Efficient and choreographed quality-of- service management in dense 6G verticals with high-speed mobility requirements

2.1Optimum QoS management solutions in dense 6G verticals

First, technologies at physical level have been reported. In this approach, complex parametric models for radio channel capacity (throughout) [20] or received radio power [21] are proposed. But some of these models do not have closed-form expressions, so the only feasible option to evaluate those models is through exhaustive simulations, which required very large processing periods. That is totally incompatible with high-speed mobility requirements. Some authors have proposed employing neural networks, including adversarial and/or generative networks [9], to deal with these not closed-form expressions [22], but in many cases the resulting numerical problems are nonconvex [23] and then the convergence time for these artificial intelligence approaches is too much higher than usual. So high-speed mobility requirements are not met neither.

Intelligent solutions are also used at link or network level [24]. Supervised learning is usually employed at the lowest level, in controllers for channel estimation [28] or interference management [29]. Unsupervised learning, on the other hand, typically operates at network level within node clustering algorithms [30] and multipath tracking protocols [31]. However, in these intelligent schemes, the Universal Approximation Theory only guarantees the approximation errors tend to zero as the calculation steps (and the number of neurons, is applicable) go to infinite, just if the optimal QoS distribution is a deterministic and continuous function [20]. But when high-speed mobility requirements are considered, QoS is not deterministic, but probabilistic. Intelligent solutions, then, tend to be unprecise and non-convergent. Our proposal addresses this open challenge.

Other solutions based on graph theory [19] and traditional traffic engineering mechanisms have also been studied [33]. Mainly, queue management algorithms including Markov models [17], queue theory [55], traffic classification [35], self-adaptive approaches [14] and/or congestion control [36] have been proposed. In general, however, these ad hoc solutions are specifically designed for a particular device density and speed. And, more importantly, they are only able to optimize one QoS indicator (usually throughput or communication delay). But 6G verticals show multidimensional dynamic QoS requirements and restrictions that need a more flexible and holistic approach to QoS management. This work fills this gap.

Table 1 summarizes the main approaches for QoS management in 6G networks reported in the state of the art.

2.2Mobility management solutions in 6G

Mobility management is one of the key challenges in mobile communications systems. Traditional approaches to this area focus on mitigating the impact of mobility on radio signals or network protocols [37]. But in dense 6G verticals, the impact of the large number of mobile devices moving around may be unpredictable and may even cause the base stations to become congested and collapse [38]. Then, mitigation is not enough, and new proactive management techniques are being studied and proposed.

Two basic approaches to mobility management in 6G networks have been reported [39]: handover management and location management.

Handover management techniques are focused on reducing the required time to complete a handover. It is the most time-consuming control process, as it requires around fifty second to succeed, while (for example) high-speed trains only need eleven seconds to go through the coverage area of a standard base station [40]. Smart signalization solutions have been proposed at the physical level, where implicit (doppler) information in radio signals is used to reduce the exchange of information between user devices and base stations have been proposed [40]. Other mechanisms at link level propose new protocols for 6G handovers with a reduced number of messages to be exchanged [41]. Some of these schemes even enabling low-latency communications [44]. Other solutions consisting of innovative networks architectures have also been reported. Schemes can be found where specific severs and databases manage mobile devices [42] and solutions where handovers are device-to-device with reduced network intervention [43].

But those previous works present some disadvantages. First, they focus on scenarios with a reduced or standard device density. But in dense 6G verticals, the handover processing delay is negligible compared to the context update delay in base stations (which is not optimized), so no real significant improvement can be achieved through these methods.

Besides, those works are only able to improve one QoS (delay), but not all verticals present hard restriction with latency, and other indicators (bitrate, reliability, etc.) may be relevant instead. Finally, most of these proposals, networks cannot follow commercial or scientific standards, which is undesired.

Some works specifically focused on dense 6G verticals can be found, but they are sparse and totally focused on increasing network throughput [45]. More general solutions are required, and, moreover, some authors have warned that any realistic solution for 6G dense verticals needs to consider QoS and resource management together [46].

