Optimizing Service Areas in 6G mmWave/THz Systems with Dual Blockage and Micromobility

Abstract

The modern 5G millimeter wave (mmWave) New Radio (NR) systems as well as future terahertz (THz) radio access technologies (RAT) will heavily rely on beamforming to combat the excessive path losses. Additionally, both RATs target similar bandwidth-greedy non-elastic traffic and are affected by the blockage phenomena. To improve service reliability in these systems multiconnectivity can be utilized to dynamically hand over the ongoing sessions between two technologies. In this article, we investigate the association strategies in collocated deployments of mmWave/THz systems and evaluate the impact of the utilized antenna arrays. Our results show that accepting sessions to THz BS that may experience outage in blocked conditions is preferable when multiconnecitvity is utilized as compared to accepting them to mmWave BS. However, extending the coverage of THz base station (BS) by increasing the number of antenna elements slightly affects performance metrics. Nevertheless, there is still non-negligible probability of dropping sessions accepted for service, implying that in 6G deployments the support of fully reliable microwave technology such as sub-6 GHz NR is vital.

1. Introduction

Nowadays, when standardization of 5G New Radio (NR) technology operating in millimeter wave (mmWave) and microwave ($\mathsf{\mu }$Wave) bands is completed and network operators are beginning their rollouts, the emphasis of the research community is shifting towards 6G systems. There is a common agreement that the new radio access technology (RAT) will utilize the lower part of the terahertz band (THz, 100–300 GHz) which may potentially provide tens of consecutive gigahertz of bandwidth, reaching tremendous capacity of tens or even hundreds of gigabits-per-second at the air interface [1].

Both mmWave and THz access systems are subject to the same type of impairments—extremely large free-space propagation losses and blockage phenomenon. The principle difference is the magnitude of this effect with blockage causing much higher attenuation in THz band. Thus, the principles developed during 5G NR standardization will be applied to THz RAT design. In particular, to overcome severe propagation losses, even more directional antenna arrays will be utilized in the THz band [2]. By utilizing extremely directional arrays, it will be possible to extend the coverage area of THz BSs, dynamically providing an additional degree of freedom when utilizing both mmWave and THz BSs to serve the users.

Due to the inherent capacity, both mmWave and THz RATs target the same type of traffic at the last mile—the one requiring high bitrates and characterized by limited elasticity (adaptivity to changing rate conditions). These include long-awaited virtual/augmented reality (VR/AR), telepresence and tactile Internet services. The rest of the technologies such as Long Term Evolution (LTE) are characterized by much smaller available resources and will be used to serve conventional types of traffic. Furthermore, as shown in [3,4], the use of LTE to temporally offload mmWave sessions results in drastic performance degradation of elastic traffic served at the LTE interface. To improve service reliability, 6G user equipment (UE) may need to utilize the standardized multiconnectivity option to dynamically switch between two inherently unreliable technologies [5]. However, due to the flexibility of the radio part configurations and quantitative difference between mmWave and THz interfaces, the optimal association scheme is an open question.

To the best of the authors’ knowledge and based on the detailed review presented in Section 2, there were no studies investigating user- and system-centric performance and optimal service areas of collocated 5G/6G mmWave/THz systems. The goal of our study is to address these research questions. To address these questions, we consider collocated deployment of mmWave and THz BSs serving UEs that are impaired by the dynamic blockage phenomenon. To ensure session continuity, we assume inter-RAT multiconnectivity between THz and mmWave systems and evaluate the effect of user association policies under a wide range of antenna configurations. To this aim, we apply the tools to stochastic geometry and queuing theory with random resource requirements.

The main contributions of our study are:

• Mathematical model capturing session service process in joint 6G mmWave/THz deployments with multiconnectivity functionality under dynamic blockage impairments;
• Results showing that: (i) accepting sessions that may experience outage due to blockade at THz BS improves service reliability; (ii) under realistic load conditions performance of association schemes are almost independent of the antenna arrays at THz BS.

The rest of the paper is organized as follows. We give an overview of related work in Section 2. Furthermore, we introduce our system model in Section 3. We analyze it and evaluate our metrics in Section 4. Numerical results are presented in Section 5. Conclusions are drawn in Section 6.

