resistance to jamming and interference, less background noise, and a certain degree of multipath resilience depending on the code sequence characteristics. Furthermore, DSSS allows for multiple users to access the same channel simultaneously in synchronous or asynchronous mode. In the WiNoC literature, this technique was adopted by [28], demonstrating promising results over conventional NoCs. However, simulations and performance estimations provided in [START_REF] Vidapalapati | NoC architectures with adaptive Code Division Multiple Access based wireless links[END_REF] were only considering an ideal wireless channel.

3) Time-Diversity Scheme (TDS): implies that the same data is transmitted repeatedly at different time schedule. Thus, considering a channel with multi-path propagation, there are multiple copies of the same signal transmitted according to the number of multi-path components. Therefore, as depicted in Fig. 5, DSSS also takes advantage of this characteristic assuming L correlators between the input data signal y(t) and code sequences delayed by i = 0 . . . L -1 chip periods. The correlator outputs are combined using a diversity combining rule with their respective weighting coefficients (G i ). On the other hand, since this technique collects the energy from the received signal components to provide diversity, it is often called the RAKE receiver.

V. ARCHITECTURE OF THE WIRELESS INTERFACE

This section presents the WiNoC and wireless transceiver architectures considered in this work.

A. WiNoC Architecture 1) Topology: The adopted topology is based on a wired 2-D mesh conventional NoC architecture, divided into N clusters including a wired sub-network. Each cluster has one Wireless Interface (WI) connected to a dedicated router/switch, responsible for providing wireless access to the cores placed in the same cluster. Fig. 6 illustrates a 20mm × 20mm chip example composed of 8 × 8 cores. The WiNoC architecture is divided into N = 4 clusters of 16 cores with a WI located at the center of each cluster.

2) Wireless Multiple Access: Due to the availability of multiple channels, the synchronous DSSS technique is adopted for channelization to achieve simultaneous multiple communications among the WIs. Each cluster i uses a dedicated code sequence C i for data transmission and knows the code sequence of the other clusters for data demodulation at the receiver side. Besides, we consider that signal synchronization is performed only once in the WI to open the different simultaneous channels.

B. Wireless Interface Architecture

The adopted WI architecture is similar to the one explained in Section IV-A. However, the digital domain part is modified to comply with the proposed techniques. Fig. 7 depicts the global architecture of the digital transceiver, which is divided into three parts classified by clock frequencies: low 1 , medium 2 and high 3 . Furthermore, zero-forcing equalization and time diversity scheme are implemented using DSSS as a baseline architecture. Therefore, in our simulation and synthesis results, we tested three main architecture configurations detailed in this section and shown in Fig. 7: DSSS, TDS with DSSS, and ZF with DSSS. Additionally, DSSS needs an analog-to-digital converter (ADC) block to distinguish each code-channel. Consequently, to avoid excessive area cost and power consumption, we propose to adopt a 10 Giga-samples-per-second Time-Interleaved Successive Approximation Register (SAR) ADC [START_REF]22.3 A 20GHz-BW 6b 10GS/s 32mW time-interleaved SAR ADC with Master T&H in 28nm UTBB FDSOI technology[END_REF] instead of a flash ADC. This ADC provides eight 4-bit words in parallel at 1.25 GHz corresponding to eight consecutive samples.

Despite the use of serializer (SER) and de-serializer (DESER) blocks is mandatory in any wireless communication, previous WiNoC literature rarely details information about these blocks. Therefore, we propose to adopt a SER/DESER binary MUX tree topology with half-rate architecture [START_REF] Clarke | 140 Gb/s Serializer Using Clock Doublers in 90 nm SiGe Technology[END_REF], [START_REF] Mohammed | 6-Gb/s serial link transceiver for NoCs[END_REF], which uses a 625 MHz half-rate clock source to generate 1.25 Gb/s data rate. In addition, this architecture is a good compromise between higher data rates and risks of duty-cycle distortion and clock skew. 1) DSSS Architecture: is divided into two main functional blocks: encoder and decoder. Furthermore, the code sequence adopted in this architecture is a Hadamard binary code on 8 bits (SF = 8). As each cluster has a dedicated code sequence, the design of the encoder block is very simple. The encoder is composed of registers whose outputs are arranged according to the Hadamard code sequence assigned to the considered cluster.

