On the Spatial Consistency of Sub-Terahertz Channel Characteristics for Beyond-6G Systems

On the Spatial Consistenc y of Sub-T erahertz Channel Characteristics for Be yond-6G Systems Hossein Amininasab 1 , Huda Farooqui 1 , Dmitri Moltchanov 1 , Serge y Andree v 1 , Michele Polese 2 , Mikko V alkama 1 , Josep M. Jornet 2 1 Unit of Electrical Engineering, T ampere W ireless Research Center , T ampere Uni versity , Finland 2 Department of Electrical and Computer Engineering, Northeastern Univ ersity , Boston, MA, USA Contact author’ s e-mail: hossein.amininasab@tuni.fi Abstract —Ray tracing is a versatile appr oach for precise sub-terahertz (sub-THz, 100–300 GHz) channel modeling when designing new mechanisms for beyond-6G cellular systems. Theo- retically , wireless channels may exhibit variations over wa velength distances. In the sub-THz band, close-to-millimeter wavelengths thus require extremely large computational efforts for ray-tracing modeling. However , in practice, channel characteristics may re- main quantitatively similar over much larger distances, which can drastically decr ease computational efforts. The aim of this study is to experimentally characterize the degree of spatial consistency in sub-THz channel characteristics. T o this end, we performed a large-scale measurement campaign in the 140–150 GHz frequency band in an indoor-hall (InH) envir onment and characterized the channel at separation distances from 2.5 mm up to 1 m. Our results show that channel characteristics including delay spr ead, angular delay spread, and K-factor change only slightly over multiple tens of centimeter distances. This implies that, in the considered InH envir onment, the mesh grid can be in the range of 10–50 wav elengths (at 145 GHz) along stable line-of-sight (LoS) directions, while a finer resolution is needed in regions not dominated by LoS. For coarser grids, advanced interpolation is r equired to capture rapidly varying scatter ed components. Index T erms —Bey ond-6G; sub-terahertz; spatial consistency; multipath; delay spread; angular delay spreads; K-factor . I . I N T R O D U C T I ON The utilization of high-frequency bands, such as the sub-THz (100–300 GHz), in be yond-6G cellular systems is vital for fun- damental improvements in access rates at the air interface [1]. These bands, providing hundreds of megahertz of contiguous bandwidth at the air interface, can potentially enable future applications characterized by extreme rate demands [2]. Sub-THz frequency band shares a number of propaga- tion properties with millimeter-w av e band (mm-W av e, 30– 100 GHz) including diffuse dif fraction, sensitivity to materials in urban deployments, blockage, etc. [3]. Howe ver , further decrease in the wa velength makes sub-THz wav e propagation ev en more sensitiv e to en vironmental specifics such as the type of materials and geometrical properties of surrounding micro-scale objects. In the context of beyond-6G communica- tion systems, the wav elength also affects the size of antenna elements, requiring larger arrays at base stations (BS), resulting in narrower beamwidths and making the system more sensitive to beam misalignment ev ents [4], [5]. T o take decisive steps tow ard the dev elopment of beyond- 6G systems, fine-grained propagation models are required. Con ventional propagation models, such as urban-micro/macro (UMi/UMa) and indoor -hall (InH), predict the a verage receiv e signal strength at a giv en distance from the transmitter [6]. Although sub-THz counterparts of such models hav e recently been proposed [7], these models do not capture time-related characteristics of wireless channel and thus fail to pro vide de- tailed characterization of the propagation en vironment required to design physical-layer mechanisms. Three-dimensional (3D) cluster channel models inherently account for multipath prop- agation and random delays representing the recei ved signal strength as a random v ariable, see, e.g. [8]. Ho wev er , these models require complex procedures to account for spatial con- sistency , such as ensuring that there is a dependency between the receiv ed signal strength observed at adjacent distances [9]. Ray tracing is nowadays a de-facto approach for precise modeling of mmW ave/sub-THz communications systems [10]. Theoretically , channel response is expected to