2. Related Work

Stochastic geometry is one of the main methods for link-level performance analysis of future 6G THz systems. The main focus so far has been on characterizing the performance bounds and the impact of the unique effects of THz band-blockage and micromobility. For example, in [6,7], by explicitly accounting for blockage and directional antennas, the authors investigated interference and signal-to-noise ratio (SINR) at UE. Further, these studies have been extended to capture various deployment specifics. For example, the authors in [8,9] considered 3D deployments, while Wu et al. in [10] considered indoor deployments, etc. Moreover, in [11], the authors investigated the effect of 3GPP multi-connectivity in dynamic blockage conditions. In [12], the authors extended these efforts by accounting for the micromobility effect discussed in [13]. Applying the stochastic geometry tool, researchers often choose capacity and the outage probability as the main metrics of interest. In general, the studies agree that multiconnectivity improves these metrics but cannot guarantee completely reliable operation while the capacity is far from the advertised theoretical bound [14].

There are not many studies that have investigated THz/mmWave joint operation at the system level. Of particular note is a study [15] which formulates the problem of optimizing user association to improve UE capacity in a joint THz/mmWave system. Another similar study was conducted in [16]. The authors investigated users’ associations, but also considered the coexistence of systems below sub-6 GHz ($\mathsf{\mu }$Wave) and THz. UE heuristic association algorithms have been proposed using system level modeling. Notably, most of such studies have considered elastic traffic patterns.

THz and mmWave systems can, in fact, be utilized together; however, one has to account for the type of traffic they are intended for. Due to the large amount of resources provided, both RATs target non-elastic, rate-greedy applications such as AR/VR, 8/16K streaming, holographic telepresence, etc. [17]. It should be noted that both RATs are subject to dynamic blockage, and THz systems further suffer from micromobility. In this context, the study in [18] investigates non-elastic traffic patterns in mmWave systems, while the work in [4] reflects the performance of joint $\mathsf{\mu }$Wave/mmWave systems with multiconnectivity support. It is also shown in [4] that the temporary offloading of high-speed connections to $\mathsf{\mu }$Wave systems leads to negative consequences for UEs with only a $\mathsf{\mu }$Wave interface.

We also note that in addition to principal connectivity challenges addressed in this paper, wireless communications in these mmWave/THz high-frequency bands is challenging and appropriate measures need to be taken to ensure that the flow of data is received in sequence and uncorrupted. The critical issue here is the choice of the modulation and coding schemes that are not set in stone yet for 6G systems. However, the application of low-density parity-check codes (LDPCs) promises to enable lightweight hardware-based decoding for 6G systems ensuring high forward error correction capabilities [19,20].

3. System Model

3.1. Deployment

We consider the mature deployment stage of mmWave NR systems and concentrate on a single mmWave BS cell of circular shape with radius $R_M$, see Figure 1, where $R_M$ is such that blockage at the cell edge does not lead to outage. Collocated with mmWave BS is THz BS characterized by coverage radii $R_{T,1}$ and $R_{T,2}$, where the former radius is such that no sessions that are inside $(0,R_{T,1})$ experience outage in case of blockage, while those from the ring $(R_{T,1},R_{T,2})$ may experience outage in cases of blockage. These radii depending on antenna configuration are computed by utilizing two propagation models in Section 4. The height of BSs is the same, $h_A$. UE height is $h_U$. The mmWave and THz BS bandwidth are $B_M$ and $B_T$.

3.2. Traffic

The session arrival process is Poisson with intensity ${\lambda }_A$ sess./s·m${}^2$. The geometric locations of sessions are assumed to be uniformly distributed in the mmWave coverage area. The session service times are exponentially distributed with parameters $\mathsf{\mu }$. Each session requires bitrate of $R_b$ Mbps.

