Heterogeneous Quality of Experience Guarantees Over Wireless Networks

Jianyu Wang, Wenchi Cheng＊

State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710000, China

Abstract: Quality of experience (QoE), which is very critical for the experience of users in wireless networks, has been extensively studied. However, due to different human perceptions, quantifying the effective capacity of wireless network subject to diverse QoE is very difficult, which leads to many new challenges regarding QoE guarantees in wireless networks. In this paper, we formulate the QoE guarantees model for cellular wireless networks. Based on the model, we convert the effective capacity maximization problem into the equivalent convex optimization problem.Then, we develop the optimal QoE-driven power allocation scheme, which can maximize the effective capacity. The obtained simulation results verified our proposed power allocation scheme, showing that the effective capacity can be significantly increased compared with that of traditional QoE guarantees based schemes.

Keywords: wireless network; effective capacity; power allocation; heterogeneous; quality of experience; quality of service

I. INTRODUCTION

Recent studies show that although service providers and researchers have done a number of works on quality of service (QoS) to optimize the performance of the network, most of QoS indicators such as throughput, packet loss rate,and transmission delay are based on technical performance and not sufficient to measure the users’ experience. Therefore, with the increasing requirement for wireless transmission such as mobile media services and applications,more researchers and service providers are committed to developing user-centric strategies and place more emphasis on perceived end to end quality, which is referred as quality of experience (QoE).

Generally, the evaluations of QoE parameter can be divided into two categories: objective assessment and subjective assessment [1].Evaluating QoE with objective assessment refers to estimating users’ satisfaction according to technical parameters, such as rate, delay,and packet loss, etc. Based on mathematical analyses and experimental measurements, researchers have built some models to evaluate the relationships between QoE and QoS. For example, the authors of [2] proposed the linear and exponential functions based QoE measurements, which are evaluated by experiments.Using the mean opinion score (MOS) model,the authors of [3] established the mapping relationships between the response time of the web server and the QoE parameter, while the authors of [4] show the relationships between the experience of users and QoS parameters for video service. As for the subjective assessment, it is mainly related to the user’s subjective feeling of service, thus need much time to collect date. The MOS based model is widely used in subjective QoE assessment. MOS is a real number between 1 and 5, with higher number corresponding to better QoE

Traditionally, QoE guarantees for wireless networks is homogeneous, that is, each link in wireless networks only needs to take its own QoE requirement into account, rather than QoE requirements corresponding to other links. However, due to the diversity of many kinds of traffics, it is highly desired to jointly consider the QoE guarantees for all links,which is the heterogeneous QoE guaranteeing for wireless networks.

In order to achieve heterogeneous QoE guarantees, we can borrow ideas from the schemes of heterogeneous QoS provisioning for wireless networks, which has been extensively studied. The authors of [5] proposed the optimal power allocation for base station (BS)with QoS requirements in cooperative wireless networks, while the heterogeneous QoS provisioning scheme has been extended to D2D network in [6]. Taking the energy saving into account, the authors of [7] investigated the QoS-aware energy efficiency optimization in 5G wireless networks. Also, an QoS guarantees method is proposed for full duplex D2D communications in 5G networks [8], while the authors of [9] and [10] made great efforts for guaranteeing the QoS indicators in multiple input multiple output (MIMO) networks. It is expected that future communication terminals will have higher mobility [11], and the authors of [12] proposed a modified doppler frequency trajectory undergoing varying velocities for high speed rail (HSR) communications, which provided effective support to guarantee the QoS requirements of users with high mobility.Moreover, with regard to machine-to-machine communications, an improved access scheme was proposed in [13] to downgrade the expected delays. Alternatively, QoS indicators guarantees for high frequency communication network with diversity is discussed in [14].However, since QoE metrics consider human factors, the performance optimization in wireless networks with heterogeneous QoE guarantees imposes new challenges.

Fig. 1. The system model for downlink transmissions in wireless cellular network.

