An Analytical Model for CBAP Allocations in IEEE 802.11ad

Chiara Pielli; Tanguy Ropitault; Nada Golmie; Michele Zorzi

arXiv:1906.07097·cs.NI·June 18, 2019

An Analytical Model for CBAP Allocations in IEEE 802.11ad

Chiara Pielli, Tanguy Ropitault, Nada Golmie, Michele Zorzi

PDF

TL;DR

This paper presents a Markov Chain model for CBAPs in IEEE 802.11ad, analyzing their performance and interference to optimize transmission scheduling in millimeter wave WiFi networks.

Contribution

It introduces a novel Markov Chain model that accounts for directional communication challenges and interference, aiding in efficient resource allocation.

Findings

01

Analytical expressions for throughput, delay, and packet drops.

02

Impact assessment of transmission parameters on performance.

03

Guidelines for designing transmission schedulers based on analysis.

Abstract

The IEEE 802.11ad standard extends WiFi operation to the millimeter wave frequencies, and introduces novel features concerning both the physical (PHY) and Medium Access Control (MAC) layers. However, while there are extensive research efforts to develop mechanisms for establishing and maintaining directional links for mmWave communications, fewer works deal with transmission scheduling and the hybrid MAC introduced by the standard. The hybrid MAC layer provides for two different kinds of resource allocations: Contention Based Access Periods (CBAPs) and contention free Service Periods (SPs). In this paper, we propose a Markov Chain model to represent CBAPs, which takes into account operation interruptions due to scheduled SPs and the deafness and hidden node problems that directional communication exacerbates. We also propose a mathematical analysis to assess interference among stations.…

Tables2

b_{0, 0}

= {\begin{matrix} \frac{2 ​ (1 - 2 ​ p) ​ (1 - p)}{W_{0} (1 - {(2 p)}^{m + 1} (1 - p) + (1 - p^{m + 1}) (1 - 2 p)} if ​ m \leq m^{'} \\ \frac{2 ​ (1 - 2 ​ p) ​ (1 - p)}{W_{0} ​ (1 - {(2 ​ p)}^{m^{'} + 1}) ​ (1 - p) + 2^{m^{'}} ​ W_{0} ​ (p^{m^{'}} - p^{m}) ​ (1 - 2 ​ p) ​ p + (1 - p^{m + 1}) ​ (1 - 2 ​ p)} if ​ m > m^{'} \end{matrix}

(4)

Table 2. Table I: Simulation parameters.

BI structure
BI duration	$B I$	100 ms
BHI duration	$B H I$	2 ms
EDCA parameters [1]
Minimum contention window size	$W_{0}$	16
Maximum contention window size	$2^{m^{'}} W_{0}$	$1024$
Maximum $#$ retransmission attempts	$m$	$6$
Slot duration	$σ$	$5$ $μ$ s
SIFS	$S I F S$	$3$ $μ$ s
DIFS	$D I F S$	$13$ $μ$ s
Propagation delay	$δ$	$100$ ns
Packets size [1]
MAC header	$H_{M A C}$	$320$ b
PHY header	$H_{P H Y}$	$64$ b
RTS size	$L_{R T S}$	$20 * 8$ b
CTS size	$L_{C T S}$	$20 * 8$ b
ACK size	$L_{A C K}$	$14 * 8$ b
Data size	$E [L]$	$7995 * 8 b - H_{M A C}$
Noise
Noise figure	$F_{d B}$	$10$ dB
Bandwidth	$W$	$2.16$ GHz
Path loss exponent	$η$	$3$

Equations73

P_{rx} = P_{tx} \frac{g _{tx} ( θ _{tx} , φ _{rx} ) g _{rx} ( θ _{tx} , φ _{rx} )}{A d ^{η}}

P_{rx} = P_{tx} \frac{g _{tx} ( θ _{tx} , φ _{rx} ) g _{rx} ( θ _{tx} , φ _{rx} )}{A d ^{η}}

p_{t} = \frac{T _{L}}{T _{CBAP} / N _{CBAP}} .

p_{t} = \frac{T _{L}}{T _{CBAP} / N _{CBAP}} .

b_{i, k} = \frac{W _{i} - k}{W _{i}} p b_{0, 0},

b_{i, k} = \frac{W _{i} - k}{W _{i}} p b_{0, 0},

τ = i = 0 \sum m b_{i, 0} (1 - p_{t}) = \frac{1 - p ^{m + 1}}{1 - p} (1 - p_{t}) b_{0, 0} .

τ = i = 0 \sum m b_{i, 0} (1 - p_{t}) = \frac{1 - p ^{m + 1}}{1 - p} (1 - p_{t}) b_{0, 0} .

π_{tx} = \frac{τ E [ T _{tx} ]}{τ E [ T _{tx} ] + ( 1 - τ ) E [ T _{ntx} ]} .

