Deep Learning for Intelligent Wireless MAC: Exploiting Real Data Sampled on 2.4GHz Frequency Band

06/18/2021 ∙ by Jiantao Xin, et al. ∙ Shenzhen University 0

The existing medium access control (MAC) protocol of Wi-Fi networks (i.e., CSMA/CA) suffers from poor performance in large networks due to its incapability of handling transmission collisions. This drawback dramatically reduces the spectrum efficiency of Wi-Fi networks. To cope with this issue, we investigate a deep-learning (DL) based intelligent wireless MAC protocol, referred to as DL-MAC, to improve the spectrum efficiency of Wi-Fi networks. The goal of DL-MAC is to enable not only intelligent channel access, but also intelligent rate adaption to increase the throughput. Notably, our DL-MAC protocol is designed for the 2.4GHz frequency band and exploits the real wireless data sampled from actual environments that consist of many working devices. We design a deep neural network (DNN) that is trained using the sampled real data after data processing and exploit the trained DNN to implement our DL-MAC. The experimental results demonstrate that the DL-MAC protocol can achieve high throughput than CSMA/CA channel access and traditional rate adaptions.

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I Introduction

The rapid increase of Wi-Fi devices poses a huge challenge to the performance of Wi-Fi networks. However, the performances of Wi-Fi networks are severely limited by the current Industrial, Scientific, and Medical (ISM) frequency bands that are already extremely crowded. To improve the performances of Wi-Fi networks, it is required to increase the spectrum efficiency of Wi-Fi networks.

An efficient medium access control (MAC) protocol is essential to improve the spectrum efficiency of Wi-Fi networks. The main functionality of a wireless MAC protocol needs to determine when to access the allocated spectrum channels and how to match the transmission rate with the physical quality of the underlying spectrum channel. Therefore, a high-performance and robust MAC protocol not only allows devices to fairly, orderly, and efficiently access spectrum but also flexibly adapt to changes its transmission rate in the wireless environment. However, to design such a high-performance and robust MAC for Wi-Fi networks is quite challenging. For example, it is known that the classic Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) MAC protocol of Wi-Fi cannot handle transmission collisions among a large number of Wi-Fi devices so that the performance of CSMA/CA in Wi-Fi networks that contain many devices extremely deteriorates [1]. Moreover, on the 2.4GHz ISM frequency band, there are many devices from other wireless networks, (e.g., Bluetooth (BT/BLE), ZigBee, LTE-U) that heavily interfere with Wi-Fi devices; however, the CSMA/CA MAC protocol of Wi-Fi networks cannot operate normally with the MAC protocols of other networks [3, 9]. As a result, the current CSMA/CA MAC protocol of Wi-Fi networks no longer able to satisfy the requirement of highly efficient and robust channel access performances.

There exist many investigations that aim at improving the MAC protocol of Wi-Fi networks. The methods proposed in [18, 17, 15, 2] improve the backoff mechanism or the adaptation of contention windows size to achieve performance improvements for CSMA/CA. Recently, learning-based approaches are applied to design or improve MACs for Wi-Fi/Wi-Fi-like wireless networks. For example, learning-based approaches are used to adjust the parameters of CSMA/CA in works [5, 6] and enable channel access prediction in works [22, 21, 24, 23]. Moreover, works [14, 4] proposed learning-based rata adaption approaches for wireless works. However, we point out that without considering many practical issues, all these works that use learning approaches to improve MAC simplify the target problem and model. For example, works [24, 23]

assumed that the learning-based MAC can observe perfect information about the channel states at the MAC layer, i.e., the channel state is a binary variable with two possible values of idle and occupied. Moreover, the solutions proposed in these works all are verified using simulations with man-made data. Therefore, it is not clear whether these learning-based MACs can achieve real performance improvements in practical wireless networks. To make learning-based MAC evolve towards practical uses, we aim to design a learning-based MAC using the wireless data sampled on the 2.4GHz band from real wireless environments.

