3GPP-Compatible Channel Generation Framework for FR2-2 Indoor Short-Range Communication

This study proposes a 3GPP-compatible channel generation framework for ultra-wideband and indoor short-range communication realized by the fifth-generation (5G) new radio operating in the frequency range (FR) of 52.6–71.0 GHz. The addition of this band, coined “FR2–2,” to the 5G specification allows foreseeing the use cases of shorter-range communications with ultra-wide bandwidth. However, the current focus of the 3GPP channel model on longer-range communication hinders link-level simulations of this use case. To fill this void, we develop a channel generation framework compatible with the 3GPP channel model and applicable to the FR2-2 indoor short-range use case based on real channel measurements. We highlight that even with appropriate parameters for this use case, the 3GPP channel model does not necessarily reproduce similar characteristics of the measured channel impulse response (CIR) owing to the lack of uniformity of cluster angle of arrival (AoA) and power dispersion in intra-cluster subpaths. Based on this finding, an amendment is proposed, where cluster AoA is uniformly distributed, and the intra-cluster power dispersion term is introduced. We demonstrate the feasibility of the proposed framework for reproducing the real CIR characteristic by showcasing an agreement of root-mean-square delay and angular spreads with the measured CIR.

the joint reproduction of the angle of arrival (AoA), excess delay, and power of intra-cluster subpaths are necessary because adjacent intra-cluster subpaths with even small intracluster excess delay and AoA dispersion can be resolved in terms of the usage of large bandwidth and directional antennas, respectively [13]. The 3GPP channel model in technical report 38.901 [8] partially contributes to this objective by describing the two-step procedure, where the delay spread, angular spread, and Rician K-factor, referred to as largescale parameters (LSPs), are generated first, followed by the CIRs including AoA, excess delay, and power of intracluster subpaths generated based on the LSPs. However, the 3GPP model reports the parameter set to generate the former LSP only for the urban macro, UMi, indoor office, and indoor factory, where the assumed communication distance is over several tens of meters. Moreover, even if the parameter sets are available to reproduce the LSPs, it is questionable whether the framework for reproducing the CIR based on the LSPs in the 3GPP model is valid for the FR 2-2 indoor short-range scenario. To summarize, there are no complete channel generation frameworks to reproduce CIRs consistent with 3GPP channel models.
To fill this void, this study develops a complete 3GPPcompatible channel-generation framework based on real indoor measurements. This study primarily focuses on the second issue of the 3GPP model by proposing the generation flow of AoA, excess delay, and power of the intra-cluster subpaths. More specifically, this study addresses the following two research questions: 1) Given the generated LSPs, can the 3GPP channel model generate similar characteristics to the measured CIRs for the FR2-2 indoor short-range use case? 2) If not, how can we amend the channel generation framework to retain the real characteristics of the measured CIRs for the use case?
Note that there are many existing measurement campaigns to build a 3GPP-consistent channel model in this scenario [14], as surveyed in Section II-B. However, these works primarily focused on measuring the LSPs suited for this scenario; the generation mechanism of the CIR has not been intensively addressed. We address this issue by proposing a channelgeneration flow to reproduce the CIRs by reporting the necessary amendment of the 3GPP model based on the measured CIRs. In more detail, the salient contributions and insights provided by this paper are summarized as follows: • We highlight that for the FR2-2 indoor short-range scenario, the current 3GPP channel model does not necessarily reproduce CIRs exhibiting similar characteristics to the measured CIRs, even if the LSPs suited for the scenario are available (Section IV). More technically, the CIR generated by the 3GPP channel model is shown to lack the uniformity of the cluster AoA and the power dispersion of the intra-cluster subpath. To the best of our knowledge, this insight was not provided in the literature targeting the same scenarios in FR2-2 [14], where only the parameters to generate LSPs have been reported; the characteristics of the generated CIR (i.e., AoA, excess delay, and power) were not analyzed. • We propose a 3GPP-compatible channel-generation flow by providing guidelines to amend the current 3GPP channel model for FR2-2 indoor short-range scenarios (Section V). This guideline is supported by our in-depth observations of the mismatch between the measured CIRs and the CIR generated by the 3GPP model. Moreover, we demonstrate the feasibility of the improved accuracy of the proposed flow in the statistical characteristics of the CIR filtered by directional antennas, thereby confirming the validity for link-level simulation usages (Section VI). The remainder of this paper is organized as follows. Section II summarizes the related studies focusing on the channel model that generates the CIR for mmWave link-level simulations. Section III describes the measurement experiment for the FR2-2 indoor short-range scenario, which is the basis for developing the proposed channel generation framework. Section IV discusses the flow of the proposed 3GPP-compatible channel generation for FR2-2 indoor shortrange communication. Section V compares the generated CIR between the current 3GPP channel and the proposed framework. Section VI provides the concluding remarks.

II. RELATED WORKS
Numerous measurement campaigns were performed for the indoor-short-range scenarios in the FR2-2 band. We briefly introduce the previous works and discuss their differences from these existing works. Note that the measurement campaigns in other scenarios (e.g., outdoor [15] or indoor scenarios with longer receiver (RX)-transmitter (TX) distances [16], [17]) are excluded from the following discussion. Moreover, our focus is on generating CIRs in a static environment because the user equipment is likely to be static in the FR2-2 use case, similar to the devices in IEEE 802.15.3c WPANs. Hence, the measurements for additional features exhibiting dynamic events (e.g., cluster dynamics, human blockage events, and Doppler shifts) are not included in the following discussion.