π_{tx} = \frac{τ E [ T _{tx} ]}{τ E [ T _{tx} ] + ( 1 - τ ) E [ T _{ntx} ]} .

π_{j} = \frac{T _{j} b _{j}}{\sum _{ℓ \in J_{tx}} T _{ℓ} b _{ℓ}} j \in J_{tx},

π_{j} = \frac{T _{j} b _{j}}{\sum _{ℓ \in J_{tx}} T _{ℓ} b _{ℓ}} j \in J_{tx},

q_{1}

q_{1}

q_{2} = \frac{1 - ( 1 - π _{tx} ( π _{R_{v}} + π _{R_{c}} ) ) ^{n_{O, 2}}}{T _{CBAP} / T _{BI}} .

q_{2} = \frac{1 - ( 1 - π _{tx} ( π _{R_{v}} + π _{R_{c}} ) ) ^{n_{O, 2}}}{T _{CBAP} / T _{BI}} .

q_{3} = \frac{1 - ( 1 - π _{tx} ( π _{R_{v}} + π _{R_{c}} + π _{O} ) ) ^{n_{O, 4}}}{T _{CBAP} / T _{BI}} .

q_{3} = \frac{1 - ( 1 - π _{tx} ( π _{R_{v}} + π _{R_{c}} + π _{O} ) ) ^{n_{O, 4}}}{T _{CBAP} / T _{BI}} .

p_{c, 1} = 1 - (1 - q_{1}) (1 - q_{2}) (1 - q_{3}) .

p_{c, 1} = 1 - (1 - q_{1}) (1 - q_{2}) (1 - q_{3}) .

p_{c, 2} = \frac{1 - (( 1 - p _{acc} ) ^{n_{I, 2} + n_{I, 4}} ) ^{T_{R_{v}} / T_{A}}}{T _{CBAP} / T _{BI}} .

p_{c, 2} = \frac{1 - (( 1 - p _{acc} ) ^{n_{I, 2} + n_{I, 4}} ) ^{T_{R_{v}} / T_{A}}}{T _{CBAP} / T _{BI}} .

E [T_{tx}]

E [T_{tx}]

+ (T_{A} + T_{R_{v}} + T_{F}) (1 - p_{c, 1}) p_{c, 2}

+ (T_{A} + T_{R_{v}} + T_{O} + T_{F}) (1 - p_{c, 1}) (1 - p_{c, 2}) p_{e}

+ (T_{A} + T_{R_{v}} + T_{O} + T_{S}) (1 - p_{c, 1}) (1 - p_{c, 2}) (1 - p_{e}) .

p_{f} = 1 - \frac{T _{CBAP}}{T _{BI}},

p_{f} = 1 - \frac{T _{CBAP}}{T _{BI}},

p_{i} = (1 - π_{tx} (π_{A} + π_{R_{c}} + π_{R_{v}} + π_{O}))^{n_{I, 1} + n_{I, 3}} (1 - π_{tx} π_{O})^{n_{I, 2}},

p_{i} = (1 - π_{tx} (π_{A} + π_{R_{c}} + π_{R_{v}} + π_{O}))^{n_{I, 1} + n_{I, 3}} (1 - π_{tx} π_{O})^{n_{I, 2}},

E [T_{ntx}] = σ + \frac{( 1 - p _{i} ) E _{tx}}{1 - p _{f}} .

E [T_{ntx}] = σ + \frac{( 1 - p _{i} ) E _{tx}}{1 - p _{f}} .

S = n \frac{π _{tx} ( 1 - p ) E [ L ]}{π _{tx} E [ T _{tx} ] + ( 1 - π _{tx} ) E [ T _{ntx} ]}

S = n \frac{π _{tx} ( 1 - p ) E [ L ]}{π _{tx} E [ T _{tx} ] + ( 1 - π _{tx} ) E [ T _{ntx} ]}

E [D] = i = 0 \sum m Pr (TX (i) ∣ success) E [D_{i}]

E [D] = i = 0 \sum m Pr (TX (i) ∣ success) E [D_{i}]

E [D_{i}] = i T_{c} + T_{s} + E [T_{ntx}] j = 0 \sum i ℓ = 0 \sum + \infty p_{t}^{ℓ} k = 0 \sum W_{j} - 1 \frac{k + 1}{W _{j}}

E [D_{i}] = i T_{c} + T_{s} + E [T_{ntx}] j = 0 \sum i ℓ = 0 \sum + \infty p_{t}^{ℓ} k = 0 \sum W_{j} - 1 \frac{k + 1}{W _{j}}

= i T_{c} + T_{s} + \frac{E [ T _{ntx} ]}{1 - p _{t}} j = 0 \sum i \frac{W _{j} + 1}{2}

= i T_{c} + T_{s} + \frac{E [ T _{ntx} ]}{2 ( 1 - p _{t} )} (2^{m i n (i, m^{'}) + 1} - 1 + max (i - m^{'}, 0) 2^{m^{'}}) W_{0}

T_{s}

T_{s}

T_{c}

d \leq (\frac{P _{tx} g _{tx} ( θ _{tx} , φ _{rx} ) g _{rx} ( θ _{tx} , φ _{rx} )}{γ _{th} A N})^{1/ η} .

d \leq (\frac{P _{tx} g _{tx} ( θ _{tx} , φ _{rx} ) g _{rx} ( θ _{tx} , φ _{rx} )}{γ _{th} A N})^{1/ η} .

