M2M energy saving strategy in 5G millimeter wave system

Machine to Machine technology has a broad application prospect in the 5G network, but there is a bottleneck in the energy consumption of intelligent devices powered by the battery. In this paper, we study the energy-saving strategy in the 5G millimeter-wave system. Firstly, a Discontinuous Reception scheme based on Beam Measurement (BM-DRX) is proposed to avoid unnecessary beamforming. Secondly, we modified the frame structure and optimized the beamforming to short the beamforming time and save the power consumption. Finally, based on the European Telecommunications Standards Institute data model, we used the semi-Markov process to analyze the BM-DRX by considering the beam misalignment events as a Poisson distribution. Simulation results show that the proposed scheme can not only meet the delay performance, but also save the energy consumption of the system.


Background
In the Fifth Generation (5G) communication networks, some strategies are used to satisfy growing data capacity, data rate, and the best quality of service requirements. Firstly, to improve the data bandwidth and connection efficiency, achieve better download and upload speed with less latency, bands are specified in two Frequency Ranges (FR) in 3GPP Release 15. FR1 ranges from 450 to 6000 MHz, known as cmWave. FR2 ranges from 24,250 to 52,600 MHz, known as mmWave. Secondly, some related technologies to 5G are also proposed. Reference [1] proposed an integrated multipleinput multiple-output (MIMO) antenna solution for Long Term Evolution (LTE) and Millimeter-Wave (mm-wave) 5G wireless communication services.
Moreover, some technology such as beamforming is used in the 5G network. References [2,3] show that the millime- ter wave spectrum can support high-speed data rate by using beamforming technology with multi-antenna arrays. Efficient beamforming is helpful to improve spectrum efficiency, reduce system interference and enhance wireless communication security.
At the same time, with the rapid development of electronics and computers, intelligent devices can fulfill the requirement of higher bandwidth service [4]. M2M (Machine to Machine) communication is widely used in the 5G Internet of Things (IoT) [5], including the fields of industrial vehicle network, automation, smart grid, telemedicine, etc. With the exponential growth of the number of M2M intelligent devices, the data flow is expanding rapidly. The increasing of M2M devices will not only affect Access Networks (ANs), but also Core Networks (CNs). Because most of the devices are powered by batteries, such as intelligent wearable devices, UAVs (unmanned aerial vehicles) [6], intelligent electric meters, power-saving is a crucial issue for the 5G M2M network. Thus, increasing energy efficiency in mobile networks will reduce the costs of capital and operational expenditures. It makes energy efficiency extremely important.

Problem statement
There are many energy-saving technologies for 5G/B5G wireless networks. Some recent researches on green 5G/B5G technology and communication energy harvest are reviewed in reference [7][8][9]. Some new technologies are also discussed related to energy-saving, including User-Centric Design, intelligent devices On/Off switching, interference management, power control, etc. Discontinuous Reception (DRX) is also a kind of energy-saving scheme in the 4G network, which allows user equipment (UE) to make the signaling free transitions between sleep and awakened states. Considering 3GPP supports DRX integration [10], Reference [11] proposed to apply the beam-aware Discontinuous Reception (DRX) mechanism to manage the power consumption and temperature of UE simultaneously, so we study DRX related energy-saving strategy of M2M in 5G Millimeter-Wave System, combing with beamforming and optimization of 5G frame structure.
In this paper, we focus on the following four aspects to improve the energy and delay performance of M2M communication in the 5G network.
1. Beam strategy. In the multi-beam millimeter-wave scenario, beamforming is unnecessary after each DRX sleep process. The user device measures the current beam pair's level after DRX sleep to decide whether to beamform. Specifically, a threshold value of beam pair level is set in advance. If the measured level is higher than it, the beam is aligned, and the intelligent device can effectively decode PDCCH data and signaling. Otherwise, the beam is out of alignment, and beamforming is required. 2. Optimize 5G frame structure. A flexible 5G frame structure can realize the balance of spectrum efficiency, air interface delay, and reliability [12,13]. In this paper, the short frame structure is adopted to reduce the time of beamforming and listening to PDDCH channel, so as to reduce power consumption and delay. 3. Optimize DRX configuration. Based on LTE-DRX, two sleep-ready timers are set for different sleep states (light sleep and deep sleep). In the sleep state of DRX, after a successful beamforming, it does not turn into the active state, but enters the sleep-ready state. When the sleepready timer expires with beam alignment and no data arrives, then go to sleep state. It can reduce the impact of the beam misalignment in the case of no data arrival, and turn into the sleep state as frequently as possible to save energy. 4. Select data model. In this paper, the ETSI data model [14] is adopted, and the Poisson process of beam misalignment events is defined to make the model closer to reality.
A Semi-Markov model of eight states is established to evaluate the impact of beam misalignment events on the performance of the whole DRX scheme.