A. CHANNEL PARAMETER MEASUREMENTS FOR 3GPP-INCOMPATIBLE CHANNEL MODELS
In the standardization activity in the IEEE 802.15.3c task group (TG), channel measurements and modeling were performed in [18], [19] for WPAN scenarios in the 60 GHz band. Therein, indoor measurements with a transmission distance of several meters were performed, and the channel model merging the Salah-and-Velenziela model [20] with the two-path line-of-sight (LoS) path model was developed. Subsequently, MATLAB codes were developed and have been widely publicized to generate the AoA, excess delay, and power of the intra-cluster subpaths [21]. This standardization activity of using 60 GHz bands is followed by IEEE 802.11ad TG to build WLAN systems operating in this band. Accordingly, a channel model was developed to fit this scenario [22], and measurement campaigns were performed [23], [24]. Therein, AoAs in the elevation angle are additionally characterized because the WLAN access points are likely to be developed at a higher place than stations to avoid human blockage events. Based on these measurements, ray-tracing simulations were conducted to derive the statistical characteristics of cluster AoAs, excess delays, and power [22]. However, these channel models are incompatible with the 3GPP model, where CIRs are directly generated by statistical modeling without generating LSPs. These models are cast as the most site-general models [13] and differ from the 3GPP models. Our focus is on developing 3GPPcompatible channel models at the same site-specificity level, and the addressed problem differs from these works.
In addition to standardization activities, measurements and modeling for this scenario were performed in [25], [26], [27], [28], [29], [30]. In [25], indoor measurements at 60 GHz bands were conducted, where the statistical characteristics of the time of arrival, AoA, and path loss were derived. In [26], indoor measurements were performed, and the Rician K-factor and path loss were derived. In [27], the angular spread, delay spread, and path loss were measured in the 60 GHz and 80 GHz bands. The characteristics of a measured cluster were reported in [28]. However, these works did not address the channel generation applicable to linklevel simulations, where the objective differs from this work. For channel generation, in [29], [30], a statistical model to reproduce the CIR was developed for short-range communications. In clause 3.3.4 in [14], statistical modeling of the intra-cluster subpaths was performed similarly as in IEEE 802.15.3c. Although the CIR can be generated from these  models, these models are not compatible with the 3GPP models as in the IEEE 802.15.3c and 11ad models.

B. CHANNEL PARAMETER MEASUREMENTS FOR 3GPP-COMPATIBLE CHANNEL MODELS
Channel models compatible with the 3GPP model in the FR2-2 scenario were developed in various communities. In [31], the statistical parameters of the LSPs in the 3GPP models were derived by measurement in an indoor office scenario in the 60 GHz band. However, this work does not detail the channel-generation flow, where the same channelgeneration flow in the 3GPP model was applied to the capacity analysis. In [14], the statistical parameters of the LSPs were reported in a manner consistent with the 3GPP model, and the channel generation flow was detailed. This channel model was implemented in [32] as the available code. However, this work mostly followed the channel generation flow of the 3GPP model, and the insights into the mismatch between the real measured and generated CIRs were not provided. Going beyond this work, we discuss how the 3GPP channel generation flow yields a mismatch based on an in-depth comparison between the measured and generated CIRs.

A. MEASUREMENT SETUP
The propagation measurements were conducted using the settings listed in Table 1. In the channel sounding system shown in Fig. 1, the RX employed a rotatable horn antenna with the half power beamwidth of 10.74 • to obtain power delay profiles (PDPs) with an angular characteristic for the AoA. We mechanically rotated the horn antenna through 360 • in steps of 5 • to obtain fine-grained AoA characteristics with full coverage. The TX employed an omnidirectional antenna to obtain the complete multipath characteristics in an indoor room for measurement. To measure the PDPs, we employed the Keysight channel sounding software that performs a sliding correlator-based PDP measurement customized for a channel bandwidth of 2.16 GHz. The sounding signal with the center frequency of 3 GHz and the bandwidth of 2.16 GHz is up-converted to an RF frequency of 58.32 GHz on the TX side and is down-converted to the same center frequency on the receiver side to be inputted to the oscilloscope. Thereafter, the oscilloscope samples the received sounding signal calculates the PDP based on the channel sounding software.
As shown in Fig. 2, we conducted the measurements in an indoor room, where the TX and RX were placed at distances ranging from 0.7 m to 3 m. The approximate size of the room was 5.8 m × 7.1 m × 3.0 m. The TX was placed on one of the rectangular desks located in the room. The height of the TX was 0.15 m from the top of the desk. The RX was placed around the edge of the desk while maintaining the distance depicted in Fig. 2. This setting is similar to the WPAN desktop scenario performed in the IEEE 802.15.3c standardization in [18], [19]. However, our objective was to develop a 3GPP-compatible channel generation framework for the scenario, which has not been performed in the literature, including [18], [19]. Therefore, performing measurements in indoor and short-range settings is sufficient for investigating the validity of our proposed channel-generation flow. Moreover, this setting, consistent with [18], [19], facilitates the validation of the measured data and extracted parameters; hence, we decided to perform the measurement in this setting.
The measured PDPs were processed to estimate the CIR for each RX position. This is done by deconvolving the PDPs with known horn antenna patterns and RX-TX filter patterns as shown in Fig. 3. In the recorded PDP shown in the upper part of Fig. 3, the continuous power spreads, which shapes the horn antenna pattern, are observed in the angular domain around power peaks. This is due to the overlapped observation of one incoming path, whose effect is eliminated in this procedure. First, the maximum peak search is conducted, and subsequently, the continuous power spread around the peak is subtracted by the known joint patterns of the horn antenna and time-domain RX-TX filter. These patterns are pre-obtained by an anechoic room measurement. This procedure is iterated until the power peak larger than a power threshold cannot be found in the PDP The threshold is set to be −50 dB relative to the LoS component in this study because the 95% of the power contributions lay in this range. Finally, the delay, horn-antenna angle, and power of each peak are regarded as the delay, AoA, and power of each impulse.
It should be noted that throughout this paper, we mainly use this estimated CIR for performance evaluations.
Recalling that the effect of the horn antenna patterns and RX-TX filters are eliminated in the CIR, these effects are not concerned in the following evaluations.
Subsequently, each impulse is clustered, and the parameters consistent with the 3GPP channel model (e.g., delay spread, angular spread of AoA, and K-factor) were calculated. The procedures specific to this measurement are detailed in the Appendix because this study primarily focuses on the channel generation framework, given the complete parameter set compatible with the 3GPP channel model, rather than the parameter extraction method.

