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Auto-Generated Summaries for Stochastic Radio Channel Models
... In order to overcome these challenges, a host of estimation methods have been proposed recently that circumvent the need for extracting multipath components and clustering [14]- [21]. In [16], [18], a method of moments estimator is proposed for the Saleh-Valenzuela [2] and the Turin model [1], respectively. ...
... In [19] a multilayer perceptron is used to estimate parameters in the Saleh-Valenzuela model. The methods in [14], [20], [21] are based on approximate Bayesian computation (ABC) [22], which is a likelihood-free inference method that relies on summary statistics of the channel measurements to approximate the likelihood function. It is possible to use automatically generated summary statistics, as shown in [21], although these did not perform as well as handcrafted summaries. ...
... The methods in [14], [20], [21] are based on approximate Bayesian computation (ABC) [22], which is a likelihood-free inference method that relies on summary statistics of the channel measurements to approximate the likelihood function. It is possible to use automatically generated summary statistics, as shown in [21], although these did not perform as well as handcrafted summaries. In [15] a kernel-based distance metric is used in the ABC algorithm, which alleviates the need for summary statistics at the cost of choosing a kernel. ...
Stochastic radio channel models based on underlying point processes of multipath components have been studied intensively since the seminal papers of Turin and Saleh-Valenzuela. Despite of this, inference regarding parameters of these models has remained a major challenge. Current methods typically have a somewhat ad hoc flavor involving a multitude of steps requiring user specification of tuning parameters. In this paper, we propose to instead adopt the principled framework of Bayesian inference to conduct inference for the Saleh-Valenzuela model. The posterior distribution is not analytically tractable and we therefore compute approximations of the posterior using Markov chain Monte Carlo (MCMC) methods specific to point processes. To demonstrate the flexibility of our approach, we additionally propose a new multipath model and apply our inference method to it. The resulting inference methodology is computationally demanding and our successful implementation relies critically on our novel multipath component updates within the MCMC sampler. We demonstrate the usefulness of our approach on simulated and real radio channel data.
... Modern channel modelling aim to overcome these limitations by integrating DL algorithms which are capable of learning and estimating radio propagation channel parameters [12]. More particularly, artificial neural networks (ANNs) have been 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 widely used in an effort to replace ray tracing simulators. ...
... We further validated our results with goodness of fit parameters (Table.1) like root mean square 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 error (RMSE) and mean absolute error (MAE) by using (12) and (13). ...
Radio wave propagation in an intra-vehicular environment is markedly different from other well studied indoor scenarios such as an office or a factory oor. Millimeter Wave (mmWave) based intra-vehicular communications promises large bandwidth and can achieve ultra-high data rate with lower latency. However, exploiting the advantages of mmWave communications largely relies on proper characterization of the propagation channel. Channel characterization is most accurately done through an extensive channel sounding, but due to hardware and environmental constraints, it is impractical to test channel condition for all possible transmitter and receiver locations. In this paper, we use artificial neural network to aid channel sounding. Based on some real-world sounding data we show that it is possible to accurately estimate channel transfer function (CTF) and power delay profile (PDP) in an intra-bus scenario. Such artificially generated models can help in extrapolation in other relevant scenarios for which measurement data is unavailable. The proposed model can also be used for tapped delay line based bit-error-simulations as well.
... They have been used to calibrate the Turin model [1], the Saleh-Valenzuela (S-V) model [2] and the polarized propagation graph (PG) model [15]. These calibration methods rely either on a Monte Carlo approximation of the likelihood [16], [17], the method of moments [18], [19], or a summarybased likelihood-free inference framework [20]- [23] such as approximate Bayesian computation (ABC). First developed in the field of population genetics in 1997, ABC has since become a popular method for calibrating models with intractable likelihoods in various fields, see [24] for an overview. ...
... We encounter this to be a non-trivial task, and it may not even be possible for the more elaborate channel models. Similar problems exist in [20]- [22] where a low-dimensional vector of statistics should be redesigned or trained using an autoencoder [23] for the channel model at hand, which is not always trivial and may not generalize to other models. Moreover, summarizing the data leads to information loss that can hamper the accuracy of the parameter estimates. ...
