Performance analysis based Markov chain in random access heterogeneous MIMO networks
Introduction
Future wireless networks will be dominated by heterogeneous devices supporting various numbers of antennas. This is due to increasingly diversified devices. Devices that differ in the number of antennas can contend for not only time, but also for spatial degrees of freedom, so as to improve the overall network throughput [4]. However, existing designs of IEEE 802.11 WLAN adopt random channel access only in time domain, i.e., a single device can transmit at a time, and fail to make the use of diversified devices and antennas configurations [1].
Recently, there has been a growing interested in how to fully realize the benefits of MIMO in WLAN. In IEEE 802.11ac standard [2], downlink multi-user MIMO (DL-MU-MIMO) technique is proposed to allow an AP to simultaneously transmit to multiple clients in the downlink transmission. To improve the efficiency of transmission and boost the capacity of WLAN, the next generation standard IEEE 802.11ax supports uplink MU-MIMO (UL-MU-MIMO) transmission using orthogonal frequency division multiple access (OFDMA) technology [3]. Although MU-MIMO technique in both DL and UL can improve the network throughput compared with single-user MIMO, the capacity improvement is bounded by the number of AP’s antennas, whichever is smaller in the heterogeneous MIMO network.
To further fully utilize the spacial resource, Kate et al. [4] proposed a multi-dimensional carrier sense random channel access protocol, which extends random access into spatial domain and enables multiple nodes equipped with different numbers of antennas to transmit concurrently. Unlike 802.11 which stops contending after a node wins the contention, in multi-dimensional carrier sense, nodes with more antennas than the contention winner can continue to carrier sense and contend for the medium as if the medium is free. This access scheme was later improved in [5], where both the client’s and the AP’s antennas share the responsibility of canceling the interference between them and increasing the number of concurrent transmission steams. NetMIMO is another schemes achieved the concurrent transmission among independent nodes [6], [7]. A node that has obtained the access to the channel becomes the lead AP and enables other APs to beamform their signals and communicate with their clients on the same channel, forming a virtual multipoint-to-multipoint MIMO. However, NetMIMO requires multiple APs participating transmission to accurately synchronize their initial phase and time.
In this paper, we summarize the key features of the MDCSMA-based heterogeneous MIMO WLAN proposed by Lin et al. [4].
To improve the efficiency, the optimal transmission probability is adopted instead of the constant transmission probability in each dimension carrier sense. Then, a theoretical model is developed to characterize the saturation throughput and mean access delay in heterogeneous MIMO WLAN. The contribution of this paper are as follows.
- (1)
We adopts a simple backoff algorithm called p-persistent CSMA contend the medium in each dimension carrier sense. Since the number of nodes allowed to contend the concurrent link varies in each dimension carrier sense, we dynamically turn the p values (i.e., the average size of the contention window in the IEEE 802.11 protocol) that maximizes the throughput in current dimension carrier sense, which is related with the number of nodes allowed to participate in contend the shared medium and the remaining duration of data transmission.
- (2)
A analytical model based on Markov chain is developed to characterize the throughput and mean access delay in heterogeneous MIMO WLANs. Different from the existing Markov chain model which models the backoff process to derive the transmission probability in a slot. Our Markov chain is built up to evaluate the probability that nodes are allowed to contend for each dimensional transmission opportunity.
- (3)
Comparisons between analytical and simulation results are conducted to verify our model. Numerical examples are presented to show that our analytical model provides a close estimation of the network throughput. The accuracy of our model is high especially for the network with less number of antennas. Then, the network performance is evaluated through the developed analytical model.
The rest of paper is organized as follows. In Section II we describe the related work. In Section III we provide the main features of the multidimensional carriers sense MAC protocol in heterogeneous MIMO WLANs. In Section IV a theoretical model is derived to compute the saturation throughput and mean access delay of the donwlink channel. In section V, numerical analysis is carried out to validate the model accuracy with respect to different parameters. Then, network performance is evaluated by means of the developed model in Section VI. Finally, Section VII concludes this paper.
Notation: bold upper and lower letters denote matrices and column vectors, respectively; and the symbol ( · )T for the transpose. The norm of vector x is denoted ‖x‖.
Section snippets
Related works
There have been remarkable research works on the design of MAC protocol to support multiple nodes transmission in WLAN. In [8], the authors propose TXOP sharing mechanism based on 802.11e which allows primary access category (AC) to share the TXOP with the secondary ACs and transmit simultaneously. In IEEE 802.11ac [2], TXOP sharing called MU-TXOP is introduced to implement DL-MU-MIMO, which enables the transmission of multiple packets from primary AC to multiple directions or multiple packets
Multi-dimension carrier sensing based random access in heterogeneous MIMO WLANs
In this section we summarize the main features of a multi-dimension carrier sensing based heterogeneous MIMO WLAN. Assume that each client can only associate with one AP at a time and the downlink channel is considered throughout this paper.
