Auxiliary beam pair enabled initial access for mmWave D2D networks

Physical Communication xxx (xxxx) xxx

Contents lists available at ScienceDirect

Physical Communication journal homepage: www.elsevier.com/locate/phycom

Full length article

Auxiliary beam pair enabled initial access for mmWave D2D networks Sadaf Nawaz a , Syed Ali Hassan a , Haejoon Jung b , a b

∗

School of Electrical Engineering and Computer Science (SEECS), National University of Sciences & Technology (NUST), Islamabad, Pakistan Department of Information & Telecommunication Engineering, Incheon National University, Incheon, 22012, Korea

article

info

Article history: Received 30 July 2019 Received in revised form 28 January 2020 Accepted 30 January 2020 Available online xxxx Keywords: mmWave Beamforming gain Device-to-device Initial access Auxiliary beam pair Discovery delay

a b s t r a c t In this paper, we propose two auxiliary beam pair (ABP) schemes, i.e., auxiliary-half (AH) and auxiliaryfull (AF) to improve the initial access (IA) mechanism in a millimeter wave (mmWave) device-to-device (D2D) network. In AH, a uniform linear array (ULA) is split equally to form two simultaneous beams at both transmitter (TX) and receiver (RX) for device detection. The detection process takes place through the generation of antenna scan sequences. On the other hand, AF utilizes the full antenna array to form one beam at a time at RX and TX and searches the same sector twice in a time division manner. We also employ beamforming (BF) technique in the already existing schemes in literature, i.e., oblivious directional neighbor discovery (ODND) and Polya’s Necklaces. We compare all the schemes and it is shown that both AH and AF exhibit a high dependence on the separation between the beam pair. We also prove the dependence of discovery delay (DD) on the signal-to-noise ratio (SNR) which is contrary to the worst-case DD upper-bound given by ODND. For a reasonable value of beam separation, high SNR threshold and high TX–RX separation, AH achieves a lower DD than all other schemes. Moreover, AF outperforms all other schemes in terms of probability of miss detection (PMD) and for a considerable beam separation, low SNR threshold and low RX–TX separation, it also achieves a lower DD than ODND, Polya’s Necklaces and AH. © 2020 Elsevier B.V. All rights reserved.

1. Introduction The millimeter wave (mmWave) frequencies (30–300 GHz), which can achieve data rates of multigigabits, have been used for point-to-point communication. Recently, mmWave is being analyzed for cellular networks as well. However, this new application poses many challenges with respect to propagation losses and strict constraints on cost, size and power consumption. Given the scarcity of available sub-6 GHz band, along with increasing demand for wireless and broadband data services, mmWave technologies for cellular systems have attracted intense interest in the recent years [1]. The mmWave deployment will utilize beamforming (BF) through a large transmit and receive antenna array to ensure adequate received signal power. The antenna arrays can be steered in different directions to achieve high BF gains. Hence, directional transmission not only ensures high gains but compensates for attenuation, absorption and high path loss [2]. In this scenario, initial access (IA) becomes a key parameter in mmWave systems and is the focus of our work. IA is a mechanism where both transmitter (TX) and receiver (RX) direct their beams in a suitable direction to ensure subsequent communication [3]. ∗ Corresponding author. E-mail addresses: [email protected] (S. Nawaz), [email protected] (S.A. Hassan), [email protected] (H. Jung).

Recently, BF techniques have been discussed in literature for wide variety of applications, however, we restrict ourselves to only the IA mechanism for mmWave systems. An ABP scheme is constructed at the TX [4] and at both TX and RX in [5] and [6] by generating two beams in a desired scan region. The TX sends orthogonal signals via two beams in a particular direction and the RX computes the channel state information. After the signal is received, the RX calculates a ratio metric by comparing the amplitude of each beam. The quantized version of ratio metric is fed back to the TX and based on the received feedback, the TX adjusts its BF direction and finally the data transmission starts. A high performance with respect to angle estimation under various SNR levels and channel conditions is achieved. In our previous work [7], we proposed two novel ABP schemes, i.e., auxiliary-half (AH) and auxiliary-full (AF) for IA in a mmWave system. We employ a uniform linear array (ULA) at the TX and omnidirectional antenna at the RX for both schemes. In AH the antenna array is divided into two equal parts and each part generates a separate beam. The two beams are generated simultaneously in a certain direction to detect a user. The two beams scan the entire region in a sequential manner for user detection. If a user is detected before the beam sweeping process ends, then the search stops. Otherwise, the beams sweep the entire region and the search ends with a missed user detection. On the other hand, in AF, the full antenna array generates two beams in a time-division

https://doi.org/10.1016/j.phycom.2020.101039 1874-4907/© 2020 Elsevier B.V. All rights reserved.