On the other hand, location management technologies aim to capture the devices’ location, so the network can be optimally configured to that geographical distribution. At the physical level, solutions have been reported for base stations that work with millimetric waves to adjust the radiated power to the number of devices in their coverage area [47]. But the most common work in this area is focused on the non-terrestrial segment [49]. Schemes are being investigated to ensure that 6G networks can locate and follow moving elements such as planes or satellites [48] and guarantee they are correctly served. Although reported proposals are preliminary (focused on challenges, possible solutions, etc.) and only prospective [49]. Anyway, these mechanisms are very application-specific and cannot be implemented in all 6G dense verticals.

Finally, some authors are exploring techniques to predict the future location of mobile devices, so 6G networks can prepare in advance to the future system situation. Typical approaches to that problem are based on Bayesian networks [50], which can be combined with other technologies such as neural networks [51] to improve the precision. These techniques have proven to be successful, but too slow for high-speed mobility scenarios. On the contrary, faster mechanisms based (for example) on Markov chains [52, 57] achieve much lower precision.

Table 1 summarizes the main solution for mobility management in 6G networks.

In this paper, we fill this gap, with a holistic approach to mobility, QoS, and resource management. All these three dimensions are considered together. Besides, to harmonize models with a good precision but lightweight enough to operate at real-time in scenarios with high-speed mobility restrictions, a choreographed and collaborative calculation process is proposed.

3.1Mobility diagnosis

A dense 6G vertical with high-speed mobility requirements is composed of a set 𝒟 of ND devices, diEq. (1). These devices are distributed across a geographic area, 𝒜. Besides, in this area, a set ℬ of NB 6G base stations bj Eq. (2) is deployed to cover the region and serve all devices within the vertical.

Every device di is communicating with the base stations through OFDM (Orthogonal frequency-division multiplexing) radio signals, si⁢(t) Eq. (3.1). In these radio signals, Xki are complex symbols obtained through a channel coding or modulation (Quadrature Amplitude Modulation -QAM-, Quadrature Phase Shift Keying -QPSK-, etc.) applied to the original binary baseband signal. Besides, fci is the carrier frequency and Ti is the OFDM symbol period. Finally, Ci represents the number of subcarriers within the OFDM radio channels. Both parameters C and T can only take specific values described in the standards.

Radio channels are usually linear and time-invariant, but mobile devices with high speed induce a Doppler frequency shift into the radio spectrum which cannot be described with a time-invariant impulse response. Then, under those conditions, radio channels are still linear but randomly time-variant. Then, the OFDM output signal of a time-variant radio channel yi⁢(t) can be calculated using an integral linear operator and the kernel system function K𝑠𝑦𝑠i⁢(t,μ) Eq. (4) [53]. Without loss of generality, we can make a variable change Eq. (5), so the kernel system function takes the form of a time-variant impulse response in a sort of convolution sum Eq. (3.1). Then, both variables (t and τ) belong to the time domain.

In our scenario, time-variant radio channels cause two basic effects: a propagation delay (because of the distance between every device and radio stations) and a Doppler frequency shift because of the fast movement. But this bidimensional kernel function belongs to the time domain, whereas Doppler effects are much easier to describe in the frequency domain. Then we describe the kernel system function as the inverse Fourier transform of a Delay-Doppler-Spread (DDS) function H𝐷𝐷𝑆i⁢(τ,f) Eq. (7). In this DDS function, parameter τ is used to describe the propagation delays, while parameter f is employed to represent the Doppler frequency shift. Then, OFDM output signal may be finally calculated through this DDS Eq. (3.1).

Figure 2.

Speed estimation: Block diagram.

As devices move at very high speed, radio signals show multipath propagation (direct path, scattered paths and reflected paths, mainly). In our model for the DDS function, we assume P different paths. Besides, each path r presents a different propagation delay tri, a different Doppler frequency shift fri and a different attenuation αri. Delays and frequency shifts are considered constant within each subcarrier, so they can be modeled using the Dirac delta Eq. (9). So, finally, the OFDM radio signal yi⁢(t) actually received by base station can be deducted Eq. (3.1).

The first parameter to describe the current mobility state of devices is speed vi⁢(t). The mobility diagnosis is repeated every Tm⁢d seconds (measurement period). This time must be short enough, so the devices’ speed is constant. Besides, although elevated, the speed of mobile devices is negligible compared to the propagation speed of radio signals in the atmosphere. Under those conditions, the Doppler frequency shift is directly proportional to the devices’ speed Eq. (3.1), being cr the radio signal propagation speed along the path r. But, in general, radio propagation media are isotropic, and propagation speed for all of them can be replaced by the light speed in the vacuum c, with an error lower than 0.03% Eq. (3.1).