B. RESULTS OF EXTRACTED CHANNEL MODEL PARAMETERS
The 3GPP model parameters calculated from these measurements are listed in Table 2. As a reference, Table 2 lists the parameters of indoor office scenarios reported in [8] for ease of understanding our results by comparing them with the existing parameters under the same indoor conditions. The parameters for the non-LoS (NLoS) scenario were calculated by removing the LoS components from the extracted multipath components. As detailed in Section III, the channel statistics in Table 2 are yielded in the power range from −50 dB to 0 dB relative to the observed LoS component. Hence, the valid power range for the channel generation detailed in the subsequent section is also from −50 dB to 0 dB for LoS cases. In NLoS cases, the valid power range is from −30 dB to 0 dB relative to the first cluster power because in the measurement, the power difference between the LoS component and the first cluster was approximately 20 dB.
In Table 2, the noticeable difference lies in the smaller delay spread and the higher intra-cluster angular spread. These differences can be attributed to the smaller size and emptiness of the room relative to the 3GPP indoor office scenario that considers an office with a size of 50 m × 120 m (see [8, clause 7.2]) with more multipath richness. For instance, the smaller delay spread can be explained by the strong multipath components that concentrate on the lower part of the propagation delay owing to the close reflective objects (i.e., walls and desks). This characteristic can be significantly different from the 3GPP indoor office scenario, where reflective objects can be distributed at relatively larger distances from the RX, and the multi-path components are not concentrated with strong power, as in the presented measurement. The higher intra-cluster angular spread can also be attributed to the close reflective objects, which leads to the observation of diffuse scattering components with a higher power.

IV. REVIEW OF 3GPP CHANNEL GENERATION FLOW AND COMPARISON WITH MEASURED RESPONSE
In this section, we compare the measured CIR with a CIR generated by the 3GPP channel generation procedure [8]; thereby visualizing the mismatch as stated in the first contribution in Section I. First, we review the 3GPP channel generation flow reported in [8]. Second, we visualize the generated and measured CIRs and demonstrate the mismatch that lies between them.

A. REVIEW OF 3GPP CHANNEL GENERATION FLOW 1) OVERVIEW
Firstly, we detail the current 3GPP channel generation flow in view of the CIR generation for the indoor short-range communications. For simplicity, we consider point-to-point links, where multiple channels subject to distance correlation are not considered. Moreover, as the standardization history for shows (e.g., IEEE 802.15.3c [9] and IEEE 802.11ad [10]), indoor short-range communication in this band is likely to be used statically; hence, we consider a static environment, where the Doppler shift was not considered in the CIR generation.
The generated components are summarized as follows: 1) the number of clusters N, 2) the number of subpaths per cluster M, 3) cluster excess delays τ 1 , . . . , τ N , 4) exponentially decaying cluster power P 1 , . . . , P N , 5) cluster angle of arrival φ 1 , . . . , φ N , 6) intra-cluster excess delays τ n,1 , . . . , τ n,M for n ∈ {1, . . . , N}, 7) exponentially decaying power of intra-cluster subpaths P n,1 , . . . , P n,M , for n ∈ {1, . . . , N}, and 8) intra-cluster AoA φ n,1 , . . . , φ n,M n ∈ {1, . . . , N}. These variables are used to yield one realization of the CIR, as follows: where δ(·) denotes the Dirac delta function. The last equation is used because we consider the normalized power gain so that developers can use arbitrary path loss models. In the above CIR model, the delay and AoA are normalized such that the subpath with t = 0 s and φ = 0 • indicates the time of arrival and AoA of the LoS ray, respectively. Subsequently, we detail the procedure for generating delay, AoA, and power information for subpaths of the current 3GPP model [8]. We omit the generation procedure for the numbers of clusters and intra-cluster subpaths because these values are always provided in parameter tables.

