594 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 1, JANUARY 2019
Fig. 1. Dense mmWave network architecture.
beamforming gain G is
G (α, ϑ)=
2π −(2π −α)
α
, if |ϑ|≤
α
2
,
, otherwise,
(1)
where α is the beamwidth of the mainlobe in radian, ϑ is the
beam offset angle to the mainlobe in radian, is the gain of the
sidelobe and 0 < 1.
For analytical tractability, we assume that the number of
beams of AP and STA is limited, and each beam covers a
unique direction in a non-overlapping way. Then, the maxi-
mum number of beams of AP and STA could be b
AP
=
2π
α
AP
and b
STA
=
2π
α
STA
, respectively, where α
AP
and α
STA
are the
beamwidths of AP and STA, respectively.
B. Efficient Beamforming Training Mechanism for Dense
mmWave Network
As shown in Fig. 1, when an STA is covered by multiple
APs (e.g., STA c is covered by SAP i and SAP j), in order
to allow the STA to select a suitable AP (e.g., SAP j) among
all APs for connecting in terms of smaller interference, the
STA should perform BFT with its surrounding APs in advance.
However, the BFT mechanism in IEEE 802.11ad/ay focuses on
the BFT between one AP and one STA or between one AP and
multiple STAs. If the BFT mechanism in IEEE 802.11ad/ay
is directly applied into dense mmWave network, there will be
serious collision problem when multiple APs begin to perform
BFT simultaneously [19], [21], [35], [36]. Otherwise, if all APs
are forced to perform BFT one by one to avoid collision, the
BFT will be inefficient in dense mmWave network. As shown
in Fig. 2 and Fig. 3, according to the BFT in IEEE 802.11ad/ay
we propose an efficient BFT mechanism to coordinate the BFT
processes of every AP and STA so that many duplicated BFT
processes can be merged. The details of our proposed efficient
BFT mechanism are shown as below:
Fig. 2. Step 1: Beamforming training between MAP and SAPs.
Step 1: BFT between MAP and SAPs.
1) MAP transmits directional multi-gigabit (DMG) Beacon
frames in all its beams to perform initiator sector sweep
(ISS).
2) Each SAP selects a training slot (i.e., association beam-
forming training slot i n IEEE 802.11ad/ay) to perform re-
sponder sector sweep (RSS) by transmitting sector sweep
(SSW) frames in all beams (the training results of ISS are
contained in SSW frames).
3) MAP transmits SSW-Feedback frames (i.e., “FB” in
Fig. 2) to the SAPs who have finished RSS through the
best beams indicated in the training results of ISS. In ad-
dition, the best beam of each SAP will be contained in
SSW-Feedback frames.
Step 2: BFT between APs and STAs.
1) Each AP transmits SSW frames in all beams t o perform
BFT of the AP side. At this moment, all the STAs are
staying in quasi-omni listening mode.
2) Each STA selects a training slot (i.e., association beam-
forming training slot in IEEE 802.11ad/ay) to perform
BFT of the STA side by transmitting SSW frames in all
its beams (the training results of the AP side are contained
in SSW frames). At this moment, all the APs are staying
in quasi-omni listening mode.
3) After receiving the SSW frames from STAs, each SAP
will transmit the training results to MAP through “SAP
FB” frame. Thus, MAP can obtain the BFT information
of every STA.
4) MAP transmits the BFT information of every STA to SAPs
through “MAP FB” frames.
5) At last, one SAP will be selected based on the BFT infor-
mation to transmit a “FB” frame to each STA. The “FB”
frame will inform the STA the best beams between itself
and its surrounding APs.
It is worth noting that, after finishing Step 1 and Step 2, only
the transmit BFT of APs and STAs were performed, while the
receive BFT of APs and STAs did not [21], [35], [36]. According
to the reciprocity of directional beams in mmWave band, we can
conclude that both transmit BFT and receive BFT are done in a
similar way [1], [36]. However, if receive BFT is needed, beam
refinement protocol (BRP) phase in IEEE 802.11ad/ay can be
performed by applying the similar modifications of Step 1 and
Step 2. For more details (e.g., training processes and specific
frame formats), please refer to [19], [21], [36].
We assume each AP performs BFT one by one to avoid the
collision, and the detailed BFT processes can refer to [19], [21],
[36]. Since each AP and STA can generate b
AP
and b
STA
beams,
respectively, for the BFT mechanism in IEEE 802.11ad/ay, t he