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

2

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

manner. For example, during time slot 1, one beam is generated at a specific angle in a certain search sector to locate a user. If the user is not detected in time slot 1, then in time slot 2 another beam is generated in the same sector but at a slightly different angle. In this way, two beams are generated in the same search sector but during two different time slots to locate the user. The beams sweep the entire region for user detection and if the user is not detected after the entire region is scanned, a missed detection occurs. However, the proposed AH and AF schemes were used in cellular region where a BS performs IA with a cellular user. In this study we perform IA for two users which operate in device-to-device (D2D) mode. To achieve a high-quality cellular network, the short-distance technology, known as D2D has attracted significant research interest recently. D2D is also gaining popularity for device-centric communications [8]. However, large scale deployment of D2D is still under consideration, mainly due to insufficient bandwidth in the microwave band and severe interference. Recently, mmWave is being exploited for D2D to cater these challenges. The D2D communication with respect to line-of-sight (LoS) mmWave link is discussed in [9]. The D2D selects between a mmWave and microwave band for data transmission. For a distributed mmWave communication, D2D users detect a LoS link along with beam forming direction. The performance is analyzed through stochastic geometry and it is concluded that the performance gain of proposed algorithm is high as compared to single band communication. The mmWave performance in a clustered D2D network is also analyzed in [10] where the D2D transceiver location is modeled as a Poisson cluster process. The coverage probability with respect to intra-cluster interference is investigated and by choosing an optimal number of D2D pairs, the area spectral efficiency can be maximized. Directional antenna for neighbor discovery in a distributed wireless network has also been studied in [11]. An oblivious directional neighbor discovery (ODND) algorithm is devised that guarantees device discovery with minimal worst-case discovery delay in an asynchronous heterogeneous network. The algorithm ensures device discovery irrespective of the antenna bandwidth and node positions in a bounded time. In this scheme, an antenna scan sequence is generated to point one TX and one RX beam in a particular direction. The nodes keep scanning the entire region according to their respective scan sequences. During this scanning process, when the beams of both TX and RX get aligned, only then the devices would discover each other. It is shown that the devices always discover each other within minimal worst-case discovery delay. Device discovery is also ensured by Hunting-based Directional Neighbor Discovery scheme for mmWave systems in [12]. The nodes rotate their beams continuously in either clockwise or anticlockwise direction at a fixed angular velocity. A node in the scheme scans the entire region for its neighbors. The algorithm ensures device discovery and a bound for worst-case discovery delay. Neighbor discovery is also analyzed in autonomous unmanned aerial vehicles. A fully uncoordinated matrix-based channel hopping algorithm is proposed in [13]. When the channels overlap, the device discovery is guaranteed. A probability based dynamic discovery algorithm is also discussed for varying channels and it is shown that the algorithm ensures timely rendezvous with high probability. For D2D communication, neighbor discovery in a mmWave system is discussed in [14]. A device discovery algorithm is proposed that uses the concept of necklaces to minimize the worstcase discovery delay. The device discovery process is based on the generation of antenna scan sequences as discussed in [11] but the worst-case discovery delay is calculated through Polya’s Necklaces. The algorithm reduces the worst-case discovery delay

as compared to [11] by utilizing the Fredricksen, Kessler and Maiorana (FKM) Algorithm. Hence, shorter and efficient scan sequence further improves neighbor discovery in a decentralized network. In this paper, we propose to use the two BF techniques, i.e., AH and AF to further improve the performance of IA in D2D communications in terms of PMD and DD. In our previous work [7], the idea of BF through AH and AF techniques was exploited in a cellular network. The BS was scanning the entire region in a sequential manner to search for a user in its vicinity. However, in this paper, we employ BF through ULA at both TX and RX for a D2D network. Furthermore, both TX and RX scan the region randomly according to the newly proposed antenna scan sequences. We generate scan sequences for beam pairs unlike the single beam scan sequence given in [11]. The well structured beam pairs in a D2D system help acquire low DD and low PMD under various SNR levels, beam separation values, number of antenna elements and TX–RX separation. In particular, the main contributions of this work are summarized as follows

• We propose two ABP schemes, i.e., AH and AF in a D2D system. In AH, the antenna array is split into two equal parts to generate two simultaneous beams, whereas, AF utilizes the full antenna array to form two beams in a time division manner. AH and AF are employed at both TX and RX of a D2D pair. • The already existing techniques of ODND and Polya’s Necklaces lack BF in a D2D network. Hence, we develop a mathematical model for BF in these existing schemes for a comprehensive analysis and generate new antenna scan sequences for beam pairs in AH and AF that help both TX and RX to scan the region in a non-sequential manner. • Through BF at both TX and RX, we further prove that the upper-bound for worst-case discovery delay proposed in ODND scheme [11] might not always be true. We show through our evaluations that the DD is highly dependent on the SNR, whereas the upper-bound of ODND is independent of SNR. Hence, the worst-case DD cannot be upper-bounded as proved in ODND. • We perform an extensive study by analyzing the DD and PMD for all D2D search algorithms with respect to variable SNR levels, beam separation values, number of antenna elements and TX–RX separation. The rest of the paper is organized as follows. In Section 2, we propose the two new schemes through BF and antennas sequence generation. We also review the ODND and Polya’s Necklaces schemes with respect to BF. Section 3 evaluates the performance of all the algorithms with respect to PMD and DD. Finally, the main findings are summarized in Section 4. 2. Initial access schemes In this section, we discuss our proposed algorithms, i.e., AH and AF with respect to antenna scan sequences and BF techniques. We also employ BF methods in the previously known algorithms, i.e., ODND and Polya’s Necklaces for a comprehensive approach. First, we will discuss the BF techniques in all four schemes, i.e., AH, AF, ODND and Polya’s Necklaces. Later, the antenna scan sequence generation along with BF will be explained in detail. 2.1. Beamforming 2.1.1. Auxiliary-half The basic design principle of RX and TX antenna BF is first illustrated. It is assumed that both TX and RX employ a ULA. The

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

3

according to the antenna scan sequence. The generation of antenna scanning sequence includes both random and deterministic components [11,15]. The scan region for both TX and RX is divided into a number of search sectors, i.e. NtAH and NrAH search sectors for TX and RX, respectively. Mathematically, NrAH = Fig. 1. Beamforming for auxiliary-half scheme.

NtAH =

TX and RX simultaneously form two beams, i.e., beamt α , beamt β are generated at the TX and beamr α , beamr β are formed at the RX as shown in Fig. 1. The total antenna elements, Nr , in the RX ULA are divided into two equal parts such that beamr α and beamr β occur simultaneously. Mathematically, Nr = Nr1 + Nr2 ,

(1)

where Nr1 and Nr2 are the antenna elements forming beamr α and beamr β , respectively. The vector contribution from elements Nr1 and Nr2 can be summed as Nr1 −1 ∑ 1 Xr1 (θ ) = √ e(−j2π d(n) sin(θ ))/λ , Nr1

(2)

∑ 1 Xr2 (θ ) = √ e(−j2π d(m) sin(θ ))/λ , Nr2

(3)

n=0 Nr2 −1

m=0

where d and λ are the spacing between antenna elements and wavelength, respectively. Also, θ ∈ [−π/2, π/2] is the angle-ofarrival (AoA). The chosen θ range helps avoid the grating lobes [12]. The beamr α and beamr β are steered in different directions, φr α and φr β , such that 1

Nr1 −1

e(j2π d(n) sin(φr α ))/λ ,

(4)

∑ 1 W (φr β ) = √ e(j2π d(m) sin(φr β ))/λ , Nr2

(5)

W (φ r α ) = √ Nr1

∑ n=0 Nr2 −1

180◦ ◦ BWrAH

180◦ ◦ BWtAH

Yr α = Xr1 (θ ) × W (φr α ),

=

Yr β =

sin(Nr1 π d(sin(θ ) − sin(φr α ))/λ)

Nr1 × sin(π d(sin(θ ) − sin(φr α ))/λ)

,

sin(Nr2 π d(sin(θ ) − sin(φr β ))/λ) Nr2 × sin(π d(sin(θ ) − sin(φr β ))/λ)

.