2) LSP GENERATION
As a preparation step, the LSPs, that is, the delay spread, angular spread, and K-factor, are sampled from the lognormal distributions. Let DS, ASA, and K denote the delay spread, angular spread of azimuth AoA, and Kfactor, and let l denote the vector of these parameters, i.e., l := [lgDS, lgASA, K] T . The LSPs are drawn by: where In the above equation, cov(·, ·) is the covariance between the variables, calculated using the correlation of the variables and the standard deviation of each variable. K is on the dB scale. Hereafter, the K-factor in the linear scale is written as K lin .

3) CLUSTER AND INTRA-CLUSTER EXCESS DELAY GENERATIONS
Cluster Excess Delay: Cluster excess delays are drawn from exponential distributions with a rate parameter of 1/r τ DS, where r τ is the delay scaling factor [8]. For the NLoS cases, the cluster excess delay τ n is drawn as follows: where In the above equations, sort n (·) indicates the operation that sorts the arguments and extracts the nth sample, i.e., the resultant excess delays form the order statistics of the exponential distribution Exp(1/(r τ DS)).
In the LoS cases, additional scaling of τ n was performed. This procedure is expressed as follows: where The notation "←" indicates the replacement of the lefthand side by the right-hand side.
Intra-Cluster Excess Delay: As determined in clause 7.6.2.2, in the 3GPP model for a large-bandwidth use case [8], intra-cluster excess delays are drawn from a uniform distribution. For the mth subpath inside the nth cluster, the intra-cluster excess delay τ n,m is drawn as follows: where In (13), c DS is the intra-cluster delay spread, which can be found by measurements.

4) CLUSTER POWER AND INTRA-CLUSTER SUBPATH POWER GENERATIONS
Cluster Power: Cluster powers were calculated using the exponential decay profile added by a random log-normal shadowing term. First, in the NLoS cases, the cluster powers P n for n = 1, . . . , N are calculated as: where

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In the above equation, z n ∼ N (0, ζ 2 ), where ζ is the per-cluster shadow fading standard deviation presented in Table 2. For τ n in (15), the excess cluster delay without scaling in (4), that is, the delay in (8), must be used even in LoS conditions. This note can be found in [8, clause 7.5].
In the LoS cases, the cluster power was scaled by the Rician K-factor generated in the previous section. This procedure was performed as follows: The LoS ray with a power of K lin /(K lin +1) is added to the first subpath in the first cluster in the generation procedure for intra-cluster powers, which is detailed below.
Intra-Cluster Subpath Power: For the NLoS and LoS cases, the intra-cluster powers are calculated by the exponential decay profile using a random log-normal shadowing term. Specifically, the intra-cluster powers are calculated by where In the above equation, α n,m ∼ uniform(−2, 2) denotes the term determining the intra-cluster AoA.
In the LoS cases, the LoS ray is added to the first subpath in the first cluster. This procedure is expressed as follows: Accordingly, the cluster power of the first cluster is modified as: This substitution of the first cluster power is performed after the intra-cluster subpath power generation.

5) CLUSTER ANGLE OF ARRIVAL AND INTRA-CLUSTER ANGLE OF ARRIVAL GENERATIONS
Cluster AoA: The 3GPP model sets cluster AoAs deterministically to ensure consistency with the generated angular spread ASA and to form the angular spectrum as a wrapped Gaussian function [8]. Mathematically, the procedure for generating cluster AoAs in the 3GPP model is as follows: where φ n = 2(ASA/1.4) √ − ln(P n / max P n ) In the above equation, Bern(prob) indicates a sampling operation from the Bernoulli distribution with the probability of prob, and C φ is a constant value for scaling presented in [8]. In the LoS cases, φ 1 is enforced to be 0 • .
Intra-Cluster AoA: The intra-cluster AoAs are sampled from a uniform distribution scaled by the cluster AoA spread c ASA . This procedure is expressed as follows: where α n,m ∼ uniform(−2, 2).
In the LoS cases, α 1,1 is enforced to be 0 • because the first subpath in the first cluster represents the LoS ray. This is formally expressed as α 1,1 ← 0 • .

B. COMPARISON BETWEEN GENERATED AND MEASURED CHANNEL RESPONSES
Figs. 4 and 5 show the AoA and power characteristics of the subpaths with respect to the excess delay. Note that we set the "FR2-2 indoor short-range" parameters listed in Table 2 for the channel generation instead of using the default parameters in [8] to ensure fair comparison.
AoA Characteristics: Fig. 4 shows the polar plot representing the AoA characteristics of the CIR measured at the location "1m (East)" in Fig. 2(a) and the CIR generated by the 3GPP model. The polar angle represents the AoA, and the radial distance represents the excess delay relative to the LoS ray. From Fig. 4(a), we can identify the following two characteristics of the measured CIR. First, the intra-cluster AoA dispersion ranged approximately from 10 • to 90 • . Second, the cluster AoA was distributed uniformly at every angle. However, the CIR generated from the 3GPP model in Fig. 4(b) does not exhibit the second characteristic, meaning that the cluster AoAs are not distributed uniformly and are biased at approximately 120 • or 230 • . This fact clearly shows that the function that determines the cluster AoAs in (21)-(24) should be amended for this scenario.
Power Characteristics: Fig. 5 shows the power of the subpaths in the CIR measured at the same location and the CIR generated by the 3GPP model with respect to the excess delay of each subpath. From Fig. 5(a), we can identify the following two characteristics of the measured CIR in the intra-cluster subpath powers. First, the cluster power, that is, the sum of the subpath power in each cluster, decays exponentially. Second, in each cluster, the powers of the subpaths broadly fluctuate and lie in −50 dB to −15 dB. However, the CIR generated from the 3GPP model in Fig. 5(b) lacks the second characteristic of the large dispersion of the subpath power in each cluster. This drawback is due to the generation mechanism of the intra-cluster subpath power in (18), where the intra-cluster subpath power decays monotonously in the decibel domain. This is clearly in contrast to the measured CIR exhibiting more intensive dispersion in the intra-cluster subpath powers.