The contributions of this work can be summarized as follows. First, we design a new intelligent wireless MAC protocol based on deep learning (DL), referred to as DL-MAC. The most important technical contribution of this work is that we design our DL-MAC for the actual 2.4GHz frequency band and exploit it to improve the spectrum efficiency of real wireless networks working on this frequency band. We design a deep neural network (DNN) to implement DL-MAC. We train the DNN using the real wireless data sampled on the 2.4GHz frequency band from Shenzhen University and Shenzhen Baoan International Airport. Rather than directly sending the raw data to the DNN for use, we preprocess the data so that we can use the sampled wireless data in a supervised learning framework. The trained DNN can take the previous data as the inputs and decide whether the device can access the spectrum channel next time. Moreover, besides the channel access, we also incorporate rate adaption into our DL-MAC, which enables the joint channel access and rate adaption to further provide an additional gain in the spectrum utilization. Finally, we experimentally verify the performance of our proposed DL-MAC protocol using the sampled real data. Benchmarked to the CSMA/CA channel access and the traditional rate adaption schemes

[12, 7], the experimental results demonstrate that our designed DL-MAC protocol can enable more efficient channel access with higher transmission rates.

Ii System Descriptions

We consider a Wi-Fi network working on the 2.4GHz ISM frequency band. The Wi-Fi network consists of a group of traditional Wi-Fi devices and one AI device. The traditional Wi-Fi devices employ the CSMA/CA MAC protocol to access the channel on the 2.4GHz ISM frequency band; the AI device employs our DL-MAC to coexist with the traditional Wi-Fi devices on the same channel. Besides these devices of the Wi-Fi network, there also may exist many other devices operating under other different wireless protocols, such as BT/BLE, ZigBee, LTE-U. These wireless devices employ their own MAC protocol to access the 2.4GHz ISM band. Since the MAC protocols of the different networks are not compatible with the CSMA/CA MAC of the Wi-Fi network, the wireless devices of other different networks usually cause interference to the traditional Wi-Fi devices and the AI device. Fig. 1 illustrates the wireless scenario of the 2.4GHz ISM band under our consideration. In the following, we briefly talk about the CSMA/CA MAC protocol of Wi-Fi networks and rate adaptation mechanism.

Fig. 1: The wireless scenario of the 2.4GHz ISM band where many devices under different wireless protocols coexist to use the same band.

Ii-a Csma/ca Mac

The basic principle behind CSMA/CA is the “listen before transmit” [8]

. Before each packet transmission, the node senses the channel. If the channel is sensed idle for a period of Distributed Inter-frame Spacing (DIFS), the packet will be transmitted; if the channel is sensed occupied, the node keeps silent and listens to the channel until the channel is sensed idle for another DIFS period. Specifically, after the channel is sensed occupied, the node generates a random backoff interval before transmitting the packet. The random backoff not only minimizes the possible collisions of the probability with packets transmitted by other nodes but also provides fairness in competing channels among nodes.

CSMA/CA adopts an exponential backoff scheme. That is, the backoff interval is generated uniformly from the range of , where the contention window that is determined by the number of failed transmissions for the packet. The contention window is initialized as a minimum contention window at each packet’s first transmission, and is doubled after each failed transmission. For each failed transmission, the contention window is doubled until reaches a maximum value , where is the maximum backoff exponent and represents the upper limit on the number of the backoff for transmission attempts. During the backoff phase, the counter is decreased by one each time slot only if the channel is sensed idle, until the counter decreases to zero a packet transmits immediately. When the channel is sensed occupied by other nodes during the backoff period, the backoff counter is frozen and reactivates after the channel is sensed idle again for a DIFS period.

The above CSMA/CA MAC is unable to coordinate the channel access by a large number of devices, due to that the back-off time is greatly increased by transmission collisions [1].

Ii-B Rate Adaptation

Besides the channel access mechanism of MAC, rate adaptation (RA) [12, 7] is another important mechanism that determines the spectrum efficiency of Wi-Fi networks. In this work, we only consider selecting modulation and coding scheme (MCS) to realize RA. Other factors such as changing channel bandwidth, the number of spatial streams will be considered in future work.

MCS Index Modulation
Coding
Rate
Rate
(Mbps)
0 BPSK 1/2 6.5
1 QPSK 1/2 13
2 QPSK 3/4 19.5
3 16-QAM 1/2 26
4 16-QAM 3/4 39
5 64-QAM 2/3 52
6 64-QAM 3/4 58.5
7 64-QAM 5/6 65
8 256-QAM 3/4 78
TABLE I: THE RATES OF MCSS FOR A SINGLE SPATIAL STREAM OVER A MANDATORY 20MHZ CHANNE IN 802.11AC.