(6)

HPBW ◦rAH =

Yt α =

Yt β =

Nt1 × sin(π d(sin(θ ) − sin(φt α ))/λ) sin(Nt2 π d(sin(θ ) − sin(φt β ))/λ) Nt2 × sin(π d(sin(θ ) − sin(φt β ))/λ)

, .

,

(11)

50.8◦ (Nx dcos(ϕ )/λ)

,

(12)

where Nx ∈ {Nr1 , Nr2 }, ϕ is the scan angle, i.e., ϕ = φr α or ϕ = φr β . The HPBW changes at different scan angles and the smallest value is achieved at ϕ = 0◦ . Therefore, for simplicity, the HPBW is fixed according to 0◦ for our entire analysis. Furthermore, the search beamwidth1 is determined from the HPBW as ◦ ◦ BWrAH = HPBWrAH + δ,

(13)

where δ is the separation between beamr α and beamr β . Similarly, the beamwidth for TX is calculated as ◦ ◦ BWtAH = HPBWtAH + δ.

(14)

2.1.2. Auxiliary-full The design principal of AF is similar to AH with the only difference that in AF two beams are formed in two different time slots with a separation of δ between the beams. Both TX and RX form a beam with all antenna elements, i.e., Nt and Nr , respectively. The TX and RX scan each sector twice in a time division manner as shown in Fig. 2. For the RX, the radiation pattern in different time slots is calculated as sin(NrAF π d(sin(θ ) − sin(φr α ))/λ)

Yr α (t1 ) =

NrAF × sin(π d(sin(θ ) − sin(φr α ))/λ)

Yr β (t2 ) =

NrAF × sin(π d(sin(θ ) − sin(φr β ))/λ)

sin(NrAF π d(sin(θ ) − sin(φr β ))/λ)

,

(15)

,

(16)

where t1 and t2 are two different time slots in which beams are ◦ ◦ formed. The HPBWrAF and BWrAF is given as HPBW ◦rAF =

(7)

50.8◦ (NrAF d cos(ϕ )/λ)

,

(17)

◦ ◦ BWrAF = HPBWrAF + δ.

Similarly, the radiation pattern for TX is given as sin(Nt1 π d(sin(θ ) − sin(φt α ))/λ)

(10)

where the scanning region is limited to 180◦ to avoid grating ◦ ◦ lobes and BWtAH , BWrAH are the TX and RX search beamwidths, respectively. The RX half power √ beamwidth (HPBW) is obtained by equating (6) or (7) to 1/ 2 and solving for θ [16], such that

m=0

where W (φr α ) and W (φr β ) are the weights adjusting the signal phase. Hence, the array factor or radiation pattern is given as

,

(18)

(8)

The TX beamwidth is calculated in a similar way as (15)–(18).

(9)

2.1.3. ODND and Polya’s Necklaces ODND and Polya’s Necklaces employ beamforming by utilizing all antenna elements of the ULA. Both TX and RX form one beam at a time to scan a given sector. In ODND, the array factor for RX is calculated as

where θ ∈ [π /2, 3π /2] is the angle-of-departure (AoD). For IA, both RX and TX need to discover each other. RX and TX search for each other by forming beams in different directions. When the beams of RX and TX get aligned and there is sufficient signal power, only then both the devices discover each other. The mechanism of BF in a particular direction is a pseudodeterministic process, where the beam direction is determined

Yr =

sin(NrOdnd π d(sin(θ ) − sin(φr ))/λ) NrOdnd × sin(π d(sin(θ ) − sin(φr ))/λ)

.

(19)

1 A sector or search beamwidth is defined by the HPBW of beam (beam ) rα rβ plus the separation between beamr α (beamr β ) and beamr β (beamr α ).

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

4

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

Fig. 2. Beamforming for auxiliary-full scheme.

The search area is divided into NrOdnd sectors such as NrOdnd =

180◦ ◦ BWrOdnd

=

180◦ ◦ HPBWrOdnd

.

(20)

◦ ◦ are equal in this case. Similar calcuand BWrOdnd The HPBWrOdnd lations follow for TX part of ODND and Polya’s necklaces.

2.2. Antenna scan sequence The antenna scan sequence generation for ODND and Polya’s Necklace is well discussed in [11,14,15]. We modify the scan sequence for the generation of ABP in our proposed algorithms. 2.2.1. ODND In ODND, there are M devices in the network that can only discover each other when their antenna beams get aligned. For example, there are Am number of antennas per device, m refers to device index, m ∈ {0, 1, . . . , M − 1}. Based on Am , each device scans the search region according to the beamwidth Bm , where (0 < Bm < 2π ). Each device has Nodnd = 2π/Bm search sectors. For example, in Fig. 3, Node a has 3 sectors and Node b has 4 sectors. Both devices point their beams in different sectors based on a scanning sequence. The scanning sequence is used to direct the antenna beam towards a specific sector in a given time slot. The scenario given in Fig. 3 is described in Fig. 4 with respect to the discovery process and scanning sequence. It is clear from Fig. 4 that the devices discover each other when device a points its beam in sector 2 and device b directs it in sector 1. Each device has a unique ID, known as device ID, which can be represented as a binary number. The minimum number of bits for a device ID is determined by the total number of devices in the network. For example, for a network with M devices, the least number of bits must be ⌈log2 (M)⌉. Each device can construct its extended address using this device ID. The extended address is created such that it is mutually cyclically rotationally distinct for each device, i.e., each extended address is unique and cannot be obtained by cyclic rotation of any other extended addresses. This condition ensures neighbor discovery for arbitrary device orientations that may not be synchronous. The extended address length Lodnd is a key parameter in determining the neighbor discovery latency. The construction of extended ID sequence proposed in [11] is summarized as follows.

