Uniform Analysis of Multipath Components From Various Scenarios With Time-Domain Channel Sounding at 300GHz

Knowledge of the wireless channel remains crucial for the development of applications such as joint communication and sensing, intelligent reflective surfaces or terahertz communications that are currently discussed as fundamental part of the sixth generation of mobile systems. To benefit from synergies, a uniform and collaborative data evaluation of measurement sets from two different time-domain channel sounders is presented in this paper. Based on a common signal processing that extracts discrete multipath components, the properties of the propagation channel are analyzed. The channels show a great variety of characteristics depending on the scenario, the line-of-sight condition and the signal-to-noise ratio requirements of the prospective communication system. Considering the impact of a realistic antenna array, the radio channel that is ultimately relevant for the communication system is examined. Having less impact due to the spatial filtering, the different characteristics of multipath propagation still emphasize the brought range of terahertz channels. The extracted multipath components are published as research data to serve the community for future analytical studies and simulations in relevant scenarios for the sixth generation of mobile systems.


I. INTRODUCTION
O NE VISION of the sixth-generation (6G) mobile system standard is the achievement of a wireless data transfer with a data rate of up to 1 Tbps [1]. At the same time, novel applications and use cases are envisioned that will benefit from technologies such as joint communication and sensing or intelligent radio environments like intelligent reflective surfaces (IRSs) [2]. For all applications in this context, the wireless channel and its exploration has a key role for a successful implementation and integration.
A promising approach to achieve a 100-fold capacity increase of the data rate lies in the expansion of the frequency spectrum to the terahertz (THz) band that covers a range from 0.1 THz to 10 THz [3]. The THz communication has received growing attention in the recent years [4]. Promising frequency bands in the lower THz band are the D-band (110 GHz to 170 GHz) and H-band (220 GHz to 330 GHz) due to their specific low atmospheric attenuation properties, that is favorable for wireless communications [5]. Moreover, an overall bandwidth of 137 GHz was identified for land mobile and fixed services between 275 GHz and 450 GHz at the World Radio Conference 2019 [6]. Besides, first standardization activities in the THz band have released a standard for fixed point-to-point THz links defining a single carrier transmission over 69 bands in the range from 252.72 GHz to 321.84 GHz with bandwidths ranging from 2.16 GHz to 69.12 GHz [7].
In the context of the genesis of 6G, the THz band gains more and more attraction. Nevertheless, there are still many open questions that affect the design of systems, algorithms and components. For instance, the role and impact of multipath propagation on the THz communication link is one central research topic. Depending on the application, the number of relevant multipath components (MPCs) might change significantly. Also, the filtering effect of directional antennas and the interplay of multipath propagation and antenna side lobes will determine the characteristics of the effective radio channel [8].
Channel measurements lay the foundation for the development of modern communications systems giving insights on the radio environment [9]. The increasing advances on the system design and functionalities also augment the necessary knowledge production and level of detail of the wireless channel. Research groups from all over the world contribute to push the knowledge on the propagation characteristics in diverse application scenarios [10] as, for example, for device-to-device (D2D) communication [11], for kiosk-downloading [12], in data centers [13], in office scenarios [14], and in outdoor environments [15].
In the recent years, channel sounding via time-domain correlation became available that allows for an instantaneous capture of the radio channel. The individually designed measurement systems make it more difficult to compare measurement results from different measurement campaigns by contrast with measurements performed with a vector network analyzer (VNA) [16]. Since measurement campaigns are costly and time-intensive, the community would profit from shared and exchangeable data based on a common reference [17].
The contribution of this paper is threefold: • Two correlation-based time-domain channel sounders (CSs) are compared and a coordinated measurement evaluation based on a coherent signal processing and use of MPCs extraction technique is shown that brings the measurements to a same level of evaluation. • A uniform analysis of a wide range of application scenarios of THz communication is performed considering temporal and spatial channel characteristics. We draw conclusions on the propagation channel and show the impact on future communication systems evaluating the radio channel that takes into account a realistic patch antenna array. • The discrete MPCs that are extracted from 56 measurement positions are published as research data such that the community can profit from realistic information on THz channels [18].
The remainder of the paper is structured as follows. Section II briefly introduces the most common channel sounding techniques and discusses the challenges of time-domain channel sounding. Then, Section III compares the CSs of Fraunhofer Heinrich Hertz Institut (HHI) and Technische Universität Braunschweig (TUBS) and the respective signal processing in detail that yields comparable and exchangeable measurement results of both systems. Afterwards, Section IV illustrates the scenarios that are examined in the collaborative measurement evaluation presented in Section V. Finally, Section VI concludes the contribution of this paper.