change ev ery wa velength distance thus requiring extreme computational ef- forts to characterize realistic cellular deployments [11]. How- ev er , in practical conditions, the channel characteristics may remain approximately the same ov er much lar ger distances that may significantly simplify computational efforts or facilitate efficient interpolation techniques. Thus, it is critical to identify the distance ov er which channel characteristics remain approx- imately the same. T o the best of our knowledge, this paper presents the first experimental study on the spatial consistency of sub-THz channel characteristics at distances smaller than 1 m, con- ducted through a comprehensi ve and lar ge-scale measurement campaign in the open scientific literature. Measurements were carried out in the 140–150 GHz frequency band within an InH environment, in vestigating variations in channel properties ov er separation distances ranging from 2.5 mm to 1 m to assess spatial consistency across multiple scales. The analysis utilizes spatial autocorrelation of k ey channel characteristics, including the power delay profile (PDP), root-mean-square (RMS) delay spread (DS), RMS angular spreads (AS), and K- factor . These findings provide insights for parameterizing sub- THz ray tracers for indoor propagation modeling, quantifying modeling errors, and dev eloping channel prediction algorithms. The main contributions of our study are: • W e present measurements and an analysis of sub-THz channel characteristics in the 140–150 GHz frequency band to assess spatial consistency in InH en vironments. • W e provide empirical observations showing that: (i) chan- nel metrics such as delay spread, angular spread, and K-factor remain stable over small-scale displacements ( ≤ 10–50 λ ), indicating strong local spatial consistency; and (ii) spatial de-correlation at larger separations pri- marily arises from v ariations in non-line-of-sight (NLoS) multipath components (MPCs), highlighting the need for adaptiv e meshing in ray-based modeling and for robust beam-tracking strategies in future InH sub-THz systems. The paper is or ganized as follows. W e be gin with related work in Section II. The measurement setup, experiments, and data processing are described in Section III. Results and discussion are pro vided in Section IV. Conclusions are drawn in the last section. I I . R E L A T E D W O R K The wav e propagation at sub-THz band already recei ved significant attention from the research community . The existing efforts in [12], [13] ha ve focused on lar ge-scale propagation including path loss, delay spread, and material interactions in indoor and outdoor environments. These studies report that, in the presence of LoS transmission, the Path Loss Exponent (PLE) is in the range of 1.8–2.2 depending on environmental conditions. Howe ver , in a NLoS en vironment, PLE could increase up to 3.6, due to diffraction loss, penetration through materials, and blockage [13], [14]. In addition, an extra at- tenuation of 10–30 dB is commonly observed due to beam misalignment or structural obstructions. Although there has been substantial ef fort on large-scale propagation, only few authors studied spatial or temporal consistency [15], [16]. At lo wer mm-W a ve bands ( ≤ 100 GHz), standardized models such as 3GPP TR 38.901 and NYUSIM [17] define reference correlation distance of approximately 10– 15 m for shadow fading, delay spread, and angular spreads. These values are obtained from extensiv e measurement cam- paigns and serve as a reference for ev aluating channel varia- tions caused by displacement. At the sub-THz bands, the correlation distance is expected to decrease as displacement-induced variations increase, par- ticularly in environments where directionality is significant. Ray-based deterministic channel modeling studies have sho wn that narrow-beam antennas are more lik ely to increase PLE, whereas wide-beam antennas reduce PLE at the expense of a longer delay spread [18]. These observations indicate that the antenna beamwidth strongly affects channel statistics that are closely related to spatial consistency . Precise metrology in the 200–300 GHz range demonstrates that e ven submillimeter dis- placements can lead to measurable channel variations. Spatial correlation may change drastically due to en vironmental f actors