Fig. 3. Antenna configuration of Node a and Node b with 3 and 4 antenna sectors, respectively.

• Let m denote the ID of device m, which is la bits long binary sequence and m(k) denoting the kth bit of m. Typically, la is chosen such that la = ⌈log2 (M)⌉. • Let m1 and m2 represent the sequence from m(1) to m(ka − 1) and from m(ka ) to m(la − 2), where ka = ⌊la /2⌋. • The extended ID sequence E and its length Lodnd is calculated as E = [0(lb ), m1 , 1, 0, m2 , 1(lc )],

(21)

Lodnd = la + lb + lc + 2,

(22)

where 0(lb ) and 1(lc ) are string of all zeros and ones of length lb and lc , respectively. lb and lc are chosen such that the total length of Lodnd is odd and minimum. The antenna scan sequence is given as

⎧ ⎨t mod pm , Ut = t mod qm , ⎩

rand(Nodnd − 1),

et m = 0 and t mod pm < Nodnd . et m = 1 and t mod qm < Nodnd .

(23)

otherwise,

where pm is the smallest odd prime number not less than Nodnd and co-prime to Lodnd . qm is the smallest power of 2 not less

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

5

Fig. 4. Example of antenna scan sequences where Node a and Node b discover each other in time slot 2.

Fig. 5. Example of antenna scan sequences where TX and RX discover each other in time slots 3 and 10.

• Alternatively, necklaces can also be represented as binary strings, i.e., black and white beads are represented by 0 and 1, respectively. • Hence, the total number of necklaces that can be generated according to b and c, is calculated by Polya’s Enumeration theorem as Fig. 6. Two unique necklaces with different colored beads (bits).

N(b, c) = than Nodnd and et m denotes a bit in E at a given time instant and rand(Nodnd − 1) is uniform random integer in [0, Nodnd − 1]. The worst-case discovery delay between two devices, i.e., RX and TX, is dependent on Lodnd and is upper-bounded by W = Lodnd max{pr qt , pt qr }.

(24)

The generation of antenna scan sequence and user discovery can be well understood by Fig. 5. Here, both TX and RX have 7 search sectors each and the extended IDs, pm , qm , Lodnd and W is calculated according to (21)–(24). It is shown that the nodes can discover each other only when their beams point in search sector 3. Hence, the devices get aligned in time slots 3 and 10 for successful discovery. 2.2.2. Polya’s Necklaces Polya’s Necklaces is another device discovery technique based on antenna scan sequence. The antenna sequence is generated in a similar way as ODND. However, the algorithm is more energy efficient by its reduced worst-case discovery delay. The length of extended address Lpoly is calculated in a different way. The algorithm proposed in [14] is summarized as follows.

• It is a technique where necklaces employ b beads with c different colors, connected circularly and invariant to rotation. For example, in Fig. 6 two necklaces can be created if b = 1 (one bead in each necklace) and c = 2 (two colors, black and white).

v 1∑

b

ϕ (gm )eb/gm ,

(25)

m=1

where gm represents the v divisors of b and ϕ is the Euler’s totient function which can be expressed as

ϕ (g) = g

v ∏ n=1

(1 −

1

ρm

),

(26)

where ρm represents the v distinct prime factors of g. For example, if g = 8, then there are three numbers that are co-prime to g, i.e., 1, 3 and 7. Hence ϕ (8) = 3. • To determine the smallest odd Lpoly , the Polya’s Necklaces method is used where Lpoly = minimize b s.t. N(b, 2) ≥ M , and mod (b, 2) = 1.

(27)

• Once the Lpoly is selected, the extended addresses can be assigned to generate all the binary necklaces through FKM algorithm.2 2.2.3. Auxiliary-half In AH, two beams are formed simultaneously. Therefore, two antenna scan sequences will be generated at a given time instant. The number of scan sectors is determined by NAH and both beams are formed within one main scan sector as shown in Fig. 7. 2 FKM algorithm is not explained due to lack of space. See [14] for details.

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

6

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

To determine the total BF gain of RX, GBFR , first we calculate the BF gains of beamr α and beamr β and then the total RX BF gain is given as

Fig. 7. Antenna configuration of RX and TX with 3 main sectors (NAH = 3) each having 6 subsectors. Devices discover each other when sectors 2, 3 of both TX and RX get aligned.

Gr α = |Yr α |2 ,

(33)

Gr β = |Yr β |2 ,

(34)

GtotalR = Gr α + Gr β ,

(35)

It is assumed that the RX BF gain remains constant in a search sector at a given time instant. Hence, GBFR is calculated as GBFR (db) = max (GtotalR ) − 3db.

(36)

The BF gain of TX (GBFT ) is calculated in a similar way. Hence, the total antenna gain G is given as The antenna sequences generated for subsectors Uα and Uβ are given as

⎧ m ⎪ ⎨2(xpm mod pm ), et = 0, 0 ≤ 2(xpm mod pm ) ≤ 2(NAH − 1). Uα = 2(xqm mod qm ), et m = 1, 0 ≤ 2(xqm mod qm ) ≤ 2(NAH − 1). ⎪ ⎩2y, otherwise, (28) ⎧ m ⎪ ⎪ ⎨2(xpm + 1 mod pm ) − 1, et = 0, 1 ≤ 2(xpm + 1mod pm ) − 1 ≤ 2NAH − 1. Uβ = 2(xqm + 1 mod qm ) − 1, et m = 1, 1 ≤ 2(xqm + 1mod qm ) − 1 ≤ 2NAH − 1. ⎪ ⎪ ⎩ 2y + 1, otherwise,