II. CHANNEL MEASUREMENT TECHNIQUES
The purpose of channel sounding and respectively performing channel measurements is the radio channel's observation at certain frequency bands. The observation aims at receiving the radio channel's system functions, such as the channel impulse response (CIR) or transfer function. Performing the channel measurements can be done with two different measurement principles: time-domain and frequency-domain channel sounding. Frequency domain channel sounding aims at the channel transfer function, whereas time-domain aims at the CIR. The realization of these two principles can vary [19].
In general, four techniques of channel measurements are popular: channel sounding with a signal generator and a spectrum analyzer, time-domain spectroscopy, channel sounding based on a VNA, and correlation-based channel sounding [20].
While the first method provides only power-based measurements, time-domain spectroscopy is mainly used for short channels and material characterization [22]. On the contrary, the VNA equipped with frequency extenders is a very popular equipment for channel sounding. In recent years, correlation-based time-domain channel sounding has become available offering new possibilities which make it attractive for channel measurements. In the following section, we will briefly introduce the concepts of channel sounding with a VNA and channel sounding with a time-domain correlation approach. Fig. 1 visualizes the two channel measurement techniques.

A. FREQUENCY SWEEP
The VNA is one realization of frequency-domain channel sounding and measures the complex S-parameters as a function of frequency [23]. The VNA approach aims for the channel transfer function and therefore combines the measured S21/S12 parameter over the measurement bandwidth to determine it.
The VNA creates a narrowband continuous wave stimulus with a selectable measurement bandwidth that is fed into the channel, the transmitted and received signals are recorded and compared. Sweeping the wide bandwidth of interest successively for a selectable number of measurement points, the VNA records the amplitude and phase at each frequency bin resulting in the transfer function of the channel. The CIR is obtained via inverse Fourier transform.
The off-the-shelf measurement equipment is available from various vendors and represents a matured technology. In addition, frequency extenders can be purchased for a wide range of frequency bands. Reliable calibration techniques take care for a correct compensation of hardware specific properties and make the measurement results of different VNAs directly comparable.
In comparison to the time-domain correlation channel measurement technique, that is explained in the following section, the VNA combines both the transmitter (TX) and receiver (RX) in one instrument, which on the one hand is an advantage in the means of hardware and a disadvantage in the means of untethered channel measurements.

B. TIME-DOMAIN CORRELATION
Correlation-based channel sounding is, besides the pulsebased approach, one main realization of time-domain channel sounding. The CS is a distributed system, mainly separated into one (or multiple) TX and RX (with many components). The sounding system delivers CIRs and observes the whole channel bandwidth simultaneously.
For THz frequencies, it is so far realized as individual construction with single-unit production in research projects because of the high requirements on circuit design due to the high bandwidth and carrier frequency. Also, the synchronization of the components is challenging regarding the very high bandwidth of the signals.
The working principle is as follows: A TX generates a (periodic) test signal, also known as sounding sequence, with good or even perfect autocorrelation characteristics, and transmits the sequence (continuously) at a desired carrier frequency. Ideally the sounding sequence is broadband and covers the band of interest. A RX captures the transmitted sequence for one or multiple periods. Through the correlation of the received signal with the original signal, the CIR is obtained.
In static environments, an increase of the dynamic range can be achieved by averaging multiple CIRs. To compensate for system specific impairments, a system characterization is performed by a calibration procure that is realized with a back-to-back (B2B) measurement and a calibration network.
One advantage of the time-domain correlation principle is, that mobile measurements where the channel is time-variant with separated TX and RX are possible. These measurements require a synchronized reference.

III. MEASUREMENT EQUIPMENT AND METHODOLOGY
The following sections introduce the CSs from TUBS and HHI that were used for performing the channel measurement campaigns and thereby gathering the measurement data.
Both CSs are based on the previously described principle of time-domain correlation and operate in the H/J-band [5] around 300 GHz. Although the two CSs's core characteristics are equal, there are many particularities that make the measurement systems differ from each other.
Therefore, their working principle, the measurement methodology and the signal processing is explained pointing out common features and differences. This comparison lies the bases for a common and comparable measurement evaluation.