The decoder, depicted in Fig. 8, is a dedicated block used to retrieve the information forwarded by other clusters. As a consequence, the decoder is composed of one correlator for each block with which it communicates, using the respective code sequence assigned to the considered cluster. As an example, for the architecture of Fig. 6 with four clusters, three correlators will be used in each cluster. Each correlator receives eight 4-bit words D j in parallel from the ADC, with D j ∈ {0, 1, ..., 15} and j = {0, 1, ..., 7}. These D j input values are directly compared with the jth bit of code C i, j related to the ith cluster. Consequently, the value of D j is turned to negative if the jth bit is 1, and remains positive otherwise. Then, the correlator performs addition or subtraction operations to calculate

Corr = ±D 0 ± D 1 ± D 2 ± D 3 ± D 4 ± D 5 ± D6 ± D7. (2)
The final step is to make a decision based on the resulting value of Corr, using a threshold detector. The optimal threshold value for DSSS with OOK modulation using Hadamard codes is 0. In our case, the decoder output is 1 when corr < 0 and 0 when corr > 0. This decision operation is simplified by connecting the sign bit (the MSB as we consider two's complement representation) of the resulting value of Corr directly to the decoder block output.

2) TDS with DSSS architecture: uses the same encoder block architecture, as explained in the previous section. However, the decoder, depicted in Fig. 9, increases the number of correlators used by cluster code sequence according to the number of significant multi-path components (MPC) estimated from the CIR. As the architecture is designed using the CIR Figure 9: Decoder architecture of the time diversity scheme. studied in Section III with α = 60%, two correlators are used by code sequence to retrieve the forwarded information from one cluster. The first one compares the input values D j with the jth bit of code C i, j related to the ith cluster and the second one compares D j with a time-shifted version of C i, j . Then the correlation results are combined using a diversity combining rule, called Maximum Ratio Combining (MRC). The MRC uses weighting coefficients obtained from the CIR to combine the correlator outputs. Finally, the sign bit (MSB) of the resulting combination value obtained from MRC computation is connected directly to the decoder block output.

To illustrate the correlator and MRC operations,

Corr 0 = -D 0 -D 1 -D 2 -D 3 + D 4 + D 5 + D6 + D7 Corr 1 = D 0 -D 1 -D 2 -D 3 -D 4 + D 5 + D6 + D7 M RC = G 0 × Corr 0 + G 1 × Corr 1 (3)
3) TDS Decoder Optimization: is performed by grouping the similar bits of the code sequences and their time-shifted version, as shown in Fig. 10. Generally, Hadamard codes contain similarities with their time-shifted version. Therefore, this characteristic is exploited to decrease the number of operations in a correlator by rewriting Eq. 3 as

Corr 0 = -D 1 -D 2 -D 3 + D 5 + D6 + D7 Corr 1 = -D 0 + D 4 M RC = G 0 × (Corr 0 + Corr 1 ) + G 1 × (Corr 0 -Corr 1 )
4) Zero Forcing with DSSS Architecture: uses the same encoder block as the simple DSSS architecture. The decoder block, as illustrated in Fig. 11, is composed of three main subblocks: a circular buffer (CB), a ZF filter to mitigate multi-path propagation and a DSSS correlator with a code sequence. The coefficient values of the ZF filter are calculated from Eq. 1 using the CIR of Section III with α = 60%.

VI. RESULTS

To evaluate the performance metrics of the different techniques studied in Section V, an end-to-end wireless communication system has been implemented for simulation and hardware synthesis. The effectiveness of each technique is evaluated adopting the multi-path channel characteristics described in Section III. The system under study is first simulated in MATLAB to estimate the BER performance. Then, the different architectures are modeled in C/C++ for High-Level Synthesis (HLS). Each architecture is synthesized to RTL using Catapult HLS and to the gate level by Synopsys Design Compiler. A 28-nm FDSOI technology library is used during hardware synthesis as a target with a supply voltage of 1 Volt. Finally, power consumption is estimated with Synopsys PrimeTime tool after activity extraction from a back-annotated gate-level simulation using 3.2 × 10 5 random input data.

