同济大学：《传播信道特征估计和建模》课程教学资源（教案讲义）Chapter 08 Measurement based statistical channel modeling.pdf_大学文库

8 Measurement based statistical channel modeling 8.1 General modeling procedures The measurement-based stochastic channel modeling is usually conducted following the flow-chart presented in Fig. 8.1. 8.1.1 Channel measurement The first block is the channel measurement. Channel measurement, usually called channel sounding, is carried out to collect the received electromagnetic waves at the receiver site when an electromagnetic wave with certain known formats is transmitted at the transmitter side. The objectives of channel measurements can be classified into two categories. First, measurements are made to investigate the mechanism of the propagation of electromagnetic waves in specified environments or media. Second, measurement data are analyzed in such a way that the values of some parameters of predefined mathematical models can be found. The applicability of these models in explaining the general characteristics of the propagation has been evaluated. The parameters need to be estimated from the measurement data by using estimation algorithms or techniques. Measurement Campaign planning Equipment calibration Measurement campaign Parameter estimation Generic model definition Estimation algorithm Designing Parameter extraction Stochastic channel modeling Statistic parameter computation Distribution extraction Model evaluation Fig. 8.1 The channel modeling approach The second objective of channel measurements is our major concern here. The block of channel measurement as shown in Figure 8.1 consists of three parts, i.e. measurement campaign planning, equipment calibration, and measurement itself. The planning of campaign is performed to determine the specifications of measurement equipments and the purposes of the measurements, e.g. in terms of which kinds of models to be expected to generate. The calibration of the measurement equipments are needed to make sure e.g. whether the transmission power of the signals is high enough to support the coverage in the area where the transmitter and the receiver are located. Furthermore, it is important to understand the behavior of the measurement equipments themselves, because the This is a Book Title Name of the Author/Editor c XXXX John Wiley & Sons, Ltd

222 Measurement based statistical channel modeling Propagation Transmission Modulation Digital RF, ant. Mod. Demod. Equalization Interleaving coding Deinterleaving Air interface RF, ant. decoding Fig. 8.2 The components in a RF channel response of the RF channel includes the responses of the measurement equipments. It is necessary to “isolate” the impact of the equipments when extracting the characteristics of the propagation. Calibrations can be performed in accordance with the purposes of the measurements. For example, if the measurements are conducted for extracting the wideband characteristics in terms of finding the parameters characterizing propagation paths, it is then necessary to have the responses of the measurement equipments, which include: • The responses of the transmitting and receiving antennas. Notice that if the sounding signal is transmitted or received through antenna arrays, the responses of the antennas need to include the impact of the coupling among antennas. • The responses of the RF chains. When a switch is used to activate the antennas to transmit or receive signals, the RF chain needs to be calibrated with the switch included. In addition, the cables used to connect the RF output from the transmitter or receiver to the multiple ports of a switch or to the antenna ports should also be considered as parts of the RF chain. • When a multiple-antenna array is used to measure the spatial channel’s responses, if a switch is applied, we also need to know the responses of the switch in the time domain. This means that the calibration needs to be performed with the same settings as in the real measurement. The switch needs to be working as in the real measurements. Figure 8.2 depicts the components included in the RF chain. It can be seen that the RF channel actually includes many parts with their specific responses. It is necessary to mitigate the impact of the system responses on the estimation of the channel characteristics. 8.1.2 Parameter estimation In the second block of the flowchart, channel parameter estimation needs to be carried out. We may split the channel parameters into three classes, i.e. • the so-called narrowband parameters, which include the fading coefficients, usually obtained when the channel measurement equipments do not have large bandwidth • the wideband profiles of the channel, including the channel impulse responses in time domain, the response in the spatial domain • the high-resolution channel parameters that are defined for individual components in the channel responses. The channel estimation block also consists of three steps: generic model selection, algorithm selection, and parameter extraction. Generic models include the models described in Chapter 3. A popular model is the specular path model which describes the channel impulse response as the combination of many specular path components. For time-variant case, it is necessary to use time-evolution model. For the case where the data samples are limited, the power spectral density model can be considered. Furthermore, the power spectral density model, which models the power spectral density of the channel, can be used to estimate the dispersive components in the power spectral density