In the base station, OFDM signals are processed with a hybrid receptor mixing a partial OFDM demodulator and an FM receptor (see Fig. 2).

First, signal yi⁢(t) is demodulated and filtered as in any standard OFDM receptor Eq. (3.1), to remove the main carriers’ power from the radio signal. Filter H𝑂𝐹𝐷𝑀⁢(f) is a lowpass filter with cut frequency f𝑐𝑢𝑡, which is consider an ideal filter in our model Eq. (3.1). The resulting signal zi⁢(t) is, later, introduced in a bank of C FM receptors, each one tuned at the frequency of one OFDM subcarrier, kTi.

Figure 3.

Trajectory calculation: Block diagram.

These receptors may be implemented using several different techniques (filters and envelope detectors, voltage-controlled oscillators, etc.), but (mathematically) all of them apply a differential operation over the zik⁢(t) signal’s phase Eq. (3.1). The output for each subcarrier wik⁢(t) is a continuous signal codifying the Doppler frequency shift f𝑑𝑜𝑝𝑝𝑙𝑒𝑟i,k Eq. (16).

Now, considering the relation between the Doppler frequency shift and the devices’ speed, we can obtain a linear Eq. (3.1) with only one unknown variable (the current devices’ speed). But we obtain a similar equation for each OFDM subcarrier, so we get a system of C linear equations with only one unknown variable Eq. (3.1). The solution vin of the resulting equation system can be calculated by minimizing the Mean Square Error (MSE) Eq. (3.1) through iterative numerical methods.

On the other hand, the same OFDM radio signal yi⁢(t) is received by 6G stations through ultra-directive antennas. In 6G base stations, antennas are intended to use Gaussian Orbital Angular Momentum (OAM) radiation patterns [34]. These patterns show several modes (orthogonal gaussian beams). Each mode may, at the same time, include several non-interfering sub-beams. In that way, each mode may be tuned for a different carrier frequency, while sub-beams are spatially distributed to cover the entire geographical area, 𝒜. In our model, each mode in an OAM 6G antenna Gk⁢(θ) is composed for a set of MB gaussian sub-beams Gsk⁢(θ) with a width of θB radians and separated θe⁢l radians in azimuth Eq. (3.1), being θ the azimuth angle and G0 the antenna’s gain. MB must be an even number.

The OAM antenna is, then, connected to a bank of envelope detectors and logarithm amplifiers, so the devices’ trajectory can be calculated (see Fig. 3). If we exclude devices moving vertically (a very unusual situation), this trajectory (the movement direction) is represented by the reception azimuth angle θir⁢x. This angle is embedded into the received signal yi⁢(t) after going through each sub-beam Eq. (21).

Then, for each sub-beam, an envelope detector is employed to get a new signal ois,k⁢(t) that depends only on the amplitude of signal uis,k⁢(t) Eq. (22).

Then, signals ois,k⁢(t) are processed using a logarithm amplifier, to get a new set of signals ais,k⁢(t) depending on the devices’ trajectory, θir⁢x Eq. (3.1), being A1i,k and A2 real numbers.

Finally, these signals ais,k⁢(t) are combined in pairs and subtracted one from each other Eq. (3.1). Given an OAM antenna with MB sub-beams, the number of combinations is given by the combinatory number (MB2). Where A3s1,s2 and A4s1,s2 are real numbers. If we assume the diagnosis time Tm⁢d is short enough to keep the trajectory constant, then a set of (MB2)linear equations with only one unknown variable is obtained Eq. (3.1). These equations are solved using numerical method and the minimization of the MSE as target function, just as explained for the speed estimation process Eq. (3.1). The resulting solution θin describes the devices’ trajectory.

3.2Movement prediction

After the mobility diagnosis phase, every base station is provided with a set of two parameters {vin,θin} describing the mobility state of the i-th device. Besides, each base station defines a regular M𝒜⋅N𝒜 rectangular grid representing the 6G vertical’s geographical area (see Fig. 4). Thus, the position of any device pi within the vertical may be described using only two coordinates Eq. (3.2). Hereinafter we are naming pi⁢(n) the position of the i-th device at time instant t=n⋅Tm⁢d

Figure 4.

Movement prediction: Rectangular grid.

