Early Warning of mmWave Signal Blockage and AoA Transition Using sub-6 GHz Observations

TL;DR

This paper demonstrates that lower-frequency sub-6 GHz signals can serve as early indicators of mmWave signal blockage or recovery, enabling proactive mitigation in 5G networks through physics-based simulations.

Contribution

It introduces a physics-based simulation approach showing sub-6 GHz signals lead mmWave signals in detecting blockages, enabling early warning systems without relying on specific topologies.

Findings

Sub-6 GHz signals lead mmWave signals by several to tens of milliseconds.

The approach works across various transition scenarios including LoS to NLoS.

Prediction of AoA and strongest multipath component is feasible using sub-6 GHz observations.

Abstract

The susceptibility of millimeter-wave (mmWave) signals to physical blockage and abrupt signal strength variations presents a challenge to reliable 5G communication. This work proposes and examines the feasibility of utilizing lower-frequency signals as early-warning indicators of mobile mmWave signal blockage or recovery. A physics-based channel simulation tool incorporating Fresnel diffraction and image sources is employed to demonstrate that sub-6 GHz signals "lead" mmWave signals in reaching a specific signal-strength threshold by several to tens of milliseconds at mobile speeds, suggesting early-warning systems are viable. This predictive approach stems from frequency-dependent properties of diffraction and does not assume a specific topology or mobile and obstacle speeds. Realistic simulations that include transitions from line of sight (LoS) to non-line of sight (NLoS) and reflection scenarios are employed to verify the proposed prediction capabilities. Moreover, prediction of the strongest multipath component and its angle of arrival (AoA) using sub-6 GHz observations is investigated.

Figures

Equations

$$\begin{array}{rl}{h}_k(t)& =\sum _{m=0}^M{h}_{k,m}(t)\text{ with }\\ h_{k,m}(t)& =A_{k,m}(t)e^{j(2\pi f_{dm,k}tcos(Ao{A}_m(t))+{\varphi }_{k,m}(t))}\end{array}$$

$$\begin{array}{rl}& h_{k,m}({\mathbf{r}}_{rx})=\frac{-0.25{\Re }_m{e}^{j(2\pi r_m{f}_k/c+{\varphi }_{k,m})}|{\mathbf{r}}_{refl,m}-{\mathbf{r}}_{eff,m}|}{|{\mathbf{r}}_{refl,m}-{\mathbf{r}}_{eff,m}|+|{\mathbf{r}}_{rx}-{\mathbf{r}}_{refl,m}|}\\ & \ast \frac{Fr(w_{u_1},w_{u_2})Fr(w_{v_1},w_{v_2})Fr(w_{u_{1tx}},w_{u_{2tx}})Fr(w_{v_{1tx}},w_{v_{2tx}})}{|{\mathbf{r}}_{txaper}-{\mathbf{r}}_{tx}|+|{\mathbf{r}}_{refl,m}-{\mathbf{r}}_{txaper}|}.\end{array}$$

$$\begin{array}{r}Fr(w_{u_1},w_{u_2})=C(w_{u_2})-C(w_{u_1})-jS(w_{u_2})+jS(w_{u_1}),\\ C(w)={\int }_0^{w}cos(\frac{\pi q^2}{2})dq\text{ and }S(w)={\int }_0^{w}sin(\frac{\pi q^2}{2})dq,\end{array}$$

$$w_{{\xi }_{\zeta },k,m}=\sqrt{\frac{2f_k}{c{\rho }_m}}({\xi }_{\zeta ,m}-{\xi }_{0,m})=\sqrt{\frac{2}{{\lambda }_k{\rho }_m}}({\xi }_{\zeta ,m}-{\xi }_{0,m})$$

$$\frac{1}{{\rho }_m}=\frac{1}{|{\mathbf{r}}_{refl,m}-{\mathbf{r}}_{eff,m}|}+\frac{1}{|{\mathbf{r}}_{rx}-{\mathbf{r}}_{refl,m}|}.$$

$$\tau (Th)=t_{f_2}(Th)-t_{f_1}(Th)(seconds),$$

Full text

I Introduction

The emerging generation of cellular communications111This paper has supplementary ”media” material provided by the authors. This includes a 2 MB pdf file with further explanations and derivations, cited as [SM §section]. The model code is at a link from www.physics.ncsu.edu/optics, 5G, will utilize frequencies in the range of 30 - 300 GHz (mmWave) to overcome the bandwidth limitations inherent to current 4G systems (sub-6 GHz) [1]. However, mmWave communication signals do not diffract as strongly and thus are more susceptible to blocking by physical objects than sub-6 GHz signals [2]. Such effects are especially detrimental in mobile communications or with moving obstacles [3, 4, 5].