A. MEASUREMENT HARDWARE AND PARAMETER
Since both CSs are based on the same principle, their composition resembles one another. The setups can be divided into TX and RX and an extra clock/impulse generator. The TX consists of a test sequence generator that generates the sounding sequence and one or multiple upconverter stages for upconversion to the radio frequency (RF) band via an intermediate frequency (IF). The RX consists of one or multiple down-converter stages and an analog-to-digital converter (ADC) that samples the received sounding sequence. Fig. 2 illustrates the composition of the measurement systems.
For a deeper understanding of the CSs, the following section describes the setup, the hardware's interconnections and lists the main parameters. Being able to handle up to four TXs and four RXs, a base unit of the TUBS system creates a common clock of 9.22 GHz that is distributed to all TXs and RXs in order to guarantee the synchronization. In contrast, the HHI Synchronomat creates a 10 MHz reference signal that is fed to the TX and the RX. The HHI Synchronomat, that was developed within the Fraunhofer society, enables a distribution of a common 10 MHz reference signal to multiple measurement instruments and also enables a trigger generation for multiple measurement instruments for coherent sampling. Unlike most clock generators, the HHI Synchronomat is synchronizable with another HHI Synchronomat for untethered channel measurements via a rubidium standard. This means that the setup is separable for coherent measurements over large distances.
The internal arbitrary waveform generator (AWG) of a vector signal generator of the HHI system generates a Frank-Zadoff-Chu (FZC) test sequence with a bandwidth of 2 GHz and a sequence length of 200.000 chips. The probe signal is internally up-converted to the IF band at 12 GHz. An analog signal generator generates a local oscillator (LO) signal for the TX frequency extender at a frequency of 8 GHz. All components are fed by separate power supplies. In comparison, the TUBS system generates an M-sequence in the TX ultra-wide band (UWB) modules with 4095 chips and a bandwidth of 8 GHz in the IF band from 5.22 GHz to 13.22 GHz. Frequency extenders can convert the test signal via frequency doublers, amplifiers and a subharmonic mixer either to the mmWave band from 60.54 GHz to 68.54 GHz or to the low THz band from 300.26 GHz to 308.26 GHz making use of the common clock signal as LO. The power supply for all components is provided by the base station [24].
Comparing the different test sequences, the FZC sequence offers better correlation properties due to the generation of a complex signal with a constant amplitude [25]. On the other hand it causes a more sophisticated generation procedure compared to the M-sequence that is created with a linearfeedback shift register.
The HHI system also uses external frequency converters that are a Fraunhofer in-house design. The front-ends are based on transceiver (TRX) modules developed by the Fraunhofer IAF that follow the principle of single sideband conversion. The TRX front-end can operate both as up-and down-converter. For the TX-side, only the up-converter path is used. The signal is radiated at 300 GHz with an equivalent isotropic radiated power (EIRP) of 11 dBm by an open waveguide with an antenna gain of 6 dBi and a half-power beam width (HPBW) of 90°in both, E-and H-plane. Highpass filters in the TUBS frequency extenders similarly assure a single side band transmission before the signal is radiated with an EIRP of 2.7 dBm by horn antennas with a gain of 26.4 dBi and a HPBW of 8.5°in both, E-and H-plane.
For the down-conversion of the signal that is received with a 20 dBi horn antenna, the HHI CS uses another TRX front-end. An analog signal generator creates the LO signal at a frequency of 8.15 GHz and the IF signal at a frequency of 6.6 GHz is sampled with a vector signal analyzer (VSA). The VSA uses a sampling rate of 2.5 GHz which corresponds to a measurement bandwidth of 2 GHz and stores the inphaseand quadrature-(I-/Q-)samples internally on the instrument. In theory, the mentioned sampling rate and sequence duration result in a measurement rate of 10 000 CIR/s after signal processing. The bottleneck in achieving the measurement rate is the instrument's internal random access memory (RAM) [26].
Accordingly, the TUBS RX side downconverts the received signal that is amplified by a variable gain amplifier to assure the allowed input power and sampled with 14-bit ADCs in the RX UWB modules using a coherent subsampling scheme [27] with a factor of 128 resulting in a measurement rate of 17 590 CIR/s.

B. MEASUREMENT PROCEDURE AND METHODOLOGY
The TUBS CS offers two operation modes: an averaged mode and a high-resolution mode. In the high-resolution mode, the maximum measurement rate of 17 590 CIR/s is achieved and the I-/Q-samples of the transmit and received signal are directly stored on a solid state drive (SSD). This mode enables time-variant measurements with a maximum Doppler frequency of 8.795 kHz making movements of the TX, of the RX or of scatterers possible [28]. The correlation of the recorded TX signal and the recorded RX signal is performed offline during the post-processing. In the averaged mode, the correlation with the original TX signal is performed by the UWB modules. A programmable number of CIRs between 64 and 262 144 is averaged and transferred to the control laptop. This way, a high number of measurements with high dynamic range can be stored in a data-efficient way while the I-/Q-samples before correlation are not directly accessible.
Comparable to the high-resolution mode of the TUBS system, the HHI CS records a multitude of sequence periods -usually 250 to 500 sequences per measurement that are often denoted as snapshots. After a one time trigger that is generated by the HHI Synchronomat, the test sequence is transmitted continuously by the TX. The sampling at the RX is coherent to the sequence transmission on the TX side and starts with another trigger signal from the Synchronomat. The VSA samples the received I-/Q-data and records the baseband samples internally on the RAM of the VSA that limits the number of snapshots to 500 corresponding to a measurement duration of 50 ms. After each measurement, the data is stored on the SSD of the VSA. For further processing, the data is loaded from the VSA to MATLAB ® after a certain series of measurements.
Both CSs usually use a B2B configuration in order to calibrate the absolute delay and path gain and to compensate for the antenna gain and hardware specific impairments. The calibration network consisting of manual direct reading precision attenuators with known waveguide attenuation is dimensioned in such a way that the waveguide attenuation corresponds to the minimal expected path loss in the measurement scenario. For low TX-RX-distances the maximum rating of the specification of the equipment have to be assured in order to avoid an RF overload. Alternatively, the CSs are calibrated in an over the air (OTA) configuration with known distance between TX and RX. Here, the antenna matching is considered in the calibration measurement, while the elimination of the influence of the environment is challenging.
Depending on the channel characteristics of interest, the TXs and RXs of both CSs can be mounted on different tools that support an accurate measurement procedure. Automated rotation units scan a programmable angular range with an adjustable step size. Rotational measurements are usually performed with an angular step size that corresponds to the HPBW of the antenna [29]. Both parties use a vertical polarization of the antennas for azimuth scans, that minimizes the antenna side lobes in the azimuth plane. In this way, an antenna de-embedding can be avoided in a first order approach. The TUBS system performs doubledirectional measurements scanning the angle of departure (AoD) and angle of arrival (AoA) and the HHI system keeps a fixed AoD with a broad-beam antenna and scans the AoA. Alternatively, tripods allow for an accurate height adjustment and a rail system for precise axial displacements that are measured with a laser meter.