3.3. mmWave Propagation

For mmWave path loss, we utilize the 3GPP Urban Micro (UMi) propagation model defined in [21], i.e.,

$$\begin{array}{c}\hfill L_{dB}\left(y\right)=32.4+{\zeta }_{M,i}10{log}_{10}\left(y\right)+20{log}_{10}{f}_{M,c},\end{array}$$

(1)

where y is the UE-BS distance measured in meters while $f_{M,c}$ is the carrier frequency in GHz, ${\zeta }_{M,1}$ and ${\zeta }_{M,2}$ are propagation constants for line-of-sight (LoS) and non-LoS states [21].

We assume 15 dB of blockage-induced attenuation. Thus, the signal-to-interference plus noise radio (SINR) in linear scale at the mmWave UE can be written as

$$\begin{array}{c}\hfill S\left(y\right)=\frac{P_M{G}_{M,A}{G}_{M,U}}{N_0{B}_M+M_{M,I}}\left[\frac{y^{-{\zeta }_{M,1}}[1-p_B\left(y\right)]}{A_{M,1}}+\frac{y^{-{\zeta }_{M,2}}{p}_B\left(y\right)}{A_{M,2}}\right],\end{array}$$

(2)

where $A_{M,1}={10}^{2{log}_{10}{f}_{M,c}+3.24}$, $A_{M,2}={10}^{2{log}_{10}{f}_{M,c}+4.74}$, $P_M$ is mmWave BS emitted power, $G_{M,A}$ and $G_{M,U}$ are the mmWave BS and UE gains, $N_0$ is the thermal noise, $B_M$ is the bandwidth of mmWave BS, $M_{M,I}$ is the interference margin, y is 3D UE-BS distance and $p_B\left(y\right)$ is the blockage probability given by [22]

$$\begin{array}{c}\hfill p_B\left(y\right)=1-{exp}^{-2{\lambda }_B{r}_B\left[\sqrt{y^2-{(h_A-h_U)}^2}\frac{h_B-h_U}{h_A-h_U}+r_B\right]},\end{array}$$

(3)

where ${\lambda }_B$ is the intensity of blockers, $r_B$ and $h_B$ are the blockers’ radius and height, $h_U$ is the height of UE. Blockers are assumed to move according to the random direction mobility model (RDM) with speed $v_B$ and mean run time ${\tau }_B$.

3.4. THz Propagation

The principal differences between THz and mmWave frequencies are: (i) higher propagation losses and (ii) atmospheric absorption. Similarly to [6], we account for the latter factor in (2) by introducing exponential attenuation factor $e^{-Ky}$, where K is the absorption coefficient that can be estimated from the HITRAN database. The former factor requires modification of propagation constants $A_{T,1}$, $A_{T,2}$, ${\zeta }_{T,1}$ and ${\zeta }_{T,2}$. By following [23], these constants are $A_{T,1}={10}^{2{log}_{10}{f}_{T,c}+14.7}$, $A_{T,2}={10}^{2{log}_{10}{f}_{T,c}+17.7}$, ${\zeta }_{T,1}=2.0$, ${\zeta }_{T,1}=3.2$, where the blockage losses are 30 dB.

3.5. Antenna

By following [6], at both BS types we use the directional cone antenna model, where the width of the beam coincides with the radiation pattern’s half-power beamwidth (HPBW). The mean gain over the HPBW is [24]

$$\begin{array}{c}\hfill G=\frac{1}{{\theta }_{3db}^{+}-{\theta }_{3db}^{-}}{\int }_{{\theta }_{3db}^{-}}^{{\theta }_{3db}^{+}}\frac{sin(N_{(·)}\pi cos\left(\theta \right)/2)}{sin(\pi cos(\theta )/2)}d\theta ,\end{array}$$

(4)

where $N_{(·)}$ is the number of antenna elements.