(29) where y = rand(NAH − 1), xpm = t + pm and xqm = t + qm . Both TX and RX detect each other if the beams of both devices face each other as shown in Figs. 7 and 8. In Fig. 8, both TX and RX form two beams simultaneously. When the beams are formed in subsectors 2 and 3 of TX and RX, it is assumed that the devices have discovered each other. It is to be noted that discovery time for AH is lower (1 time slot) than ODND (3 time slots) because the number of search sectors in AH is reduced when two simultaneous beams are formed. Based on the antenna scan sequence, we implement BF at both TX and RX. It is to be noted that when BF is implemented, (24) may no longer be valid. This is because the worst-case discovery delay is independent of the SNR, τ in (24). However, τ plays a vital role in device discovery and is the main focus of our study. The system model is summarized as follows. The search area spanned by two RX beams at a given time instant is found as

(

Uα

)

θe◦α

◦ BWAH , θs◦α = 90◦ − 2 ( ) Uα + 1 ◦ = 90◦ − BWAH ,

θe◦β

◦ θsβ = 90 − BWAH , 2 ( ) Uβ + 1 ◦ = 90◦ − BWAH ,

(30)

2

◦

◦

(

Uβ

)

(31)

2

where θsα , θeα and θs◦β , θe◦β mark the start and end of beamr α and beamr β , respectively. The direction of both the beams is given as ◦

◦

δ φr α = θe◦α + , 2

δ φr β = θs◦β − . 2

G(dB) = GR + GT + GBFR + GBFT ,

(37)

where GR , GT are the receive and transmit antenna gains, respectively. Now, the signal passes through a channel which is either LoS or non-line-of-sight (NLoS). The path loss can be calculated as

{ PL(dB) =

ρ + 10ψL log(r) + χL , if LoS . ρ + 10ψN log(r) + χN , otherwise,

(38)

where ρ is the fixed path loss factor, r denotes the distance between the receiver and transmitter, ψN and ψL are the NLoS and LoS path loss exponents, respectively. χN and χL denote the zero mean lognormal random variables for NLoS and LoS links, respectively, which represent shadowing. When a signal is received at the RX, then the received power is calculated as Pt Gζ , (39) Pr = PL where Pt is the transmit power and ζ is the squared envelope of multipath fading channel. The envelope follows a Rician or Rayleigh distribution depending on whether the link between the BS and UE is LoS or NLoS, respectively. The SNR is thus calculated as Pr τ = 2, (40)

σ

where σ 2 is the noise variance. A decision regarding the RX–TX link establishment is made according to the SNR threshold, γth , such that if

{

τ ≥ γth , link is established. τ < γth , otherwise.

(41)

The TX and RX start searching for each other by pointing their beams in a particular sector according to the antenna scan sequence. Both RX and TX send a synchronization signal, Tsyn , with ◦ ◦ beamwidth BWrAH and BWtAH , for Tsig seconds (s) in a particular sector. If the beams of RX and TX get aligned and τ ≥ γth , then both devices have discovered each other. However, if τ < γth , then both TX and RX wait for Tper (s) and then the search process continues according to the antenna scan sequence. It is to be noted that if τ < γth , it takes Tsig (s) for each TX and RX beam to scan the sector. Hence, the discovery delay is defined as the total time it takes for TX or RX to scan a given region (Tsig ) and the waiting time between scanning (Tper ). TX and RX keep scanning the regions until τ ≥ γth with which the discovery process stops. Mathematically, DDAH (t) = (t + 1)Tsig + (t)Tper ,

(32)

subject to :

(42)

τ ≥ γth

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

7

Fig. 8. Example of antenna scan sequences where TX and RX discover each other in slots 1 and 9.

Fig. 9. Example of TX and RX beam alignment in slot 1 but no device discovery as τ < γth . Devices discover each other in slot 9 when τ ≥ γth .

where t ∈ {0, 1, . . . , T } is the number of time slots. It is to be noted that unlike the worst-case discovery delay given by ODND scheme in (24), the DD for AH cannot be upper-bounded. It is because the DD is highly dependent on the SNR as shown in Fig. 9. 2.2.4. Auxiliary-full In AF, two beams are created in two different time slots but within one main sector as shown in Fig. 2. The beams formed within the subsectors are δ distance apart from each other. Thus, the antenna scan sequence for two beams is calculated as ⎧ m ⎪ ⎨2(xpm mod pm ), et = 0, 0 ≤ 2(xpm mod pi ) ≤ 2(NAF − 1). m Uα (tev en ) = 2(xqm mod qm ), et = 1, 0 ≤ 2(xqm mod qi ) ≤ 2(NAF − 1). ⎪ ⎩ 2y, otherwise, (43)

Uβ (todd ) =

⎧ ⎪ 2(z mod pm ) + 1, et −1 m = 0, 1 ≤ 2(zpi mod pm ) + 1 ≤ 2NAF − 1. ⎪ ⎨ pm 2(zqm mod qm ) + 1,

⎪ ⎪ ⎩

2y + 1,

et −1 m = 1, 1 ≤ 2(zqi mod qm ) + 1 ≤ 2NAF − 1.

starting time index is assumed to be t = 0 or any even index. However, if the starting time index is odd then (43) and (44) are interchanged, i.e., (43) is used for odd indices and (44) is used for even index calculation. Similar to AH, the search area spanned by both RX and TX is calculated according to (30)–(32). However, the BF gain at RX and TX is calculated independently in each time slot, i.e., Gα−BFR (t1 ) = |Yr α (t1 )|2 ,

(45)

Gα−BFT (t1 ) = |Yt α (t1 )|2 .

