Multi-Connectivity for Indoor Terahertz Communication with Self and Dynamic Blockage

Terahertz (THz) communication has been envisioned as a highly promising paradigm to support wireless data applications which demand ultra-high-speed transmission [1]. These applications, such as wireless virtual reality, augmented reality, and ultra-fast wireless local-area-networks, are beyond the reach of millimeter wave (mmWave) communication. This undoubtedly drives the need of communication at 0.1-10 THz band. Built on the major progress in THz hardware design and THz communication standardization over the past decade, it is anticipated that indoor THz communication systems will be brought to reality in the near future [2].

Despite the promise, designing ready-to-use THz communication systems brings new and pressing challenges that have never been seen at lower frequencies [3]. For example, THz signal propagation suffers from very high spreading loss and molecular absorption loss [4]. Particularly, the latter is highly frequency-selective and divides the THz band into multiple ultra-wideband transmission windows. Notably, the bandwidth of each transmission window shrinks with longer transmission distance [5]. Moreover, the THz signal propagation is highly vulnerable to blockage, including the blockage caused by the user itself, moving humans, and inherent indoor constructions (e.g., walls and furniture) [6]. All such factors lead to unique propagation characteristics at the THz band, which mandates the design and development of new communication and signal processing mechanisms.

One promising solution to addressing the reliability degradation caused by blockage in THz communication systems is to use multi-connectivity (MC) strategies. Under MC, users are allowed to maintain dynamic association with available access points (APs) for ensuring user session continuity. Due to its importance, the impact of MC on the performance of mmWave communication systems has been examined in recent studies, e.g., [7, 8, 9, 10]. Particularly, if the reactive MC (R-MC) strategy is adopted, where the user switches its communication from the current AP to another AP only when the current AP is blocked, has found considerable improvement in the outage probability and capacity [9, 10]. However, given the fundamental difference between mmWave channels and THz channels, the feasibility of using the R-MC strategy in THz communication has not been investigated, which is one of the motivations of this work.

In this paper, we present new analysis to evaluate the impact of MC strategies on the performance of an indoor ultra-wideband THz communication system where the user equipment (UE) suffers from both self-blockage and dynamic human blockage. For this system, we establish a three-dimensional (3D) propagation model where we consider both the spreading loss, determined by 3D propagation distances, and the molecular absorption loss, reflecting the shrinking usable bandwidth nature of the ultra-wideband THz channel. Under such consideration, we derive new expressions for the connection probability and the average ergodic capacity for two MC strategies, namely, closest line-of-sight (LOS) AP MC (C-MC) strategy and R-MC strategy. Different from the R-MC strategy, the UE under the C-MC strategy always communicates with the closest LOS AP, while maintaining association with several APs. Here, the connection probability is defined as the probability that at least one associated AP is LOS such that the UE can connect and communicate with. Aided by numerical results, we demonstrate that our analysis is accurate and a considerably improved connection probability is achieved by MC strategies, relative to the single connectivity (SC) strategy. Moreover, we find that the C-MC strategy achieves a significantly higher capacity gain over the SC strategy than the R-MC strategy. Furthermore, we reveal that when the UE is associated with more APs, the capacity gain achieved by the C-MC strategy increases while that achieved by the R-MC strategy decreases, sometimes even below zero. This worsening capacity behavior for the R-MC strategy demonstrates the impracticality of using it for THz communication, especially at low density of APs, which is different from the conclusion for mmWave communication. Finally, we clarify that there is an optimal density of APs to maximize the capacity gain of MC strategies, the value of which can be determined by using our analysis.

In this work, we consider a 3D THz communication system, as depicted in Figs. 1 and 2. Specifically, Fig. 1 shows the top view of the considered system where a UE associates with THz APs that are not blocked by the UE itself nor by moving humans, while Fig. 2 shows the side view of a single link from an AP to a UE. The UE is of height $h_{\textrm{U}}$ and assumed to be stationary. The APs are of fixed height $h_{\textrm{A}}$ and their location follows a Poisson point process (PPP) in $\mathbb{R}^{2}$ with the density of $\lambda_{\textrm{A}}$. Moving humans in the area of interest acts as potential blockers. These humans are modeled as cylinders with the radius of $r_{\textrm{B}}$ and height of $h_{\textrm{B}}$ and their location follows another PPP with the density of $\lambda_{\textrm{B}}$. Considering the practicality of THz communication system, we assume that $h_{\textrm{A}}>h_{\textrm{B}}>h_{\textrm{U}}$.