In this paper, we explore the utilization of sub-6 GHz-band channel state information (CSI) to provide early warning of blockage and other received signal strength (RSS) variations of mmWave signals far ahead into the future. The proposed method is suitable for hybrid communication systems, where the sub-6 GHz and mmWave bands are employed simultaneously [6, 7, 8]. Using the fact that diffracted sub-6 GHz signals reach a specified RSS threshold much earlier than mmWave signals [9],we employ the threshold crossing of the former to forecast blockages and other rapid changes in the latter several to tens of msec (several to hundreds of slots) ahead in mobile communications systems. The proposed predictive approach would provide hybrid mobile communication systems with sufficient time to adapt the data rate, search for a new beam, or perform a handover between the two frequencies before a significant change of the mmWave signal occurs. The insights and results in this paper are based on our physical model [10, 11, 14], which uses the method of images and Fresnel diffraction [9]. Our analysis and simulation results demonstrate the proposed early warning capability in typical mobile communication environments. Moreover, we show that the strongest multipath component of the mmWave signal and its AoA can be predicted using sub-6 GHz observations, thus aiding a mmWave beam search.

Related Work Research on *predicting blockage *includes using beams with overlapping zones to create correlations that aid in beam selection in response to a blockage [3]. However, this method does not provide early warning of an upcoming blockage. A machine learning-based method [4] uses training data on base station handoffs in a static environment, identical to that of the mobile user, to predict that user’s handoffs, presumably due to blockage of LoS. A handover method [5] uses blockage of neighboring paths to predict loss of the primary one, but requires slowly moving obstacles, a scattering-rich environment, and tracking of several mmWave antenna beam formations. In contrast to [4, 5], the method described in this paper does not assume a specific environment, obstacle motion, or speeds.

While the references above employ only in-band mmWave channel observations, *out-of-band *information was exploited in [6, 7, 8, 12, 13]. However, we compare the mmWave and sub-6 GHz signals at different time instances (or locations), not at the same time instance as in the referenced works. These references aim to reduce the antenna beam search or detect existing blockage at mmWave, not warn of an upcoming blockage or an abrupt RSS or AoA change. Our results in section III.C corroborate the findings in [7, 12, 13], but the main contribution of this paper is demonstration of the early warning capability of the sub-6 GHz observations, which has not been reported previously in the literature.

Finally, the physical model used used in this paper was validated using measured data in [10, 14]. These results pertained to long-range prediction (LRP) of multipath fading at sub-6GHz frequencies and demonstrated that the model captured the channel variation in a more realistic way than conventional, stationary channel models. In this paper, the same physical model accurately characterizes the hybrid channel and the early warning capability of sub-6 GHz signals. We emphasize that this model differs significantly from ray tracing [18], statistical [8, 12], geometric [7], and point cloud models [15]. First, one key element in mmWave propagation is the importance of small reflectors, such as sign posts, since their sizes are comparable or larger than the mmWave wavelength and thus they might produce strong reflections. A very dense set of rays must be used and placed carefully in a ray-tracing model to ensure that at least some rays intercept the small reflectors [16]. Since our model is based on calculation from every reflector, a reflection is never missed and always handled accurately. Second, while the hybrid channel model in [7] relied on qualitative observations from measurements, our model accurately captures frequency-dependent diffraction even close to an object, uses full Fresnel formalism to avoid quantization onto rays, includes diffraction modification to the non-reflected component, and models small reflectors, which are not addressed in [17] or enhanced ray tracing [18].