(46)

From the gain calculated in time slot 1, SNR is determined following (36)–(41). It is to be noted that unlike AH, the BF gain is not the sum of gains obtained from beamα and beamβ . Similar to AH, AF is also dependent on SNR for device discovery as shown in Fig. 10. Thus, the DDAF is calculated according to (42) for each time slot. 3. Performance analysis

otherwise,

(44) where Uα (tev en ) and Uβ (todd ) are the beamα and beamβ formed at even and odd time slots, respectively, y = rand(NAF − 1), zpm = xpm − 1 and zqm = xqm − 1. It is to be noted that the

In this section, we analyze the performance of AH, AF, ODND and Polya’s Necklaces in terms of DD and PMD. Both transmitter and receiver employ a ULA with Nr = Nt = 4 antenna elements. The search beamwidth is calculated independently for each scheme. For simplicity, we have assumed a fixed distance r

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

8

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

Fig. 10. Example of antenna scan sequences where TX and RX discover each other in slots 8 when τ ≥ γth .

Fig. 12. DD for ODND and AH with variable δ .

Fig. 11. PMD for ODND and AH with variable δ . Table 1 System parameters. Parameter

Value

Parameter

Value

Parameter

Value

fc Pt GT GR

73 GHz 30 dBm 0 dBi 0 dBi

αL αN

2 2.5 200 µs 10 µs

r

15 m 70 dB 5.2 dB 7.2 dB

Tper Tsig

ρ

Std(χL ) Std(χN )

between TX and RX. The channel is generated either as a NLoS or LoS by following a Bernoulli distribution and the results are approximated using 105 Monte Carlo simulations via MATLAB. The simulation parameters are summarized in Table 1. 3.1. ODND vs. AH Fig. 11 shows the PMD performance for ODND and AH against

γth . The values of Lodnd = LAH = 3 is calculated according to

(22) for ODND and AH. For two devices, E is calculated according to (21) such that et r = 101 and et t = 100. During one Monte Carlo simulation, both TX and RX keep scanning the region until the devices have not discovered each other or the worst-case discovery delay is not reached according to (24). For AH, we calculate the worst-case delay in a similar way as given in (24) for better understanding of the DD upper-bound proposed in [11]. In ODND, the RX and TX utilize all the antenna elements to form one beam, hence, the PMD is low for ODND. The BF gain at both TX and RX is high and there is high probability of device detection since the SNR is high. On the other hand, the PMD=0 for lower values of γth when AH scheme is employed. Although the BF gain is low for AH but for lower values of γth , both TX and RX keep scanning the region for maximum time slots (W = LAH pr qt ) and detect each other within this time. However, as the γth increases beyond 22 dB, it becomes difficult for AH to detect the devices

Fig. 13. Time slots required for device discovery in ODND and AH with variable δ.

because of low BF gain. Hence, even after scanning the region for maximum time slots, TX and RX cannot find each other all the time. So, the PMD is higher as compared to ODND. It is to be noted that the worst-case discovery delay does not ensure 100% device discovery for both ODND and AH. Hence, the upper-bound given in (24) is not always valid. The discovery process in highly dependent on the SNR. In [11] the SNR parameter is not considered while calculating the upper-bound, hence worstcase discovery delay does not always ensure device detection. Fig. 12 shows that the DD is the least for AH with δ = 25◦ . It is because the beamwidth has increased due to increased separation between beamα and beamβ . This in turn increases the coverage

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

9

Fig. 14. PMD for ODND and AF with variable δ .

Fig. 16. PMD for Polya’s necklaces and AH with variable δ .

Fig. 15. DD for ODND and AF with variable δ .

Fig. 17. DD for Polya’s necklaces and AH with variable δ .

area. Hence, it takes less time to scan the region. However, it is to be noted that for lower values of γth , AH with variable δ still performs better than ODND. It is due to the fact that the γth value is low and even with low BF gain, AH can discover the devices. But for γth = 26 dB it is seen that ODND starts performing better than AH with δ = 0◦ , 5◦ , 10◦ . It is because since the γth is high, it becomes difficult for AH to detect a device because of low BF gain. AH has to scan maximum time slots (as shown in Fig. 13) to detect a device, hence it takes more time during each Monte Carlo simulation. Whereas, since the BF gain is high for ODND, it can scan and detect the user within short span (does not need to scan region for maximum time slots) as shown in Fig. 13. It can detect a user quickly as compared to AH, so the DD is low for ODND. However, for γth > 30 dB, even ODND cannot detect the devices because the BF gain is not enough, so ODND takes more time to scan a region as compared to AH (as shown in Fig. 13). Therefore, the DD is highest for ODND at γth > 30 dB.

In Fig. 15, for lower values of γth , AF performs better than ODND because AF scan a sector twice, hence the probability of detection in a short span increases. Therefore, DD is low. For higher values of γth , AF with δ = 0◦ , 5◦ , 10◦ , performs worse than ODND because the separation between two beams is not significant. AF keeps scanning one sector twice, hence the number of time slots increases as compared to ODND. On the other hand when δ = 15◦ , then the beamwidth is high and AF can scan a region in less time as compared to ODND, so the DD is low.

3.2. ODND vs. AF Fig. 14 shows that for lower values of SNR, both ODND and AF performs the same. However, for γth > 26 dB, AF performs better than ODND because AF is scanning one sector twice which increases the probability of detection. Also, for γth = 40 dB, both ODND and AF show similar results since the γth value is very high and the signal strength for both ODND and AF is low, hence the PMD is high.

3.3. Polya’s Necklaces vs. AH In Polya’s Necklaces scheme, the length of extended address in reduced i.e. Lpoly = 1. We analyze both Polya’s Necklaces and AH schemes with respect to this new length. Fig. 16 shows that the PMD is the lowest for Polya’s scheme because BF gain is high. All antenna elements combine to form one beam at TX and RX, therefore the signal strength is higher for Polya’s Necklaces. Whereas, the AH utilizes two simultaneous beams with reduced BF gain, hence the PMD is high. Fig. 17 shows that the DD is low for all values of δ in AH. It is because the beamwidth increases by increasing δ , hence it takes short time to scan a region. Whereas, the DD is high for Polya’s Necklaces for all values of SNR. Here all antenna elements form a beam which is a narrow beam as compared to AH. Therefore, it takes more time to discover a device. It is to be noted that when the length of extended address

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

10

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

Fig. 18. PMD for Polya’s necklaces and AF with variable δ .