φ_{lim} (d_{i}) = ⎩ ⎨ ⎧ π - \frac{θ _{S}}{2} - arcsin (\frac{d _{i}}{d _{t}} sin (\frac{θ _{S}}{2})) if d_{i} \leq d_{t} π - \frac{θ _{S}}{2} - arcsin (\frac{d _{t}}{d _{i}} sin (\frac{θ _{S}}{2})) if d_{i} > d_{t}

φ_{lim} (d_{i}) = ⎩ ⎨ ⎧ π - \frac{θ _{S}}{2} - arcsin (\frac{d _{i}}{d _{t}} sin (\frac{θ _{S}}{2})) if d_{i} \leq d_{t} π - \frac{θ _{S}}{2} - arcsin (\frac{d _{t}}{d _{i}} sin (\frac{θ _{S}}{2})) if d_{i} > d_{t}

R_{R} (d_{t})

R_{R} (d_{t})

= π R^{2} - 2 \int_{0}^{d_{t}} (π - \frac{θ _{S}}{2} - arcsin (\frac{r}{d _{t}} sin \frac{θ _{S}}{2})) r \partial r

- 2 \int_{d_{t}}^{R} (π - \frac{θ _{S}}{2} - arcsin (\frac{d _{t}}{r} sin \frac{θ _{S}}{2})) r \partial r

E [R_{R}]

E [R_{R}]

R_{C} = \int_{0}^{R} \int_{φ_{AP} - θ_{AP}}^{φ_{AP}} r \partial θ r \partial r = π R^{2} = \frac{θ _{AP}}{2} R^{2} .

R_{C} = \int_{0}^{R} \int_{φ_{AP} - θ_{AP}}^{φ_{AP}} r \partial θ r \partial r = π R^{2} = \frac{θ _{AP}}{2} R^{2} .

R_{R, C} (d_{t}, φ_{AP})

R_{R, C} (d_{t}, φ_{AP})

\mathrm{E}\left[{\mathcal{R}}_{R,C}\right]=\int_{0}^{R}\frac{2d_{t}}{R^{2}}\Bigg{(}\int_{0}^{\theta_{\rm AP}}\frac{1}{\theta_{\rm AP}}{\mathcal{R}}_{R,C}(d_{t},\varphi_{\rm AP})\partial\phi_{\rm AP}\\ +\int_{0}^{\theta_{\rm AP}}\frac{1}{\theta_{\rm AP}}{\mathcal{R}}_{R,C}(d_{t},\varphi_{\rm AP})\partial(\theta_{\rm AP}-\phi_{\rm AP})\Bigg{)}\,\partial d_{t}\,.

\mathrm{E}\left[{\mathcal{R}}_{R,C}\right]=\int_{0}^{R}\frac{2d_{t}}{R^{2}}\Bigg{(}\int_{0}^{\theta_{\rm AP}}\frac{1}{\theta_{\rm AP}}{\mathcal{R}}_{R,C}(d_{t},\varphi_{\rm AP})\partial\phi_{\rm AP}\\ +\int_{0}^{\theta_{\rm AP}}\frac{1}{\theta_{\rm AP}}{\mathcal{R}}_{R,C}(d_{t},\varphi_{\rm AP})\partial(\theta_{\rm AP}-\phi_{\rm AP})\Bigg{)}\,\partial d_{t}\,.

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Full text

An Analytical Model for CBAP Allocations

in IEEE 802.11ad

Chiara Pielli, Tanguy Ropitault, Nada Golmie, and Michele Zorzi Chiara Pielli ([email protected]) and Michele Zorzi ([email protected]) are with the Department of Information Engineering, University of Padova, Padova, Italy.Tanguy Ropitault ([email protected]) and Nada Golmie ([email protected]) are with the National Institute of Standards and Technology (NIST), Gaithersburg, MD, US.

Abstract

The IEEE 802.11ad standard extends WiFi operation to the millimeter wave frequencies, and introduces novel features concerning both the physical (PHY) and Medium Access Control (MAC) layers. However, while there are extensive research efforts to develop mechanisms for establishing and maintaining directional links for mmWave communications, fewer works deal with transmission scheduling and the hybrid MAC introduced by the standard. The hybrid MAC layer provides for two different kinds of resource allocations: Contention Based Access Periods (CBAPs) and contention free Service Periods (SPs). In this paper, we propose a Markov Chain model to represent CBAPs, which takes into account operation interruptions due to scheduled SPs and the deafness and hidden node problems that directional communication exacerbates. We also propose a mathematical analysis to assess interference among stations. We derive analytical expressions to assess the impact of various transmission parameters and of the Data Transmission Interval configuration on some key performance metrics such as throughput, delay and packet dropping rate. This information may be used to efficiently design a transmission scheduler that allocates contention-based and contention-free periods based on the application requirements.