such as human body blockage, furniture, plants, and weather conditions [15], while controlled studies show that path loss, delay spread, and cluster statistics often exhibit more gradual ev olution with displacement. Recent research provides e vidence of these trends. In [19], the authors conducted measurements at 142 GHz within an urban microcell, capturing key large- and small-scale wireless channel properties along a 102 m rectangular path, with Rx points spaced e very 3 m. Each parameter’ s spatial autocorrela- tion w as modeled using an exponentially decaying sinusoid, rev ealing that shadow fading de-correlates rapidly , with a correlation distance of only 3.8 m, significantly shorter than the 10–13 m [20] typically observed at below 100 GHz. The delay spread and the angular spread exhibit larger correlation distances, approximately 11.8 m and 12 m, respectiv ely , similar to those seen at lower frequencies [19]. Complementing these ef forts, a large-scale indoor measure- ments campaign of 90 transmitter (Tx)-receiver (Rx) pairs [21] qualitativ ely characterized temporal and spatial consistency , in hallway and NLoS cases, and reported per-scenario PLEs, delay/angle spreads, and cluster statistics across displacement ranges of 2–30 m. The results verify that dominant MPCs persist and angle-of-arriv al (AoA) and time-of-arriv al (T oA) shift smoothly along displacement tracks, supporting the feasi- bility of beam tracking at 200+ GHz. Indoors, sev eral authors extended statistical models using 140 GHz datasets and de- veloped spatially-aware simulators (e.g., NYUSIM extensions) [22]. These works provide rich measurement databases and cluster/delay/angular spread statistics, forming a practical basis for spatial consistency modeling at frequencies abov e 100 GHz. Further studies reinforced the sensitivity of sub-THz chan- nels to displacement. At 73 GHz, fading v aries smoothly over 0.35 m [17]. Measurements at 215–225 GHz showed delay spreads of 0.16–0.83 ns, azimuth spreads of 14.65°–37.80°, and 2.57–4.14 clusters depending on displacement [23], while at 299–301 GHz in large indoor halls, delay spreads increased sharply with distance, from ≈ 7 . 5 ns at 3 m up to ≈ 35 . 6 ns at 15.6 m, accompanied by angular spreads exceeding 40° and highly non-stationary multipath behavior [24]. Narrow- beam antennas reduce delay spread but raise PLE, while wide beams broaden multipath variation [25]. High-precision chamber experiments at 200–300 GHz further show that e ven sub-millimeter shifts cause measurable delay drift [26]. Summarizing the related studies, we emphasize that little is known about the spatial consistency of sub-THz channel characteristics at distances below 1 m, which are particularly relev ant for the parameterization of ray-tracing simulations. In our paper , we focus on such smaller separation distances be- tween measurement points. W e also consider InH propagation en vironment that is subject to complex multipath propagation. I I I . M E A S U R E M E N T C A M P A I G N In this section, we describe the measurement campaign including the measurement setup using the Northeastern Uni- versity (NU) channel sounder , the experiments, and the mea- surement data ev aluation part. A. Measur ement Setup Fig. 1 illustrates block diagram of the NU channel sounder, a custom spread-spectrum sliding-correlator channel sounder IF A WG Channel Tx frontend & Antenna LO Reference 10 MHz PSG IF Rx frontend & Antenna DSO LO PSG Post- processing IF signal Generation Fig. 1. Block diagram of the NU channel sounder and the equipment in use for the channel sounding measurements. dev eloped at Northeastern Univ ersity [27]. For PDP measure- ments, WR-6.5 VDI horn antennas were employed at both Tx and Rx to radiate and capture the pseudo-random sequences with sharp autocorrelation properties ov er a 10 GHz bandwidth. The sounding sequences were generated in MA TLAB, up- loaded to an Arbitrary W av eform Generator (A WG), and fed into the intermediate frequency (IF) port of the VDI front-end. A Keysight performance signal generator (PSG) pro vided local oscillator (LO) to upcon vert the signal to 140 GHz, which was radiated through a horn antenna (21 dBi gain, 13 ◦ full 3-dB beamwidth). At the Rx, the signal was captured by an identical VDI horn antenna connected to a VDI front-end, which was synchronized with a second PSG. LO synchronization between PSGs was achiev ed using a 10 MHz reference cable. The downcon v erted IF signal was sampled at 128 GSa/s and recorded by a digital storage oscilloscope (DSO) for further processing. Considering the DSO sampling frequency , the sampling interval is T s = 7 . 