Measurement based statistical channel modeling 223 20 40 60 80 100 −150 −100 −50 0 50 100 150 −50 0 50 17 20 23 27 30 Azimuth of arrival [ ◦ ] Elevation of arrival [ ◦ ] Cycle index Delay in samples Fig. 8.3 Example of estimates of path parameters In the step of “Estimation algorithm designing”, methods or algorithms for extracting the model parameters are chosen. These algorithms have been introduced in Chapter 6 and 7. Depending on the time requirements for completing the data processing, the parameters of interest, and the modeling objectives, the algorithms are selected. The most popular methods are the beamforming method for computing the estimate of power spectral density, the specular-path model based SAGE or RiMAX, and the power spectrum density-component estimation method. After the estimation algorithm is determined, channel parameters are extracted for multiple snapshots by processing the measurement data. Usually, this step is very time-consuming. Fig. 8.3 illustrates an example of the parameters of the paths estimated from multiple snapshots. These estimation results will be used to construct models in the next block - “stochastic channel modeling”. 8.1.3 Stochastic modeling In the third block of the flowchart, stochastic model parameters are extracted based on the parameters estimated for instantaneous measurement snapshots. The stochastic model parameters can be the large-scale and the small-scale parameters. The large-scale parameters include the path loss, composite delay spread, composite angular spreads, composite Doppler frequency spread, the correlation coefficients among spatial channels or the channels separated in frequency domains, etc. The small-scale parameters are referred to the parameters describing the behavior of individual path, or individual clusters of paths. In Section ??, the clustering of paths will be explained in details. The small-scale parameters of interest, are the delay spread, angular spread, Doppler frequency spread of individual clusters. Furthermore, as the modeling of time-variant channels, and multi-link channels is getting popular, more smallscale parameters are raised in these models, such as the parameters describing the time-stationarity, the correlation coefficients of small-scale fading in delay domains, etc. The modeling procedure includes three steps: statistic parameter computation, the probability distribution function extraction, and model evaluation. In the first step, the parameters of interest are computed for multiple snapshots. Consequently, sufficient number of parameter realizations are obtained. Notice that individual snapshot may contain multiple instantaneous measurements. A so-called “data-segmentation” technique is usually needed to determine the measurements belonging to the same snapshot. Then, in the second step, the probability density functions of the parameters are extracted. It is also important to determine whether the snapshots are collected in the same type of

224 Measurement based statistical channel modeling environments. In the last step, the applicability of the pdf can be evaluated by using more observations which were not considered for constructing the models. The final output of the modeling is the stochastic channel models, such as the stochastic channel modeling based on the measurements has been adopted for generating standard channel models for standards, i.e. the 3GPP TR25.996 Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 7) (2007), the WINNER II SCME (Enhanced Spatial Channel Models) WINNER II Channel Models (IST-WINNER2. Tech. Rep., 2007), and the IMT-Advanced channel models REPORT ITU-R M.2135 Guidelines for evaluation of radio interface technologies for IMTAdvanced (2007). 