In this paper, we formulate the system model with heterogeneous QoE guarantees for downlink transmissions in wireless cellular networks.With the object of maximizing effective capacity, we construct the optimization problem as well as develop the optimal QoE-driven power allocation strategy with QoE guarantees. In addition, we also conduct simulations to evaluate our proposed QoE-driven power allocation strategy in this paper.

The remainder of this paper is structured as follows. ith Section II describes the system model. Section III formulates the optimization problem for QoE-guaranteed downlink transmissions in wireless cellular network.We also develop the QoE-driven power allocation scheme for each downlink. Section IV conducts simulation results to show the performance of our proposed power allocation scheme. The paper concludes in Section V.

We formulate the system model with heterogeneous QoE guarantees for downlink transmissions in wireless cellular networks.

II. SYSTEM MODEL

We consider the generic downlink transmissions scenario in wireless cellular networks, as depicted in Figure. 1, where the BS transmits data to N cellular users through different orthogonal division multiple access (OFDMA)sub-channels. Each downlink corresponds to one cellular user as well as being required to satisfy the user’s QoE parameters.We use the block fading channel, where the channel gain remains unchanged within one frame with the length T, but varies across different frames.The bandwidth corresponding to each downlink is denoted by B. Nakagami-m channel model, which can flexibly represent different degrees of fading by changing the parameter m, is applied. The probability density function(PDF) of Nakagami-m channel model, denoted by pN(Γ), is given by the following equation:

where Γ is the instantaneous channel signalto-noise ratio (SNR), m represents the fading parameter of Nakagami-m distribution,ϒ(·) is the Gamma function, anddenotes the average SNR received by the user.

QoE represents users’ satisfaction degree with communication services, which is derived by integrating human factors into QoS measurements. We denote by θi(1≤i≤ N)the QoS exponents for the ith downlink. The data service rate corresponding to the ith downlink transmission is defined by the sequence {Ri[k], k = 1,2,...}, a discrete-time stationary and ergodic stochastic process. k represents the time frame index of frame time whose time duration equals to T. Effective capacity is defined as the maximum constant arrival rate that can be supported by the service rate to guarantee the specified QoS exponent.If the service-rate sequence corresponding to the ith downlink Ri(k ) is time-uncorrelated and stationary, the effective capacity for the ith downlink, denoted by EiC(θi), can be written as follows [12]:

where E{·} denotes the expectation operation,Γirepresents the channel SNR corresponding to the ith downlink and Piis the instantaneous transmit power of the BS corresponding to the ith downlink.

Based on the system model, the aggregated effective capacity for downlink transmissions with heterogeneous QoS requirements, denoted by AC(θ1,...,θN), can be derived as

III. MAXIMIZING DOWNLINK AGGREGATED EFFECTIVE CAPACITY WITH HETEROGENEOUS QoE REQUIREMENTS

In this section, we formulate the relationships between QoS metrics and QoE measurements.Then, based on the model, the optimization problem is constructed to maximize the effective capacity over cellular users in wireless cellular networks with heterogeneous QoE requirements. Then, we derive the QoE-driven power allocations, which is the solution to the optimization problem. We consider to measure QoE measurements in human, techniques,context, and business aspects [13].

Human domain refers to that the human with various attributes (gender, hobby, age),and various roles (user, customer) have different satisfaction degrees with communication services. For this domain, we consider that each user’s tolerance for delay and transmission rate are different, withandrepresenting the delay and transmission rate corresponding to the maximum tolerance of user i.

Technical domain refers to all technical entities and technical roles from design to delivery of the service. We take into account the delay experienced by the source packet arriving at the user i, denoted by τi, for this domain.

Context domain represents that the environment in which human beings exchange data with technological entities can also affect the user satisfaction degree. For this domain, we consider the size of multimedia file required by user i, denoted by Si, and Γi, which is the instantaneous SNR of user i in Section II.