Fig. 20. PMD for all schemes.

Fig. 19. DD for Polya’s necklaces and AF with variable δ .

Fig. 21. DD for all schemes.

is reduced, the performance of AH is better than both Polya’s Necklaces and ODND in terms of DD.

diversity and by utilizing all the antenna elements of the ULA. AFodnd performs better than AFpoly because the number of time slots is very high in AFodnd as compared to AFpoly . It takes less time to scan the whole region through AFpoly , hence the PMD is high than AFodnd . Fig. 21 shows that AHpoly gives the best discovery delay due to reduced time slots as compared to AHodnd and all other schemes. Whereas, ODND takes more time to discover a device due to high number of time slots. Since, AFodnd scans a region twice so the probability of discovering a device in shorter time span increases. Hence, AFodnd performs better than both ODND and Polya’s Necklaces.

3.4. Polya’s Necklaces vs. AF Fig. 18 shows that for AF with variable δ , the performance is better then Polya’s Necklaces. AF scans a sector twice, which increases the probability of detection. Hence, the performance is better for any value of SNR. The DD is lowest for AF with δ = 15◦ as shown in Fig. 19. It is because the beamwidth is increased, and it takes less time to scan the region. Whereas, the DD is highest for AF with δ = 0◦ , 5◦ when γth > 35 dB because the separation between beams is not significant. The beamwidth of AF is almost similar to beamwidth of Polya’s Necklaces. Hence, when AF scans each sector twice, it takes more time to discover a device. Whereas, Polya’s Necklaces can scan the region quickly, hence the DD is low. 3.5. Probability of miss detection and discovery delay vs. SNR Figs. 20 and 21 show the behavior of PMD and DD for all schemes with δ = 15◦ , Nr = Nt = 8 and r = 50 m, respectively. In Fig. 20, it is observed that as the γth increases, the PMD starts increasing as well due to low BF gain. AH performs the worst in terms of PMD because the antenna array is split into two parts which reduces the BF gain as compared to ODND, Polya’s Necklaces and AF. However, AF performs the best due to time

3.6. Probability of miss detection vs. number of antennas Fig. 22 shows the PMD versus the number of antenna elements at both TX and RX. The values of δ , r and γth are taken as 15◦ , 40 m, and 38 dB, respectively. It is observed that the PMD is highly dependent on the number of antennas in the ULA. When the number of antennas is small, the device discovery is not possible because the BF gain is very low. Hence, the PMD is very high. However, as the number of antenna elements increases, the BF gain becomes high and the PMD starts decreasing. The AH scheme performs the worst due to wide beams and low BF gain, whereas, AF outperforms all other schemes due to narrow beams, time diversity and high BF gain with respect to various antenna elements.

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

11

also provides a lower DD as compared to ODND, Polya’s Necklaces and AH for a lower γth and r. Furthermore, we showed that the DD is highly dependent on the SNR which contradicts the worstcase DD upper-bound proved by ODND algorithm. In future, we aim to optimize the performance of ABP with respect to δ for a multi-device and multi-cell network. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement

Fig. 22. PMD for varying number of antennas.

Sadaf Nawaz: Conceptualization, Methodology, Software, Data curation, Writing - original draft. Syed Ali Hassan: Conceptualization, Visualization, Investigation, Supervision, Writing - review & editing. Haejoon Jung: Investigation, Validation, Supervision, Writing - review & editing. Acknowledgment The work of Sadaf Nawaz and Syed Ali Hassan was supported by the Higher Education Commission of Pakistan. The work of H. Jung was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Government (Grant number: NRF-2019R1F1A1047989). References

Fig. 23. Time slots required for device detection for all schemes.

3.7. Time slots vs. distance between RX and TX Fig. 23 shows the number of time slots required to detect a device for variable TX–RX separation. The values of δ , Nr , Nt and γth are taken as 10◦ , 8, 8 and 30 dB, respectively. It is observed that both AFodnd and AFpoly require the least number of time slots for device detection. Since, AF utilizes the full antenna array and time diversity, hence it can detect a device quickly when the distance between TX and RX is small. However, as the distance starts increasing, AFodnd takes more time to scan a region as AFodnd scans twice the time slots as compared to ODND. On the other hand, all other schemes can scan the entire region according to the maximum number of time slots as given by (24). The maximum time slots for ODND, Polya’s Necklaces and AH is less than AF because of time diversity in AF. 4. Conclusions and future work In this paper, we have analyzed and compared the performance of different IA schemes, i.e., ODND, Polya’s Necklaces and ABP schemes for D2D in mmWave systems. The numerical results show that the proposed ABP schemes are highly dependent on the beam separation, δ , that has a significant impact on the DD and PMD performance. AH achieves a lower DD than all other schemes for higher values of γth and r, whereas, AF outperforms all other schemes in terms of PMD for a moderate δ value. AF