C. PREPROCESSING, POSTPROCESSING AND MULTIPATH EXTRACTION
The signal processing of the measurement data is conducted in three consecutive steps. The first step is the preprocessing that results in the calibrated exchangeable measurement data. The following post-processing includes further signal processing before the discrete MPCs are extracted in the third step [17].
All processing steps are carried out offline in MATLAB ® , after the execution of channel measurements is completed. Starting point of the signal processing for both parties (TUBS and HHI) is the captured raw measurement data. Here, HHI starts with I-/Q-samples and TUBS with raw CIRs from the averaged mode that is used for rotational scanning measurements with 131 072 CIRs being recorded for each combination of AoA and AoD representing a trade-off between dynamic range and measurement duration.
The correlation and calibration can either be done in two steps, as TUBS does, or in one step, as HHI does, by correlating with a B2B calibration that is recorded before the channel measurement's execution such that the setup's influence by hardware is eliminated. In the TUBS processing, the CIRs are calibrated in terms of path gain and delay and the noise floor is cut-off with a margin of 15 dB. Due to hardware-specific impairments, the spurious-free dynamic range (SFDR) of the TUBS CS is currently limited to 14 dB. After the calibration, each CIR is cut at the level of the SFDR.
The derived exchangeable and calibrated CIRs are afterwards averaged and windowed. The HHI system applies a Kaiser-Bessel window with a β parameter of 8 and TUBS applies a Hann window from 300.2 GHz to 302.2 GHz in order to make the data comparable to the bandwidth of the HHI system. Both windows reduce side lobes in the CIR originating from the CS. Fraunhofer HHI also compensates the common phase error before averaging. The phase drift that is mainly caused by the system's phase noise is estimated and afterwards corrected. Within one measurement, for each snapshot the phase value of the main peak of the individual cross correlation function between received and transmitted signal is observed. Under the assumption of a static channel, the phase deviation throughout the snapshots can be compensated.
If the scenario can be assumed to be time-invariant over one series of measurements -which is the case for rotational measurements in static environments -all snapshots of a spatial sampling point are averaged in the post-processing resulting in an averaging gain. Overall, the averaging gain and the correlation gain together increase the dynamic range, that is defined by the range between the maximum measurable level and the noise floor, to 70 dB for both systems. The dynamic range cannot be calculated or directly derived since some noise characteristics of hardware components are unknown to the authors. Here, the HHI CS has a correlation gain of 53.0 dB due to the sequence length of 200 000 and a resulting averaging gain of 27.0 dB. The TUBS system has a correlation gain of 36.1 dB originating from the 12 th -order M-sequence with a length of 4095 and an averaging gain of 51.2 dB for the presented measurements. Table 1 summarizes the key values of the two measurement systems.
After the postprocessing, the averaged CIRs can be combined to sets of CIRs for a specific measurement position, also in double directional measurements where the angular range of the AoD is limited to 180°around the direct path in order to agree with HHI's measurements. On the basis of these sets of CIRs, the MPCs are extracted, by a local maxima search of the amplitude of the CIR in the three-dimensional space AoD×AoA×Delay for double-directional measurements and the two-dimensional space AoA×Delay for unidirectional measurements. The MPC extraction considers a threshold that is well above the noise floor. For the HHI CS this threshold is 5 dB  above the noise floor and for the TUBS CS it is 15 dB. In order to correctly detect the maxima in the spatial domain, the periodicity of the angular domain is taken into account. Finally, a list with all detected MPCs including the amplitude, delay, AoA (and AoD for double-directional measurements) is obtained that is published for the following scenarios [18].

IV. MEASUREMENT SCENARIOS
This section introduces the channel measurement campaigns carried out by Fraunhofer HHI and TUBS at 300 GHz. In the following, the authors briefly describe the indoor scenarios visualized in Fig. 3 and summarized in Table 2. The measurements in the data center and aircraft cabin scenario were carried out by TUBS. The measurements in the industrial, the shopping mall and the conference room scenario were carried out by HHI. For the common evaluation of channel parameters, only rotational scans of the azimuth plane are considered representing a comparable measurement procedure. TUBS performed double-directional scans, which means that both the TX frontend and the RX frontend are rotated stepwise in the azimuth plane, whereas HHI only rotates the RX frontend with a fixed TX frontend alignment. In total, a number of 56 measurement positions were approached and the collected and processed measurement data will be evaluated jointly. Due to the different measurement procedures, HHI contributed measurements for 48 measurement positions and TUBS contributed measurements for 8 measurement positions. The measurements scenarios consist of line-of-sight (LOS), obstructed line-of-sight (OLOS) and non-line-of-sight (NLOS) measurements. LOS is defined as a scenario with a clear direct path between TX and RX, OLOS is defined as a scenario where the direct path is adversely affected but still present and NLOS is defined as a scenario where the direct path is blocked. For detailed information on the measurement setups, the authors refer to the respective reference.