3.6. Multiconnectivity and Associations

All considered UEs are assumed to support multiconnectivity functionality [5]. As the major performance degradation in the considered future dense 6G mmWave/THz deployments is produced by the dynamic human body blockage, we consider two association schemes, mmWave preferred (mmWave_P) and THz preferred (THz_P), see Figure 2. In the former, only those sessions that do not experience outage due to blockage are accepted at THz BS. This corresponds to the circle of radius $R_{T,1}$ in Figure 1. The rest of the sessions arrive at mmWave BS and remain there till their service is completed or the session is dropped. In the THz preferred scheme, sessions arriving from the circle with radius $R_{T,2}$ are initially accepted in THz BS. Those sessions that experience outage with THz BS in the ring $(R_{T,1},R_{T,2})$ are then temporarily rerouted to mmWave BS and return back once blockage with THz BS is over. In this scheme, more traffic is initially routed to THz BS but a fraction of sessions may experience outage as a result of blockage.

3.7. Metrics of Interest

In terms of metrics of interest, we consider: (i) new session loss probability, ${\pi }_N$, (ii) ongoing session loss probability, ${\pi }_O$, and (iii) resource utilization, $\overline{R}$.

A session accepted for service at mmWave BS can be lost as a result of entering the blockage state. Although in this case, no outage happens, the amount of resources required for service increases due to the lower-order modulation and coding scheme (MCS). If mmWave BS does not have a sufficient amount of resources, a session is dropped. Sessions accepted in THz BS in the circle of radius $R_{T,1}$ are never lost. However, in the THz preferred scheme, a session experiencing blockage at THz BS in the ring $(R_{T,1},R_{T,2})$ might be lost at mmWave BS if there is no sufficient amount of resources to temporarily offload it to the mmWave BS.

4. Performance Analysis

Consider a queuing network with two nodes, namely M- and T-node, which represent a BS with dual technologies, mmWave NR and THz, respectively. Each part of the BS receives a Poisson arrival flow of sessions with intensities ${\lambda }_M$ and ${\lambda }_T$, respectively. Session service times are exponentially distributed with parameter $\mathsf{\mu }$. The arrival intensities are thus

$$\begin{array}{cc}\hfill & {\lambda }_M=(1-p_T){\lambda }_A\pi R_M^2,\hfill \\ \hfill & {\lambda }_T=p_T{\lambda }_A\pi R_M^2,\hfill \end{array}$$

(5)

where $p_T$ is the probability that a session is associated initially with the THz part. Note that $p_T=R_{T,2}^2/R_M^2$ for the THz preferred and $p_T=R_{T,1}^2/R_M^2$ for the mmWave preferred strategy. Using the introduced antenna and propagation models, $R_M$ can be found assuming the nLoS state [25,26]

$$\begin{array}{c}\hfill R_M=\sqrt{{\left[\frac{P_M{G}_{M,A}{G}_{M,U}{S}_{M,min}^{-1}}{N_0{B}_M+M_{M,I}}\right]}^{2/{\zeta }_{M,2}}-{(h_A-h_U)}^2},\end{array}$$

(6)

where $S_{M,min}$ is the SINR outage threshold [27]. Note that $R_{T,1}$ and $R_{T,2}$ are found similarly to (6), utilizing the THz path loss model from Section 3.4. Note that in $R_{T,2}$ additional human body blockage attenuation is accounted for.

Since the amount of resources at the THz part of the BS is assumed to be sufficient to handle the traffic load, the T-node is modeled as an infinite server queuing system and the M-node as a resource loss system (ReLS [28]) with N servers and R primary resource blocks (PRBs). Each session arriving at the M-node requires a server and a random amount of resources according to the pmfs $\left\{p_{1,r}\right\}$ and $\left\{p_{2,r}\right\}$, $r\ge 0$, in cases of initial arrival and rerouting from the T-node, respectively. These pmfs are computed using SINR as defined in Section 3.3 and Section 3.4, and NR MCS [27] as described in [25,26]. Note that $\left\{p_{1,r}\right\}$ represents resource requirements of sessions arriving from $(R_{T,1},R_{T,2})$, and $\left\{p_{2,r}\right\}$ from $(R_{T,2},R_M)$, see Figure 1. If the amount of resources is not sufficient to meet the resource requirements upon arrival or rerouting of a session, the session is dropped.