The business factors of service (advertisement, pricing, promotions) directly affects the experience of users. In general, a larger energy loss leads to a higher pricing. Therefore, for business domain, we consider the total energy loss corresponding to the ith downlink, denoted by Liand given by

where Ridenotes the instantaneous transmission rate of the ith downlink.

We employ MOS function [14] to characterize the mapping relationships between QoE and QoS as well as quantify QoE parameters.The MOS measurement function for the ith downlink, denoted by Mi, can be estimated using

The relationships model between QoE and QoS has attracted extensive attention. The authors of [15] pointed out the logarithmic nature of QoE assessment. An extensively discussed relationships between QoE and QoS can be given as follows [15]:

where QoEMOSand QoS are the QoE parameter that quantified by MOS function and the QoS indicator, respectively. a, b, and c are logarithmic model parameters. Therefore, for the ith downlink, the relationships function between QoS and QoE can be derived as follows :

where ai, bi, and ciare defined as the logarithmic model parameters for user i. Eq. (7)can also be written as follows:

Combining Eq. (3), the aggregated effective capacity for the transmission from the BS to N cellular users with heterogeneous QoE requirements can be rewritten as

Since θmin=min{θ1,...,θN}θmax=max{θ1,...,θN}, and Γ = (Γ1,...,ΓN),there is an optimal unique value θ0(θmin≤θ0≤θmax) that can be found to formulate the equivalent function for(θ1,...,θN)[16], denoted by(θ1,...,θN)and given by

where EΓ{·} denotes the expectation over Γ .

Maximizing the aggregated effective capacity for the downlink transmissions with heterogeneous QoE requirements, the optimization problem, denoted by P1, can be formulated as follows:

where Paveis the average power constraint for the BS; the constraint 1). implies the power allocated by BS for each downlink cannot be a negative value; the constraint 2). implies that the aggregated transmit power is limited bythe average power constraint for BS.

We can intuitively know [−log(y)/θo]decreases as y increases. Thus, the optimization problem P1 can be converted into a new problem P2 as follows:

subject to the constraints 1). and 2). given in P1. Then, we study the convexity of P2,which is given by the following lemma.

Lemma 1.The optimization problem P2 is strictly convex.

Proof. Because the left side function of the constraint 2). in P1 is linear with respect to the space spanned by (P1,...,PN), analyzing the convexity of P2 is equivalent to study the convexity of the function defined as

Then, the second-order derivative and partial derivative of G(P1,...,PN) can be derived as

The Hessian matrix of G(P1,...,PN), denoted byK, can be given by

where

The following equation holds for any non-zero vectorυ=(υ1,υ2,...,υN):

Based on the above analysis, the unique optimal power allocation for problem P2 can be obtained. We denote by J the Lagrangian function of P2 as the following equation:

where µ is the Lagrangian multiplier corresponding to the constraint 2). in P1. The derivative of J with respect to Pi(1≤i≤N )can be numerically obtained as:

Setting the results of Eq. (19) to zero, the following equations can be derived:

Then, N equations expressed by Eq. (20)can be multiplied as follows:

which results in

substituting Eq. (22) into Eq. (20), the following equation can be obtained:

where µ0is defined as the optimal Lagrangian multiplier corresponding to the constraint 2).in P1, which can be derived through plugging Eq. (23) into. So far, we have derived our proposed QoE-driven power allocation scheme.

Therefore, the maximum aggregated effective capacity for transmissions from the BS to multiple cellular users with heterogeneous QoE requirements, denoted by Amax, can be derived as the equation (24) below.

Fig. 2. Relationship between QoE estimation and transmit power with different delays.

IV. NUMBERICAL SIMULATION

In this section, we make simulation to show the performance of our proposed QoE-driven power allocation scheme for the transmission from the BS to multiple cellular users in cellular wireless networks. We set the time frame length T = 2 ms, and the bandwidth corresponding to each downlink B=2 MHz.The fading parameter of Nakagami-m channel model is set to m=2. The average SNR of each channel is set to=−3dB, and we set the average power constraint for BS as Pave=1W.