A. PRODUCTION HALL
The backbone for future industries is high-performance communication for data exchange between machines, tools and work pieces, providing high reliability, high throughput and ultra-low latency. Wireless communications play an increasingly important role, allowing rapid reconfiguration of environments and connectivity between mobile robots.
Industrial environments, such as production halls, are ample areas mainly characterized by metal and concrete. In most cases, the ground, ceiling, and walls are made of concrete. Metal surfaces appear in forms of ventilation tubes along the ceiling, tracks along the ground, protective covers along the walls or around free-standing pillars and machinery enclosure.
The channel measurements were conducted for three different surroundings. The first surrounding was a production shop floor, the second a storage and prototyping area and the third a metal hallway. For each surrounding a multitude of measurement positions in LOS, OLOS and NLOS scenarios were approached and in total 18 measurement positions were captured. For the production shop floor and storage area an access point (AP) scenario was simulated by placing the TX at a height of 2.7 m and the RX on a height of 1.5 m. The TX's alignment was changed throughout the channel measurement's execution, depending on the RX's position. For measurements in and around the metal hallway, the TX and RX were placed on the same height of 1.5 m [30].

B. DATA CENTER
Additional wireless links in a data center will augment the flexibility and reconfigurability of the data center network. However, the high potential of this use case is highly connected to the reliability and data rate of the wireless links that has to be comparable to optical fibre links. Hence, measurements in a data center have investigated the propagation characteristics for inter-rack wireless links at medium height and top-of-rack level [31]. Though the two regions are located in the same environment, they differ significantly from each other. The inter-rack links at medium height face many powder-coated metal racks and glass fronts that are arranged in long aisles. In contrast, the top-ofrack region is characterized by very few obstacles apart from cable ducts and plastic curtains that separate regions of hot and cool air for an efficient cooling. Here, six measurement positions are considered. Three measurement positions belong to the links at medium height that are all placed in a LOS scenario, and three measurement positions belong to the top-of-rack links. For the latter, one position is a LOS scenario and two positions are OLOS scenarios where one and two plastic curtains obstruct the direct path, respectively [31].

C. AIRCRAFT CABIN
Connecting the passenger's personal electronic devices (PEDs) to the in-flight entertainment (IFE) system will improve the comfort of passengers during a flight. A wireless connection allows for a flexible solution and reduces the weight of the aircraft saving cables and monitors. However, a high number of passengers each requiring a high data rate make THz communications a promising candidate.
The aircraft cabin is dominated by blocking furniture like overhead stowage compartments and seats, covered in a metal fuselage. Application-oriented measurements investigate the multipath propagation for different communication link and interference link configurations [32]. Here, two measurement positions are considered that perform a full angular sweep in the azimuth plane. In the first measurement representing a LOS scenario, TX and RX are placed in the same row of seats on the opposite sides of the aircraft. In the second measurement representing an NLOS scenario, the TX was moved one row backwards so that a seat blocked the direct path.

D. SHOPPING MALL
A shopping mall or atrium-type scenario is typically characterized by wide, open spaces with high ceilings. Besides usually tiled floors and glass walls, concrete pillars and metallic surfaces, for example at elevators, are part of the environment.
The measurements were conducted in a company building's atrium with a room size of 15 m×50 m and a ceiling height of 20 m. The TX was placed centrally on one end of the atrium and the RX was moved along a well defined grid of measurement positions. Both TX and RX were placed on the same height of 1.5 m to simulate a D2D communication. Throughout the measurement scenario's execution, the TX's alignment was not changed and in total a number of 22 measurement positions were approached, for all of which a LOS was present [33].

E. CONFERENCE ROOM
A typical scenario for simulating a wireless network in a small indoor environment is the AP scenario in a conference room. By placing the TX in one corner on an elevated plane of the conference room with an alignment to the room's center, the mobile AP is imitated. Besides glass fronts, and concrete walls, a conference room usually consists of furniture like chairs and a huge table. To simulate typical user equipment (UE) positions in the conference room, the RX was placed on various positions on the table, that is located in the conference room's center. The TX was placed on a height of 1.9 m and the RX on 0.9 m. The angle-resolved measurements were carried out in one of HHI premise's conference room and approached 8 measurement positions in total. For all measurement positions a LOS was present [34].