A. Bit Error Rate Evaluation

The end-to-end system modeled in MATLAB considers a half-duplex communication and consists of four wireless interfaces to open three code-channels simultaneously. Each code-channel uses a dedicated orthogonal Hadamard code of 8 bits. The channel model employed in simulation was tworay time-invariant frequency-selective channel with AWGN.

The modulation scheme simulated was coherent OOK. The simulated model considers the quantization noise (QN) added in the demodulation process by a 4-bit ADC at the side [START_REF] Kiyani | Performance analysis of ook modulated signals in the presence of adc quantization noise[END_REF]. The average BER, which considers three parallel code-channels, is estimated by Monte-Carlo simulation with a confidence interval of 95%.

Simulation results are reported in Fig. 12 for four different architectures: DSSS, DSSS with ZF using 3 taps and 11 taps, and DSSS with TDS. The considered techniques are compared with the single channel simulated BER of OOK with multi-path using α = 60%, and without multi-path channel (OOK Theory in Fig. 12). The results indicate that the average BER of the DSSS technique, without channel compensation, stays high even with an SNR per bit of 27 dB. This poor BER performance is due to the impact of the CIR on the code orthogonality, and consequently on the misdetection rate. Nevertheless, associating DSSS with TDS or ZF improves performance compared with the technique without compensation. Indeed, part of the channel degradation was corrected, thus decreasing the mis-detection rate. Furthermore, comparing ZF filter using 3 taps with the other architectures on an average BER of e.g. 10 -6 , shows that TDS and ZF with 11 taps improve the SNR by 5 and 8 dB, respectively. However, despite ZF with 11 taps provides best performance, its complexity is much higher compared to the other architectures.

B. Synthesis Results and Discussion

The different blocks of the digital transceiver as depicted in Fig. 7 have been synthesized from C/C++ using HLS and logic synthesis. Digital interfaces with the router are designed considering a 32-bit bus width, which is serialized at 1.25 Gbit/s by the 32-bit SER/DESER blocks described in Section V-B. The DSSS Encoder block encodes each data bit in a parallel stream of 8 bits, before being serialized at 10 Gbit/s by the 8-bit SER block.

Four different architectures (DSSS, DSSS with 3-tap ZF, DSSS with 11-tap ZF, and DSSS with TDS) are synthesized separately. Each architecture configuration is capable to retrieve data from N -1 clusters among N. Synthesis results of each architecture with N = 4 and other blocks of the wireless interface are summarized in Table I. Codec in the table means both the encoder and the considered decoder architecture configuration. The Optimized TDS Codec corresponds to the scheme proposed in Section V-B3.

The total power consumption of each block reports both the static and dynamic power consumed. However, static power represents less than 1% of the total power, mainly thanks to the 28-nm FDSOI low leakage technology. To estimate an accurate dynamic power, a Pseudo Random Bit Sequence of 4 × 10 4 bits is injected into the encoder block, which generates a total of 3.2 × 10 5 bits for the decoder block.

The ADC is a key block in OOK transceivers based on DSSS and filter compensation (e.g. zero-forcing) since it consumes the bulk of area and power of the WI. Nevertheless, as performance simulations in literature only consider an ideal wireless channel, no ADC is used for digital channel compensation. The parallel architecture of time-interleaved SAR ADC, mentioned in Section V-B, allows to decrease the frequency for digital filters and therefore to improve power consumption. Based on [START_REF]22.3 A 20GHz-BW 6b 10GS/s 32mW time-interleaved SAR ADC with Master T&H in 28nm UTBB FDSOI technology[END_REF], Table I also provides area and power for the ADC block. For reference, figures extrapolated from [START_REF] Duraisamy | Multicast-aware high-performance wireless network-on-chip architectures[END_REF] of an OOK transceiver are also reported. However, Section III already showed the poor performance of this transceiver in case of multi-path CIR. [START_REF] Duraisamy | Multicast-aware high-performance wireless network-on-chip architectures[END_REF] not specified 20.8

