This paper discusses the stochastic and strategic control of 60 GHz millimeterwave (mmWave) wireless transmission for distributed and mobile virtual reality (VR) applications. In VR scenarios, establishing wireless connection between VR datacenter (called
As actively discussed nowadays, virtual reality (VR) or augmented reality (AR) applications have received a lot of attention by industry and academia research organizations [
For massive highvolume and highdefinition multimedia contents delivery, millimeterwave (mmWave) wireless communication technologies are widely discussed nowadays [
In this paper, the 60 GHz wireless channel is explored for simultaneous largescale massive multimedia information delivery based on following reasons:
Based on the 60 GHz wireless communication technologies, this paper proposes a strategic and stochastic queue control algorithm to minimize the timeaverage expected power consumption (which is equivalent to maximizing the timeaverage expected energyefficiency) subject to queue stabilization. The VRS calculates the amount of transmit power allocation for transmitting data (from the transmission queue in VRS) to its associated VRD. If the amount of transmit power allocation at VRS is quite high, more bits will be processed from the queue within the VRS. Then, the queue should be more stable whereas power (or energy) management is not efficient. On the other hand, if the amount of transmit power allocation is relatively small, the small number of bits will be processed from the transmission queue within the VRS. Processing insufficient number of bits results in queue overflows in the VRS queue, which is not allowed because it will lose VR information at the VRS. The VR information loss should induce users’ unsatisfactory experiences. Therefore, an energyefficient stochastic transmit power allocation algorithm is required to transmit bits with the concept of the joint optimization of
The last sections of this paper are as follows: the reference distributed VR network platforms is introduced in Section
Current VRDs support 360degree video applications to allow users to interact with digital environments and objects. For example, according to users’ head motions such as pitching (leaning forward/backward), yawing (rotating left/right), and rolling (spinning clockwise/counterclockwise), the stateoftheart VRDs offer corresponding video images to the users. Oculus GearVR [
However, unfortunately, it is hard to agree that current VRDs are providing the truly immersive VR experiences that have been an aspiration of many. That is because the truly immersive VR systems should have three essential features: quality, responsiveness, and mobility [
Extensive research efforts have been invested to overcome the limitations of the current VR systems, thereby meeting the aforesaid requirements. For example, Facebook has proposed the dynamic streaming technique to provide 6K video streaming service [
Nevertheless, the truly immersive VR systems do still have a major challenge, the highspeed VR network. As rising resolution of video applications including various parallaxes of each single image, the video applications require a lot of data and delivery of these experiences across the Internet presents the inevitable challenge on network (i.e., even 6K resolution used by the GearVR may be 20 times the size of 4K videos). We have searched on the most possible solutions and eventually determined that the mmWavebased network is the strongest candidate for the near future VR system.
Our proposed model of the VR system including mmWavebased VR network is described in Figure
Concept of the proposed VR system exploiting the mmWavebased VR network.
This section mathematically calculates the maximum speed (i.e., upper bound) of wireless data transmission over 60 GHz mmWave channels and eventually defines the quality of VR video streaming, through the following steps: (i) calculating the received signal strength at VRD, (ii) obtaining maximum wireless data transmission speed, and (iii) defining the quality of streaming. The maximum wireless data transmission speed will be derived with two possible ways: (i) using Shannon capacity equation and (ii) using the level of supportable modulation and coding scheme (MCS) defined in IEEE 802.11ad specification and its associated wireless data transmission speed.
The received signal strength in 60 GHz mmWave wireless channels that depends on distance between VRS and VRD (denoted by
According to the 60 GHz IEEE 802.11ad lineofsight (LOS) pathloss [
Based on the calculation result of the received signal strength in VRD, the interfering signals are added to the desired transmission through the main wireless link from VRS to VRD. Therefore, signaltointerference plus noise ratio (SINR) in a dB scale, denoted by
In (
Figure
Interference scenario with directional transmit antennas.
In order to obtain the maximum wireless data transmission speed, two possible methods may exist: (i) using Shannon capacity equation (refer to Section
Based on the SINR calculated in (
This subsection uses
IEEE 802.11ad singlecarrier MCS table [
Receiver  Selected MCS indices 

Sensitivity  (Data rates, unit: Mbps) 