V. EVALUATION OF MULTIPATH COMPONENTS
Starting point of the collective evaluation of MPCs, which for this work means a collaborative evaluation between TUBS and HHI, is the processed data of the previously discussed channel measurement campaigns in Section IV. The MPCs are extracted individually as described in Section III-C. This section focuses on how to evaluate the extracted MPCs further, by introducing a common reference plane for a collective evaluation. The authors aim at deriving further channel parameters that can afterwards be analysed collectively. As already mentioned in Section III-A the realization of both CSs differ and therefore also the signal processing approach. Nevertheless, both CSs are based on the principle of time-domain channel sounding with the aim of angleresolved channel measurements, so a common processing reference plane is achievable.
A coherent signal processing and the MPC detection are the basis for a joint evaluation of the measurement data from different equipment, scenarios, and positions. The following section defines the channel parameters that are investigated and provides a description of the joint evaluation of all scenarios. Thereafter, the propagation channel (sometimes denoted physical channel), is analyzed followed by an analysis of the radio channel (sometimes denoted effective channel) that incorporates a realistic antenna at the RX side and thus provides significant implications on the design guidelines for wireless communication systems at low THz frequencies.

A. CHANNEL PARAMETERS
The following section introduces all channel parameters whose derivation is part of the collaborative MPC analysis. Each parameter is described and defined, based on the L discrete MPCs characterized by their respective amplitude A l , delay τ l and AoA ϕ l .

1) CHANNEL GAIN
The channel gain corresponds to the maximum of the amplitudes of the MPCs

2) POWER-DELAY PROFILE
The power delay profile (PDP) builds the basis for most of the channel parameters and describes the path gain of the different MPCs as a function of the delay. The PDP P τ is given by the combination of the square of the amplitudes located at the respective delays where δ(·) denotes the Dirac function. Consequently, a superposition of multiple MPCs at the same delay yields the sum of the squared amplitudes.

3) DELAY SPREAD
The root mean square (RMS) delay spread (DS) is the square root of the second central moment of the PDP and given by [35] where τ i denotes the delay of the i-th component of the PDP.

4) POWER-ANGULAR PROFILE
As a counterpart of the PDP in the angular domain, the PAP describes the path gain of the different MPCs in the angular domain where ϕ l denotes the AoA of the l-th MPC. Similarly, a superposition of multiple MPCs at the same AoA yields the sum of the squared amplitudes.

5) ANGULAR SPREAD
The angular spread (AS) describes the standard deviation of the angular distribution of the MPCs. In order to avoid an ambiguity due to the periodicity of the angular domain and the dependency on the orientation of the coordination system, the AS is defined by the circular standard deviation in directional statistics and can be expressed by [36] where ϕ i denotes the AoA of the i-th component of the PAP. The PAP and AS can also be defined for the AoD and the elevation plane. Because of the lack of measurement data for the elevation plane and the AoD in the azimuth plane for all measurement positions, we limit the evaluation to the AoA in the azimuth plane.

6) K-FACTOR
The K-factor is defined as the ratio of the power of the strongest path in relation to the power of the remaining MPCs

7) MAXIMUM EXCESS DELAY
The maximum excess delay (MED) is defined as the time difference of the delay of the MPC with the maximum delay τ L and the first MPC τ 1

B. OVERARCHING SCENARIO EVALUATION
An overarching evaluation of the extracted MPCs for all measurement campaigns that were introduced in Section IV is beneficial, because channel measurement campaigns are time-intensive and costly. For this reason, a great potential lies in a cooperative and joint data evaluation based on exchangeable measurement data from different parties.
To guarantee the interchangeability, HHI and TUBS implemented a coherent signal processing that is compliant with a reference model [17] and allows for the calculation of channel parameters based on discrete MPCs. This means, that all measurement positions and measurement campaigns can be uniformly evaluated, independent from its contributing party. Besides the mentioned synchronized signal processing, the similar measurement procedures that HHI and TUBS utilize enable a collaborative evaluation if the measurement results. One main feature in the measurement procedure that allows the presumption of results with quasi omnidirectional antennas at the RX side, is the rotation of the RX frontend in correspondence to the RX antenna's HPBW. After the local maxima detection (MPC extraction), the obtained components can be regarded as received with an omnidirectional antenna. By summing up MPCs with same delay for one measurement position, a pseudo-omnidirectional PDP is achieved. Fig. 4 presents the PAP and PDP for two measurement positions, from two distinguishing measurement scenarios, one carried out by TUBS and the other one by HHI. One measurement is an inter-rack link at medium height in the data center and the other one a possible UE position on a table of a conference room. The joint depiction demonstrates the exchangeable representation of measurement results that is reached by the implemented signal processing. The measurement results from HHI and TUBS in the delay domain and angular domain can be presented in a similar and comparable way laying the foundation for a uniform evaluation that is applied to all channel parameters.
The basis for the following channel analysis for prospective applications at low THz frequencies consists of 56 measurement positions from five scenarios of which 48, 5, 3 are LOS, OLOS and NLOS, respectively. One scenario, e.g., an industrial environment, can comprise measurement positions in LOS, OLOS and NLOS configurations and can therefore differ in itself significantly with regard to the channel characteristics. Hence, a blended examination or modeling neglecting the LOS condition will not lead to meaningful results. On the other hand, a pure classification depending on the LOS condition regardless of the environment might also lead to the risk of misinterpretation of relations since the fundamental impact of the geometry and materials of the environment are ignored. Therefore, it is reasonable to process a joint examination of all measurement points from all scenarios and represent the information in a detailed and differentiated way. With a coherent evaluation of all measurement positions, the variety and multitude of channels within the scenarios and among each other can be demonstrated. It is noteworthy that this approach is not confounded with a pure stochastic analysis since the mean and the variance of all measurement positions from all scenarios are a figure of merit with very little significance. Here, in the context of a collective analysis, the distributions of the channel parameters are of interest showing the diversity of the channels. Details of the individual scenario evaluation and scenario specific modeling approaches have been presented in dedicated analysis of the environments [30], [31], [32], [33], [34].