Remark 1 (Problem Identification of the 3GPP Channel Generation Flow for FR2-2 Indoor Short-Range Communications):
The 3GPP channel generation flow fails to capture the following two characteristics: 1) the uniformity of cluster AoA and 2) intra-cluster subpath power dispersion ranging from −50 dB to −15 dB This mismatch can lead to an inaccurate evaluation of physical layer performances since the physical layer simulations are often conducted by convolving the waveform of interest with the generated CIR. Hence, this problem should be addressed by amending the mechanisms of generating cluster AoAs and intra-cluster subpath powers, which is detailed in the next section.

V. PROPOSED FLOW FOR 3GPP-CONSISTENT CHANNEL GENERATION FOR FR2-2 INDOOR SHORT-RANGE COMMUNICATIONS
Based on the insight found in the previous section, we propose an amendment for the mechanism for cluster AoAs and intra-cluster subpath powers. In Fig. 6, the proposed channel generation flow for FR2-2 indoor short-range communications is shown, where the difference from the 3GPP channel generation flow is highlighted. In this section, we focus only on the two amended mechanisms for CIR generation.
We do not amend other parts of the 3GPP channel generation flow motivated by the focus of this study. One of the goals of this study is to develop a channel generation flow in a compatible manner to the 3GPP model for the indoor short-range communications, thereby discussing the feasibility of such a channel generation flow. Hence, the amendment should be kept minimum, and we amend only the above two parts, that is, the mechanisms to generate cluster AoAs and intra-cluster subpath powers as detailed below.

A. GENERATION MECHANISM FOR CLUSTER AOA
Based on the observation in the previous section, cluster AoAs are sampled from a uniform distribution instead of wrapped Gaussian function in eq. (21)- (24), where the sample range is from 0 • to 360 • . This mechanism is formally written as: Exceptionally, in the LoS cases, φ 1 , is substituted by 0 • because the first cluster contains the LoS ray, which is formally written as φ 1 ← 0 • .
For the validation of the uniform distribution for cluster AoAs, we plot the cumulative distribution function (CDF) of the measured cluster AoAs and uniform distribution in Fig. 7. The distribution of the measured cluster AoAs well matches the uniform distribution, implying the validity of this assumption, at least in the measured scenario.
Moreover, this assumption for uniform distributions can be applied as long as considered scenarios are indoor. This can be attributed to the following two facts. First, the clusters can be explained by the first-or-higher-order reflections from walls in this band; hence, the cluster AoAs can generally scatter in [0 • , 360 • ) for each RX-TX location. Secondly, given that cluster AoAs are defined relative to the LoS component, they can take every value in [0 • , 360 • ) depending on RX-TX locations. The same assumption can be found in the existing channel generation framework in this band for indoor scenarios in [18] and [30].
It should be noted that the assumption of the uniform distribution does not mean that the clusters arrive from every direction with equal powers. In the channel generation flow, the cluster AoAs and cluster powers are independently sampled as shown in Fig. 6. Hence, even if the cluster AoAs are sampled from the uniform distribution, simulated channels are fundamentally directive to some directions in which a large cluster power is sampled.
Indeed, this proposal may violate the consistency in the measured angular spread and that calculated from generated CIRs. However, this problem can be alleviated when the generated CIRs are filtered with directional antenna patterns. Moreover, when the CIRs are filtered by directional antenna patterns, this mechanism rather leads to a better match to the measured angular spread. This fact is also shown in Section IV-B.

B. GENERATION MECHANISM FOR INTRA-CLUSTER SUBPATH POWERS
To involve a large dispersion of the intra-cluster subpath powers, we propose to add intra-cluster shadow-fading term to the intra-cluster power decay. More formally, (18) in the 3GPP channel generation flow is replaced with the following equation: intra−cluster shadow fading (28) where z n,m ∼ N (0, ζ 2 ) denotes the intra-cluster shadow fading term. The standard deviation, ζ , is determined by a linear regression in the dB scale, where the squared error between the regression line and the observed intracluster power is minimized. In our measurement, the standard deviation is found to be ζ = 12.8 dB.

VI. RESULTS OF CIR GENERATION
The performance of the proposed flow for CIR generation was evaluated by comparing the generated CIRs with the measured CIRs in terms of their characteristics. To provide holistic evaluations, we compared the following two viewpoints: 1) an outlook of the snapshot of a generated CIR and 2) statistical characteristics of the generated CIRs.