8125 ps. The fundamental delay resolution of the channel sounding is bandwidth-limited to ∆ τ = 1 / B = 200 ps for a bandwidth of B = 10 GHz. The Rx front-end and horn antenna were mounted on a mo- torized rotary table, controlled via MA TLAB through a serial interface, allo wing systematic sweeps of the Rx orientation in both azimuth and elev ation. B. Description of Experiments The channel sounding measurements were conducted at Northeastern Univ ersity’ s Ultrabroadband Nanonetworking Laboratory (UNLab), EXP Building, 7th floor , in a room resembling typical classroom (20 × 12 × 3 m 3 ), see Fig. 2. The Tx was placed 5 m from the wall and 10 m from the front windows, while the Rx was initially placed at the room center , 5 m from the Tx. The Rx was then moved along a cross-shaped trajectory composed of two orthogonal 1-meter lines intersecting at the center , as sho wn in Fig. 2 and Fig. 3. The spatial sampling resolutions used are coarse (10 cm), fine (1 cm), and ultra-fine (2.5 mm). The room contained several tables and pieces of equipment distributed around its perimeter that resemble a typical classroom. This configuration enabled analysis of variations in MPCs and PDPs across different Rx positions, allo wing in vestig ation of whether measurable differences occurred at spatial interv als comparable to the sub- THz wa velength. Both Tx and Rx antennas were mounted at a height of 1 . 5 m. The Tx antenna remained fixed and oriented towards the center Rx Tx Crossline 1.8 m Fig. 2. Channel sounding measurement en vironment (UNLab, EXP Building, 7th floor) resembling a classroom, sho wing the cross-shaped trajectory , dis- tances between tables, and the NU channel sounder setup. of the cross-shaped trajectory for the entire experiment. At each Rx sampling point, the Rx antenna was swept in azimuth and elev ation with 10 ◦ increments, spanning from − 100 ◦ to 100 ◦ in azimuth and from − 20 ◦ to 20 ◦ in elev ation. Each transmission was repeated ten times per Rx position and sweep angle, enabling noise reduction through coherent averaging and improving the robustness of the extracted channel parameters. The Rx antenna was intentionally not fully swept over the full 360 ◦ . While weak MPCs from far-wall reflections may exist in principle, their contribution was assumed ne gligible for the considered link budget and measurement sensitivity , and thus unlikely to affect the dominant channel characteristics analyzed in this work. The transmitted sounding waveform w as generated by map- ping an 8191-chips-long m-sequence header (maximum-length sequence) followed by three repetitions of a 4095-chips-long m-sequence onto binary pulse amplitude modulation (2-P AM) symbols. The resulting sequence was pulse-shaped using a square-root-raised-cosine (SRRC) filter with a high roll-off factor to preserve the Nyquist intersymbol-interference-free property and was digitally upcon verted to an IF of 5 GHz Pos1 Pos2 Pos3 Pos4 Pos5 Pos15 Pos16 Pos17 Pos18 Pos19 Pos20 Pos21 Pos22 Pos23 Pos24 Pos25 Pos26 Pos27 Po28 Pos29 Pos30 Ultra-fine points group- 2.5 mm Fine points group- 1 cm Tx Coarse points group- 10 cm Fig. 3. Measurement points along the cross-shaped trajectory . Black circles indicate coarse sampling with 10 cm spacing, while green and red ribbons denote fine and ultra-fine regions with 1 cm (from position 5 tow ard 15) and 2.5 mm (from position 15 tow ard 5) spacing, respectively . at a symbol rate of 5 GSym/s. This design yields a wav eform with a sharp autocorrelation function, making it well-suited for high-resolution channel sounding. At the Rx, the observ ed signal consists of the transmitted sequence as distorted by the propagation channel, including multipath effects. Cross-correlating the recei ved signal with the kno wn transmitted sequence yields the channel impulse re- sponse (CIR). The squared magnitude of this cross-correlation yields the PDP , where strong and weak peaks correspond to LoS and MPCs, respectiv ely . C. Data Pr ocessing The first step was to process the measured data to obtain well-shaped PDPs, which serve as the basis for extracting key propagation metrics, including RMS delay spread, RMS angular spread, K-factor , and coherence bandwidth for prop- agation channel ev aluation. T o this end, the received signal was correlated with a locally generated m-sequence to extract the CIR. The CIR is then coherently averaged over the 10 repetitions to reduce the observable noise floor and suppress spurious detections. 