II Physical Channel Modeling

Consider an omnidirectional, narrowband transmission. The equivalent low-pass received signal at a frequency $f_{k}$ is given by $r_{k}(t)=h_{k}(t)s(t)+n(t)$, where $s(t)$ is the transmitted signal, $n(t)$ is additive noise, and

[TABLE]

is the complex channel coefficient, where $h_{k,0}(t)$, is the ’direct,’ or non-reflected, multipath component, $h_{k,m}(t)$ for $m>0$ corresponds to reflections in the modeled environment from the $M$ reflectors, $A_{k,m}(t)$ and $\phi_{k,m}(t)$ are the time-dependent envelope and phase, respectively, of the $m^{th}$ multipath component, and $f_{dm,k}=f_{k}v/c$ is the maximum Doppler shift for a mobile with speed $v$ and speed of light $c$. The angle of arrival $AoA_{m}(t)$ is the angle between the reflector-to-mobile or the transmitter-to-mobile direction and mobile direction for $m>0$ and $m=0$, respectively. The $A_{k,m}(t)$ and $\phi_{k,m}(t)$ account for the propagation delays of each reflector $m$ and phase shifts in the diffraction process. We employ an image and Fresnel diffraction-based calculation tool [10, 11] to model and simulate the frequency-dependent coefficient $h_{k}(t)$ in (1) in various channel environments. While this earlier work employed the model to enable long-range prediction on multipath fading [14] and UWB template design [11], in this paper we use the physical model to characterize the hybrid channel and to investigate frequency-dependent diffraction effects. To achieve this goal, we have updated the calculation tool to perform two diffraction calculations: one from the transmitter to the reflector, and one from the effective source to the receiver. The model naturally and accurately transforms the $m$=0 (non-reflected) component $h_{k,0}(t)$ in (1) from the LoS to a NLoS (diffracted) signal or vice-versa. Identically-sized and located apertures substitute reflectors, while effective sources are created and positioned using the image method as in [10].

The model calculates the spatial coefficient $h_{k,m}(x,y)$ point-by-point along a specific trajectory for a chosen configuration of M curved or flat reflectors of different sizes. It can be converted to time for straight-line mobile motion $h_{k,m}(t)=h_{k,m}(x(t),y(t))=h_{k,m}(x_{0}+v_{x}t,y_{0}+v_{y}t)$ in (1) via the receiver’s starting ($t=0$) position $(x_{0},y_{0})$ and speed $\textbf{v}=(v_{x},v_{y})$. Curved reflectors are relatively unimportant compared to LoS or even diffraction from a small, flat reflector except when the mobile is adjacent to the curved reflector [SM §III], so they are not included in our scenarios. In addition, while the model is capable of 3-d, a 2-d simulation is used in this work since 3-d is more complex but unlikely to result in qualitative differences [SM §III]. Scenarios with a LoS component along the entire path are not considered since the LoS component dominates, making these paths useful but not interesting.

An example of a model scenario is shown in Fig. 1(a). The transmitter aperture is given by the gap in the brick wall. A receiver (car) moves from NLoS to LoS along a horizontal path. Four reflectors $m=1-4$ are shown in this example ($M$=4). For each reflector $m$ in the general $M$ case, we define the parameters for the calculation, including its location and the effective source location, as in Fig. 1(b). The coordinates in the (reflector or transmitter) aperture plane are denoted by $u,v$, with $v$ normal to the page, and are measured relative to the intersection of that plane with the straight line from the effective source location $\mathbf{r}_{eff,m}$ to the mobile location $\mathbf{r}_{rx}$. Each reflector $m$ at location $\mathbf{r}_{refl,m}$ has reflectance $\Re_{m}$ and phase $\phi_{m}$. All positions, $\mathbf{r}_{rx}$, $\mathbf{r}_{refl,m}$, $\mathbf{r}_{eff,m}$, $\mathbf{r}_{tx}$, $\mathbf{r}_{txaper}$, can be varied along individual straight-line paths, and reflectors rotated, although in this work we only vary $\mathbf{r}_{rx}$ within each model evaluation. The two back-back Fresnel diffractions [9] from a point source then give the electric field complex amplitude at $\mathbf{r}_{rx}$:

[TABLE]

The Fresnel Integral $Fr$, and definitions, are given by

[TABLE]

[TABLE]

for $\xi\in\{u,v\}\text{ and }\zeta\in\{1,2,1tx,2tx\}$. All $w$ parameters in (2) and (3) have a $k,m$ dependence as in (4), $\lambda_{k}$ the wavelength, and $\rho_{m}$ a distance parameter. For the second diffraction,

[TABLE]

In 2-d, the aperture is only along the u-direction, so the v-direction does not have diffraction, and thus $v_{1}=-\infty,v_{2}=\infty$, which causes $C(w_{v_{2}})=S(w_{v_{2}})=-C(w_{v_{1}})=-S(w_{v_{1}})=0.5$ and $Fr(w_{v_{1}},w_{v_{2}})=Fr(w_{v_{1tx}},w_{v_{2tx}})=(1-j)$ for all $m$.