Paper organization
The rest of the paper is organized as follows: In Sect. 2, we reviewed some related works about M2M energysaving technology, include DRX related methods. In Sect. 3, we described the multi-beam sleep scheme include the system model, beam and frame structure, and the beam measurement-based DRX scheme (BM-DRX). The details of the analytical model of BM-DRX and the procedures of protocol execution are presented in Sect. 4. The simulation research and performance evaluation of the proposed protocol are presented in Sect. 5. Finally, the concluding remarks and future work are presented in Sect. 6. Table 1 lists the symbols and notations used in this paper.

Energy-saving technology
There are many energy-saving methods in M2M systems by considering different protocol layers. In the physics layer, power control is one of the important effect factors. In [15], a method named Energy Transfer and Transmission Adaptation (ENTRADA) is proposed to determine the optimal transmission power of users. Suppose that each user is associated with a utility function that represents its QoS requirements. The distributed power control problem is defined as the utility maximization problem of each user to determine the optimal transmission power of the user and meet their QoS requirements. A wireless powered communication networking (WPCN) technology is discussed in [16], where the battery of wireless communication devices can be remotely replenished by microwave wireless power transfer (WPT) technology. An overview of the key networking structures and performance-enhancing techniques is provided to build an efficient WPCN, and points out new and challenging future research directions for WPCN. Based on the wireless powered communication (WPC) technique, an energy-aware clustering and resource management framework are proposed to extend the operation time of the whole M2M network [17].
In the data link layer, many energy-saving methods are proposed. Reference [18] studies the energy-saving design by considering the quality of service (QoS) in the long-term evolution (LTE) network for M2M/H2H coexistence scenario. The problem of resource allocation is described as the maximization of bit capacity per joule based on effective capacity under statistical QoS configuration. An implicit weed optimization (IWO) algorithm is proposed to satisfy energy efficiency and QoS requirements. A MAC layer scheduling method combining with beam awareness is proposed in [19] by considering the interval between channel measurement and data transmission. The BS processes the scheduling according to the result of channel measurement instead of every slot. The simulation results and mathematical expression demonstrate that the beam-aware media access control (MAC) framework improves throughput under power constraints. A new scheduling algorithm is also proposed in [20] to improve battery life and ensure better spectrum efficiency by reducing energy consumption. Based on Non-orthogonal Multiple Access (NOMA) technology [21], proposed a novel energy-efficient resource allocation algorithm to optimize the energy efficiency of M2M communication. Reference [22] considered a Wireless sensor network with aggregated nodes and proposed an optimal partial aggregation technique for tradeoff the compromise of energy and delay.