8.2 Methods for constructing stochastic channel models In this section, methods for constructing stochastic channel models are briefly summarized. These methods include the widely-used geometry-based stochastic channel modeling method, and the novel power spectrum modeling method. Geometry-based stochastic channel modeling The generic WINNER II channel models, the spatial channel models (SCM’s) proposed by TR25.996, and some other models follow a geometry-based stochastic channel modeling approach. This approach allows creating of an arbitrary double directional radio channel model. This model is independent of the communication systems. The channel matrix for different MIMO scheme and antenna responses can be created using this model. The values of the model parameters are determined stochastically, based on statistical distributions extracted from channel measurement. The statistical distributions extracted are for the delay spread, delay values, angle spread, shadow fading, and cross-polarization discrimination. For each snapshot or the so-called “drop” of the channel, the model parameters are calculated from the distributions. After determining the model parameters, the propagation paths with the specified model parameters are created and summed up to generate channel realizations. Each path is characterized by its delay, power, azimuth-of-arrival, azimuth-of-departure and polarization matrix. The stochastic channel models generated by using the geometry-based approach have different model parameters, depending on the typical characteristics in the scenarios. These models are usually composed of multiple path clusters. In the next section, we introduce the random-cluster modeling, which is an extension of the conventional geometry-based method e.g. the method used to create the WINNER II SCME channel models. Clustered-delay-line models Compared with the cluster-based models, the clustered-delay-line (CDL) models have reduced complexity, mainly for rapid simulation. In the CDL models, a cluster is centered at each delay tap. Each cluster is comprised of the vector sum of equal-powered multi-path components (MPC’s). All the MPCs have the same or close to same delay. The complex attenuation of these paths, i.e. the MPCs, are varying. However, the angle (azimuth of departure and azimuth of arrival) offsets of the paths are fixed. These fixed offsets realize the Laplacian power azimuth spectrum. The powers and delays of the clusters can be non-uniform. They are determined in such a way that the desired overall channel rms delay spread can be achieved. Power spectrum modelling with a generic model of dispersive path components Another approach to construct stochastic channel models is similar with the geometry-based method but the model parameters are associated with dispersive path components, instead of clusters. Clustering paths is an efficient method to group the great amount of paths. However, some of the estimated paths may not have their counterparts in reality. These paths are obtained due to the model mismatch between the discrete specular-path model and the inherent dispersive behavior of the real channel. Therefore, an alternative method for estimating the channel characteristics accurately is to use a generic model suitable for describing the dispersive path components in the channel. The model parameters include the spreads of dispersion of path component in different dimensions. The distribution of these parameters can be calculated from the parameter estimates obtained from multiple measurements. The realizations of channel can be created stochastically from the distributions

Measurement based statistical channel modeling 225 8.3 Clustering algorithm based on specular path models The propagation paths are grouped into clusters based on the parameter estimates of the paths. Then the statistics of the clusters, such as the center of gravity and the spreads of the clusters is extracted. The statistics of the paths within individual clusters is also important for modeling. Those information are used to setup a stochastic channel model, which is composed of multiple probability density functions (PDFs) of a number of parameters. By using a random number generator, it is possible to construct the random channel realizations based on the PDFs specified in the model. The organization of this section is as follows. First Subsection 8.3.1 introduces the widely used clustering approach for channel modeling. Subsection 8.3.2 discusses the details of the clustering algorithm used in this work to group the multipaths. Subsection 8.3.3 shows some clustering results based on the measurement data. Subsection ?? introduces the method we use to determine the data segment during which the channel is stationary. In the subsections ?? to ??, the procedures of extracting the statistics of the cluster parameters, including the average power, the average delay and AoA, the AoA spread, the AoA offsets within clusters, the cluster spread ratio and the cluster XPD, are presented. Experimental results obtained by processing Oulu data are also reported. 