Next, we illustrate the frequency-dependent properties of diffracted signals and provide insight into the early warning capabilities of sub 6-GHz signals. In Fig. 1(c, d), the spatial images of $|h_{k,1}(x,y)|$ are shown at sub-6 GHz and mmWave frequencies, respectively, for the same 0.5 m long reflector rotated 160∘ counter-clockwise from the x-axis and positioned 0.1 m to the right and 2.5 m above the bottom of the 10 m x 10 m diffracted-signal region shown. The specular reflection of the transmitter, which is 1000 m to the left, is along the direction of the bright line through the pattern. The color scale is 0-1 (numerical max is $\sim$1.3 in the region) referenced to the transmit signal strength. As the receiver moves along the line shown or other paths through the region, we observe an earlier and more gradual transition in RSS at lower frequencies than at higher frequencies. To quantify this observation, consider the set of points $(x,y)$ for which $|h_{k}(x,y)|=Th$, where $Th$ is the threshold. Given the trajectory and speed, we define the threshold delay for frequencies $f_{1}$ and $f_{2}>f_{1}$ as

[TABLE]

where $t_{f_{k}}(Th)$ is the time when $|h_{k}(t)|$ = $Th$ for frequency $f_{k}$. The threshold delay can be expressed as a distance by multiplying the terms of (6) by the mobile’s speed. In this paper, we assume a vehicular speed of 20 m/s and $f_{1}$ = 2.4 GHz, $f_{2}$ = 30 GHz. In Fig. 1(c, d), only the reflected component $m=1$ is shown. The set of points where $|h_{k,1}(x,y)|=Th$ forms a line at threshold (sufficiently far from the reflector) at an angle from specular reflection, which we call the diffraction angle: $\theta_{diffractionangle}(Th)=w(Th)\sqrt{cr_{m}/(2f_{k}r_{1,m}r_{2,m})}$ where $r_{1,m}=|\mathbf{r}_{refl,m}-\mathbf{r}_{eff,m}|$, $r_{2,m}=|\mathbf{r}_{rx}-\mathbf{r}_{refl,m}|$, and $r_{m}=|\mathbf{r}_{rx}-\mathbf{r}_{eff,m}|$ [SM §IV]. The $w(Th)$, as in (4) is a frequency-independent constant determined from $Th$ via inversion of the Fresnel terms (3) in (2). Note that the diffraction angle decreases with frequency. Thus, the mobile path intersects the $Th$ (dotted line) earlier for 2.4 GHz ($t_{2.4GHz}(Th)$, Fig. 1(c)) than at 30 GHz ($t_{30GHz}(Th)$, Fig. 1(d)), illustrating the early warning potential of the sub-6 GHz signals. While the above discussion focused on the reflected ($m>0$) components in (1), the LoS/NLoS transition ($m=0$) has similar dependencies.

III Simulation Results

In this section, we employ our physics-based simulation tool (section II) to demonstrate the capability of lower-frequency observations to predict mmWave signal-strength changes. The RSS values $|h_{k}(t)|$ in (1) were calculated for $f_{1}=2.4$ GHz and $f_{2}=30$ GHz for several topologies chosen to highlight typical propagation scenarios and challenging cases for the proposed ’early warning’ concept. For each topology, we computed $\tau(Th)$ in (6) for appropriately chosen threshold values. We also provide a statistical analysis that demonstrates the impact of reflector roughness on early-warning capabilities.