A. OUTLOOK OF GENERATED CIR REALIZATIONS
To verify that the generated CIR exhibits the real characteristics of the measured CIRs, we first visualized a snapshot of the measured CIR and a CIR generated by the proposed flow. In the same manner as done in Section IV, we show AoA and power characteristics of the subpaths with respect to the excess delay in Figs 8 and 9, respectively, which are detailed as follows.
AoA Characteristics: Fig. 8 shows the polar plot representing the AoA characteristics of the measured CIR and a CIR generated by the proposed flow. Note that the Fig. 8(a) is the same as Fig. 4(a) in the previous section. As shown in Fig. 8(b), the proposed flow overcomes the drawback of the 3GPP channel generation flow in Remark 1 by sampling the cluster AoAs from a uniform distribution as in (27), where the proposed model well simulates the above characteristics of the real CIR in this metric.
Power Characteristics: Fig. 9 shows the power of the subpaths in the measured and generated CIRs with respect to the excess delay of each subpath. Note that Fig. 9(a) is the same as Fig. 5(a). As shown in Fig. 9(b), the proposed model overcomes this drawback of the 3GPP channel generation flow in Remark 1 by introducing the dispersion term of the subpath powers in each cluster in (28), thereby simulating the real characteristics of the measured CIR.

B. EVALUATION OF THE STATISTICAL CHARACTERISTICS
We also evaluated the statistical characteristics of the generated CIR in terms of RMS delay and angular spreads. This evaluation investigates the statistical characteristics of the omnidirectional CIR, i.e., H(τ, φ) in Eq. (1) and directional CIR, where the omnidirectional CIR H(τ, φ) is filtered by the directional antenna pattern in the receiver. This evaluation allows us to gain insight into the usefulness of our proposed flow for link-level simulation in the FR2-2 band because previous communication systems in this band (e.g., IEEE 802.15.3c [9] and 11ad [10]) always employed directional antennas, and the 5G NR communication systems in this band are also likely to leverage directional antennas.
Let H directional (τ, φ) denote the directional CIR. Formally, the directional CIR is given by where A(φ, φ bore ) is the receiver antenna pattern with boresight angle φ bore . In this evaluation, we employed a two-dimensional version of the antenna model in 3GPP TR 37.840 [33], where the antenna pattern is represented by the summation of multiple array element patterns. Following [33], the receiver antenna pattern is calculated as: In the above equation, A E (φ) is the element factor given by: where φ 3dB = 65 • is the half-power beamwidth, and A m = 30dB is the front-to-back ratio. The terms x and y represent the indices of the vertical and horizontal array elements, respectively. X and Y denote the numbers of antenna elements in the vertical and horizontal domains, respectively. The terms v x,y and w n,m are the corresponding elements of the antenna steering and weighting matrices, respectively, and are given by: and where d = 2.5mm and λ = 5.1 mm denote the element spacing and wavelength, respectively. The evaluation results are as follows. Note that to ensure fair comparison, the same array antenna settings should be applied to the measurement data regardless of the fact that we conducted the measurement with a horn antenna. To this end, we leverage the estimated CIR in Fig. 3 in Section III-A, where we apply the same array antenna configuration to the estimated CIRs to yield directional CIRs. Namely, we replace H(τ, φ) in eq. (29) with the estimated CIR in the measurement and calculate the RMS delay and angular spreads in the same manner as those for the CIRs generated by the conventional and proposed channel generation flows.
RMS Delay Spread: Fig. 10 shows the CDF of the RMS delay spread in the measured and generated CIRs. As shown in Fig. 10(a), neither model yielded a clear difference in terms of the RMS delay spread in the generated omnidirectional CIRs. Meanwhile, as shown in Fig. 10(b), the RMS delay spread generated by the proposed flow was close to that of the measured CIRs, whereas the 3GPP model vastly underestimated the RMS delay spread. As stated in the previous section, this can be attributed to the biased AoA cluster. As shown in Fig. 10, in the 3GPP model, no clusters except for the first cluster lie around an AoA of 0 • , where almost all cluster powers are filtered out by the directional antenna pattern. This resulted in a lower RMS delay spread in the 3GPP model. Recalling that the measured CIR and the CIRs generated by the proposed flow distribute the cluster uniformly in terms of the cluster AoA, this effect does not occur in either case, which results in a more accurate CDF of the RMS delay spread in the proposed flow.
RMS Angular Spread: Fig. 11 shows the CDF of the RMS angular spread in the measured and generated CIRs. As shown in Fig. 11(a), the CDF of the RMS angular spread in the 3GPP model was close to that of the measured CIRs. This is because the 3GPP model determines the cluster AoAs such that the RMS angular spread in the generated omnidirectional CIRs is consistent with that in the measured CIR by applying (22). That is, the 3GPP model strictly enforces consistency. The proposed model relaxed this requirement by applying a uniform distribution. Hence, in terms of the omnidirectional CIR, the 3GPP model achieved a more accurate distribution in the RMS angular spread.
However, for the directional CIR, the CDF of the RMS angular spread generated by the proposed flow was closer to that of the measured CIRs. This can be attributed to the same reason as that for the RMS delay spread. In the directional CIR in the 3GPP model, almost all clusters were filtered out by the directional antenna pattern, which resulted in an underestimation of the RMS angular spread. This does not occur in the proposed model with cluster AoA generation leveraging a uniform distribution, which is the reason for the accurate CDF of the RMS angular spread.