[1] Z. Pi, F. Khan, An introduction to millimeter-wave mobile broadband systems, IEEE Commun. Mag. 49 (6) (2011) 101–107, http://dx.doi.org/10. 1109/MCOM.2011.5783993. [2] A. Alkhateeb, Y. Nam, M.S. Rahman, J. Zhang, R.W. Heath, Initial beam association in millimeter wave cellular systems: Analysis and design insights, IEEE Trans. Wirel. Commun. 16 (5) (2017) 2807–2821, http: //dx.doi.org/10.1109/TWC.2017.2666806. [3] C.N. Barati, S.A. Hosseini, M. Mezzavilla, T. Korakis, S. Panwar, S. Rangan, M. Zorzi, Initial access in millimeter wave cellular systems, IEEE Trans. Wirel. Commun. 15 (12) (2016) 7926–7940, http://dx.doi.org/10.1109/TWC.2016. 2609384. [4] D. Zhu, J. Choi, R.W. Heath, Auxiliary beam pair design in mmWave cellular systems with hybrid precoding and limited feedback, in: 2016 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2016, pp. 3391–3395, http://dx.doi.org/10.1109/ICASSP. 2016.7472306, ISSN: 2379-190X. [5] D. Zhu, J. Choi, R.W. Heath, Auxiliary beam pair enabled AoD and AoA estimation in mmWave FD-MIMO systems, in: 2016 IEEE Global Commun. Conf. (GLOBECOM), IEEE, 2016, pp. 1–6, http://dx.doi.org/10.1109/GLOCOM. 2016.7841616. [6] D. Zhu, J. Choi, R.W. Heath, Auxiliary beam pair enabled AoD and AoA estimation in closed-loop large-scale mmWave MIMO system, IEEE Trans. Wirel. Commun. 16 (7) (2017) 4770–4785, http://dx.doi.org/10.1109/TWC. 2017.2702617. [7] S. Nawaz, S.A. Hassan, Auxiliary beam pair enabled initial access in mmWave systems: Analysis and design insights, in: 2019 IEEE Conf. on Commun. Worshops (ICC), IEEE, 2019, pp. 1–6, http://dx.doi.org/10.1109/ ICCW.2019.8757105, ISSN: 2474-9133. [8] R.I. Ansari, C. Chrysostomou, S.A. Hassan, M. Guizani, S. Mumtaz, J. Rodriguez, J.J.P.C. Rodrigues, 5G D2D networks: Techniques challenges and fututre prospects, IEEE Syst. J. 12 (4) (2017) 3970–3984, http://dx.doi.org/ 10.1109/JSYST.2017.2773633. [9] N. Bahadori, N. Namvar, B. Kelley, A. Homaifar, Device-to-device communications in the millimeter wave band: A novel distributed mechanism, in: 2018 Wireless TeleCommun. Symposium (WTS), IEEE, 2018, pp. 1–6, http://dx.doi.org/10.1109/WTS.2018.8363940. [10] W. Yi, Y. Liu, A. Nallanathan, Modeling and analysis of D2D millimeterwave networks with Poisson cluster processes, IEEE Trans. Commun. 65 (12) (2017) 5574–5588, http://dx.doi.org/10.1109/TCOMM.2017.2744644. [11] L. Chen, Y. Li, A.V. Vasilakos, On oblivious neighbor discovery in distributed wireless networks with directional antennas: Theoretical foundation and algorithm design, IEEE Trans. Netw. 25 (4) (2017) 1982–1993, http://dx. doi.org/10.1109/TNET.2017.2673862.

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.

12

S. Nawaz, S.A. Hassan and H. Jung / Physical Communication xxx (xxxx) xxx

[12] Y. Wang, S. Mao, T.S. Rappaport, On directional neighbor discovery in mmWave networks, in: 2017 IEEE Conf. on Distributed Computing Systems (ICDCS), IEEE, 2017, pp. 1704–1713, http://dx.doi.org/10.1109/ICDCS.2017. 229, ISSN: 1063-6927. [13] B. Yang, M. Liu, Z. Li, Rendezvous on the fly: Efficient neighbor discovery for autonomous UAVs, IEEE J. Sel. Areas Commun. 36 (9) (2018) 2032–2044, http://dx.doi.org/10.1109/JSAC.2018.2864422. [14] A. Riaz, S. Saleem, S.A. Hassan, Energy efficient neighbor discovery for mmWave D2D networks using Polya’s necklaces, in: 2018 IEEE Global Commun. Conf. (GLOBECOM), IEEE, 2018, pp. 1–6, http://dx.doi.org/10. 1109/GLOCOM.2018.8647419, ISSN: 2576-6813. [15] L. Chen, Y. Li, A.V. Vasilakos, Oblivious neighbor discovery for wireless devices with directional antennas, in: 2016 IEEE Int. Conf. on Computer Commun. (INFOCOM), IEEE, 2016, pp. 1–9, http://dx.doi.org/10.1109/ INFOCOM.2016.7524570. [16] T.C. Cheston, J. Frank, Array Antennas, The Johns Hopkins University, Applied Physics Laboratory, Silver Spring, Marylan, 1968.

Syed Ali Hassan received his PhD in Electrical Engineering from Georgia Institute of Technology, Atlanta USA in 2011. He received his MS Mathematics from Georgia Tech in 2011 and MS Electrical Engineering from University of Stuttgart, Germany in 2007. He was awarded BE degree in Electrical Engineering from National University of Sciences and Technology (NUST), Pakistan, in 2004. His broader area of research is signal processing for communications with a focus on cooperative communications for wireless networks, stochastic modeling, estimation and detection theory, and smart grid communications. Currently, he is working as an Associate Professor at the School of Electrical Engineering and Computer Science (SEECS), NUST, where he is the director of Information Processing and Transmission (IPT) Lab, which focuses on various aspects of theoretical communications. He was a visiting professor at Georgia Tech in Fall 2017 and also holds senior membership of IEEE. He also held industry positions, in Cisco Systems Inc. CA, USA, and Center for Advanced Research in Engineering, Islamabad, Pakistan.

Sadaf Nawaz received the B.E. degree in Telecommunication engineering from COMSATS Institute of Information Technology, Pakistan in 2010 and the M.S. degree from University of Engineering and Technology, Pakistan in 2013. She is currently a PhD scholar in National University of Science and Technology, Pakistan. Her main research interests include downlink modeling and analysis of mmWave systems, Massive MIMO, antenna arrays and heterogeneous networks.

Haejoon Jung received the B.S. degree (Hons.) from Yonsei University, South Korea, in 2008, and the M.S. and Ph.D. degrees from the Georgia Institute of Technology (Georgia Tech), Atlanta, GA, USA, in 2010 and 2014, respectively, all in electrical engineering. From 2014 to 2016, he was a Wireless Systems Engineer at Apple, Cupertino, CA, USA. Since 2016, he has been an Assistant Professor with Incheon National University, Incheon, South Korea. His research interests include communication theory, wireless communications, wireless power transfer, and statistical signal processing.

Please cite this article as: S. Nawaz, S.A. Hassan and H. Jung, Auxiliary beam pair enabled initial access for mmWave D2D networks, Physical Communication (2020) 101039, https://doi.org/10.1016/j.phycom.2020.101039.