1) P ower Delay Pr ofile: Measurements performed with di- rectional antennas yield directional CIR. By averaging CIRs ov er repetitions, the directional PDPs are obtained as P ( τ , Φ , θ ; d ) = | h avg ( τ , Φ T x , θ T x , Φ Rx , θ Rx ; d ) | 2 , (1) where the terms Φ T x , θ T x , Φ Rx , and θ Rx denote the azimuth angles and the elev ation angles of the Tx and Rx antennas, respectiv ely . Here, h avg ( . ) represents the average directional CIR ov er repetitions and τ is the delay bin. In this work, the delay axis was truncated using a fixed temporal gate of τ n = 85 ns, corresponding to the maximum excess delay associated with first-order reflections in the con- sidered indoor geometry . This delay gate defines the temporal support of the propagation channel used for subsequent metric extraction. The max-directional PDP is the strongest received power at each delay bin τ for a giv en separation distance d , regardless of the specific Tx and Rx pointing directions, obtained by P max − d ir ( τ ; d ) = max Φ T x , Φ Rx , θ T x , θ Rx P ( τ , Φ T x , θ T x , Φ Rx , θ Rx ; d ) . (2) The omnidirectional PDP is obtained by selecting the strongest path at each azimuth angle and av eraging o ver ele v a- tion angles, providing a comprehensi ve channel representation. In this campaign, only the Rx antenna was swept while the Tx antenna remained fixed and aligned with the LoS direction. The omnidirectional PDP is therefore giv en by [28]: P omni ( τ ; d ) = max Φ T x , Φ Rx ∑ i ∑ j P ( τ , Φ T x , θ i T x , Φ Rx , θ j Rx ; d ) , (3) where i ∈ { 1 , 2 , 3 , 4 , 5 } represents the ele v ation index for the Rx sweep angles {− 20 ◦ , − 10 ◦ , 0 ◦ , 10 ◦ , 20 ◦ } and j = 1 as the Tx antenna is fixed towards the center of the cross-shaped trajectory . T ABLE I P A R A ME T E R S F O R D E TE C T I ON . Parameter V alue ε 6 dB α 0 . 4 N t rain 31 samples N guard 15 samples τ n 85 ns 2) MPC Detection: The MPCs were extracted from the both omni- and maxi-directional PDPs. The strongest peak was identified as the LoS component, while additional MPCs were detected based on adaptiv e threshold v alidation as T h ( τ ) = ε [ α ˜ µ med ( τ ) + ( 1 − α ) µ t rain ( τ )] , (4) where ε is the offset factor , ˜ µ med ( τ ) is the local median of the noise floor estimated in a sliding guard–training window around the delay bin τ , µ t rain ( τ ) is the local mean of the training samples, N t rain , in the noise region (i.e., 10% tail in the late delay bins), and α is the weighting factor ( 0 ≤ α ≤ 1 ) that balances between the median-based and mean-based noise estimates. This approach ensures robust and consistent MPC detection at all Rx positions, enabling reliable extraction of subsequent channel metrics. The local noise floor was estimated using a sliding training–guard window combined with moving median filtering, and the detection threshold was set to ε dB abo ve this local noise estimate, as summarized in T able I. 3) Channel Metrics: The RMS delay spread, σ τ , quantifies the dispersion of the channel in the temporal domain. It provides a measure of the v ariability of the mean delay and is calculated as the second central moment of the PDP , as [28] σ τ = s ∑ N − 1 i = 0 ( τ i − ˆ τ ) 2 P i ∑ N − 1 i = 0 P i , (5) where i = 0 and N denote the indices of the first and last delay bins abov e the noise threshold, τ i represents delay , and P i is the power received from the path i . The mean delay ˆ τ is ˆ τ = ∑ N − 1 i = 0 τ i P i ∑ N − 1 i = 0 P i . (6) Similarly , the RMS angular spread ( AS RM S ) characterizes the spatial multipath richness of the propagation channel and is computed as [28]: AS RM S = s ∑ N − 1 i = 0 ( θ i − ˆ θ ) 2 P i ∑ N − 1 i = 0 P i , (7) where θ i is the AoA of path i and ˆ θ is the mean AoA: ˆ θ = ∑ N − 1 i = 0 θ i P i ∑ N − 1 i = 0 P i . (8) The Rician K-factor characterizes the power distribution between