I Introduction

Ratified in December $2012$ , the IEEE 802.11ad amendment to the IEEE 802.11 standard targets short range millimeter wave (mmWave) communications in local area networks [1]. It is the fist amendment of 802.11 that concerns mmWaves, and more specifically it targets the $60$ GHz ISM unlicensed band [1]. MmWaves have been recently gaining a lot of momentum in telecommunications thanks to the wide spectrum available, which allows for channels with higher capacity and has the potential to eliminate the congestion issues encountered in the overcrowded sub- $6$ -GHz bands.

The propagation environment in the mmWave spectrum is significantly different from that at sub- $6$ -GHz frequencies, and is characterized by a high propagation loss and a significant sensitivity to blockage. Blockage refers to very high attenuation due to obstacles; the human body for example could yield a penetration loss in the $20-35$ dB range [2]. Note, however, that the high attenuation may be an advantage for applications with short range, since it makes interference from farther transmissions negligible. The coverage range can be increased through beamforming, by focusing the power (both in transmission and in reception) towards the chosen direction, yielding a so-called directional link. This can be obtained by properly steering the elements of the antenna arrays. Also, the antenna arrays can be extremely compact and easily embedded into sensors and handsets, since the inter-antenna distance is proportional to the signal wavelength. Directional communication significantly attenuates interference among concurrent transmissions, yielding high potential for spatial sharing. Beamforming is a delicate process, and requires efficient beamforming training and beam tracking algorithms to establish and also maintain directional links, since poorly trained beams lead to extreme throughput loss: using the lowest Modulation and Coding Scheme (MCS) defined by IEEE 802.11ad yields a drop of almost $95\%$ compared to the highest achievable data rate of $6.76$ Gbps [3].

Because of the characteristics of the mmWave propagation environment, protocols designed for lower frequencies cannot simply be transposed to the mmWave band, but major design changes are required for both PHY and Medium Access Control (MAC) layers. While extensive research is ongoing to develop efficient beamforming training and beam tracking mechanisms [4, 5], it is also necessary to understand how to access the wireless medium and use the beamformed links efficiently to transmit data. The MAC layer of 802.11ad presents several features which yield an outstanding scheduling flexibility: it is possible to have both contention-based and contention-free allocations, and an additional mechanism built on top of the defined schedule allows to dynamically allocate channel time in quasi real-time. However, the standard [1] only provides rules for channel access; to the best of our knowledge, efficient scheduling schemes that exploit this hybrid MAC layer and match each traffic pattern to the most appropriate allocation is yet to be developed. To realize an adaptive scheduler able to optimally allocate the channel time resources and accommodate disparate Quality of Service (QoS) requirements, it is first necessary to assess the performance that can be obtained with the mechanisms available in 802.11ad.

A mathematical model allows to understand the tradeoffs between the various system parameters and how they affect the network performance. However, building a complete model is extremely challenging because there are several components to consider. In this paper we only focus on the performance that can be obtained in Contention Based Access Period (CBAP) allocations, taking into account the presence of Service Periods (SPs) allocations. This is intended to represent a first step in the process of understanding and characterizing the various types of allocations that can be used in 802.11ad with the ultimate goal of designing an efficient allocation scheduler able to cope with heterogeneous traffic patterns and requirements. In particular, we propose a variation of Bianchi’s seminal model for the Distributed Coordination Function (DCF) mechanism in legacy WiFi networks [6]. Such variation addresses the main novel features of the 802.11ad standard and, unlike most of the works proposed in the literature, takes into account the deafness and hidden node problems, which are exacerbated by directional transmissions [7]. Our model is based on a division of the area around a considered station (STA) into regions, similarly to what done in [8]: STAs belong to different groups based on whether they can overhear the messages sent by the STA to and/or received from the Access Point (AP), according to their respective positions and beams. However, [8] does not specify how to determine such regions; we instead explain how to compute the area of the regions mathematically, providing also the formulation for its expectation over the location of the considered station. This classification of STAs is needed to characterize the probability of collision, and thus to evaluate performance metrics such as throughput, latency and dropping rate. Note that, although in directional communication systems the STAs rarely interfere with each other, the carrier sensing mechanism is not as effective, causing STAs to access the channel while the AP is already involved in ongoing communications with other STAs.

The rest of the paper is structured as follows. Sec. II gives an overview of the 802.11ad standard. Sec. LABEL:sec:scheduling explains the scheduling problem and introduces the related works. The proposed model and the metrics used to evaluate the performance are described in Secs. IV and V, respectively. Sec. VI explains how to compute the interference regions when constant-gain beam shapes are used. Sec. VII shows the numerical evaluations and, finally, Sec. VIII concludes the paper.