8.3.1 Conventional stochastic-cluster modeling Definition of “clusters” The random-cluster modeling is based on stochastically generating the parameters of the so-called path clusters. The cluster parameters are perceived as random variables, whose probability density function (pdf) can be estimated from measurement data. The essential concept that the random-cluster modeling relies on is the “cluster” of paths. According to Czink’s argument Czink et al. (2007), a cluster of paths is referred to as a group of paths that have similar parameters. A large amount of paths can be separated into certain number of clusters by using some clustering algorithms. Different cluster-based modeling The concept of “cluster” exists already for a long time. The cluster delay line (CDL) model is a typical channel model making use of clusters to represent the spread of the channel components. The 3GPP spatial channel model (SCM) and the WINNER SCME models are also based on clusters. In these models, dispersion of a cluster is extended from delay domain to include spatial domain, i.e. the directions of departure and the directions of arrival. WINNER modeling also uses a cluster-based method. However, the cluster-concept was used differently in the considered scenarios. This is probably because for some of the measurements /scenarios, the equipment was not able to resolve e.g. the paths in angular domain. For example, clusters with delay and angular spreads are used for modeling the small-scale characteristics of propagation in “A1 - Indoor office”, “A2-Indoor-to-Outdoor”, “B1-Urban microcell”, “D1 ´lC Rural macro-cell”. For scenario “C1 Suburban macro-cell”, the “zero-delay-spread cluster(ZDSC)” was used. This means the clusters are only dispersive in the angular domain. For scenarios such as “C2 Urban macrocell”, taps instead of clusters are used for channel modeling. Clusters were not used for modeling the channel in the scenarios B2, B3, B4 Outdoor to indoor, B5 Stiationary feeder, C3 Bad urban macro-cell, and C3 Bad urban macro-cell. An updated version of the clustering approach, called Random-clsuter modeling (RCM), is elaborated in Czink (2007). In the sequel, we briefly discuss the difference of this modeling scheme with the conventional schemes, as it will be used for modeling propagation channels in our work. Diffuse multiple component in the RCM The RCM has considered modeling of the Diffuse Multiple Component (DMC), which was not the case in the classical cluster-based channel models. The DMC has impact on the channel diversity, so it is important to include the DMCs into the channel modeling. In the RCM described in Czink (2007) the DMC is only considered in the delay domain. The characteristics of the DMC in the directional domain and in the Doppler frequency domain have not been discussed. A prerequisite to include the spatial-domain DMCs into e.g. the geometry-based stochastic model Kyösti et al. (2007) or the RCM Czink (2007) is to investigate the parametric characterization of DMCs in space-time-frequency based on extensive measurement campaigns. Cluster’s lifetime considered in the RCM According to Czink (2007), the RCM uses two time bases to define the lifetime of a cluster: • ∆ts denotes the channel sampling interval. In these time steps, clusters move. The channel matrices are calculated on this basis

226 Measurement based statistical channel modeling • ∆tΛ denotes the cluster lifetime interval. Cluster lifetimes can only be a multiple of this value. The reason for this is that newly born clusters have to fade in and dying clusters need to fade out smoothly. Note that ∆tΛ is an integer multiple of ∆ts. Model evaluation issues As proposed in Czink (2007), evaluation of a channel can be performed in the following ways: 1. Mutual information 2. Channel diversity 3. Demmel condition number of the MIMO channel metrics 4. Environment Characterization Metric (ECM) comparing directly the discrete propagation paths in the channel Clustering methods Four methods can be used for clustering paths: • the hierarchical tree clustering • the KPowerMeans clustering • Gaussian-mixture clustering • Estimating clusters directly in the impulse response. Gaussian mixture (GM) clustering superimposes a specific structure on the clusters. The cluster parameters are assumed to be Gaussian distributed, showing a higher path density in the centre than in its outskirts. For MPC clustering, this approach can be easily combined using path powers. Unfortunately, it turned out that this clustering method has its shortcomings when trying to track clusters since the clustering results are quite unstable. The fourth method is the “potato”-based approach, which is originally proposed for estimating the spreads of a dispersive paths. Notice that the term “dispersive path” is used rather than clusters here. However, a dispersive path can be viewed as consisting of many non-separable paths. In such a sense, the definitions of cluster and a dispersive path are similar. 