The DSSS codec shows lower area and power consumption overhead than the other techniques. However, as shown in Fig. 12, its average BER is lower than for the other techniques with channel effect compensation. On the other hand, the ZF with 11 taps shows the best performance in terms of average BER, at the cost of highest power and area overhead. Finally, the average BER performance of the Time Diversity Scheme (TDS) based on the RAKE receiver is situated between ZF with 11 taps and 3 taps. In addition, the area and power consumption overhead of the optimized TDS codec is better than any k-tap ZF codec.

Furthermore, as shown in Fig. 2, decreasing α, the amplitude of the second path of the CIR, improves BER performance. Therefore, any technique applied with α less than 60% will enhance BER too. However, the area and power consumption of each architecture will be approximately the same (overhead may depend upon the coefficient values), but the TDS performance will become closer to the 11-tap ZF. Under these conditions, the TDS technique offers the best trade-off between BER performance and area/power over the other techniques.

VII. CONCLUSIONS

Emerging WiNoC communication technology is considered as a very viable solution for facing scalability and energy issues in multicore architectures. However, communication reliability through realistic wireless channel cannot be ensured by adopting conventional transceiver architectures. Therefore, in this paper, we show the impact of a semi-realistic multipath wireless channel over conventional WiNoC modulation scheme. Our study demonstrates the significant unreliability of an OOK transceiver, even for a channel with low dispersion. To overcome this issue, we propose to combine the DSSS coding scheme with channel compensation blocks. Among the solutions studied, the TDS receiver represents the best trade-off between bit-error rate performance and area/power overhead, when compared with different Zero-Forcing equalizers. The area (and power) overhead of the TDS block for a four-cluster receiver is only 317µm 2 (and 0.63mW ), which represents less than 1% (2%) of the wireless interface. Therefore, the gain in performance of our proposed scheme is significant at the cost of a very low area/power overhead. The TDS, unlike an error-correcting code, offers more throughput as the number of users sharing the wireless channel increases. We believe that the introduction of the proposed solution opens interesting scenarios to combat channel effects in WiNoC.

Figure 1 :

 1 Figure 1: Channel impulse response with α = 60%

Figure 2 :

 2 Figure 2: Scaling of BER performance according to the SNR per bit (E b /N 0 ) for different reflected-path gains in the OOK scheme.

Figure 3 :

 3 Figure 3: A conventional Wireless Interface of a WiNoC.

Figure 4 :

 4 Figure 4: Demodulation performance BER according to the SNR per bit (E b /N 0 ) using Zero-Forcing equalizer with different number of filter taps.

Figure 5 :

 5 Figure 5: Diversity demodulator for spread-spectrum signals over multi-path channels.

Figure 6 :

 6 Figure 6: Wireless interface distribution among a clustered WiNoC hybrid topology with N = 4 clusters.

Figure 7 :

 7 Figure 7: Enhanced digital-domain transceiver architecture with three decoder configurations.

Figure 8 :

 8 Figure 8: DSSS decoder architecture.

  Figure 10: Time-diversity scheme optimization.

Figure 11 :

 11 Figure 11: ZF equalizer with DSSS decoder architecture.

Figure 12 :

 12 Figure 12: Demodulation performance BER scaling according to SNR for the considered techniques with α = 60%.

Table I :

 I Synthesis results (area and power consumption) of the different Wireless Interface architectures using 28-nm FDSOI.

	WI Block	Area (µm 2 )	Power (mW )
	DSSS Codec	313.18	0.43
	TDS Codec	401.63	0.82
	Optimized TDS Codec	317.42	0.63
	3-tap ZF with DSSS Codec	490.41	0.98
	11-tap ZF with DSSS Codec	1967.37	4.04
	8-bit Serializer (10 Gbps)	21.8	0.1741
	32-bit Serializer (1.25 Gbps)	49	0.04391
	32-bit Deserializer (1.25 Gbps)	50	0.044
	4-bit ADC [29]	9000	16
	OOK Transceiver