C. PROPAGATION CHANNEL
The evaluation of the MPCs for the propagation channel is directly linked to the concept introduced in the previous section. On the basis of quasi omnidirectional measurements at the RX side, the channel is analysed with regards to the listed channel parameters. Firstly, an observation of all extracted MPCs and secondly, a statistical evaluation in the form of cumulative density functions (CDFs) for the introduced channel parameters is done.
For the observation of all extracted MPCs, a normalization and sorting of all MPCs with regards to the strongest path within the set of MPCs is done. After the normalization, the strongest path corresponds to an MPC index of 0 and a magnitude of 0 dB. As an example of a measurement with present LOS, the direct (LOS) path is normalized to 0 dB and 0 MPC index, followed by the residual MPCs in a decreasing order with regards to the magnitude, but an increasing order with regards to the MPC index.
For the MPC observation, a threshold of 30 dB at maximum below the strongest path is chosen. For each measurement position, a multitude of MPCs are detected within the threshold. The following observation limits the number of MPCs after the strongest path to 15. Fig. 5 visualizes the extracted MPCs for the mentioned threshold below the strongest path for all scenarios. The figure also illustrates the 10 % and 90 % quantiles as red boxes behind the MPCs, that are illustrated as red dots.
The figure denotes, that mostly 2 MPCs besides the strongest path are observable, in the range of 10 dB below the strongest path. By increasing the range considered to 20 dB, the number of MPCs present increases to 8. In the range of 30 dB below the strongest path, over 15 MPCs are observable.
Regardless of LOS, OLOS or NLOS, in 90 % of cases the second strongest MPC is at least 4 dB below the strongest path. With progressing MPC index, the decrease in path gain is exponential and flattens around the 10 th MPC.
Considering the deployment of a wireless network in an indoor environment or the implementation of a mobile standard for such, at least 2 MPCs beside the strongest path are present even with low signal-to-noise ratio (SNR) condition of 10 dB. Fair way, this result regards a "worst-case" scenario with an omnidirectional RX antenna and a non-directional TX antenna.
The following analysis of the channel parameters visualized as CDFs provides a differentiated picture and examines the channel characteristics as a function of the SNR requirements. Besides the differentiation between the 56 measurement position, a threshold of 10 dB, 20 dB and 30 dB with regard to the strongest path in the respective measurement positions is introduced that limits the MPCs considered for the calculation of the channel parameters. With the introduction of those extra threshold, a low, medium and high SNR of a prospective communication system is simulated. The radio channel and the requirements of future communication systems on the channel such as the SNR have to be seen and analyzed together. Fig. 6 visualizes the CDF of the DS, AS, MED and K-factor based on the MPCs in the region of the previously introduced thresholds. For all CDFs, the observation for the 10 dB threshold corresponds to blue, for 20 dB to red, and for 30 dB to yellow.
For DS, AS and K-factor, MPCs between 20 dB and 30 dB are less significant since the curves have a very similar shape and therefore only show slight variations. The MED behaves differently, because the parameter is dependent on the maximum value without a weighting of the components.
For the DS, a wide range of values from 0 ns to 40.75 ns is observed. In 48 % of all cases, there is only one path for a threshold of 10 dB, resulting in a DS of 0 ns. For 90 % of cases, the DS for a considered threshold of 10 dB, is below 10 ns. Considering a threshold of 20 dB to 30 dB, the DS is well below 17 ns in 80 % of cases and below 35 ns in 90 % of cases. 57 % of the measurement positions have an AS of 0°with a considered threshold of 10 dB, meaning that all MPCs are incident from the orientation towards the TX. This corresponds partly to the DS value of 0 ns (only one significant path), but implies also, that some measurements have a significant MPC following the strongest path from the same direction. For all threshold conditions, in 80 % of cases the AS is below 45°.
The highest values of the MED augments from 142 ns to 218 ns and to 256 ns for a threshold of 10 dB, 20 dB, and 30 dB, respectively. In 80 % of cases, the MED is below 9 ns, 69 ns and 120 ns, respectively.
A DS of 0 ns results in K-factor of infinity. Due to the introduced thresholds, the K-factor is below 30 dB, before converging towards infinity. The K-factor gives an insight, on how much of the total received power is in the strongest path. In over 90 % of cases, not matter the considered threshold, the strongest path is 10 dB higher than the residual power.
The propagation channel's observation shows that the MED will have a higher impact on the design of a future communication system for THz communication, than the power distribution of the MPCs. As already mentioned, the propagation channel represents the worst case simulation for a communication network, because there is no spatial filtering.