We assume that the mobility of humans follows the random directional model (RDM). Based on this model, a moving human randomly selects a direction to travel in and a time duration for this travel [11]. Similar to [10], in this work we assume that the moving speed is $v_{\textrm{B}}$. If a blocker is moving as per the RDM model in a given area in $\mathbb{R}^{2}$, the probability density function (PDF) of the location of blockers is uniform over time [11]. As such, at any given time instant, the location of blockers forms PPP with the same density, $\lambda_{\textrm{B}}$.

In this section, we present numerical results to evaluate the impact of MC strategies and parameters on the performance of the considered system with SC being the benchmark. The values of the parameters used in this section are summarized in Table I, unless specified otherwise.

Fig. 5 plots the connection probabilities of the SC strategy with $N=1$ and the $N$-degree MC strategy with $N=2$, $3$, and $4$ versus the density of APs, $\lambda_{\textrm{A}}$. We first observe that the connection probability significantly increases when $N$ becomes higher. This demonstrates the reliability performance improvement brought by the MC strategy relative to the SC strategy. Second, we observe the profound increase in the connection probability when $\lambda_{\textrm{A}}$ is larger. This implies that a denser deployment of APs can effectively overcome the detrimental impact of self-blockage and dynamic human blockage. Notably, when $\lambda_{\textrm{A}}$ is large, e.g., $\lambda_{\textrm{A}}=1.5\times 10^{-2}$, it is possible to achieve a high connection probability, e.g., $95\%$, even for $N=2$. Third, we observe that our analysis well match the simulations, especially for the SC strategy with any $\lambda_{\textrm{A}}$ and for the MC strategy with low and medium $\lambda_{\textrm{A}}$, which demonstrates the correctness of our analysis. When $\lambda_{\textrm{A}}$ is high, our analysis for the MC strategy slightly overestimate the connection probability. This is due to the fact that our analysis is under the assumption that the blockage process from different APs are independent of each other. However, for high $\lambda_{\textrm{A}}$, non-negligible dependencies appear such that the LOS blockage zones of different AP-UE links overlap with each other, which yields the slight overestimation.

Fig. 6 plots the average ergodic capacity of the C-MC strategy versus $\lambda_{\textrm{A}}$ considering the transmission window of $0.99-1.09~{}\textrm{THz}$ and the total transmit power of $P_{\textrm{T}}=20~{}\textrm{dBm}$. As expected, the average ergodic capacity becomes noticeably higher when $N$ increases from $1$ to $2$, which shows the benefits of the MC strategy relative to the SC strategy. Moreover, we note that the average ergodic capacity gain brought by further increasing $N$ from $2$ to $4$ is marginal. This marginal gain in capacity, along with the profound increase in connection probability when $\lambda_{\textrm{A}}$ is larger, which is observed in Fig. 5, implies that for the MC strategy, it may not be worthwhile to allow the UE to associate with more than two closest APs at higher AP densities. Furthermore, we again observe the benefit of a denser deployment of APs and the correctness of our analysis.

In order to precisely examine the performance improvement brought by the MC strategies relative to the SC strategy, we now define the capacity gain of the MC strategies relative to the SC strategy as