In the following, we present the Intel Iwl-Mvm-Rs algorithm that is widely used for the MCS selection in Wi-Fi networks. In Wi-Fi, there are 9 MCSs that are indexed in ascending order according to their transmission rates, as shown in Table I. Table I shows the MCSs defined in the 802.11ac standard and their corresponding transmission rates of a single spatial stream over a mandatory 20MHz channel. The algorithm has three decisions for selecting the MCS that will be used in the next packet transmission, i.e., increasing the MCS index, decreasing the MCS index, and maintaining the current MCS index. The algorithm begins with the lowest MCS index, and the operation of MCS selection is made based on a comparison between the measured throughputs of the current MCS and the adjacent MCSs. The measured throughput for each MCS is obtained by multiplying the success ratio of packet transmissions with the theoretical throughput when using this MCS. The theoretical throughputs of MCSs had been calculated and hardcoded into the system. The success ratio is calculated from the last 62 packet transmissions using this MCS, and at least 8 successful transmissions or 3 failed transmissions are required. The detailed implementation of MCS selection in the Intel Iwl-Mvm-Rs algorithm is as follows and can be found in [7].

The Intel Iwl-Mvm-Rs algorithm begins with the lowest MCS index for transmission.

(1) If the measured throughput of the current MCS is zero, or the successful ratio of the current MCS is less than 15%, the algorithm decreases the MCS index;

(2) Elseif, the measured throughput of the current MCS (a) is better than the measured throughput of the previous adjacent MCS index, or unknown the measured throughput of the next adjacent MCS index; (b) is worse than the measured throughput of the next adjacent MCS index; (c) knows neither the measured throughputs of the previous adjacent MCS index nor the measured throughputs of the next MCS indices, the algorithm increases the MCS index;

(3) Elseif, the measured throughput of the current MCS is better than both of the measured throughput of the previous and next adjacent MCS, the algorithm maintains the current MCS index;

(4) Elseif, if the success ratio of this MCS is less than 85%, and the throughput of the previous adjacent MCS index is better than the current measured throughput, theoretically, and if the measured throughput of the previous adjacent MCS index is better or unknown, the algorithm decreases the MCS index;

(5) Else, the success ratio of this MCS is larger than 85%, then the algorithm maintains this MCS index.

The rate adaptation mechanisms of the Intel Iwl-Mvm-Rs algorithm will be used as one of the benchmarks to evaluate the performance of our DL-MAC algorithm.

Iii Proposed Deep Learning-Based Mac

This section presents the design details of DL-MAC. We first propose the data collection and data processing, which are key steps for our DL-MAC. Then, we present the DNN model and how to use the pre-trained DNN model to implement our DL-MAC protocol. Finally, we propose the benchmark with the optimal transmission rate to compare the performance of DL-MAC.

Iii-a Data Collection and Processing

Iii-A1 Raw data collection

Since the signal-to-interference-plus-noise ratio (SINR) is a good indicator of the wireless channel quality, it can be used as evidence for the channel access and MCS selection over the channel. In this work, we adopt an accessible link metric, i.e., the received signal strength indicator (RSSI) that can be served as a proxy for the real SINR. We measure and capture RSSI values on the 2.4 GHz frequency band using the spectrum analysis function of Ellisys Bluetooth Vanguard (BV1). The available 2.4GHz frequency band used by 802.11 Wi-Fi networks in Europe is from 2.401GHz to 2.483GHz [19], which can be divided into N=83 sub-bands each with a bandwidth of 1MHz. We denote the nth 1MHz sub-band by

(1)

where .

We can collect the raw data by sampling the RSSI on each sub-band with an equal sampling interval for a certain sampling duration. When we sample the RSSI on each of the sub-bands, we set the sampling interval to for a sampling duration that consists RSSI samples. The all data of the sampled raw RSSI on sub-bands can be collected into the following raw RSSI matrix:

(2)

where is the th entry of the raw RSSI matrix, is the sampling starting time, , is the th sampling time.

Note that, when we use BV1 to sample the raw RSSI data on the 2.4GHz frequency band, the collected raw data will include all potential signals from the wireless networks working on this band. The signal from networks other than Wi-Fi (i.e., LTE-U, BT/BLE, and ZigBee, etc.) will constitute external interference signals to the target Wi-Fi network.