D. RADIO CHANNEL
The radio channel that incorporates the antennas of a communication system is pivotal for a successful algorithm and system design. In this section, we apply a realistic antenna diagram to the discrete MPC at the RX and evaluate the resulting radio channel that a THz communication system would effectively face. The antenna development for THz communications is a challenging task because of the small dimensions and the high gain that is required to compensate for high channel losses. In addition, beam steering capabilities are crucial for point-to-point links in scenarios with user mobility or reconfigurable links. The non-ideal characteristics of the THz antennas will affect the THz communication systems if strong MPCs or interferes are received via a side lobe of the antenna.
To evaluate the impact of THz antenna arrays, an antenna pattern of a realistic 16×16 patch antenna array (see the Appendix) filters the MPCs at the RX. The main lobe is oriented towards the strongest path at the respective measurement position.
Compared to the propagation channel that can be interpreted as a radio channel with omni-directional antennas representing a worst case scenario with regard to channel characteristics, the selected antenna pattern represents a best case simulation. Since the angular sampling interval of both HHI and TUBS almost coincides with the minima of the antenna pattern, the antenna optimally filters the MPCs. Other steering angles and other antennas will filter in a different way that might result in radio channels lying between this best case and the worst case.
The filtering is directly visible in the resulting MPCs of the radio channel that are visualized in Fig. 7. In the majority of cases, there are only two relevant MPCs beside the strongest path. Ten measurement positions have an additional MPC above the 10 dB threshold and two measurement positions have a second MPC above the 10 dB threshold. Only one single measurement position has a third MPC that is above the threshold of 20 dB. It is also notable that the quantiles are significantly stretched showing the diversity of the MPC distribution for the first and second MPC and that the exponential decrease of the MPCs is stronger compared to the propagation channel.
Similar to the analysis of the propagation channel, Fig. 8 presents the CDFs of the DS, AS, MED and K-factor of the radio channel. The DS is limited to 2.06 ns and 6.55 ns for the 10 dB and 30 dB threshold, respectively, except for one measurement position where the DS still amounts to 46.67 ns. As expected, the AS is significantly reduced and 0°for all measurement points for the 10 dB threshold. Hence, for measurements with an AS of 0°all MPCs are incident from the angle of the direct path. Consequently, a even more focused antenna will not filter more MPCs in this case. The MED is globally reduced. The maximum value results to 142 ns that corresponds to the value of the 10 dB threshold of the propagation channel. Moreover, differences between the 10 dB threshold and the 20 dB threshold are smaller compared to the propagation channel. Regarding the K-factor, all curves share a common shape up to their respective threshold where they jump to infinity. Again, the ratio of K-factors that are infinity determines the number of measurement positions that have one single path.
We point out, that the present analysis only considers a point-to-point communication link and does not account for interference that is likely to occur if multiple THz links are active as for example in data centers or THz mesh networks [37]. Interferers that are located close to the RX might compensate the attenuation of the directional antenna. For instance, a link with a distance of 10 m will be strongly impaired by an interfering TX that is located 2 m away from the RX and cancels out the side lobe level of the antenna of 13.4 dB while benefiting from a lower propagation loss.

VI. CONCLUSION
Channel measurements yield important information for the design of future communication systems at THz frequencies.
In this paper, we have provided a brief overview of channel sounding techniques and addressed two different time-domain setups in more detail. We show a uniform measurement evaluation of data from these channel sounding systems based on an MPC detection and evaluate a series of measurements in indoor scenarios where THz communications may be of great interest in the future. The scenarios differ widely -not only in dimensions and targeted link distances, but also in the nature of the objects and surfaces that act as reflectors and blockers and thus significantly determine wave propagation. Accordingly, the measured characteristics of the wireless channels are different.
We show the variety of channel parameters in the scenarios under investigation and demonstrate the impact of the radio channel incorporating a realistic patch antenna array on design guidelines for future THz communication systems. Depending on the SNR requirements, different channel characteristics have to be considered. In several cases, MPCs typically appear 10 dB to 20 dB below the strongest path, which need to be taken into account in the system designeither by using simple, robust modulation techniques or, in the case where high spectral efficiency is desired, powerful equalization that can cope with large excess delays despite the high transmission bandwidth. In turn, these dominant reflection paths offer the potential to maintain a connection with reduced data rate in case of LOS interruption, if they are selectively excited.
These observations show that there are significant challenges using THz frequencies in mobile communications beyond fixed high-gain directional links. However, they also emphasize that quantitative statements on THz channel characteristics can only be made in the context of specific propagation environments. In order to provide scenariospecific measurement data and robust data-based channel models, conducting measurement campaigns with powerful, flexible CSs remains an important task.

APPENDIX
In order to obtain a realistic antenna pattern for THz communications, the patch antenna array from [38] is extended per simulation by INESC TEC to a realistic 16×16 patch antenna array with a gain of 26.2 dBi, a HPBW of approximately 6°a nd a side lobe level of 13.4 dB. The antenna diagram for a steering angle of 0°that is visualized in Fig. 9 is selected and applied on the discrete MPCs such that the main lobe is oriented towards the angle of the strongest MPC.