DRX methods and beam alignment
Since the mobile user device is significantly restricted by the battery capacity, most existing wireless mobile networks, such the 3G and 4G mobile communication, employ discontinuous reception (DRX) to conserve the power of mobile stations (MSs) [10,23]. In [24], DRX mechanism is applied to the IoT gateway which reduced the power consumption of IoT gateway and improved energy efficiency. If the DRX scheme is directly moved to the 5G environment, especially the millimeter-wave environment, it will get an adverse effect on DRX performance [25,26]. Data needs to be transmitted under the successful pairing of the beam pairs of the transmitter and the receiver by the beamforming, which makes the sleep time in the DRX scheme shorter and the supervision time of the PDCCH (Physical Downlink Control Channel) downlink channel longer.
Many papers focus on the research of beam alignment and misalignment. Reference [27] describes the relationship between the moving speed of intelligent devices and the probability of beam misalignment in the DRX state. When the moving speed of an intelligent device is 30 km/h, the short sleep cycle interval of DRX will be 100 ms, the probability of beam misalignment is 0.1. When the short sleep cycle interval of DRX is 300 ms, the probability of beam misalignment is less than 0.3. When the speed of the intelligent devices is 90 km/h, the probability of beam misalignment is about 0.22 and 0.47 for the same DRX configuration. Therefore, under the DRX scheme, when the intelligent device moves slowly and in the statics state, the probability of beam misalignment is very low. In [28], directional-discontinuous reception (D-DRX) is proposed for millimeter-wave enabled 5G communications, to address alignment of directional beams between base station (BS) and intelligent user devices (UD) after a sleep cycle. When the best beam pair is searched, the beam search process is stopped instead of the full beam search, and the energy consumption is reduced by 10%.
An M2M paging scheme combined with DRX is proposed to reduce the network load and signaling overhead between BS and UD in the 5G network [29] with less power consumption. In [30], the interoperable hybrid H-DRX scheme is proposed in the 4G/5G core network. When a 4G core network finds 5G data arriving, it sends beamforming prompt information to 5G intelligent devices, to reduce unnecessary beamforming and save power consumption. Because these devices need to connect to both 4G and 5G networks, they will also increase power consumption.
Based on the study of [28], an extended HD-DRX scheme is proposed in [31], which adds a single active state of a packet between the states of sleep and awake. In this state, user devices can receive packets during sleep within a certain threshold without switching to the active state to save power. Therefore, the user devices can directly receive short burst packets without beam searching procedure, thus reducing the beam searching time. In [32], a DRX scheme of beam sensing in M2M scenario is proposed. When the best matched beam pair is searched in DRX state, the beam pair is always used for data transmission, while other unauthorized beams are not used. Although this scheme can reduce the time of beamforming, it has poor flexibility without considering the changes of the surrounding environment. In [33,34], a dynamic beam-aware DRX scheme is proposed, which could be applied along with dynamic mmWave beam configuration for better energy efficiency.
In [35], a fast beam tracking DRX scheme is proposed in the UAV scenario with a D2D structure, focusing on analyzing system performance from sleep rate and average packet delay. In [36], based on the DRX scheme of 5G, beam training and feedback are adopted, which points out that frequent beamforming in the DRX state is unnecessary. They use Poisson modeling without considering the self-similarity of the data. The simulation shows that the energy-saving effect is

System model
We consider a system shown in Fig. 1 which consists of 5G base station (BS) with M beams and many small intelligent user devices (UD) with N beams, including sensors and actuators which are connected through the network. The network provides communication means for sending and receiving data in a periodic form of M2M-based communication. At one moment, only one transmit and receive beam pair can be established between BS and a UD. The purpose of beamforming is to find the best beam pair and establish the connection between the BS and UDs.
According to Friis free space path loss, RF coverage distance is inversely proportional to the carrier frequency square. In the 5G network, intelligent devices, base station gains, RF bandwidth, coding, and modulation techniques determine cell coverage. In our paper, the path loss can be estimated according to the specific channel model in reference [37]. Compared with 3G and 4G, 5G uses millimeterwave works in a higher frequency band, so it needs to overcome huge path loss [38]. Fortunately, the millimeterwave antenna array can focus narrow beam and propagate towards the target direction by using beamforming technology. It can reduce path loss and reduce interference [39,40].
As shown in Fig. 1, UD performs a full beam search. It needs to search M * N beam pairs to find the best beam and transmit data with the best channel quality. To keep the beam alignment, a UD checks the channel status periodically on the given beam pair and appropriately changes the beam not to be misaligned.
There are many reasons for beam misalignment, such as the mobility of UD, the drastic changes of communication channels, and the collision due to competing millimeter-wave channels with other UD in beamforming.

Beam and frame structure
Reference [27] tells us that in the case of low mobility of UD, the probability of beam misalignment is very low in DRX state, and Reference [33] shows that frequent beamforming is unnecessary in DRX state. In our scheme, a level threshold T h needs to be set, which is the minimum level value to ensure the beam pairing and data transmission between BS and UD. In the DRX state, UD immediately measures the current beam pair after its sleep. If the beam pair level is greater than T h, UD sends a feedback to BS to establish the channel between the BS and UD. Otherwise, beamforming is required until the beam pair level is greater than T h, instead of full beam search. The beamforming time is related to the frame length L, which is at millisecond level in 5G standard. The time for full beam search is M * N * L and the average statistical time required for best beam search is M * N * L/2. Assuming that the threshold level T h is half of the best beam level, and the level of each beam pair is not equal to each other, the average time required for the beam search is M * N * L/4. 5G supports flexible frame structure. As expected for 5G communication networks [12], shorter frame size will be used. The proposed solution encompasses flexible multiplexing of users on a shared channel with dynamic adjustment of the transmission time interval (TTI) in coherence with the service requirements per link. It can optimize the fundamental trade-offs between spectral efficiency, latency, and reliability for each link, as well as the efficient machine-type communication support. The short frame structure can reduce the beam search time, save the power consumption of UD in DRX state, and reduce the delay caused by beamforming can also be reduced.
In this paper, we will consider different frame structures, which can adapt to different application scenarios. We assume that the number of beams and time slots in the frame structure of the 5G base station can access all intelligent devices in the cell, beam-forming after beam misalignment can find the beam pair to establish the connection of the uplink and downlink channels.