Figure 2 shows the QoE estimation versus allocated powers for the user under τ=2ms,τ=8ms, and τ=10ms. In this simulation, we set the file size for the user as 200 Kb and the user’s maximum tolerance of delay as 10ms. The user’s maximum tolerance of transmission rate is set to 400Kbps, and the transmit power varies from 0.2W to 2W.Based on Figure 2, we can observe that the power allocated to the user directly affects the the user’s experience. Moreover, we can also find the relationships between allocated power for the user and the QoE estimation for the user is consistent with the logarithmic nature.Besides, if τ=10ms, allocating 2W, which is double the average power constraint of BS,to the user can only make QoE achieve 2.7.Under this circumstance, enhancing the value of τ can significantly improve the user experience. For example, when the allocated power to the user is 2W, decreasing τ from 10ms to 2ms can rapidly increase QoE from 2.7 to 4.5.

Figure 3 illustrates the logarithmic relationships between the QoS exponent θ and average QoE with our developed QoE-driven power allocation. The file sizes transmitted to users are randomly set between 200Kb and 800 Kb. The delay requirements of users are randomly set between 1ms and 5ms, and user’s maximum tolerance of transmission rate are randomly set between 400Kbps and 800 Kbps. As illustrated in Figure 3, when θ is very loose, QoE rapidly increases as θ increases. However, when θ is very stringent, QoE slightly increases as θ increases.For example, changing θ from 0 to 0.01 can make the QoE of the curve corresponding to N=2 rapidly increase from 1 to 3.4. However, changing θ from 0.09 to 0.1 only make the QoE of the curve corresponding to N=2 slightly increases from 4.3 to 4.4. On the other hand, we can know that the estimation of QoE decreases as the number of users increases.This is because the resource that allocated to each downlink decreases as the number of users increases. Also, we can observe that the increasing of QoE is slower as the number of users increases.

The allocated power for users in cellular network using our proposed heterogeneous QoE-driven power allocation scheme is depicted in Figure 4, where we set N=2,M1=2,and M2=3.5. As shown in Figure 4, because the user corresponding to the downlink with M1=2 corresponds to the lower QoE requirement, it has been allocated more power than the user corresponding to the downlink with M2=3.5, which corresponds to the higher QoE requirement.

Figure 5 shows the aggregated effective capacity versus various M1and M2corresponding to our proposed heterogeneous-QoE-driven power allocation and the homogeneous-QoE-driven power allocation,where we set N=2. As depicted in Figure 5,the aggregated effective capacity with homogeneous QoE guarantees scheme can approach the aggregated effective capacity with heterogeneous QoE guarantees scheme near the plane M1=M2, implying that the QoE guaranteeing corresponding to homogeneous is only a special case of QoE guaranteeing corresponding to heterogeneous. On the other hand, the aggregated effective capacity corresponding to heterogeneous QoE guarantees is always larger than the aggregated effective capacity corresponding to homogeneous QoE guarantees, implying that our proposed heterogeneous-QoE-driven power allocation can significantly enhance the performance of wire-less networks as compared with traditional homogeneous QoE guarantees scheme.

Fig. 3. Relationship between average QoE and QoS with our developed QoE-driven power allocation.

Fig. 4. Heterogeneous-QoE-driven power allocation scheme.

Fig. 5. Comparison of the aggregated effective capacities using heterogeneous-QoE-driven power allocation and homogeneous-QoE-driven power allocation schemes.

V. CONCLUSION

In this paper, we solved the problem of how to guarantee heterogeneous QoE requirements in wireless cellular networks. We built up the effective capacity model with heterogeneous QoE requirements. Then, we develop the optimal power allocation to maximize the effective capacity as well as satisfy the user QoE requirements. Simulation results show that our proposed power allocation scheme can significantly increase the aggregated effective capacity.

ACKNOWLEDGEMENT

This work was supported in part by the National Natural Science Foundation of China(Nos. 61771368 and 61671347) and Young Elite Scientists Sponsorship Program by CAST (2016QNRC001).