III-A LoS to NLoS Transition: Blockage

This section is devoted to sudden blockage of the mmWave LoS signal due to poor diffraction around obstacles in the environment, one of the primary limiting factors of base station coverage and causes of interrupted mmWave communication [1, 2]. Figure 1(a) with reflectors removed ($M=0$ in (1)) illustrates a scenario typical in blockage. The receiver is moving from the LoS to the NLoS region (right to left) along the horizontal dashed line. A brick building (the transmitter aperture) eventually blocks the LoS, and the received signal is determined by the diffraction. Figure 2 depicts the RSS for both frequencies along the path, and the lower frequency is impacted much earlier than the mmWave frequency as discussed in section II. We also observe the more abrupt transition to NLoS at the mmWave frequency, illustrating sudden blockage. The threshold $Th$ is chosen to be 70% of the average LoS value for this LoS/NLoS transition, and $\tau$ = 38 ms (0.76 m) (6). This threshold delay is sufficiently long to provide an early warning (tens to hundreds of slots) of the upcoming transition to NLoS and blockage of the mmWave signal using observations at the lower band, even in vehicular communications. Note that other threshold values can be chosen, but $Th$ = 50% should not be used since the RSS profiles at all frequencies intersect at 50% for edge diffraction, where the Fresnel integral argument $w$ (4) is zero [SM §II]. Moreover, when the mobile moves from left to right in Fig. 1(a), i.e., a NLoS to LoS transition (signal recovery), $Th$ = 30% of LoS RSS is used in (6), and the threshold delay is $\tau$ = 44 ms (0.88 m), again demonstrating early warning capability.

III-B Reflection into Shadow Region

A strong reflected mmWave signal can enable reliable communications in a NLoS environment, thus alleviating the effects of blockage for mmWave transmission. We explore the early warning of an upcoming strong reflection in NLoS using sub-6 GHz observations in the second scenario, which models a signal being reflected into the region shadowed from LoS as shown in Fig. 1(a). The transmitter aperture has been shortened from 10 m to 5 m to ensure that the calculation path is entirely within the NLoS region. The mobile moves from the left along the horizontal dashed line within the NLoS region and receives a signal from four reflectors at different locations on the mobile path. From left to right, the reflector locations (x, y) in meters are (4.5, -1), (2.5, 1), (6, 2), (18, -3); their sizes are 1.5 m, 0.5 m, 2.0 m, 1.5 m; and their angles counter-clockwise (CCW) from positive x-axis are 135°, 120°, 120°, and 135°, respectively. These could represent, e.g, a sign, mailbox, parked car, and dumpster. The sum in (1) has five components ($m=0,...,4$), and each reflected component $h_{k,m>0}$(t) is sufficiently strong and persistent to produce a viable communication signal for 0.5-2 m or 25-100 ms at vehicle speeds as the mobile crosses the corresponding reflection lobe while the direct component $h_{k,0}(t)$ is weak (NLoS). Early warnings of an upcoming strong reflection ($Th$ = 30% of average LoS value) and sharp decline of its RSS ($Th$ = 70%) are investigated, and the delays are shown in Fig. 3(a) and its caption.

The shapes of the reflections vs. position in Fig. 3 (bottom) vary with the regime of diffraction. Near-field diffraction, exhibiting oscillations at the top and a sharp, monotonic decline (in the absence of multipath fading), occurs for $w>\sim 3$ in (4), i.e., for a large reflector ($(\xi-\xi_{0})$ term), small distances from the reflector ($\rho_{m}$), or a higher frequency ($f_{k}$). The diffraction regime can change from near- to far-field by varying any one of these three parameters [SM §VII]. Far-field diffraction is characterized by a broad, featureless lobe, when $w<\sim 0.8$. The intermediate transition regime is marked by large sidelobes. We find that $\tau(Th=30\%)$ is long when the mobile is in the far-field of the reflector at the lower frequency, e.g., the $2^{nd}$ reflection in Fig. 3 (bottom), $w_{2.4GHz}$ = 0.8, or when the $Th$ intercepts a sidelobe in the transition regime as for the $1^{st}$ reflector, $w_{2.4GHz}$ = 2.3. When reflectors 2-4 are removed, multipath fading is reduced, and the sidelobe of the first reflection at 2.4 GHz falls below the threshold. The resulting threshold delay (shown in the right-most bar of Fig. 4) is smaller, $\tau$ = 6 ms, and is due to the wider main lobe at sub-6 GHz compared to mmWave frequencies (as discussed at the end of section II and shown in Fig. 1(c,d)). The main-lobe-induced delay also occurs when both frequencies exhibit near-field diffraction, as for the $3^{rd}$ reflection in Fig. 3 (bottom) $w_{2.4GHz}$ = 3.2, $w_{30GHz}$ = 11. The effects of multipath fading are also discussed in [SM §VIII].