Iii-A2 Time and Frequency domain processing

Before training DNN with the data, we need to process the raw RSSI samples in both the time and frequency domains.

First, we deal with the RSSI samples in the time domain. The time length of one RSSI sample is ; the time length of one mini-slot in the CSMA/CA protocol of Wi-Fi networks is [16]

. To align with the time units of CSMA/CA and our data, we perform up-sampling via the linear interpolation with an up-sampling factor

. In particular, the RSSI interpolation on sub-band is given by

(3)

where is the time index of the interpolated RSSI between the RSSI samples at time and , and is the result of interpolation at on sub-band .

After the time-domain data processing, we also have frequency-domain data processing. There are 14 overlapping and staggered channels on the 2.4GHz frequency band, and the first 13 channels are widely used in most parts of the world. Therefore, we only consider the first 13 channels in our DL-MAC. Similarly, we need to interpolate RSSI values on 83 sub-bands into the Wi-Fi channels. The th channel’s center frequency of Wi-Fi networks can be written as

(4)

We perform down-sampling via average interpolation with a down-sampling factor of 23. Consider channel 6 as an example. The 2.437GHz is the center frequency of channel 6 that occupies the 23 sub-bands from 2.426GHz to 2.448GHz . We calculate the average of the RSSI values sampled from these 23 sub-bands as the interpolated RSSI value of channel 1. In particular, we can express the interpolated RSSI of channel at time as

(5)

Finally, the RSSI matrix obtained after the time and frequency domain processing is shown below:

(6)

Iii-A3 Data labeling

In this work, we use supervised learning to train a DNN that implements DL-MAC. After the time and frequency domain processing are completed to obtain the RSSI data matrix in (6), we need to label the data contained in the matrix. Our approach of data labeling is to use the history RSSI to decide whether the AI device can access the spectrum channel in the next transmission time of a packet and which MCS to adopt if it determines to access.

We consider that the transmission time of a packet is 120 mini-slots, where each mini-slot is . We use the RSSI data of three previous consecutive packets up to the current time t on channel (i.e., the 360 RSSI data ) as the input of DNN; and the output of DNN (the label to the input data) is the optimal result of the channel access and MCS selection adopted in the next packet transmission time (i.e., from time to ) over this channel. Fig. 2 presents an illustration of data labeling over one particular channel. The RSSI data of the previous 360 mini-slots are used as the input of DNN, and the optimal result of channel access and the MCS adopted in the next packet transmission time is used as its label.

Fig. 2: The illustration of data labeling over a particular channel in Wi-Fi networks.

We now present how to determine the label for the input data, i.e., the optimal result of channel access and the MCS adopted in the next packet transmission time. We define the optimality as the highest transmission rate that can be achieved below a target packet error rate (PER). Note that in 802.11ac standard for Wi-Fi networks, there are 9 MCSs with different transmission rates and these MCSs are indexed from 0 to 8. Then, we add an MCS index of -1 to represent that the DL-MAC decides to not access the channel in the next transmission time of a packet, as shown in Table II (Thus, we now have 10 MCSs in total). Now, our data labeling problem is to determine the optimal MCS index in Table II for the next packet transmission time (i.e., the next 120 mini-slots) from the RSSI data of the 3 previous packet transmission time (i.e., the previous 360 mini-slots). The specific process of data labeling is given as follows:

i) First, at the time , we calculate the average RSSI, , of the next transmission time of a packet (i.e., from to ) as .

ii) Then, we transfer the calculated average RSSI, , into SINR. We suppose that the transmitter of the AI device operates with a fixed transmission power, such as 18dBm, and the power of the signal received by the receiver is , supposed to be -60dBm. Thus, the SINR can be calculated and given by:

(7)

iii) Finally, we set a target PER and find the MCS that achieves a PER under this target and maximizes the transmission rate. The target PER used is 0.1 in our work. For a given MCS, we can calculate the SINR that gives the target PER of 0.1 as the SINR lower bound. After calculating the 10 SINR lower bounds for the 10 MCSs, we can obtain 10 SINR ranges, as shown in Table I. Within each SINR range, there is a particular MCS that can achieve the highest transmission rate and has a PER blew the target of 0.1.