Beam measurement based DRX scheme (BM-DRX)
In this section, we propose a beam measurement based DRX scheme (BM-DRX). UD measures the current beam pair after its DRX sleep. If the measured value is greater than the threshold T h, beam can be thought as aligned and UD  Fig. 2, OFF state indicates that UD is asleep, and ON state indicates that UD is active. According to Fig. 2, the flow of BM-DRX scheme is as follows: • Step 1. Initialization stage of beamforming. Base station BS sends M beams, UD sends N beams, both sides search the best beam pair and establish wireless connection. • Step 2. Start the data transmission state, UD starts the inactive timer t i . If the beam pair is aligned and the inactive timer times out, no data is sent to UD, and then go to step 3. Otherwise start the inactive timer, and go to step 2; if the beam is not aligned, go to step 1. • Step 3. Enter DRX energy-saving state. The sleep-ready timer 1 is started, and UD will continue to listen to the channel. If the beam pair is aligned and the sleep-ready timer times out, and no data arrives at UD, UD will shut down the RF unit, and turn to the light sleep state, then go to step 4; otherwise, go to step 2. If the beam pair is not aligned before the sleep-ready timer 1 times out, go to step 1. Based on the above discussion, we will study following 3 DRX schemes. If the beamforming strategy is full beam search, we call it F-BM-DRX. If the beamforming strategy is best beam search, we call it B-BM-DRX. If the beamforming strategy is based on the beam threshold T h, we call it T-BM-DRX.
Based on Fig. 2, the algorithm of BM-DRX scheme is as follows: Algorithm of BM-DRX scheme Step  Inter-misalignment idle time,t α Exponential 1/α

BM-DRX and its analytical model
In the process of 5G M2M millimeter-wave communication, beam misalignment is inevitable. Poisson distribution is suitable for describing the number of random events occurring in unit time (or space), such as the number of machine failures, the number of natural disasters, the number of product defects, the number of accidents on the highway, etc. We know from reference [27] that under the DRX scheme, when the intelligent device moves slowly or in a static state, the probability of beam misalignment is very low. The beam misalignment rate is also the number of misalignments per unit of time, so the hypothesis that beam misalignment events are Poisson is reasonable. In order to analyze the influence of beam misalignment on DRX performance, we assume that the beam misalignment events follow the Poisson distribution with parameter α which represents the misalignment rate [36]. Then the time interval of beam misalignment event indicates that the beam is not misaligned, which obeys the exponential distribution, and the mean value is 1/α. The misalignment rate represents the number of random beam misalignment events per unit time. We use ETSI data model instead of simple Poisson distribution. Some parameters are shown in Table 2.
According to the algorithm of BM-DRX scheme, we propose an eight states mathematical analytic model based on a semi-Markov chain to describe the UD behavior below.
• S1, UD is in the active state; • S3, S8, UD enters the sleep-ready state, and listens for any incoming data; • S2, S5, S7, UD is in beamforming states, and sends feedback to BS; • S4, UD is in a light sleep state and periodically wakes up to listen for any incoming data; • S6, UD is in a deep sleep state and periodically wakes up to listen for any incoming data.