LoS and NLoS components, showing concentration of power in the dominant path relati ve to the remaining MPCs 0 10 20 30 40 50 60 70 80 Excess Delay (ns) -90 -80 -70 -60 -50 -40 -30 Power (dBm) Pos. 1 (30 MPCs) Pos. 20 (28 MPCs) Pos. 15 (28 MPCs) Pos. 21 (30 MPCs) Pos. 30 (28 MPCs) Gate (2.3 ns) Fig. 4. Max-directional PDPs at the center and four endpoints of the trajectory (positions 15, 1, 20, 21, and 30; see Fig. 3), showing the discrete MPCs resolved within the observation windo w . in the channel. This metric provides insight into the channel fading characteristics and is defined as κ 1 = P ( τ 1 ) ∑ τ N τ k = τ 2 P ( τ k ) , (9) where τ 1 is the LoS delay and τ k are the delays of the remaining MPCs ordered by magnitude. The coherence bandwidth B c is estimated from the RMS de- lay spread using the approximation B c ≈ 1 / ( 5 σ τ ) (correspond- ing to a 0.5 correlation threshold). It defines the frequency range ov er which the channel can be considered flat fading. I V . R E S U LT S A N D D I S C U S S I O N W e begin with the PDP statistics, which highlight the overall behavior of the channel at different measurement locations. W e then analyze the channel statistical parameters, followed by an examination of the spatial autocorrelation [19] statistics among the channel parameters. Fig. 4 presents max-directional PDPs at five positions along the measurement trajectory , including the center point and the four endpoints, see Fig. 3. The PDPs reveal a highly directional channel dominated by the LoS path. The vertical line at 2 . 3 ns marks reflections from nearby setup components such as the table and mountings. This feature appears consistently across the measured PDPs within the same excess delay range, and no other reflecting surfaces were present in proximity to the setup within the corresponding distance that could reasonably account for such reflection. Channel metrics were deriv ed from the gated and denoised max-directional PDP , except for the RMS angular spread, which was obtained from the directional PDPs. In this work, MPCs originating from reflections off the measurement setup (e.g., the table and mounting structures) were e xcluded to better capture the intrinsic characteristics of the propagation channel. As a result, channel metrics were computed based on this definition. While the av erage RMS delay spread across all Rx Line 1 Center Line 2 0 5 10 15 20 25 30 Measurement Position Index 14 16 18 20 22 24 26 28 30 K-factor (dB) / RMS Delay Spread (ns) 2 4 6 8 10 12 14 16 18 RMS Angular Spread (degrees) K-factor RMS Delay Spread Azimuth Spread Elevation Spread Coarse (10cm) Fine (1cm) Ultra-fine (2.5mm) Fig. 5. K-factor , RMS delay spread, and RMS angular spreads versus position index along 30 measurement points. Background colors denote coarse (blue), fine (green), and ultra-fine (yellow) spacing interv als. positions is 6.1 ns when including all detected components, the reported value (22.3 ns) corresponds to the intrinsic channel definition adopted in this work. Similarly , the mean measured K-factor is 16 dB when all components are considered, whereas a v alue of 18.5 dB is obtained under the same definition. Both metrics consistently indicate a highly directional, LoS- dominated channel. Fig. 5 shows the spatial distribution of channel metrics along the cross-shaped trajectory . Based on the RMS delay spread, the av erage coherence bandwidth is estimated to be 9 MHz. These results are consistent with the directional nature of the PDPs, confirming that the channel exhibits strong directivity . The RMS angular spreads further indicate a highly directional channel, with an RMS azimuth spread of 7 . 4 ◦ ( ± 1 . 2 ◦ ) and an elev ation spread of 7 . 6 ◦ ( ± 0 . 