II 802.11ad

In this section we briefly describe the 802.11ad standard, with a special focus on the data transmission mechanisms.

II-A Physical layer

The nominal channel bandwidth in 802.11ad is $2.16$ GHz, and there are up to $4$ channels in the ISM band around $60$ GHz, although channel availability varies from region to region. Only one channel at a time can be used for communication. There are $32$ different MCSs available, grouped into three different PHY layers, namely Control PHY, Single Carrier PHY and OFDM PHY, which differ for robustness, complexity, and achievable data rates. The standard also includes an energy-saving mode for battery-operated devices, which uses the low power Single Carrier PHY.

II-B Beamforming training

802.11ad introduces the concept of antenna sectors, which correspond to a discretization of the antenna space and reduce the number of possible beam directions to try. The standard supports up to four transmitter antenna arrays, four receiver antenna arrays, and 128 sectors per device. Beamforming training is realized in two subsequent stages: the Sector-Level Sweep (SLS) phase and the Beam Refinement Protocol (BRP) phase, that aim at setting up a link between the stations and maximizing the gain, respectively. This mechanism can be performed between two STAs or a STA and the PCP/AP; 111Besides the traditional WiFi network topology, 802.11ad can also be used for Personal Basic Service Sets (PBSSs), i.e., network architectures for ad hoc modes. The central coordinator of 802.11ad networks can then be either a PBSS Control Point (PCP) or an AP; accordingly, it is generally denoted as PCP/AP to include both infrastructures. the two devices are denoted as initiator and responder depending on who starts the SLS phase. The initiator sequentially tries different transmit antenna sector configurations, while the responder has its received antennas configured in a quasi-omnidirectional pattern and gives a feedback on each sector tried by the initiator, so as to determine the best coarse-grained antenna sector configuration. The SLS phase can be used also to inspect different configuration of the receiving antenna sectors: in this case, the initiator transmits multiple frames on the best known sector and the pairing node switches receiving sector. After a directional link has been established, the BRP phase is used to inspect narrower beams and, possibly, to optimize the antenna weight vectors in case of phased antenna arrays. Since the BRP phase follows the SLS one, a reliable frame exchange is ensured.

II-C Beacon Intervals

Medium access time is divided into Beacon Intervals (BIs), with maximum duration of $1$ s (but typically chosen around $100$ ms [3]). Each BI consists of a Beacon Header Interval (BHI) and a Data Transmission Interval (DTI), as shown in Fig. 1. The BHI replaces the single beacon frame of legacy WiFi networks and is used for synchronization and network management operations and to establish and maintain directional communication links between the STAs and the PCP/AP through beamforming training and beam tracking mechanisms; the DTI is used for data transmission and for beamforming training with the PCP/AP and between STAs.

The BHI includes up to three access periods, all of them optional: the Beacon Transmission Interval (BTI), the Association-Beamforming Training (A-BFT), and the Announcement Transmission Interval (ATI). The BTI is used for SLS beamforming training of the PCP/AP’s antennas and network announcement: the PCP/AP broadcasts beacon frames iterating through different sectors, performing the first part of the SLS phase with the STAs, which have their receiving antennas configured in a quasi-omnidirectional pattern since they do not know a-priori the direction to use to receive the beacons. The SLS phase started in the BTI is completed in the A-BFT, which is divided into slots during which STAs separately train their antenna sectors for communication with the PCP/AP, and provide feedback to the PCP/AP about the sector to use for transmitting to them. Finally, the ATI is used to exchange management information between the PCP/AP and associated and beamtrained stations, such as resource requests and allocation information for the DTI.

II-D Data transmission

The DTI is made up of contention-free SPs for exclusive communication between a dedicated pair of nodes222Technically, spatial sharing allows communication for multiple pair of nodes, but interference among pairs is checked to be basically null. and CBAPs where stations compete for access. SPs and CBAPs can be in any number and combination, and their scheduling is advertised by the PCP/AP through beacons in the BTI and/or specific frames in the ATI. An allocation is defined by several fields, including the type of allocation (SP or CBAP), the addresses of the source and destination STAs involved in the allocation (which can be unicast, multicast or broadcast), its total duration and starting time and the number of blocks it is made of, beamforming training information if needed, and whether the allocation is pseudostatic, meaning that it recurs in subsequent BIs [1]. Note that this schedule is set up prior to the beginning of the DTI. In addition, a dynamic channel time allocation mechanism allows STAs to reserve channel time in almost real-time over both SPs and CBAPs.

Contention-based access. CBAPs follow the Enhanced Distributed Channel Access (EDCA) mechanism, which is an enhanced DCF that includes functionalities to handle traffic categories with different priorities, frame aggregation and block acknowledgments. Stations compete for access and can obtain Transmission Opportunities (TXOPs) (contention-free periods) by winning an instance of EDCA contention or by receiving a Grant frame; the TXOP duration depends on the traffic category.