where $\Psi\in\{\textrm{C},\textrm{R}\}$. Fig. 7 plots ${\Delta}C_{\textrm{C}}^{N}$ and ${\Delta}C_{\textrm{R}}^{N}$ versus $\lambda_{\textrm{A}}$ for the transmission window of $0.99-1.09~{}\textrm{THz}$ with $P_{\textrm{T}}=20~{}\textrm{dBm}$. Moreover, the zero capacity gain is plotted in this figure. We first observe that relative to the SC strategy, the C-MC strategy achieves a large capacity gain while the R-MC strategy achieves a small capacity gain, e.g., ${\Delta}C_{\textrm{C}}^{N}\approx 10\%$ while ${\Delta}C_{\textrm{R}}^{N}\approx 2\%$ when $\lambda_{\textrm{A}}=1.5\times 10^{-2}$ and $N=2$. This observation indicates that the C-MC strategy significantly outperforms the R-MC strategy in THz communication systems. This observation is due to the fact that under the C-MC strategy, the UE always communicates with the closed LOS AP but under the R-MC strategy, the UE may communicate with a farther LOS AP. Indeed, the distance is a key factor governing the performance of THz communication systems given that it narrows the usable bandwidth and increases molecular absorption loss. Second, we observe that when $N$ increases, ${\Delta}C_{\textrm{C}}^{N}$ increases but ${\Delta}C_{\textrm{R}}^{N}$ decreases. The observation for the C-MC strategy is expected since under this strategy, associating with more APs gives the UE more opportunities to maintain the high-capacity communication when the current AP is blocked. Differently, under the R-MC strategy, associating with more APs gives the UE a higher chance to communicate with a farther LOS AP. This leads to the fact that the percentage of time that the UE communicates with the closest LOS AP reduces, thus decreasing the capacity. Third, we observe that for some cases, e.g., $N=4$ and small $\lambda_{\textrm{A}}$, ${\Delta}C_{\textrm{R}}^{N}$ gain is less than 0. This shows the impracticality of using the R-MC strategy for the THz communication system with a low density of APs. Finally, we observe that there exists the optimal density of APs which maximizes the capacity gain for both MC strategies. Notably, this optimal density can be determined by using our analysis.

To evaluate the capacity gain within a different transmission window, Fig. 8 plots ${\Delta}C_{\textrm{C}}^{N}$ and ${\Delta}C_{\textrm{R}}^{N}$ versus $\lambda_{\textrm{A}}$ for the transmission window of $3.34-3.49~{}\textrm{THz}$ with $P_{\textrm{T}}=30~{}\textrm{dBm}$. Once again, we observe in Fig. 8 that ${\Delta}C_{\textrm{C}}^{N}>{\Delta}C_{\textrm{R}}^{N}$, increasing $N$ increases ${\Delta}C_{\textrm{C}}^{N}$ but decreases ${\Delta}C_{\textrm{R}}^{N}$, and the optimal density of APs maximizes the capacity gain, which is similar to Fig. 7. Apart from these similar observations, we further observe that although $P_{\textrm{T}}$ increases from $20~{}\textrm{dBm}$ in Fig. 7 to $30~{}\textrm{dBm}$ in Fig. 8, the capacity gains achieved by the C-MC and R-MC strategies are worse when the transmission window increases from $0.99-1.09~{}\textrm{THz}$ to $3.34-3.49~{}\textrm{THz}$. This implies that, using wider transmission windows of higher THz band as compared to transmission windows of lower THz band, do not yield any additional improvement in capacity gain for MC strategies, due to the increased molecular absorption loss at higher THz frequencies. In addition, we observe that the capacity gains achieved by the R-MC strategy is negative even for medium $\lambda_{\textrm{A}}$, which is dfferent from Fig. 7. This is due to the combined effect of the molecular absorption loss which becomes more severe when the transmission frequency increases, and the reactive switching nature of the R-MC strategy. This again shows the impracticability of using the R-MC strategy for higher THz frequencies.

We analyzed the performance achieved by MC strategies which are used to combat the non-connection effect caused by self-blockage and dynamic blockage in THz communication systems. Specifically, we developed a new analytical framework to evaluate the connection probability and the average ergodic capacity achieved by C-MC and R-MC strategies. Using numerical results, we demonstrated the accuracy of our analysis and revealed several insights. First, comparing to the SC strategy, using MC strategy leads to a considerable improvement in the connection probability. Second, the capacity gain brought by the C-MC strategy over the SC strategy is significant, while that brought by the R-MC strategy is marginal. Third, increasing the number of associated APs leads to a higher capacity gain for the C-MC strategy, but a lower or even negative capacity gain for the R-MC strategy. Thus, it may not be practical to use the “lightweight” R-MC strategy in THz communication systems, which is different from the conclusion drawn for mmWave communication systems. Fourth, the optimal density of APs that maximizes the capacity gain can be determined by using our analysis.