III-C Angle of Arrival

In a mmWave beam search, the AoA of the strongest multipath component needs to be estimated. This problem is especially challenging in NLoS environments. Thus, for the scenarios of section III.B, we show the AoA of the strongest component in (1), denoted as $\widehat{AoA}_{k}(t)$ and defined in the Fig. 3 caption. We find that $\widehat{AoA}_{k}(t)$ values change slowly when one multipath component is dominant, due to mobile motion. Note that the $\widehat{AoA}_{k}(t)$ profiles exhibit a strong degree of congruency for the two frequencies (89.4%), supporting the findings in [7, 12]. For a low-to-moderate density of reflectors, as in Fig. 1(a), the strong reflections are separated by regions of very low RSS, where the mmWave signals are always weaker than the sub-6 GHz signals, due to poorer diffraction. Noise, multipath fading and sidelobes cause the $\widehat{AoA}_{k}(t)$ instabilities in these low RSS regions. Thus, a practical method to identify $\widehat{AoA}_{k}(t)$ would employ a RSS threshold or another detection technique. We show the $\tau(Th=30\%\text{ of LoS})$ in all panels of Fig. 3. Note that the $\widehat{AoA}_{k}(t)$ stabilize after the RSS values cross $Th_{2}$, and the threshold crossing at sub-6 GHz provides an early-warning for the switch of the $\widehat{AoA}_{k}(t)$ from one $m$-value to another at mmWave frequencies.

III-D Rough Reflections

Finally, to provide robustness to the results of section III.B and to simulate realistic building materials and structures, we removed reflectors 2, 3, and 4, and converted reflector $m=1$ in Fig. 1(a) to a rough reflector at the same location by splitting it into many sub-reflectors. Figure 4 shows the results of a statistical analysis as the mobile enters (30% of LoS) the reflected signal region ($x\sim 1-6$ m) with randomized reflector roughness. Each group of bars corresponds to a different size and number of sub-reflectors, keeping the overall 1.5 m reflector size, and each bar in a group corresponds to a different range for uniform random displacement of the sub-reflectors perpendicular to the surface. The number of components in (1) increases with roughness, where roughness is greatest for the group on the left. Within a group, the greatest roughness is for the bar on the right. The mean delay $\tau$ from (6) and its standard deviation were calculated for 100 iterations of each data point. The statistical analysis in Fig. 4 shows that roughness increases the early-warning potential of the lower frequencies significantly. Here, roughness effectively stretches the lower-frequency signal in space while the mmWave signal remains largely unchanged [SM Fig. S3(b)], which is due to the two frequencies experiencing different diffraction regimes. The reduced size of the rough sub-reflectors places the mobile into their far-field regime, with broad diffraction lobes, for the sub-6 GHz signals, $w=0.8,0.6,0.5,0.3,0.2$ for sub-reflector sizes $(\xi-\xi_{0})=0.5,0.4,0.3,0.2,0.1$ m, respectively, in (4), while the mmWave remains mostly in the transition regime due to its larger frequency. In practice, reflectors usually have some degree of roughness, which enhances the early warning potential of the lower frequencies.

IV Conclusion

A Fresnel-diffraction based channel simulation tool was employed to demonstrate that sub-6 GHz signals reach a given threshold much earlier than mmWave signals for a moving receiver. Thus, sudden changes in mmWave signal strength can be predicted using sub-6 GHz observations from several to tens of ms (several to hundreds of slots) ahead in mobile communications systems. Common scenarios, including moving from a LoS region to a NLoS region (blockage), encountering a strongly reflected signal in NLoS, and rough reflections were employed to demonstrate this predictive capability. Future work will focus on measurement-based verification and implementation of robust prediction schemes and adaptive transmission, beamforming, and anti-blockage methods for hybrid 5G systems based on the early warning capabilities of the sub-6 GHz signals.