In the standard 802.11 DCF access scheme, only one AP is allowed to transmit at the same channel [2]. APs who want to transmit data enter the contention period using carrier sensing and slotted binary exponential backoff mechanism. Before data transmission,
System model
Consider a heterogeneous MIMO WLAN with M contending pairs of nodes (e.g. AP and client) that differ in the number of antennas. The set of is denoted as the APs. Note that the pairs of nodes (e.g. AP and client) have the same number of antennas. In our model, there are N types of number of antennas at the APs, which can be represented as Qi, denoted as the set . Without loss of generality, we assume that Q1 < Q2 < ... < QN. Therefore, APs can be
Model verification
To prove that the proposed analytical model can predict the performance of multi-dimensional carrier sense MAC protocol with high accuracy, in this section comparisons between the analytical results and simulation results are presented. In the simulation, all APs are randomly deployed in a area with 20meter × 10meter. Assume that the channels between users and APs experience i.i.d. time-varying Rayleigh fading without taking large-scale fading into account. Then the user distribution is not
Numerical results
First, we investigate the saturation throughput and mean access delay of the standard IEEE 802.11 CSMA/CA MAC protocol and the multi-dimensional carrier sense (MDCSMA) MAC protocol, when E[T1] is set to 2000us. There are 6 type of APs, which number of antennas at the AP is range from 1 to 6. The total number of APs, M, can be computed as where α is set to 1 and 2. The results in Fig. 5 confirm the results we obtained: 1)The standard 802.11 protocol becomes increasingly inefficient by
Conclusions
In this paper we developed a analytical model based on Markov Chain to characterize a multi-dimensional carrier sense random access in heterogeneous MIMO network, where APs equipped with different numbers of antennas are allowed to concurrently transmit in a distributed manner. Analytical models were developed to characterize the network performance in saturation throughput and mean access delay. Comparisons between simulation and analytical results confirm a close estimation of our analytical
Author Statement
We appreciate the timely review and constructive comments on our paper, entitled as “Performance Analysis based Markov Chain in Random Access Heterogeneous MIMO Networks”. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. We would like to declare that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the
Declaration of Competing Interest
The authors have declared that they have no conflict of interest to this work.
Acknowlgedgments
This research is supported Nation Natural Science Foundation of China (grant number: 61671073, 61901163). And the research is also supported by Beijing Laboratory of advanced information network.
Zhiqun Hu received the Ph.D. degrees in Information and communication Engineering from Beijing University of posts and Telecommunication, Beijing, China, in 2018, the B.E. degree in Communication Engineering from Hubei University of Technology, Wuhan, China, in 2012. She jointed the HuBei University since 2018, where she is currently an assistant professor of Computer Science and Information Engineering. Her main research interests include wireless communications, UAV, artificial intelligence
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Cited by (0)
Zhiqun Hu received the Ph.D. degrees in Information and communication Engineering from Beijing University of posts and Telecommunication, Beijing, China, in 2018, the B.E. degree in Communication Engineering from Hubei University of Technology, Wuhan, China, in 2012. She jointed the HuBei University since 2018, where she is currently an assistant professor of Computer Science and Information Engineering. Her main research interests include wireless communications, UAV, artificial intelligence (AI), performance analysis and algorithm design, V2X, deep reinforcement learning.
Hang Qi is currently a Ph.D student in Information and communication Engineering from Beijing University of posts and Telecommunication, Beijing, China. He received the B.S. degree in communication engineering from Shandong University, Shandong, Chian. His current research interests include machine learning, performance analysis, MAC protocol design, and UAV.
Xiangming Wen is the director of Beijing Key Laboratory of Network System Architecture and Convergence, where he has managed several projects related to open wireless networking. He is also the vice president of Beijing University of Posts and Telecommunications. He received both his M.Sc. and Ph.D in information and communication engineering from Beijing University of Posts and Telecommunications. His current research interests focus on radio resource and mobility management, software defined wireless networks, and broadband multimedia transmission technology.
Zhaoming Lu received the Ph.D in Beijing University of Posts and Telecommunications in 2012. He joined the School of Information and Communication Engineering in Beijing University of Posts and Telecommunications in 2012. His research includes machine learning in wireless networks, self-driven based 5G network, software defined wireless networks, cross-layer design for mobile video applications and so on.
Wenpeng Jing received the Ph.D in Beijing University of Posts and Telecommunications in 2017 and the B.S. degree in communication engineering from Shandong University in 2012. He is currently a postdoctoral in Beijing University of Posts and Telecommunications. His research interests include radio resource allocation and management, energy efficiency and interference management in HetNet, and wireless cache.