Each session on both nodes generates a Poisson flow of signals with intensity ${\nu }_M$ (M-node) or ${\nu }_T$ (T-node) that model outages caused by blockage events. A signal arrival at the T-node triggers rerouting of a session to the M-node and generating resource requirements according to the pmf $\left\{p_{2,r}\right\}$, $r\ge 0$. If there are not enough unoccupied resources at the M-node, it may cause a session drop. If the service of a rerouted session is not finished at the M-node, it returns back to the T-node. At the M-node, a signal triggers resource reallocation of a session. The session releases previously occupied resources, generates new resource requirements according to the same pmf $\left\{p_{1,r}\right\}$, $r\ge 0$ and tries to continue its service. If the resource requirements increase, the session may be dropped.

4.1. THz Preferred Strategy

4.1.1. Model Description

In this strategy, sessions that originally arrive to the T-node switch to the M-node upon arrival of signals and return back immediately when the blockage time is over. Therefore, there are two arrival flows at the T-node: (i) the initial (primary sessions) arrivals and (ii) the session that returns from the M-node (secondary sessions). Due to the memoryless property, the residual service times of secondary sessions coincide with the original service times. The arrival intensity of the secondary sessions at the T-node is ${\gamma }_T$ and the overall intensity of leaving the T-node is $\mu +{\nu }_T$. Thus, the mean number of sessions ${\overline{N}}_T$ at the T-node is

$$\begin{array}{c}\hfill {\overline{N}}_T=\frac{{\lambda }_T+{\gamma }_T}{\mu +{\nu }_T}.\end{array}$$

(7)

The service process at the M-node is modeled by an ReLS with signals [28]. Here, we define three types of sessions: (i) primary sessions initially arriving with intensity ${\lambda }_M$, (ii) secondary sessions that re-enter the M-node due to a signal arrival with intensity ${\gamma }_M$, and (iii) rerouted sessions that were rerouted from the T-node with intensity ${\gamma }_{MT}$. We will further assume that all these arrival flows are independent of each other and independent of the service process [29].

The proposed queuing formalization is illustrated in Figure 3. Let ${\overline{N}}_M$ be the average number of all sessions at the M-node, ${\overline{N}}_{M,1}$ the average number of primary and secondary sessions at the M-node, and ${\overline{N}}_{M,2}$ the average number of rerouted sessions. Then, the arrival intensity of secondary and rerouted sessions takes the following form

$${\gamma }_M={\overline{N}}_{M,1}{\nu }_M,{\gamma }_{MT}={\overline{N}}_T{\nu }_T.$$

(8)

The service intensity of primary and secondary sessions is $\mu +{\nu }_M$, while the service intensity of the rerouted sessions is $\mu +{\nu }_T$. Since the resource requirements of primary and secondary sessions are equal, they can be aggregated in a single arrival flow with the offered traffic load

$$\begin{array}{c}\hfill {\rho }_1=\frac{{\lambda }_M+{\gamma }_M}{\mu +{\nu }_M},{\rho }_2=\frac{{\gamma }_{MT}}{\mu +\beta },\end{array}$$

(9)

where $\beta =E\left[\mathsf{\Theta }\right]/\left(E\right[\mathsf{\Theta }]+E[\mathsf{\Omega }\left]\right)$ is the blockage intensity, $E\left[\mathsf{\Theta }\right]$ and $E\left[\mathsf{\Omega }\right]$ are the means of blocked and non-blocked internals provided in [30].

4.1.2. Solution and Metrics

According to [28], the stationary probabilities that there are $n_1$ of primary and secondary sessions occupying $r_1$ resources and $n_2$ rerouted sessions occupying $r_2$ resources have the following form

$$\begin{array}{cc}\hfill & q_{n_1,n_2}(r_1,r_2)=q_0\frac{{\rho }_1^{n_1}}{n_1!}\frac{{\rho }_2^{n_2}}{n_2!}{p}_{1,r_1}^{\left(n_1\right)}{p}_{2,r_2}^{\left(n_2\right)},\hfill \\ \hfill & 0\le n_1+n_2\le N,0\le r_1+r_2\le R,\hfill \\ \hfill & q_0={\left(\sum _{0\le n_1+n_2\le N}\frac{{\rho }_1^{n_1}}{n_1!}\frac{{\rho }_2^{n_2}}{n_2!}\sum _{0\le r_1+r_2\le R}{p}_{1,r_1}^{\left(n_1\right)}{p}_{2,r_2}^{\left(n_2\right)}\right)}^{-1}.\hfill \end{array}$$