8.3.2 Clustering algorithms Definition of MCD Nicolai proposes to use Multipath component distance (MCD) to quantify the difference between two paths. This MCD applies specific scaling method to scale the difference between the path parameters in different dimensions. So the parameter differences are combined with the same unit. This MCD is first introduced in Steinbauer et al. (2002) to quantify the complete multipath separation of the radio channel. MCD considers the angular domain and the delay domain. In the angular domain, the MCD between two directions Ω1 and Ω2 is defined as MCDAoA/AoD,ij = 1 2 Ω1 − Ω2 . (8.1) This value has the range of [0, 1]. The MCD of paths in delay domain can be defined as MCDτ,ij = ζτ · |τi − τj | ∆τmax · τstd ∆τmax , (8.2) where ∆τmax = maxi,j{|τi − τj |}, τstd is the standard deviation of the delays, and ζ is a scaling factor which can give more “importance” when necessary. In Czink (2007), the author suggests to choose ζ = 8. Finally the distance between the paths (i, j) is calculated as MCDij = q kMCDΩTx,ijk 2 + kMCDΩRx,ijk 2 + MCD2 τ,ij . (8.3)

Measurement based statistical channel modeling 227 Extension of the MCD in our case The Doppler frequencies of the propagation paths should be also considered when computing the distance between two paths. We can use a similar definition for the MCD in Doppler frequency domain with that of the MCD in delay, i.e. MCDν,ij = ζν · |νi − νj | ∆νmax · νstd ∆νmax , (8.4) where ζν is a scaling factor to give different “importance” to the MCD difference. It is quite difficult to understand the meaning of the multiplicative factors for scaling the so-called MCD. But just for comparison purpose, we implement this method and show the difference of the results obtained with the proposed method in the section of “Experimental result”. Per Cluster Doppler frequency spectrum In the current RCM, the Doppler frequency is added to the MPCs within a cluster in a second step, with the first step being the determination of the parameters in delay, directions and attenuations. The Doppler frequency of a cluster, actually only one single Doppler frequency value is provided for the whole cluster, which is calculated by νc = f0 c0 vc, (8.5) In the RCM, the basic version of which is the fundamental modeling method used to generate WINNER I and II models, all paths within a cluster are assigned the same rate of change of their delay (i.e., they show the same Doppler frequency characteristics), and the effects of rotating antenna arrays are neglected. We should be able to show that a good clustering method can give a good match to physical propagation scenario. The Doppler frequency spectrum obtained for a cluster, is somehow related to the movement of the Tx or Rx and direction of travel of the Tx or Rx. Anyway, these models may not be accurate when both the clusters and Tx or Rx are moving. We can do the following steps to obtain the Doppler frequency spectrum for individual clusters. 1. Using a geometric method and the ray-tracing technique, represent the scatterer with certain physical extension by multiple discrete points. Each point results in a propagation path. The Doppler frequency spectrum for such a scatterer can be calculated or derived analytically. 2. Try to parameterize the Doppler frequency spectrum using the characteristics of the scatterer. It is possible to model the scatterer’s physical shape by its center of gravity and the spreads in length and width or depth. 3. Derive a model for received signal by cooperating the parametric model of the Doppler frequency spectrum. 4. Estimate the parameters from real measurement data. MCD without weighting factors One drawback of the MCD defined in Czink (2007) is that the MCD relies on the weighting factors that give different importance to the difference between path parameters. These factors are heuristic and are proposed based on experimental experience. To avoid using heuristic factors, we can define a new multipath component distance which relies on the difference between the baseband received signals with the different path parameters. The phasors due to the parameters are compared. The difference of two phasors due to delay can be easily combined with the difference of two phasors due to Doppler frequency or angles. By doing so, it is not necessary to use heuristic settings to specify the importance of parameter distance in different dimensions. Extraction method We select 3 bursts as one data segment. The estimated paths obtained from these 3 bursts are clustered into a fixed number of clusters. These clusters are considered as the independent realizations of paths in the TR25.996. The statistical characteristics of the clusters are obtained based on these clusters. In this work, we use MCD-based method to cluster the paths