The DCF is based on Carrier Sense Multiple Access (CSMA) with Collision Avoidance (CSMA/CA): before transmission, the channel needs to be sensed idle for a minimum amount of time, namely a Distributed Interframe Space (DIFS). If the channel is sensed busy, the transmission is postponed: the STA picks a backoff counter uniformly distributed in $\{0,\ldots,W_{i}-1\}$ , where $W_{i}$ is the size of the contention window at the $i$ -th retransmission attempt. The contention window starts at a minimum value and doubles at each collision, until it saturates to a maximum value. The backoff time counter is decremented as long as the channel is sensed idle, frozen when a transmission is detected on the channel or the CBAP operation is suspended, and reactivated when the channel is sensed idle again for at least a DIFS (after that the CBAP operation has been resumed). When the backoff counter expires, the STA accesses the channel.

In 802.11ad, the channel status is determined through a combined physical and virtual carrier sensing; the former consists in energy or preamble detection over the channel, the latter is realized through Network Allocation Vectors (NAVs). The NAVs are counters based on the transmission duration information announced in Request-To-Send (RTS) and Clear-To-Send (CTS) frames prior to the actual exchange of data and maintain a prediction of future traffic on the medium.

The directional nature of communication at mmWaves makes the carrier sensing operations problematic [3] because there may be possible interference even though the medium was considered to be idle.

Contention-free access. SPs are contention-free periods assigned by the PCP/AP for exclusive communication between a pair of STAs. The directional communication enables the possibility of spatial sharing, i.e., simultaneous SPs involving different STAs can be scheduled, provided that they do not interfere with each other; this requires a preliminary interference assessment phase, which is coordinated by the PCP/AP. Note that building and updating the interference map may result in huge overhead in case of mobility.

Dynamic allocation mechanism. This mechanism is built on scheduled SPs and CBAPs with specific configuration and enables near-real-time reservation of channel time; the dynamic allocations do not persist beyond a BI. Stations can be polled by the PCP/AP and ask for channel time, which will be granted back to back.

The dynamic mechanism also includes the possibility of truncating and extending SPs, to exploit unused channel time and finalize the ongoing communication without additional delay and scheduling, respectively. When an SP is truncated, either the relinquished channel time is used as a CBAP or the PCP/AP polls STAs so that they can ask for channel time.

Resource scheduling. Evidently, there are many elements that need to be taken into account to appropriately schedule the DTI based on the QoS requirements. In addition to modeling data transmission in both CBAP and SP allocations, it is necessary to understand in which cases the dynamic allocation mechanism yields better performance than the predefined schedule. Another aspect that should be taken into consideration is power consumption: the presence of energy constrained devices may require changes in the scheduling, e.g., in the allocation order or by assigning more SP allocations. A critical issue is represented by the beamforming training (see Sec. VI-A) which introduces overhead and may degrade the network performance. Mainly, there are three knobs available to the protocol designer:

•

Contention-based or contention free allocation. This is the most meaningful choice as it impacts the way the medium is accessed and thus plays a direct role on the performance. SP allocations grant dedicated resources and the obtained performance only depends on the channel status, being therefore more predictable than when interference comes into play. Clearly, setting up the scheduled sessions introduces overhead and some latency, but the beam steering process is simplified since the receiver knows who is going to transmit and can steer its receiving beam towards the sender, and the STAs not involved in the SP can go to sleep and save power. On the other hand, CBAPs are distributed and robust and good for unpredictable bursty traffic. Nonetheless, carrier sensing may be problematic due to the use of directional antennas. Also, during CBAP period, STAs cannot go into power saving mode due to the inner nature of CSMA/CA. SP allocations are particularly suitable for periodic reporting with QoS demands, but CBAPs may be preferable in case of less stringent QoS requirements because channel resources are available to more stations.

•

Pseudo static allocation. In this way, it is possible to decide whether the allocation will recur in successive BIs. This is very useful for predictable traffic patterns as it avoids the need to schedule the allocation every time and limits the signaling overhead.

•

Dynamic allocation. It allows quasi-real-time channel use, but has a polling overhead and the scheduled allocation over which it is applied needs to satisfy certain conditions. This feature can be useful for unpredictable transmissions that need to be delivered with specific QoS requirements.

III Related work

The seminal work of [6] introduces a Markov Chain (MC) model of the IEEE 802.11 DCF. Although several variations on such model have been proposed to account for, e.g., finite number of retransmissions [10], heterogeneous QoS [11] and hidden node problem [12], none of them can be readily applied to the hybrid MAC layer of IEEE 802.11ad, as different changes are needed to account for its peculiar features.