(10)

Having obtained the stationary distribution, we can obtain the considered performance metrics. In particular, the mean number of sessions of each aggregated flow is given by

$$\begin{array}{c}\hfill {\overline{N}}_{M,i}=\sum _{0\le n_1+n_2\le N}\sum _{0\le r_1+r_2\le R}{n}_i{q}_{n_1,n_2}(r_1,r_2),i=1,2.\end{array}$$

(11)

Define the loss probabilities ${\pi }_{a,i}$, $i=1,2$ of each aggregated flow. In classic queuing systems, one can define a set of states, in which customers are lost upon arrival. In the considered ReLS, sessions may be lost in almost every state of the system with some probability depending on the volume of required resources. Thus, we derive the complementary probability that an arriving session is accepted as

$$\begin{array}{c}\hfill {\pi }_{a,i}=1-\sum _{0\le n_1+n_2\le N-1}\sum _{0\le r_1+r_2\le R}{q}_{n_1,n_2}(r_1,r_2)\sum _{j=0}^{R-r_1-r_2}{p}_{i,j},\end{array}$$

(12)

where ${\sum }_{j=0}^{R-r_1-r_2}{p}_{i,j}$ corresponds to the probability that a session is accepted if the system is in a state with $r_1+r_2$. Then, we summarize all states to obtain the complementary probability of session acceptance.

The arrival intensity of secondary sessions at the T-node equals the intensity of rerouted session from the M-node, i.e.,

$$\begin{array}{c}\hfill {\gamma }_T=\frac{{\gamma }_{MT}(1-{\pi }_{a,2})\beta }{\mu +\beta }.\end{array}$$

(13)

The probability that a session initially arriving at the M-node is lost upon arrival is given by the loss probability of the primary sessions, i.e., ${\pi }_N={\pi }_{a,1}$. The probability that a session initially arriving at the M-node is lost during the service is evaluated as the fraction of lost and accepted sessions, that is,

$$\begin{array}{c}\hfill {\pi }_{O,M}=\frac{{\overline{N}}_{M,1}{\nu }_M{\pi }_N}{{\lambda }_M(1-{\pi }_N)}.\end{array}$$

(14)

The sessions that originally arrive at the T-node can be lost only during rerouting to the M-node. So, their loss probability ${\pi }_{O,T}$ is evaluated similarly to (14), i.e.,

$$\begin{array}{c}\hfill {\pi }_{O,T}=\frac{{\overline{N}}_T{\nu }_T{\pi }_{a,2}}{{\lambda }_T}.\end{array}$$

(15)

Finally, by averaging over both nodes, the total ongoing session loss probability ${\pi }_O$ is obtained as

$$\begin{array}{c}\hfill {\pi }_O=\frac{{\lambda }_M(1-{\pi }_N)}{{\lambda }_M(1-{\pi }_N)+{\lambda }_T}{\pi }_{O,M}+\frac{{\lambda }_T}{{\lambda }_M(1-{\pi }_N)+{\lambda }_T}{\pi }_{O,T}.\end{array}$$

(16)

The mean number of occupied resources at the M-node is

$$\begin{array}{c}\hfill \overline{R}=\sum _{1\le n_1+n_2\le N}(n_1+n_2)\sum _{0\le r_1+r_2\le R}{q}_{n_1,n_2}(r_1,r_2).\end{array}$$

(17)

The performance metrics above are estimated iteratively as proposed in [29]. At the beginning, we set ${\gamma }_T$ and ${\gamma }_M$ to 0. Then, the system (9)–(12) is solved and new values of ${\gamma }_T$ and ${\gamma }_M$ are obtained according to (8) and (13). The procedure continues until the desired accuracy is achieved.