Calibrating stochastic radio channel models to new measurement data is challenging when the likelihood function is intractable. The standard approach to this problem involves sophisticated algorithms for extraction and clustering of multipath components, following which, point estimates of the model parameters can be obtained using specialized estimators. We propose a likelihood-free calibration method using approximate Bayesian computation. The method is based on the maximum mean discrepancy, which is a notion of distance between probability distributions. Our method not only by-passes the need to implement any high-resolution or clustering algorithm, but is also automatic in that it does not require any additional input or manual pre-processing from the user. It also has the advantage of returning an entire posterior distribution on the value of the parameters, rather than a simple point estimate. We evaluate the performance of the proposed method by fitting two different stochastic channel models, namely the Saleh-Valenzuela model and the propagation graph model, to both simulated and measured data. The proposed method is able to estimate the parameters of both the models accurately in simulations, as well as when applied to 60 GHz indoor measurement data.
Estimating parameters of stochastic radio channel models based on new measurement data is an arduous task usually involving multiple steps such as multipath extraction and clustering. We propose two different machine learning methods, one based on approximate Bayesian computation (ABC) and the other on deep learning, for fitting data to stochastic channel models directly. The proposed methods make use of easy-to-compute summary statistics of measured data instead of relying on extracted multipath components. Moreover, the need for post-processing of the extracted multipath components is omitted. Taking the polarimetric propagation graph model as an example stochastic model, we present relevant summaries and evaluate the performance of the proposed methods on simulated and measured data. We find that the methods are able to learn the parameters of the model accurately in simulations. Applying the methods on 60 GHz indoor measurement data yields parameter estimates that generate averaged power delay profile from the model that fits the data.
This letter proposes a machine learning based method for the calibration of stochastic radio propagation models. Model calibration is cast as a regression problem involving mapping of the channel transfer function or impulse response to the model parameters. A multilayer perceptron is trained with summary statistics computed from synthetically generated channel realizations using the model. To calibrate the model, the trained network is used to estimate the model parameters from channel statistics obtained from measurements. The performance of the proposed method is evaluated with propagation graph and Saleh-Valenzuela models using both simulated data and in-room channel measurements. Results show accurate estimation of the parameters of both models.
Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.]
This deliverable describes WINNER II channel models for link and system level simulations. Both generic and clustered delay line models are defined for selected propagation scenarios. Disclaimer: The channel models described in this deliverable are based on a literature survey and measurements performed during this project. The authors are not responsible for any loss, damage or expenses caused by potential errors or inaccuracies in the models or in the deliverable.
One of the unique characteristics of ultra-wideband channels is the clustering phenomenon resolved by the ultra-wide signal bandwidth. Channel structures extended from the Saleh-Valenzuela model, e.g., the IEEE 802.15.3a and IEEE 802.15.4a models, have been proposed to describe such phenomenon. It is, however, noticed that a clear and systematic procedure to estimate the model parameters is still missing. Based on the recently developed analytical results, a new estimation approach is proposed in the paper to resolve the inconvenience and ambiguity in previous methods. The key step is to match the statistical profiles of interests by formulating an optimization problem with an explicit analytical objective function that can be systematically solved. Numerical tests have also been conducted to demonstrate the effectiveness of the proposed method.
In measurements of in-room radio channel responses an avalanche effect can be
observed: earliest signal components, which appear well separated in delay, are
followed by an avalanche of components arriving with increasing rate of
occurrence, gradually merging into a diffuse tail with exponentially decaying
power. We model the channel as a propagation graph in which vertices represent
transmitters, receivers, and scatterers, while edges represent propagation
conditions between vertices. The recursive structure of the graph accounts for
the exponential power decay and the avalanche effect. We derive a closed form
expression for the graph's transfer matrix. This expression is valid for any
number of interactions and is straightforward to use in numerical simulations.
We discuss an example where time dispersion occurs only due to propagation in
between vertices. Numerical experiments reveal that the graph's recursive
structure yields both an exponential power decay and an avalanche effect.
Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s
(2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006),
the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative
version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo
method of Cappé et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics
example, it compares favourably with two other versions of the approximate algorithm.
This paper generalizes a propagation graph model to polarized indoor wireless channels. In the original contribution, the channel is modelled as a propagation graph in which vertices represent transmitters, receivers and scatterers while edges represents the propagation conditions between vertices. Each edge is characterized by an edge transfer function accounting for the attenuation, delay spread and phase shift on the edge. In this contribution, we extend this modelling formalism to polarized channels by incorporating depolarization effects into the edge transfer functions and hence, the channel transfer matrix. We derive closed form expressions for the polarimetric power delay spectrum and cross-polarization ratio of the indoor channel. The expressions are derived considering average signal propagation in a graph and relate these statistics to model parameters, thereby providing a useful approach to investigate the averaged effect of these parameters on the channel statistics. Furthermore, we present a procedure for calibrating the model based on method of moments. Simulations were performed to validate the proposed model and the derived approximate expressions using both synthetic data and channel measurements at 15 GHz and 60 GHz. We observe that the model and approximate expressions provide good fits to the measurement data.
Efficient and realistic mm-wave channel models are of vital importance for the development of novel mm-wave wireless technologies. Though many of the current 60 GHz channel models are based on the useful concept of multipath clusters, only a limited number of 60 GHz channel measurements have been reported in the literature for this purpose. Therefore, there is still a need for further measurement based analyses of multipath clustering in the 60 GHz band. This paper presents clustering results for a double-directional 60 GHz MIMO channel model. Based on these results, we derive a model which is validated with measured data. Statistical cluster parameters are evaluated and compared with existing channel models. It is shown that the cluster angular characteristics are closely related to the room geometry and environment, making it infeasible to model the delay and angular domains independently. We also show that when using ray tracing to model the channel, it is insufficient to only consider walls, ceiling, floor and tables; finer structures such as ceiling lamps, chairs and bookshelves need to be taken into account as well.
We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics. The method is suited to complex problems that arise in population genetics, extending ideas developed in this setting by earlier authors. Properties of the posterior distribution of a parameter, such as its mean or density curve, are approximated without explicit likelihood calculations. This is achieved by fitting a local-linear regression of simulated parameter values on simulated summary statistics, and then substituting the observed summary statistics into the regression equation. The method combines many of the advantages of Bayesian statistical inference with the computational efficiency of methods based on summary statistics. A key advantage of the method is that the nuisance parameters are automatically integrated out in the simulation step, so that the large numbers of nuisance parameters that arise in population genetics problems can be handled without difficulty. Simulation results indicate computational and statistical efficiency that compares favorably with those of alternative methods previously proposed in the literature. We also compare the relative efficiency of inferences obtained using methods based on summary statistics with those obtained directly from the data using MCMC.
The results of indoor multipath propagation measurements using 10 ns, 1.5 GHz, radarlike pulses are presented for a medium-size office building. The observed channel was very slowly time varying, with the delay spread extending over a range up to about 200 ns and rms values of up to about 50 ns. The attenuation varied over a 60 dB dynamic range. A simple statistical multipath model of the indoor radio channel is also presented, which fits our measurements well, and more importantly, appears to be extendable to other buildings. With this model, the received signal rays arrive in clusters. The rays have independent uniform phases, and independent Rayleigh amplitudes with variances that decay exponentially with cluster and ray delays. The clusters, and the rays within the cluster, form Poisson arrival processes with different, but fixed, rates. The clusters are formed by the building superstructure, while the individual rays are formed by objects in the vicinities of the transmitter and the receiver.
An urban multipath propagation experiment, involving the simultaneous transmission from a fixed site of 100-ns pulses at 488, 1280, and 2920 MHz and their reception at a mobile van, is described. A statistical analysis of the data in the resulting multipath responses is given and used as a basis for a statistical model of urban multipath propagation.
WINNER II channel models, deliverables D1.1.2 V1.2, part I: Channel models
- P Kyösti