228 Measurement based statistical channel modeling 150 155 160 165 170 175 180 185 0 0.5 1 1.5 2 2.5 3 3.5 x 10−9 delay in samples Amplitude in linear Fig. 8.4 Example of the powers of paths versus the delays of the paths. The parameters of the paths are estimated from measurement data collected in a macro suburban environment. The Tx moves at a pedestrian speed, following the first route. Fig. 8.4 depicts the power estimates of the paths versus the delays of the paths. In order to implement Nicolai’s clustering method based on the MCD, we calculate the standard deviation στ of the delays. The following equation is used to compute στ : στ = vuut 1 P X L ℓ=1 pℓ · (τℓ − τ¯) 2 (8.6) where P = PN ℓ=1 pℓ denotes the total power of all the paths, τ¯ is calculated as τ¯ = 1 P X L ℓ=1 pℓ · τℓ (8.7) For the example shown in Fig. 8.4, τ¯ is calculated to be 159.6377 delay samples, στ reads 6.4334 delay samples. In addition, ∆τmax is 30 delay samples. Thus, (8.2) can be rewritten as MCDτ,ij = 0.0357 · |τi − τj |. (8.8) It is necessary to explain what the multiplicative factor 0.0357 stands for. We now compute the maximum duration ∆νmax, the mean ν¯ and the standard deviation σν of the Doppler frequencies of the paths. Fig. 8.5 depicts the powers of the paths versus the Doppler frequencies of those paths. The following equations are used to calculate ν¯ and σν ν¯ = 1 P X L ℓ=1 pℓ · νℓ, σν = vuut 1 P X L ℓ=1 pℓ · (νℓ − ν¯) 2 (8.9) Calculation shows that ν¯ = −1.1591Hz, σν = 1.9091Hz, and ∆νmax = 13.8Hz. Thus, (8.4) turns out to be MCDν,ij = 0.01ζν · |νi − νj |, (8.10) Now we show the clustering result when the Nicolai’s clustering method based on MCD is used. The number of clusters is set to 6. The scaling factors ζτ = ζν = 5 are selected. Fig. 8.6 depicts the result obtained when applying Nicolai’s MCD-based clustering method to the estimated 500 paths in a macro suburban environment. The square marks in the plots in Fig. 8.6 indicates the centroid of the clusters. We observe from Fig. 8.6 that the overlapping of the clusters in the angular domain is significant. However, in the Doppler-Delay domain, the clusters are well separated. We have some difficulties to understand this observation. The scaling factors multiplied with |τi − τj | and |νi − νj | are much less than the scaling factor for the directions. But the above observation shows that the distance of paths in the directional domain does not change significantly for all the paths. Although the scaling factors for the delay and Doppler frequency are small, the impact of the path distance MCDτ,ij and MCDν,ij on the overall distance MCDij is more significant than the impact of MCDΩAoA,ij

Measurement based statistical channel modeling 229 −10 −8 −6 −4 −2 0 2 4 6 0 0.5 1 1.5 2 2.5 3 3.5 x 10−9 Doppler frequency in Hz Amplitude in linear Fig. 8.5 Example of the powers of paths versus the Doppler frequencies of the paths. The parameters of the paths are estimated from measurement data collected in a macro suburban environment. The Tx moves at a pedestrian speed, following the first route. Table 8.1 Parameter setting in the SAGE algorithm and in the clustering algorithm. No. of paths 20 No. of iterations 5 Dynamic range 10 dB No. of bursts in one segment 3 No. of clusters 6 8.3.3 Experimental results for path clustering We have determined that one data segment is composed of 3 consecutive bursts. The SAGE algorithm was used to process the Oulu channel measurement data. The path estimates were grouped using the MCD-based approach as described in Czink (2007). Notice that the parameter ζ is heuristically pre-defined to be 5 according to Czink (2007). We would like to verify how the clustering algorithm performs when ζ takes different values. In the following, we select the data collected in the scenario “macrocell, suburban, Pedestrian route 1” and choose ζτ = ζν = 5 and 8 for path clustering respectively. Here, ζτ and ζν denote the weighting factor, i.e. a multiplicative factor, for the distance in delay and in Doppler frequency respectively. Table 8.1 depicts the setting used in the SAGE algorithm for processing the data. Fig. 8.6 depicts the constellation of paths and the clustering results when ζτ = ζν = 1, 5, 8, 20 is selected respectively. The paths with same color belong to one cluster. We can observe that when ζ increases, the clusters are more well-separated in the delay and Doppler frequency domains. From these results, we see that ζτ = ζν = 5 to 8 is more reasonable. From Fig. 8.6 it can be observed that for ζτ = ζν = 5 or 8, the paths which can be well separated in the EoA-AoA domain belong to different clusters as expected. Paths mixed in the center of the EoA-AoA figure are split into clusters which are well separated in the Doppler frequency and delay domains. This clustering result looks quite promising. We can also observe some outliers in the EoA-AoA domain that are assigned to clusters whose centroid are far from the outliers’ locations. This is due to the limited number of clusters selected in the algorithm. Fig. 8.7 depicts the convergence rate of the clusters’ spreads in delay, Doppler frequency, azimuth and elevation of arrival, versus the iteration number. It can be observed that after 5 iterations, the values of the clusters’ spreads stabilize. This indicates that the KPower-mean approach does exhibit an excellent convergence property