4.2. mmWave Preferred Strategy

In this strategy, only those sessions that do not experience outage in case of blockage are accepted at the T-node, implying that the system is a special case of the THz preferred strategy. Specifically, we obtain performance metrics for this case by recalculating $p_T$ and setting the intensity of secondary session and signal arrivals at the T-node to 0, ${\gamma }_T=0$ and ${\nu }_T=0$. As a result, the total ongoing session loss probability is

$$\begin{array}{c}\hfill {\pi }_O=\frac{{\lambda }_M(1-{\pi }_N)}{{\lambda }_M(1-{\pi }_N)+{\lambda }_T}{\pi }_{O,M}.\end{array}$$

(18)

All other performance metrics are calculated similarly.

5. Numerical Analysis

In this section, we elaborate on the performance of the considered association schemes using Formulas (12) for ${\pi }_N={\pi }_{a,1}$, (16) and (18) for ${\pi }_O$ and (17) for $\overline{R}$. The main system parameters are shown in

Table 1. The default system parameters.

Notation	Description	Values
$f_{M,c}$	mmWave carrier frequency	28 GHz
$f_{T,c}$	THz carrier frequency	300 GHz
$B_M,B_T$	mmWave BS bandwidth	0.4/4 GHz
C	required session rate	10 Mbps
${\mu }^{-1}$	mean session service time	10 s
${\lambda }_A$	session arrival intensity	${10}^{-4}$ sess./s/m${}^2$
${\lambda }_B$	density of blockers	0.1 bl./m${}^2$
$r_B$	blocker radius	0.4 m
$h_A$	mmWave/THz BS height	10 m
$h_U$	UE height	1.7 m
$v_B,{\tau }_B$	blockers speed and run time in RDM	1 m/s, 30 s
$P_M,P_T$	mmWave/THz BS emitted power	2 W
K	absorption coefficient	0.01
${\zeta }_{M,1},{\zeta }_{T,1}$	path loss exponents in non-bl. state	2.0/3.2
${\zeta }_{M,2},{\zeta }_{T,2}$	path loss exponents in bl. state	3.19/3.2
$M_{M,I},M_{T,I}$	mmWave/THz interference margins	3 dBi
$N_{T,A,V},N_{T,A,H}$	THz BS antenna configuration	32–120 × 4
$N_{M,A,V},N_{M,A,H}$	mmWave BS antenna configuration	32 × 4
$N_{·,U,V},N_{·,U,H}$	mmWave/THz UE configuration	4 × 4
$N_0$	thermal noise power	−84 dBi

. Note that in our numerical study, we attempted to be as close to the 3GPP recommendations as possible. Specifically, we utilize the propagation coefficients provided in TR 38.901 for the UMi model and radio part and antenna parameters provided in TR 36.911. The “free” parameters have been chosen such that they reflect the most interesting conditions when the system is about to be congested and/or the considered metrics of interest are close to the maximum allowed boundaries.

We consider $N\times 4$ antenna arrays at THz BS, where $N=32,40,\cdots ,128$. The corresponding coverage of mmWave BS is $R_M=113$ m while $R_{T_1}$ and $R_{T,2}$ in meters are

$$\begin{array}{cc}\hfill & R_{T,1}=\{15,17,18,19,20,21,22,23,23,24,25,25\},\hfill \\ \hfill & R_{T,2}=\{74,79,84,88,92,95,99,102,104,107,110,112\}.\hfill \end{array}$$

(19)

We start with Figure 4 illustrating the considered metrics for two session arrival rates ${\lambda }_A$ and different association strategies. First of all, considering new and ongoing session loss probabilities in Figure 4, observe that the increase in the array size does not affect the new and ongoing session loss probabilities for the mmWave preferred strategy. The rationale is that the THz BS coverage radius, where blockage does not induce outage increases insignificantly, from 15 m to 25 m, see (19). From this point of view, this scheme does not offer any flexibility for dual-band UEs.