In the movement prediction phase, each base station must calculate a prediction for the future position of every device for which it obtained the mobility state. To do that, each base station may implement a different algorithm. Three possible algorithms are considered in our proposal: conventional probabilistic models, Markov models and Bayesian models.

In the conventional probabilistic model, the future device’s position pi⁢(n+1) depends only on the current mobility state {vin,θin} and position pi⁢(n). In this model we are only considering as possible future positions pij the ones in the locus Li Eq. (3.2). Basically, this locus includes the MLpoints pij that could be achieved by a mobile device with speed vin in Tm⁢d second.

Within this locus, the most probable future locations pimax±⁢(n+1) are those which meet the movement equations for a uniform rectilinear motion Eq. (3.2).

Other future locations may be possible as well, as the extracted current mobility state presents a certain (relative) estimation error {εiv⁢(n),εiθ⁢(n)}. This error is the remaining MSE after minimizing it during the equation solving process for the speed estimation (εiv) and trajectory extraction (εiθ). But large errors are much less probable than small errors. Therefore, we propose the probability of future locations reduces according to a logarithmic distribution Eq. (30) as they get further from the most probable future locations pimax⁢(n+1).

Parameter ξ is obtained as the geometric average of speed estimation and trajectory estimation errors Eq. (31). Besides, λj is a numeric label (natural number) associated to each possible future location pij⁢(n+1). These labels are associated through a specific function Γ⁢(pij) based on the Euclidean distance Eq. (3.2) and which associates bigger numbers to locations that are further from the most probable future locations (so the probability decreases).

Finally, in order to ensure the aggregated probability of all possible future locations pij is not higher than the unit, it is necessary to normalize the output from the logarithmic distribution Eq. (33).

Conventional probabilistic models require a low computational power to be computed and meet the requirements of ultra-dense verticals; however, are not able to learn. Therefore, the prediction error remains constant as time passes. On the other hand, the Bayesian model can integrate an a posteriori correction process, so the model is constantly improved.

The probability computed using the conventional probabilistic model may be understood as a prior probability P-⁢[pij⁢(n)] Eq. (3.2), where 𝒞⁢(pi⁢(n),pi⁢(n),vin,θin) represents the conventional probabilistic model for the given parameters.

But a much more precise estimation is provided by the posterior probability P+⁢[pij⁢(n)] Eq. (3.2). And this probability can be easily obtained through previous paths ρk employed by devices, and the Laplace’s definition of probability. First, probability P⁢[vin,θin] is unknown, but it can be calculated using the probability theory Eq. (3.2).

Additionally, the conditional probability P[vin,θin|pij(n+1),pi(n)] may be calculated using the locations that made up the previous paths ρk and the associated previous mobility states {vik,m,θik,m}, where δ⁢[⋅] is the Dirac’s delta Eq. (3.2).

Finally, the Markov model for movement prediction is based on previous observations (locations and mobility states). While conventional probabilistic models and Bayesian models are very fast to compute (faster than ultra-mobile devices), they may be not enough precise when devices show unusual behavior.

In a latent (hidden) Markov model, we assume that the i-th device may present MM different behaviors βir Eq. (38). These behaviors, including their actual number, are unknown and must be estimated.

The probability of the i-th device to be at the location pi while showing the behavior βirat instant t=n⋅Tm⁢d, and given all its previous locations pi⁢(j) and behaviors βi⁢(j), is represented by the joint probability Eq. (39).

In a Markov model, each location pi⁢(n) only depends on the current behavior βir⁢(n) showed by the device. And behavior βir⁢(n) only depends on the previous behavior βir⁢(n-1). In those conditions, the join probability can be developed as a sequence of conditional probabilities Eq. (3.2).

However, behaviors βir are not observable, so it is not feasible to use them as independent variables. Then, we can remove those parameters from the joint probability by aggregating the probability in those dimensions Eq. (3.2). Finally, the probability of the i-th device to be at the future location pi⁢(n+1) can be identified as the probability of the device to follow the path {pi⁢(1)⁢…⁢pi⁢(n+1)} Eq. (3.2). γj,r represents the conditional probability P[pi(j)|βir], πr,l is the transition probability P[βir|βil] so the i-th device show the behavior βir at time t=j⋅Tm⁢d when it showed the behavior βil at time t=(j-1)⋅Tm⁢d, which, in Markov models, is independent of the specific value of j; and finally φ1,r represents the probability P⁢[βir].