C. COMPARISON WITH IEEE 802.15.3c MODEL
Finally, we compare the proposed channel generation flow with the IEEE 802.15.3c model [19] that also targets the indoor short-range communications in the FR2-2 band. In the IEEE 802.15.3c model, cluster delay values and intra-cluster delay values are both generated by a Poisson arrival with the arrival rate and λ /ns. Cluster AoAs are generated with the uniform(0 • , 360 • ), and intra-cluster AoAs are generated by a Laplace distribution with the scale value ρ and the mean value of zero. The cluster power is generated by the exponential decay: exp(−(τ − τ 1 )/ ) · 10 −z/10 with the decay factor of , the first cluster power , and the shadowing term z ∼ N (0, σ 2 1 ) dB. Based on the generated cluster power P 1 , . . . , P N , the intra-cluster subpath power is generated by the exponential decay: P n exp(−k) exp(−(τ n,m /γ )) · 10 −z /10 with the decay factor γ , intra-cluster k-factor k, and shadowing term z ∼ N (0, σ 2 2 ) dB. Finally, the LoS ray is added in the delay and angle of zero, and the power of the LoS ray is calculated by a two-path ground reflection model, where the distance is sampled from uniform( 0.7 m, 3m), and the heights of RX and TX are set to be 0.15 m to ensure the consistency with the measurement.
To ensure fair comparison, we set the above mathematical parameters based on the measurement results in Section III, not using the default value provided in [18]. For the arrival rates, we set = 0.30 /ns and λ = 1.23 /ns, which are found by maximum likelihood estimation. For the parameters to calculate cluster powers, we set = −22 dB, decay factor = 10.2 ns, and σ 1 = 7.48 dB, which are found by leastsquares fitting in the decibel domain. For the parameters to calculate intra-cluster subpath powers, we set γ = 19.6 ns, k = 2.08 and σ 2 = 7.76 dB, which are found by leastsquares fitting in the decibel domain. For the scale value of Laplace distribution to generate intra-cluster AoAs, we set ρ = 0.38 radian, which are found by maximum likelihood estimation. Fig. 12 illustrates a CIR example generated by the IEEE 802.15.3c model. Owing to the inclusion of the intra-cluster power shadowing term z and the uniform distribution of the cluster AoAs, the CIR is similarly structured to that generated by the proposed flow shown in Figs. 8 and 9. Hence, the problem that occurred in the 3GPP model summarized in Remark 1 does not happen in the IEEE 802.15.3c model.
However, in terms of the statistical characteristics of RMS delay and angular spreads, the IEEE 802.15.3c model largely deviates from the measured values as shown in Fig. 13, which can be alleviated by the proposed flow. Note that in Fig. 13, the results of the proposed flow are the same as that in Figs. 10 and 11. As shown in Fig. 13(a), the RMS delay spread in the IEEE 802.15.3c model tends to be generated as much larger values than measured values. This can be attributed to the difference in the generation mechanisms of cluster delay. In the proposed flow, the cluster delays are sampled as an order statistic of exponential distribution while in the IEEE 802.15.3c, those are sampled as a Poisson arrival, i.e., an order statistic of uniform distribution. This means that a large delay value tends to be sampled in the IEEE 802.15.3c relative to the proposed flow, resulting in the larger RMS spread. As shown in Fig. 13(b), the RMS angular spread in the IEEE 802.15.3c model also tends to be generated as much larger values than measured values. This can be attributed to the fact that the IEEE 802.15.3c does not enforce the first cluster AoA to be zero (i.e., the LoS direction), while in reality, the first cluster can be found around the LoS direction because of multiple echoes between the RX and TX. This effect is included in the proposed model, and we can conclude that the proposed model can generate more realistic CIR samples relative to the IEEE 802.15.3c model.

VII. CONCLUSION
This study developed a channel generation framework compatible with the 3GPP model for FR2-2 indoor short-range scenarios, which generated CIRs consistent with the real measured CIRs. We first conducted the measurements where the real CIRs were obtained and derived the parameter set in a compatible manner to the 3GPP model. Additionally, based on a comparison between the measured CIRs and those generated by the 3GPP model, we identified that the 3GPP model is not necessarily suitable for channel generation in the FR2-2 indoor short-range scenario. Particularly, we highlighted that the CIR generated by the 3GPP model deviates from the measured CIR in terms of the AoA and the power of intra-cluster subpaths. Based on this analysis, we proposed an amended flow for channel generation, where the agreement with the measured CIRs in terms of the statistics of directional RMS delay spread and angular spread were demonstrated. The proposed flow and insights into accurate characteristics in directional RMS delay spread and angular spread contribute to the link-level simulations for the upcoming 5G NR operated in the FR2-2 band because the communication systems leveraging this band always use directional antennas.

APPENDIX
This Appendix details the data processing used to estimate the CIR and clusters of each impulse from the recorded PDP.