Analyzing the results further, one may observe that the mmWave preferred association scheme is characterized by smaller new session loss probability (e.g., ∼0.06 vs. $0.14$ for ${\lambda }_A={10}^{-4}$) but results in higher ongoing session loss probability. The main reason is the effect of blockers resulting in frequent changes in the amount of resources needed to support the ongoing session. Specifically, even though sessions are exposed to the temporal offloading to mmWave BS in the THz preferred scheme, the overall decrease in the load imposed on mmWave BS leads to better ongoing session loss probability. This effect is further supported by the fact that the resources of mmWave BS are much less utilized in the THz preferred scheme as shown in Figure 4c. However, as one may notice, these unloaded conditions at mmWave BS do not allow one to handle additional load of dual-band UEs as new and ongoing session loss probabilities are already quite high, e.g., ∼0.06 and ∼0.4, respectively, for ${\lambda }_A=6\times {10}^{-5}$. Thus, this residual capacity can only be utilized to serve mmWave-only UEs.

Figure 4a also shows an interesting effect, where the new session loss probability for the THz preferred system first increases and then decreases. This is caused by the interplay between the session resource requirements imposed at mmWave BS that increases with the coverage radius of THz BS and the fraction of sessions that are initially accepted at THz BS.

As the blocker density plays a critical role in the considered schemes, we now proceed to analyze the system response to this parameter illustrated in Figure 5. By analyzing new and ongoing session loss probabilities illustrated in Figure 5a, we observe that the former metric is significantly better for the mmWave preferred scheme in the whole considered range of blocker density. Specifically, curves for THz and mmWave preferred strategies almost coincide for low blocker density and then start to move apart and this parameter increases. The difference reaches 0.07–0.1 for ${\lambda }_B=0.3$ bl./m${}^2$, ${\lambda }_A={10}^{-4}$ BS/m${}^2$ and 0.03-0.05 for ${\lambda }_B=0.3$ bl./m${}^2$, ${\lambda }_A=6\times {10}^{-5}$ BS/m${}^2$. This effect, however, cannot be considered in isolation from the ongoing session drop probability. Indeed, by analyzing the results presented in Figure 5b, we observe that the THz preferred scheme shows superior performance in terms of the ongoing session loss probability. Here, the rationale is that the mmWave preferred scheme results in much more frequent session drops during the service which make resources available for new arrivals. However, these new arrivals are more likely to be dropped during the service as compared to the THz preferred scheme. This behavior confirms that the observations made for Figure 4 remain valid for any blocker density which is the major impairment for mmWave and THz communication systems. Thus, if one wants to improve session continuity, the THz preferred scheme needs to be utilized.

Finally, by analyzing the results presented in Figure 5c, we observe that the mmWave preferred schemes lead to much better mmWave BS utilization across the whole considered range of the blocker’s density. The rationale is that this scheme results in much higher traffic initially routed to this BS. However, the difference between mmWave BS utilization decreases as the blocker density increases. Here, the reason is that blockage events caused frequent session interruptions leading to higher ongoing session drop probability as seen in Figure 5b.

6. Conclusions

Motivated by the need to improve session service reliability in future 6G mmWave/THz systems, in this paper, we investigated mmWave and THz preferred association schemes. To this end, we used the tools of queuing theory with random resource requirements allowing us to simultaneously account for channel impairments and details of the resource allocation process at mmWave/THz BSs.

Our results demonstrate that changing the coverage area of THz BS by increasing the number of antenna elements does not allow one to balance new and ongoing session loss probabilities. Specifically, mmWave preferred scheme does not offer any flexibility for dual-band UEs while the flexibility offered by varying THz BS coverage is very limited for dual-band UEs. However, THz preferred association is recommended when one wants to improve service reliability of sessions accepted for service while still keeping mmWave BS unloaded for single-band UEs.

The reported results are somewhat negative in the sense that we basically demonstrate that multi-connectivity alone cannot guarantee uninterrupted session performance in mixed 5G/6G systems operating using two RATs that are both subject to outage due to the blockage phenomenon. However, we do not view this result as strictly negative considering it as a “call for enhancements” instead. Specifically, in addition to utilizations of RATs that are not susceptible for blockage (e.g., microwave 4G LTE [3]) and bandwidth reservation techniques [31], there is an urgent need for novel techniques improving session continuity in prospective 6G mmWave/THz systems.