As behaviors are not observable, all these parameters must be estimated from observable variables. In our model, these observable variables are the mobility state {vin,θin} and previous paths ρk employed by devices.

First, we are considering all behaviors have the same probability, so φ1,rfollows a uniform distribution Eq. (43). On the other hand, probabilities γj,r and πr,l are not independent (as both depend on the device behavior). We are estimating both using the Laplace’s probability definition and previous paths ρk Eqs (44) and (3.2). Function 𝒞⁢(pi⁢(j),pi⁢(j-1),vij,θij) represents the conventional probabilistic model for the given parameters.

As probabilities γj,r and πr,l are interdependent, an infinite recalculation loop could be created. Thus, we define a target objective, so this loop can finish. Typically, for Markov models the logarithmic likelihood, ℒ is employed Eq. (46).

Regarding parameter MM, it also has a variable value, depending on the convergence of the logarithmic likelihood Eq. (3.2), as usually proposed in the state of the art [27].

Algorithm 1 shows the final calculation process of the Markov mobility model.

Physical noise in the original radio signals si⁢(t) can affect the calculation of all these probabilities. Specifically, the calculated most probable location pimax±, the conditional probability P[vin,θin|pij(n+1),pi(n)] and the Markov probability γj,r are the most sensitive values to this noise, as they depend directly on the estimated speed vin and trajectory θin (see Section 3.1). According to the Error Theory, noise (error) in these variables is directly proportional to the estimation error of the speed vin and trajectory θin. But, in a MSE problem, the estimation error can be reduced as much as desired: it decreases linearly with the number of equations under consideration. Thus, a higher number of FM receptors C and/or sub-beams MB can be employed to compensate errors in the movement prediction, induced by noise radio environments.

As different base stations are using different prediction models and may get different results, the final future vertical’s situation is obtained through a choreographed majority voting algorithm. With the implementation of three different models, we ensure our proposal can operate under very different requirements: ultramobility, ultradensity, etc. But hereinafter all base stations must agree in a common movement prediction in a choreographed manner.

Being Pb⁢[pij⁢(n)] the probability calculated by base station b of the j-th location to be the location of the i-th device at time t=n⋅Tm⁢d, we can calculate the mean probability among all base stations Pa⁢v⁢[pij⁢(n)] Eq. (48) and the associated MSE εa⁢vi,j Eq. (49). Then, in order to ensure that the final probability P⁢[pij⁢(n)] only considers predictions coherent with the results obtained by the majority of base stations, we are calculating a new mean probability as final probability, but only considering those predictions Pb⁢[pij⁢(n)] that are closer to the original mean Pa⁢v⁢[pij⁢(n)] less than at⁢h⋅εa⁢vi,jEq. (3.2). Being at⁢h a free real parameter used to control the prediction precision, and u⁢(⋅) the Heaviside function.

3.3Traffic modeling

In order to trigger a QoS management algorithm, it is necessary to transform the predicted future location of devices into a prediction of the future network load or traffic. To do that, different models may be employed. Depending on the behavior of each device, it could be considered a fluid source or a discrete source.

In the proposed traffic model, devices may be in two different states: ON state and OFF state. In the ON state, devices transmit and receive data packets at a maximum (peak) bitrate ϕimax (depends on the agreed QoS), while in the OFF state no data packets are exchanged. In the fluid source model, devices change their state at any moment, while in discrete sources, they only can do it at a discrete time steps. Devices may be fluid or discrete sources depending on the user application they are supporting, and that may change with time. Applications with a traffic pattern based on packet burst (such as web navigation) are discrete, while applications based on packet flows (such as video streaming) are continuous.

Regardless of the traffic model, the effective sustainable bitrate ϕie⁢f required by the i-th device depends on the probability of ON state Pi⁢[O⁢N]Eq. (51).

On the other hand, the effective bitrate ϕie⁢f is smaller than the peak bitrate ϕimax. Then, base stations and devices must be provided with a queue to handle this excess traffic. This queue has a capacity of Ki bits, organized in data packets with mean length Lpi. Using the standard queue theory and the traffic engineering principles [4] it can be calculated the individual prior loss factor ℓi Eq. (3.3) and the delay factor di Eq. (3.3) associated with this queue and device.