A. DATA PROCESSING FOR DELAY TIME ALIGNMENT, CIR ESTIMATION, AND CLUSTERING
The recorded PDPs for each RX antenna angle were processed to finally estimate the CIR and its clusters in the joint domains of the absolute delay time and AoA. This is a general and necessary procedure to characterize the FR2-2 propagation characteristics because the FR2-2 propagation characteristics are quasi-optical. More specifically, owing to the higher reflection gain in specular components, the strong multi-path components are concentrated on a few separated regions in the joint delay time and AoA domain and form clusters. Therein, characterizing these clusters is particularly significant to understand the FR2-2 propagation characteristic. Each process is detailed in the following:

1) DELAY TIME ALIGNMENT FOR RX ANTENNA ANGLE
The recorded PDPs for each RX antenna angle were aligned with the absolute propagation delay to estimate the aforementioned clusters. However, as shown in Fig. 14, the recorded PDPs are represented by a different delay time, that is, relative to the time at which the oscilloscope observed the strongest peak. Hence, estimating the absolute propagation time and thereby aligning the PDPs for different RX antenna angles with the absolute propagation time is required.
To this end, as shown in Fig. 14, we searched for the power peak of the LoS path component for every recorded PDP and shifted the recorded PDPs such that the delay time for each recorded PDP was aligned with the LoS path component. Note that even when the pointing angle of the horn antenna was not zero degree, the power peak of the LoS component, which is captured by either main or nonmain lobe in this case, was basically visible. This fact was checked by an anechoic room measurement conducted prior to this measurement. Specifically, by letting τ angle denote the delay time where the power peak from the LoS path was found in the recorded PDP, the recorded PDP was shifted for d/c − τ angle in the delay time domain, where c and d are the speed of light and distance between the RX and TX, respectively. In the following discussion, we use this aligned PDP and refer to it as the PDP.
Indeed, if we use the clock synchronization between the RX and TX, we can obtain the absolute delay without searching for the peak of the LoS component. However, given the fact that the LoS component was visible for almost all pointing angles of the horn antenna, we did not use clock synchronizations to simplify the procedure to obtain PDPs during the measurement. This was sufficient 1 to achieve our goal of measuring the propagation characteristics in the indoor short-range communication scenario. Moreover, we validated the results of the absolute delay time estimation, which is detailed next.
1. It should be noted that this unsynchronized setting may bring other concerns about the frequency and phase offset. However, the former was negligible because, for the TX /RX local oscillators, we leveraged calibrated continuous wave signal generators, where the frequency is adjustable in the resolution of 0.01 Hz (Keysight E8267D for RX and Anritsu MG3694C for TX). Hence, the frequency error lies in this order, which is far smaller than the sounding signal bandwidth of 2.16 GHz. Moreover, the latter is not our concern because the measurement target is the PDP, which can be obtained by measuring the power of the sounding signal without concerning the phase shift. Fig. 15(a) shows an example of the angular-resolved PDP after the delay time alignment with the range from −50 dB to 0 dB relative to the LoS component. Moreover, the PDP is overwrapped by the electro-imaging with the room layout for the measurement in Figs. 15(b) and (c). The estimated delay time is shown in Fig. 15(a), which can be compared with the delay time calculated by the electro-imaging in Figs. 15(b) and (c) for first-and-second-order reflections, respectively. By this comparison, the estimated delay times well match those from the electro-imaging, which validates the delay time estimation method. Moreover, from this result, we can identify the number of clusters, which is used for the channel generation in Table 2. More concretely, we can identify one cluster of the multiple reflection echo between RX and TX, 4 clusters of first-order reflections, 3 clusters of second-order reflections, and other isolated paths. Given this, the number of clusters is over 10; hence, we set the number of clusters to be 13.

2) CIR ESTIMATION AND CLUSTERING OF INTRA-CLUSTER SUBPATH
We estimated CIR from the measured PDP. The measured PDP exhibits a continuous power spread in delays and angles owing to the finite measurement bandwidth and angular spread in the RX antenna patterns. This estimation is performed by removing this continuous power spread, thereby distilling multipath components, that is, the AoA, excess delay, and amplitude for each impulse. This procedure is already discussed in Fig. 3 in Section III.
After the CIR estimation, we performed clustering of the extracted multipath components with separation in the joint space of the propagation delay and AoA. We employed the K-power means algorithm presented in [34] for clustering, whereas we extended the algorithm to gain dimensionality. In this algorithm, we clustered the multipath components using the measure of the weighted Euclidean distance in the Euclidean space of the propagation delay, sine, and cosine of the AoA: where τ i and φ i denote the excess delay and the AoA relative to the LoS ray, respectively. The second and third spaces ensure the circular consistency of the AoA. The term β was heuristically set to three. The number of clusters was basically set to 13 to ensure the consistency of the clustering result with the reflections expected from electro imaging. Exceptionally, for RX locations of "2m (East)" and "3m," we set the number of clusters to be 16 because more multipath components are observed in these locations. Fig. 16 shows the polar plot representing the excess delay and AoA of each multipath component relative to the LoS ray. The cluster can be estimated from the isolation in terms of excess delay and AoA. Moreover, separate investigations showed that the estimated cluster matched well with the electro-imaging based on the room layout shown in Fig. 2. Hence, we estimate the parameters listed in Table 2 based on these results.