Stationary distribution
There are two situations of new packet call, one belongs to the current session process, and the other belongs to the beginning of the next session process. The number of packet calls obeys the memoryless geometric distribution. Packet data traffic consisting of packet service sessions is considered where each session comprises of one or more packet calls depending on the applications. The number of packet calls obeys the memoryless geometric distribution. When no data arrives at UD, the probability of interval t is is q 1 1/μ pc , and the probability of t i pc is q 2 1 − 1/μ pc [41] (Fig. 3) In state S1, UD is active. When no data arrives at UD, turn on the inactivity timer. Before the timeout of the inactivity timer, there are two possible events, i.e., beam misalignment and beam alignment. In the first event, the UD goes to state S2 (i.e., transition S1 → S2), and the transition probability is p 12 . In second event, if any data arrives, then transit to S1 with transition probability p 11 ; if no data arrives, the data interval may be a session interval or a packet call interval, then transit to S3 with transition probability p 13 . The transition probabilities can be calculated as: In state S3, before the timeout of sleep-ready timer, when the beam is misaligned, then transit to state S2 with transition probability p 32 . When the beam is aligned, if there is data arrival, then transit to S1 with a transition probability p 31 . Otherwise, transit to S4 with a transition probability p 34 . The analysis process of state S8 is the same as that of state S3.
The duration of timer 2 and timer 1 is t p , so the transition probabilities are as follows: In state S4, before timeout of the light sleep timer t s , when the beam is not aligned, it transits to state S5 with transition probability p 45 . When the beam is aligned, if there is data arrival, then transit to S1 with a transition probability p 41 ; Otherwise, transit to deep-sleeping S6 with a transition probability p 46 . The transition probabilities are as follows: p 46 (q 2 e −λ i pc t s + q 1 e −λ is t s )e −αt s (8) In state S6, before timeout of the deep sleep timer t l , when the beam is not aligned, it transits to state S7 with transition probability p 67 . When the beam is aligned, if there is data arrival, then transit to S1 with a transition probability p 61 . Otherwise, transit to sleep-ready state S3 with a transition probability p 63 . The transition probabilities are as follows: p 63 (q 2 e −λ i pc t l + q 1 e −λ is t l )e −αt l (11) In the beamforming states of S2, S5 and S7, if beam alignment is successful, then transit to sleep-ready states of S3 or S8 instead of S1, then listen to the channel, which helps to extend the sleep time. The transition probabilities are as follows: According to the above state transition probability matrix, the stationary distribution π i of each state can be obtained by using the following equation.

Energy model
The power consumption of UD depends on the average holding time of each Markov state. The longer the holding time of sleep state is, the lower the energy consumption of UD is. We use T i (i ∈ {1, 2 . . . . . . 8}) to express the holding time of the Markov chain state of DRX.The duration of T 1 in state S1 consists of two parts, the service time of μ p − 1 packets and the inactive time t * i t * i ≤ t i . t * i includes the time of beam-alignment and misalignment. So the average holding time of state S1 is In the state S3, T 3 includes the time of beam-alignment and misalignment, then The analysis method for T 8 of state S8 is the same as that for T 3 . We assume the duration of timer 1 and timer 2 are the same as t p , i.e.,E[ In the state of S4, T 4 is the sum of short cycles (t ds ) of UD. If timer t s expires and no data arrives, the light sleep period lasts for N s t s / t ds short cycles. Before t s timeout, the light sleep period lasts for N * si (N * si < N s ) short cycles due to arrival of downlink data or misalignment. Different transition probabilities p 41 and p 45 correspond to N * s1 and N * s5 respectively, therefore Since t i pc , t is and t α follow the memoryless exponential distribution, we can assume that N * s follows the geometric distribution with the mean value of 1 / p n . Therefore, The analysis of state S6 is similar to that o state S4.T 6 is the sum of the long cycles (t dl ) of UD. If timer t l times out and no data arrives, the deep sleep period lasts for N l t l / t dl long cycles. Before the timeout of t l , the deep sleep period lasts for N * l (N * l < N l ) long cycles due to arrival of downlink data or misalignment. Different transition probabilities p 61 and p 67 correspond to N * l1 and N * l7 respectively. Therefore, we can obtain the following equations.
States S2, S5 and S7 all represent the process from beam search to beam pairing success. t m mainly depends on the number of beam pairs and the algorithm of beam search and feedback.
We define the probability of DRX semi Markov process in state S4 and S6 as the energy-saving parameter P s . Since each DRX cycle contains a fixed monitoring cycle τ , the effective sleep time of each DRX cycle is t ds − τ or t dl − τ . Then, E[T 4 ] and E[T 6 ] can be written as follows: According to the above analysis, we can obtain the energysaving parameter of UD as follows:

Delay model
The BM-DRX sleep scheme will inevitably lead to a certain transmission delay, because some data must save at BS cache before sending to UD. Assume UD can service the arrived data timely in active state, the delay mainly results in the state of light-sleep, deep-sleep and beamforming. The probability of these three states is P L4 , P D6 and P B j respectively, therefore We use d i (i{2, 4, 5, 6, 7}) to express the delay corresponding to the Markov chain at state S i of DRX, then the total average delay is In state S4, the delay mainly depends on whether beam is aligned in this state. If beam is aligned, UD will find the arrival of data after sending feedback ACK to BS. Assuming that the arrived data of UD in the sleep state obeys evendistributed, the delay in alignment state is: If the misalignment occurs in state S4, then the delay will be increased. The data will be detected by UD after successful beamforming and sending feedback ACK to BS. If the beam misalignment occurs in the feedback stage after beamforming, it needs to go through N times of beamforming to the cyclic state of transmitting feedback. The parameter n obeys the memoryless geometric distribution, and the probability is p n e −αt f [36]. Therefore, the delay in misalignment state is: In summary, the total average delay in the S4 state is Similar to delay analysis in S6 state, the average delay in the S4 state can be estimated as: In state S2, if beam-alignment occurs in feedback state, the delay is (t b + t f )/2. If the beam misalignment occurs in the feedback state, the analysis is the same as S4. Therefore, We can use the same methods to analyze delay in state S5, S7 and state S2.

Simulation and analysis
In this paper, Matlab is used for numerical simulation, and the simulation parameters are set as follows: λ is 1/2200, λ i pc 1/30 ,λ i p 10,μ pc 5,μ p 25,μ α 10,t i 20 ms. 5G flexible frame structure can be adapted to different applications. In order to be more realistic, we consider the frame structure parameters of 5G NS-3 [42]. The frame structure length are L 10 ms, 6 ms and 4 ms. The corresponding sub-frame TTIs are 1 ms, 0.6 ms, 0.4 ms. N s N l 10,t f t m L, t i 20 ms, τ 4 * L, t s t so + i*stepsize,t l t lo + i*stepsize, step size 10 ms, t so 300 ms, t lo 400 ms. Transmitting beam of BS is M 16 (half power beamwidth 7°), and transmitting beam of UD is N 8 (half power beamwidth 15°). The number of iterations of the simulation is 100, and the duration of each simulation is 10 6 ms. The length of the light sleep timer t l The length of the deep sleep timer τ The period when UD wakes up from sleep in each DRX cycle t dsc The period when UD sleeps in each light sleep DRX cycle t dlc The period when UD sleeps in each deep sleep DRX cycle t ds The period consists of τ and t dsc t dl The period consists of τ and t dlc N s The number of light sleep DRX cycles N l The number of deep sleep DRX cycles Figure 4 shows the relationship between sleep-ready timer t P and energy-saving factor. On the same misalignment rate, the larger the sleep cycle (t ds or t dl ) is, the longer the sleep time is, and the better the energy-saving effect is. Under the same conditions, the energy-saving effect of T-BM-DRX is the best, the energy-saving performance of B-BM-DRX is the second, and that of F-BM-DRX is the worst. With the increase of t P , the energy-saving effect is almost the same. Figure 5 shows the effect of beam misalignment rate on DRX energy-saving performance under three different BM-DRX parameter settings. The energy-saving effect of various DRX schemes decreases with the increase of beam misalignment. Under the same parameter settings, the energy-saving factor of F-BM-DRX decreases sharply with the increase of misalignment rate, while that of B-BM-DRX and T-BM-DRX decreases slowly. The energy performance of the scheme proposed in reference [36] is similar to that of F-BM-DRX. Although the beam misalignment is considered, the beam optimization strategy is not adopted, and a fixed 300 ms is used as the beam search time, resulting in low energy efficiency.
Moreover, only a fixed frame length (10 ms) is adopted in [34] and [36], and the influence of the frame length on energysaving performance is not considered. In Fig. 5, we compared these schemes with different frame length (4 ms and 10 ms), and the simulation results show that the energy-saving performance of BM-DRX with short frame is better than that of BM-DRX with long frame. Compared with BM-DRX with frame length 10 ms, the energy-saving effect of F-BM-DRX with frame length 4 ms is improved by at least 10%. The greater the misalignment rate is, the more significant the improvement in energy-saving effect is. T-BM-DRX frame length 4 ms has the best energy-saving performance, and the  Effects of beam misalignment rate on energy-saving energy-saving parameter is above 92%. This is because the shorter the frame length is, the shorter the beam search and feedback time, so the energy efficiency is improved. Because 5G standard supports flexible frame structure, our scheme is meaningful in practical applications. Figure 6 shows the effect of long and short cycle (t ds and t dl ) in two sleep states on energy-saving performance of BM-DRX scheme. Under the same parameter settings, the energy-saving effect of BM-DRX is more significant with the increase of the length of long and short cycle. The energysaving effect of BM-DRX with short frame is better than that of BM-DRX with long frame. When α 0.001, short frame length L 4 ms, t ds is greater than 300 ms and t dl is greater than 400 ms, the energy-saving effect of T-BM-DRX and B-BM-DRX is above 90%. Figure 7 shows the relationship between delay and misalignment rate in the BM-DRX scheme. The delay of BM-DRX increases with the increase of the misalignment rate. It is due to the beam misalignment leads to too much beamforming, and the data arriving at UD can only be found in the sleep state after the successful beamforming, which makes the delay longer. Under the same parameter settings, the delay performance of T-BM-DRX is the best, B-BM-DRX is the second, and F-BM-DRX is the worst.
The main causes of delay are sleep, beamforming, and feedback. In references [31] and [43], beamforming is performed after each sleep state, resulting in the increase of time delay. In our scheme, the current beam pair is measured after each sleep state (the measurement time is the length of a frame) to reduce the number of beam searches. In addition, the delay performance of BM-DRX with a short frame structure is better than that of BM-DRX with a long frame structure. Because the short frame structure can reduce the beam measurement, beamforming, and feedback time, it is very beneficial to reduce the delay. Figure 8 shows the effect of long and short cycle sleep intervals (t ds and t dl ) in two sleep states on the delay performance of BM-DRX scheme. Under the same parameter settings, the time delay of BM-DRX increases with the increase of the length of long and short cycle. Using short frame structure, BM-DRX shows better delay performance, where the short frame improves the delay performance of F-BM-DRX most obviously.
In summary, we have the following conclusions, 1. The sleep-ready timer can make UD go to sleep quickly to save energy. 2. Under the same conditions, T-BM-DRX has the best energy-saving and delay effect, B-BM-DRX is the second, and F-BM-DRX is the worst. 3. Beam misalignment has a negative impact on the delay and energy-saving of the BM-DRX scheme. At a low beam misalignment rate, adopting a short frame can reduce the impact of beam misalignment and improve the performance of the DRX system. 4. Short frame can improve the delay and energy-saving performance of the system. Especially in the F-BM-DRX scheme, the energy-saving effect is very significant.