MCS0 ( 

MCS1 ( 

MCS2 ( 

MCS3 ( 

MCS4 ( 

MCS6 ( 

MCS7 ( 

MCS8 ( 

MCS9 ( 

MCS10 ( 

MCS11 ( 

MCS12 ( 
In order to estimate the quality of the wireless video streaming that depends on the derived maximum wireless data transmission speed, we use the model presented in [
For each wireless transmission from VRS to VRD, if the transmission queue in VRS is almost empty, the transmission algorithm should not need to allocate a lot of transmit power in order to transmit more bits from the queue. Then, the algorithm will allocate relatively little amount of powers into the transmitter in order to work in the energyefficient manner. On the other hand, if the transmission queue in VRS is almost occupied by VR data information (almost in the overflow situations), the transmission algorithm should allocate relatively large amount of powers into the transmitter in order to avoid the queueoverflow situations. Therefore, this section proposes a stochastic optimization framework that works for the minimization of timeaverage expected power consumption (which is equivalent to the maximization of timeaverage expected energyefficiency), while preserving queue stabilization that depends on the queuebacklog sizes in each unit time.
For each VRS
In order to formulate
Note that
The mathematical program to minimize the summation of the timeaverage expected power consumption (which is obviously equivalent to the maximization of the summation of timeaverage expected energyefficiency) is as follows:
Note the objective function in our stochastic optimization framework has the following two constraints: (i) a constraint for queue rate stability and (ii) a constraint for discretized power allocation due to radio frequency (RF) hardware design limitations (i.e., it is impossible to allocation realnumber scaled transmit powers). The first can be expressed as
The constraint for discretized power allocation can be expressed as
Now, let us introduce a new variable
The proposed algorithm involves minimizing a bound on
Parameters;
(i)
(ii)
(iii)
(iv)
(v)
(vi)
//
(i) Observes
(ii) Finds stochastic optimal power allocation
In (
According to the fact that
In (
From this given (
The entire stochastic procedure is also described in Algorithm
This section consists of (i) simulation parameter settings (refer to Section
For evaluating the performance of our proposed queuestable timeaverage expected power consumption minimization algorithm, the following simulation parameters are used:
Transmit antenna gain:
Transmit power allocation set
The number of interfering sources: 3.
For the simulation study in this paper, we have three different simulation results; those are conducted with three different
Queue dynamics and energy consumption behaviors for our proposed stochastic algorithm with various
Queue dynamics with
Energy consumption with
Queue dynamics with
Energy consumption with
Queue dynamics with
Energy consumption with
In this section, we tracked the queue dynamics and energy consumption behaviors as plotted in Figure
In Figures
Average energy consumption and queue stability point in each time slot with various





Energy consumption (unit: milliWatt) 



Queue stability point (unit: bits)  ≈1.5 × 
≈0.5 × 
≈3 × 
As shown in Table
Notice that our considering stochastic network optimization and control theory formulated in (
This paper proposes a strategic stochastic control algorithm that is for the minimization of timeaverage expected power consumption subject to queue stability in distributed VR network platforms. In distributed VR network platforms, the VRS contains VR contents that should be transmitted to the headmounted VRD. For the wireless transmission, 60 GHz mmWave wireless communication technologies are used owing to their highspeed massive data transmission (i.e., multiGbps data speed). On top of this 60 GHz wireless link from VRS to its associated VRD, a stochastic queuestable control algorithm is proposed to minimize the timeaverage expected power consumption. The VRS calculates the amount of transmit power allocation for transmitting bits from VRS to its associated VRD. If the amount of transmit power allocation at VRS is quite high, more bits will be processed from the queue. This control eventually stabilizes the queues whereas power (or energy) management is not optimal. On the other hand, the small number of bits will be processed from the VRS queue if the amount of transmit power allocation is not enough. Then the VRS queue should be unstabilized, which should introduce the queue overflows in the VRS. Therefore, an energyefficient stochastic transmit power control algorithm is necessary to transmit bits from the VRS queue under the design rationale of the joint optimization of
As one of major future research directions, realistic and automatic
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Research Foundation of Korea (NRF Korea) under Grant 2016R1C1B1015406 and ETRI grant funded by the Korean government (16ZS1210, NZV