88 ◦ ), following the same pattern as the horn antenna. Since the RMS angular spread depends on the po wer distribution across measurement angles, nearly identical v alues are e xpected, as both the Tx and the Rx emplo y conical horn antennas with comparable half-power beamwidths (HPBWs) in azimuth and elev ation. This does not imply that antenna directi vity determines the intrinsic RMS angular spread of the propagation channel. Rather , the antenna patterns act as angular filters, shaping the observed angular po wer distribution and, consequently , the measured RMS angular spread. T o assess spatial consistency between measurement points along the cross-shaped trajectory , we first ev aluated the con- sistency of indi vidual CIRs at each position. The results showed high consistency , with correlation coef ficient values ρ exceeding 0.95, confirming that the measurements are stable and not noise-dominated. Next, autocorrelation for dif ferent position pairs were analyzed in three categories based on Rx positions, with 22 coarse (10 cm), 6 fine (1 cm), and 5 ultra- fine (2.5 mm) spacing—cov ering all 435 position pairs and separations from 1.2 λ to 483 λ (2.5 mm–1 m). Each group captures a distinct scale of channel variation, with the sub- wa velength meshed group providing v aluable insight into the 1 2 5 10 20 50 100 200 500 Spatial Separation (wavelengths, 6 ) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Spatial Correlation Coefficient ; = 0.9 ; = 0.7 All Angles LoS Angles Only LoS (Stable Positions) NLoS Angles Only Fig. 6. Pairwise directional PDP spatial autocorrelation between measurement points at dif ferent distances, categorized into 15 pairwise distance groups. de-correlation distance (see Fig. 6). Omni-directional PDPs were used to assess ov erall channel correlation, while directional PDPs e valuated angular con- sistency . Spatial autocorrelation analysis showed that omni- directional PDPs exhibited near -perfect autocorrelation ( ρ ≈ 1), indicating that av eraging across directions masks the spatial and angular dependencies of the sub-THz channel. Spatial au- tocorrelation v alues for individual angular PDPs also remained near-perfect. T o further examine the origins of spatial de- correlation, directional measurements were decomposed into LoS and NLoS subsets. LoS components—empirically defined as those within 15 dB of the main beam and ≥ 50% of energy in the first 3 ns—exhibited strong spatial autocorrelation ( ρ > 0 . 8) when ev aluated at angles qualifying as LoS at both positions, confirming the stability of dominant paths. When restricting the analysis to LoS angles that remained common across paired positions (LoS stable positions), the spatial autocorrelation further increased ( ρ > 0 . 9), isolating angularly aligned and stable LoS propagation. In contrast, the all-angles spatial autocorrelation reflects the combined contribution of aligned and misaligned LoS angles together with NLoS components, resulting in consistently lower v alues than the LoS-only cases despite remaining relatively high due to LoS dominance. NLoS components showed pronounced de-correlation ( ρ ≈ 0 . 45) due to their sensitivity to sub-wa velength displacements. These findings indicate that ov erall spatial autocorrelation arises from the interplay between stable LoS and rapidly varying NLoS contributions, suggesting that ray-tracing meshing should adapt to local propagation conditions—using coarser spacing along stable LoS beams and finer resolution in scattered regions—to balance physical fidelity and computational ef ficiency . V . C O N C L U S I O N S The aim of this paper was to ev aluate the degree of spatial consistency of the sub-THz channels in a complex InH en vi- ronment. T o this end, a detailed measurements campaign was conducted in the 140–150 GHz band covering separations of up to 1 m. As measures, we utilized the spatial autocorrelation coefficient of sev eral key channel characteristics, including PDP , RMS delay spread, RMS angular spreads, and K-factor . The results show that channel characteristics—including delay , azimuth, and ele vation spread, as well as K-factor— exhibit only minor v ariations across measurement points along the cross-shaped trajectory . Increasing the separation distance between points may lead to larger v ariations in these metrics. Howe v er , consistency tests indicate that, in the considered InH en vironment and within the examined LoS re gion, the spatial correlation distance can extend up to approximately 10–50 wav elengths. Accordingly , the minimum mesh grid step size can be chosen to be about 2–10 cm (at 145 GHz) along stable LoS directions, whereas finer spatial resolution may be required in regions dominated by NLoS scattering. For lar ger mesh grid spacing, adv anced spatial interpolation techniques should be used to accurately capture rapidly varying scattered components. 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