5.
With the increase of long or short cycles, energy is saved but a delay is prolonged in BM-DRX. Therefore, it is necessary to select parameters to find a tradeoff between Fig. 8 Effects of t ds and t dl on delay delay and energy-saving, according to the specific service QoS requirements. 6. With low beam misalignment, the T-BM-DRX scheme with short frame L 4 ms can achieve more than 92% energy-saving effect, and the delay can be less than 300 ms.

Conclusion
Except the ultra-low delay requirements in some scenarios such as the Internet of vehicles and UAVs, the millisecond delay in 5G can meet the QoS requirements of the vast number of M2M Internet of things services. In our proposed scheme, unnecessary beamforming is avoided, and several methods are proposed to reduce the time of beamforming and the adverse effects caused by beam misalignment. In the case of low beam misalignment rate, our scheme can effectively improve the delay and energy-saving performance of DRX. 5G short frame structure can reduce beam search time, and UD power consumption in DRX state and delay caused by beamforming can also be reduced. When α 0.001, short frame length L 4 ms, t ds 600 ms, t dl 700 ms, the energy-saving effect of T-BM-DRX can achieve about 96% energy-saving effect, and the delay can be less than 400 ms. Short frame structure with short time slot is suitable for URLLC (Ultra Reliable and Low Latency Communication). However, in the M2M scenario, because UD competes to access BS channel, the short frame structure not only optimizes the flexibility of M2M communication throughput, but also affects multi-user UD access. UD competes with BS channel (beam) and causes beam misalignment, thus the system delay is increased. In the future, we will further study how to find the best short frame structure to obtain better system performance.