Some works in the literature propose adaptations of Bianchi’s model for 802.11ad. Most of them, however, do not model the effect of directional communication properly, as they neglect the deafness and hidden node problems. For example, [13] uses a $3$ -dimensional MC model to analyze the channel utilization and the average MAC layer delay that can be obtained in CBAPs. This model accounts for the presence of allocations other than CBAP and for the fact that backoff counters are frozen when CSMA/CA operation is suspended. However, it does not introduce the maximum contention window size, so that the contention window keeps doubling at each retransmission stage. Moreover, the model assumes that CBAPs are allocated to sectors, so that two STAs belonging to different sectors cannot compete for the channel time in the same allocation. According to the standard [1], this is not necessarily true, since any subset of stations can participate in a CBAP, with potential deafness and hidden node issues. The model also erroneously assumes that all STAs in the same sector can overhear the messages that other nodes exchange with the AP. Thus, the assumption made in [13] strongly affects the analysis of the delay and the impact of the number of sectors used by the PCP/AP on the system performance, as the role of directional transmissions and deafness is neglected.

Similar assumptions have been made in [14], which models CBAPs with a $2$ -dimensional MC for unsaturated sources considering also the contention-free allocations of 802.11ad. However, besides neglecting the deafness problem, the model assumes that the DTI is made of SP allocations followed by a single CBAP allocation at the end of the DTI, while the standard [1] envisages SP and CBAP allocations in any number and order. This assumption may strongly affect the delay, as different configurations of the DTI may yield different performance. Also [15] uses a $2$ -dimensional MC to analyze the saturation throughput in CBAP but neglects the deafness issues and assumes the same specific configuration of the DTI as in [14].

A more accurate approach to directional communication in WiFi networks is presented in [16], which however is not designed for 802.11ad so that it does not consider the presence of SP allocations and the related backoff counter freezing. The model considers an accurate model for directional transmission, with the presence of side lobes with small antenna gain and corresponding regions with different levels of interference. Also [8] takes into account deafness and hidden node problems, and subdivides the area around a STA based on the interference level; CBAPs are then modeled using a $3$ -dimensional MC.

Other works in the literature consider different aspects of the DTI. For example, [17] derives the theoretical maximum throughput for CBAPs when two-level MAC frame aggregation is used. [7] proposed a directional MAC protocol to be used on top of 802.11ad: it allows the use of sequential directional RTS messages that a STA sends in all directions and that can therefore be overheard by all other STAs. The beamforming issue is considered in [18], which proposes a joint optimization of beamwidth selection and scheduling to maximize the effective network throughput.

For what concerns SPs, an accurate mathematical model for their preliminary allocation is presented in [19]. It considers the presence of quasi-periodic structures with multiple blocks within the same allocation, the erroneous nature of the wireless medium, and the possibility of multiple consecutive transmissions within the same allocation. A $3$ -dimensional MC is used to model a Variable Bit Rate (VBR) flow with packets arriving in batches of random size at regular intervals and can be used to derive the optimal SP allocation that satisfies the QoS requirement.

IV System model

We now introduce our analytical model for CBAP operation in 802.11ad. We denote as $T_{\rm BI}$ the duration of a BI and as $T_{\rm BHI},T_{\rm CBAP}$ and $T_{\rm SP}$ the time dedicated to BHI, CBAPs and SPs during a BI, respectively. The total time $T_{\rm CBAP}$ dedicated for contention-based access in a BI is distributed among $N_{\rm CBAP}$ allocations with the same duration, while $T_{\rm SP}$ is distributed among $N_{\rm SP}$ allocations with the same duration.

We make two assumptions: i) all STAs in the network implement a single Access Category (AC) only, hence service differentiation is not considered, and ii) the beamforming training has already been performed, so that the STAs already know how to steer their antennas to communicate with the AP. Also, we only focus on the classic WiFi network where a certain number of STAs communicate solely with the AP; we consider that the RTS/CTS mechanism is used.

To assess the performance that can be obtained in a CBAP, we leverage on Bianchi’s seminal work [6] and adapt it to model the features of CBAPs in 802.11ad. First of all we explain how directionality affects the communication during the contention-based channel access, then we describe the proposed model, and finally we discuss the performance metrics used in the numerical evaluation.

IV-A Directional communication in CBAPs

Besides the need of beamforming training and beam tracking mechanisms, the directional nature of communication in 802.11ad implies substantial changes also from a data transmission perspective. As explained in Sec II-D, CBAPs are based on the EDCA; however, the traditional approaches used in the literature need to be adapted to take directionality into account, since the consequent deafness and hidden node problems may significantly affect the system performance.