Using the SINR in (7) and Table II, we can map the SINR calculated from the RSSI data of the next packet transmission time to the optimal MCS index which is treated as the label to the RSSI data of the previous three consecutive packet time.

MCS Index Modulation
Coding
Rate
Rate
(Mbps)
SINR
(dB)
-1 (IDLE) / / <9
0 BPSK 1/2 6.5 [9, 10)
1 QPSK 1/2 13 [10, 12)
2 QPSK 3/4 19.5 [12, 15)
3 16-QAM 1/2 26 [15, 18)
4 16-QAM 3/4 39 [18, 21)
5 64-QAM 2/3 52 [21, 23)
6 64-QAM 3/4 58.5 [23, 24)
7 64-QAM 5/6 65 [24, 28)
8 256-QAM 3/4 78 28
TABLE II: THE SINR THRESHOLD CORRESPONDING TO THE MCS INDEX, WITH PER 10%.

Iii-B DNN model and implementation approach for DL-MAC

This part presents the DNN model employed to implement our DL-MAC. The DNN has a feed-forward neural network structure that consists of an input layer, three hidden layers, and an output layer. The input layer has 360 neurons, and the output layer is composed of 10 neurons that represent the probability of each MCS being selected. The numbers of the neurons in three hidden layers are 1000, 2000, and 300, respectively. The batch normalization (BN) is adopted before the ReLu activation function in each hidden-layer neuron, and the SoftMax function is the activation function of the output-layer neurons.

The DNN is trained by minimizing the cross-entropy loss function via the Adam stochastic gradient descent algorithm

[11]. After the DNN is trained, we employ the pre-trained DNN to perform the joint channel access and MCS selection for the AI device.

At the beginning, DL-MAC starts with an idle state and listens to the channel. The AI device collects one RSSI data at each mini-slot and puts it into the tail of the RSSI data queue for that channel. DL-MAC feeds the recent 360 RSSI data to the DNN as its input, and the DNN outputs a selected MCS to transmit the next packet. If the index of the selected MCS is -1 (i.e., not to transmit), the AI device keeps listening to the channel and collects one RSSI data of the next mini-slot from the received signal. On the other hand, if the output of the DNN is to transmit with a MCS, the AI device cannot receive signals from the wireless channel due to the half-duplex constraint on its radio hardware. In this time, we need a RSSI replenishment operation to supplement RSSI data for the time of transmitting after the transmission is finished. In this work, we consider that the packet transmission time consists of a physical layer convergence procedure (PLCP) overhead, and a packet payload transmission time, . During the transmission, there are mini-slots occupied for one packet. Thus, we need to generate RSSI data and put them into the RSSI data queue. Suppose that the MCS is selected for transmitting the current packet. If the packet is successfully transmitted, the RSSI data are generated uniformly to ensure that the corresponding SINR is within the range between MCS to . On the contrary, when the packet transmission fails, the RSSI data are generated uniformly to ensure that the corresponding SINR is within the range between MCS to .

Iii-C Benchmark

In this work, we consider that the payload size of each packet is fixed to 1500 bytes, and thus the length of the transmitted packet will vary with the rate of the selected MCS (i.e., the higher the MCS rate, the shorter the packet length). For channel access, we employ CSMA/CA and the optimal channel access (OPT-CA) as the benchmarks to our DL-MAC. OPT-CA can be obtained by computing the average SINR of the next packet transmission time and comparing the SINR with the interference threshold. For MCS selection, we employ the standard MCS selection algorithms of Iwl [7], ARF [10], and the optimal MCS selection (OPT-MCS) as the benchmarks to DL-MAC. According to the average SINR, OPT-MCS uses the MCS with the highest rate for a successful packet transmission is used as the optimal MCS. For joint channel access and MCS selection, we exploit a global optimal search method for the joint channel access and MCS selection, referred to as global optimal scheme (GOPT). For GOPT, the packet is not necessarily transmitted at each mini-slot, but it can wait for some mini-slots before being transmitted. GOPT searches for the optimal number of the waiting mini-slots and the MCS that can complete the packet transmission earliest even it needs to wait for some mini-slots.

Iv Experiment Results

This section experimentally investigates the throughput performances achieved by our DL-MAC protocol. We first describe the data sampling environments and our experimental setup. Then we investigate the performance of DL-MAC by comparing it with the benchmarks, i.e., the CSMA/CA channel access and the traditional rate adaption schemes, and the optimal benchmark algorithms presented in Section III.C.