The most widely used approach in the literature to model the DCF and EDCA mechanisms is Bianchi’s model [6]. It takes the perspective of a target node and models the backoff process as a two dimensional MC, where state $(i,k)$ refers to the $i^{\rm th}$ backoff stage with the backoff counter $k\in\{0,\ldots,W_{i}-1\}$ , where $W_{i}$ is the duration of the contention window at the $i^{\rm th}$ retransmission attempt. The counter is decremented with probability $1$ whenever the channel is sensed idle; when it reaches [math], the STA attempts to transmit. The time spent in each state depends on what happens in the channel meanwhile, as it may be idle, used for a successful transmission, or used simultaneously by colliding STAs. The original model was proposed for omnidirectional communication, so that each STA is aware of ongoing transmissions and can defer its own when it senses the channel to be idle. Collisions only happen when multiple STAs access the channel simultaneously because their backoff counters expired (at least two STAs are in a state $(\cdot,0)$ ).

In the case of directional communication, however, STAs may not hear ongoing transmissions, resulting in a much higher collision probability. In this work, we assume that the RTS/CTS mechanism is used. Since a STA communicates only with the AP, it always has both its transmitting and receiving antenna patterns configured towards it. The AP instead listens to the channel in a quasi-omnidirectional (QO) mode, and, upon the reception of an RTS, it switches its antenna configuration to point towards the STA that sent it. Fig. 2 illustrates the direction of the various phases of the communication between a STA and the AP. Note that the messages can be heard only by a limited number of other STAs. The received power $P_{\rm rx}$ at a STA is in fact

[TABLE]

where $P_{\rm tx}$ is the power used to transmit, $d$ is the distance from the transmitter, $\eta$ is the path-loss exponent, $A$ is a normalizing path-loss term, and $g_{\rm tx}$ and $g_{\rm rx}$ are the antenna gains of the transmitter and receiver, respectively. They both depend on the direction of the antennas with respect to the line of sight between the two STAs, thus on the angles $\theta_{\rm tx}$ and $\varphi_{\rm rx}$ . If the gains are very small, $P_{\rm rx}$ may be too low in order for the receiver to decode the signal properly.

Consider a network consisting of $n$ STAs and a target STA that communicates with the AP, so that the STA and the AP point to each other, and the antenna gains in the other directions are minimal. It is possible to cluster the other $n-1$ STAs into four groups:

•

$n_{I,1}$ : STAs that can overhear the messages sent from the target STA to the AP but not those sent from the AP to the STA.

•

$n_{I,2}$ : STAs that can overhear the messages from the AP to the target STA but not those from the STA to the AP.

•

$n_{I,3}$ : STAs that can overhear the whole communication between the AP and the target STA.

•

$n_{I,4}$ : STAs that cannot overhear any messages exchanged between the AP and the target STA.

Analogously, from the perspective of a STA that listens to the channel, the other STAs can be divided into four groups $n_{O,1}$ (STAs of which it can hear the messages to the AP but not the messages that the AP sends to them), $n_{O,2}$ (STAs of which it cannot hear the messages to the AP but can hear those that the AP sends to them), $n_{O,3}$ (STAs of which it can hear all the messages exchanged with the AP), and $n_{O,4}$ (STAs whose messages exchanged with the AP cannot be heard).

Bibliography21

The reference list from the paper itself. Each links out to its DOI / PubMed record.

1[1] IEEE 802.11 WG, “IEEE 802.11ad, amendment 3: Enhancements for very high throughput in the 60 G Hz band,” Dec. 2012.
2[2] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular wireless networks: Potentials and challenges,” Proceedings of the IEEE , vol. 102, no. 3, pp. 366–385, March 2014.
3[3] T. Nitsche, C. Cordeiro, A. B. Flores, E. W. Knightly, E. Perahia, and J. C. Widmer, “IEEE 802.11ad: directional 60 G Hz communication for multi-Gigabit-per-second Wi-Fi,” IEEE Communications Magazine , vol. 52, no. 12, pp. 132–141, Dec. 2014.
4[4] S. Kutty and D. Sen, “Beamforming for millimeter wave communications: An inclusive survey,” IEEE Communications Surveys & Tutorials , vol. 18, no. 2, pp. 949–973, Second Quarter 2016.
5[5] B. Satchidanandan, S. Yau, P. Kumar, A. Aziz, A. Ekbal, and N. Kundargi, “Track MAC: An IEEE 802.11ad-compatible beam tracking-based MAC protocol for 5G millimeter-wave local area networks,” in International Conference on Communication Systems & Networks (COMSNETS) . IEEE, Jan. 2018, pp. 185–182.
6[6] G. Bianchi, “Performance analysis of the IEEE 802.11 distributed coordination function,” IEEE Journal on Selected Areas in Communications , vol. 18, no. 3, pp. 535–547, March 2000.
7[7] A. Akhtar and S. C. Ergen, “Directional MAC protocol for IEEE 802.11ad based wireless local area networks,” Ad Hoc Networks , vol. 69, pp. 49–64, Feb. 2018.
8[8] Q. Chen, J. Tang, D. T. C. Wong, X. Peng, and Y. Zhang, “Directional cooperative MAC protocol design and performance analysis for IEEE 802.11ad WLA Ns,” IEEE Transactions on Vehicular Technology , vol. 62, no. 6, pp. 2667–2677, July 2013.