Iv-a Sampling Environment and Setup

We conducted data sampling at two different indoor scenarios, our Lab at Shenzhen university, and the departure hall of Shenzhen Baoan International Airport. Fig. 3(a) and 3(b) show the layouts of the wireless sampling environments at the two scenarios, respectively. We share the collected raw RSSI data on our project website [20] for public use.

Fig. 3: The plan illustration for the wireless data sampling at two different indoor scenarios: (a) our Lab at Shenzhen University; (b) Shenzhen Baoan International Airport departure hall [13].

In our Lab, we set up 12 Wi-Fi APs and 8 BT/BLE devices when conducting data sampling. The locations of the APs and BT/BLE devices are randomly employed. Our data sampling hardware, BV1, was placed at the center position. In particular, at the airport departure hall, we sampled RSSI at 5 different locations. In our experiments, the packet transmission time is 1.080ms, and the payload size is 1500 bytes; the packet arrives according to the Poisson arrivals with rate . The interference threshold is set to -75dBm for CSMA/CA. We use the previous 60 seconds of data to train the DNN, and use the next 20 seconds of data to verify the performance of the trained DNN for the same channel.

Iv-B Throughput Performance

We define the throughput as the number of packet bits successfully transmitted per second, which is calculated over a moving window with the size of 1000 mini-slots. We also present the average throughput over every two previous seconds.

Fig. 4: The moving average transmission rate comparison in two location scenarios: (a) the average throughput on channel 6 at Shenzhen University laboratory, (b) the average throughput on channel 11 at Shenzhen Baoan International Airport departure hall.
Fig. 5: The average throughput over every two seconds comparison in two location scenarios: (a) the average throughput on channel 6 at Shenzhen University laboratory, (b) the average throughput on channel 11 at Shenzhen Baoan International Airport departure hall.

Fig. 4 and Fig. 5 present the throughput result of our proposed DL-MAC and other benchmark algorithms, respectively. We train the DNN using the data sampled from one scenario at a particular channel and test the DNN using the data sampled from the same scenario at the same channel. As we can see from Fig. 4 and Fig. 5, GOPT shows the highest throughputs since it can wait to select the best MCS to complete the packet transmission as earliest as possible. Benchmarked to traditional CSMA/CA channel access and the traditional MCS selection (Iwl and ARF), our DL-MAC can achieve better performances for both of channel access and MCS selection.

The above experiments use the sampled data to train the DNN and evaluate the performances of DNN for DL-MAC using the data from the same scenarios. However, we want to verify that the trained DNN for DL-MAC can also work for different scenarios, i.e., one trained DNN can work for both of Shenzhen University and Shenzhen Airport scenarios. Since the statistics of the data collected from the two scenarios may quite different, we fuse the two datasets into one dataset to train the model. We use both the previous 50 seconds of the sampled data on channel 6 for data fusion. Then, we use the fused data to train the DNN. After that, we verify the throughput of the DL-MAC. Fig. 6(a) and 6(b) present the result of the two-second average throughputs of the DL-MAC in which the DNN model is trained using the fused data. We can see that the DL-MAC protocol still shows good performance both at the laboratory and the airport departure hall.

Fig. 6: The average throughput over every two seconds of the DL-MAC protocol by fusion data in two location scenarios: (a) the throughput on channel 6 at Shenzhen University laboratory, (b) the throughput on channel 6 at Shenzhen Baoan International Airport departure hall.

V Conclusion

In this work, we have investigated an intelligent DL-MAC protocol that can achieve joint channel access and MCS selection. Our DL-MAC is designed using DNN under supervised learning. DL-MAC aims at improving the spectrum efficiency of Wi-Fi networks on the 2.4GHz ISM band. Our DL-MAC protocol can deal with is the real wireless data sampled on the 2.4GHz band at Shenzhen University and Shenzhen Baoan International Airport. We experimentally verify the performance of DL-MAC, and the experimental results show that the DL-MAC protocol can achieve more efficient channel access with higher transmission rates compared to the CSMA/CA channel access and traditional rate adaption schemes. Since our DL-MAC is developed from real sampled data, it is very practical and can work in real wireless networks.

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