QoS-Aware Resource Allocation for Mobile Edge Networks: User Association, Precoding and Power Allocation

QoS-Aware Resource Allocation for Mobile Edge

Networks: User Association, Precoding and Power

Allocation

Guanchong Niu

, Qi Cao

and Man-On Pun

1_{School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China, 518172} 2_{Shenzhen Research Institute of Big Data, Shenzhen, China, 518172}

3_{Shenzhen Key Laboratory of IoT Intelligent System and Wireless Network Technology, Shenzhen, China, 518172}

Abstract—Mobile edge computing (MEC) can provide com-puting and storage services to user equipments (UEs) by utilizing edge nodes known as the small base stations (SBS’s) deployed at the edge of the network. The short-distance trans-mission nature between SBS’s and UEs makes the millimeter-wave (mmWave) communication empowered with multiple-input multiple-output (MIMO) hybrid precoding techniques particularly attractive for MEC. In this work, we consider the UE-SBS association, precoding design and power allocation for MEC networks endowed with mmWave MIMO. More specifically, the user association problem is first formulated as a max-k-cut (MkC) problem and then, solved by a distributed local-search algorithm. Next, the joint optimization of precoding and power allocation is cast into the difference of two convex functions (D.C.) programming framework before an iterative rank-constrained D.C. programming algorithm is developed to maximize the weighted sum-rate (WSR) of all UEs while taking into account the quality of service (QoS) requirement of each UE. Furthermore, the monotonic convergence of the proposed iterative algorithm is analytically proven. Finally, extensive computer simulation is conducted to demonstrate the effectiveness of the proposed iterative algorithm.

Index Terms—Mobile Edge Computing, User Association, Hybrid Beamforming, D.C. Programming, Power Allocation.

I. INTRODUCTION

The explosive growth in both mobile data traffic and the number of mobile terminals as smartphones and tablets has presented major challenges on the wireless network design [1], [2]. To meet these challenges, the future networks have to minimize the transmission latency to support real-time applications without being overloaded by data exchanges between UEs and base stations [3]. To circumvent these problems, mobile edge computing (MEC) has recently been proposed as one of the most promising techniques [4]–[8]. In MEC, the computing and storage resources are deployed from the central cloud server to edge nodes (SBS’s) of the network [9]. As a result, the computing task of stringent

This work was supported, in part, by the Shenzhen Institute of Artificial Intelligence and Robotics for Society (AIRS) under grant No. AC01202005001, the Shenzhen Science and Technology Inno-vation Committee under Grant No. ZDSYS20170725140921348 and JCYJ20190813170803617, and by the National Natural Science Foundation of China under Grant No. 61731018.

†_{Corresponding author, email: [email protected].}

Cloud Server

SBS

SBS

SBS

Fig. 1. Illustration of the MEC system under consideration.

low-latency requirements can be processed by the proximate SBS’s without being sent to the cloud server. Furthermore, the close proximity between UEs and SBS’s enables the network to collect more recent UE information such as behaviors, locations and environment, which facilitates the network to provide agile services.

U

ser

A

sso

cia

tio

n

SINR Maximization

Interference

Minimization By MkC

Join

t B

eam

for

m

ing

an

d p

ow

er a

llo

cati

on

Convexity

Transformation

Rank Constrained D.C.

Programming

SBS Edge

Computing

Section

Section

Cloud Server

Fig. 2. Flowchart in this work.

analog precoding with a large number of phase shifters, and the digital precoding with a smaller number of Radio Frequency (RF) chains. By carefully designing the analog and digital precoders, it has been shown that the low-cost hybrid beamforming can achieve comparable performance as compared to the fully digital beamforming.

In addition, user association has become an important problem in MEC as SBS’s are expected to be densely deployed with each SBS covering a much smaller area as compared to the conventional macro base stations. Thus, a carefully designed user association can match each UE with the best SBS by maximizing the transmission data rate while minimizing its incurred interference [16]. However, the user association problem is NP-hard due to its combinato-rial nature. Some pioneering studies attempted to solve the problem by simplifying the deployment scenarios. For in-stance, in [17], the association problem was addressed based on the Euclidean distance without taking into account the dynamic nature of the wireless channel model. Furthermore, [18] proposed a user association algorithm based on the physical resource block (PRB) table. In both [17], [18], user association was investigated without considering the potential impact caused by multiuser interference.

Finally, power allocation is considered as one of the most effective methods to achieve required quality of service (QoS) for each UE by better managing co-channel interference in

multiuser networks [19], [20]. However, joint precoding and power allocation design is usually analytically intractable due to its non-convex nature [21]. To circumvent this obstacle, [22] proposed to optimize the power allocation for the sum-rate capacity maximization problem by utilizing the water-filling algorithm, assuming that the spatial channels of all UEs are perfectly orthogonal. Clearly, this assumption is an issue of concern in practice. In addition, the task of finding the optimal precoding and power allocation design that maximizes the spectral efficiency is very challenging due to the fact that all system parameters under consideration are highly coupled.

Motivated by the aforementioned challenges, this work studies the MEC system equipped with mmWave MIMO as shown in Fig. 1. As depicted in Fig. 2, the user association problem is first transformed into an intra-SBS interference minimization problem before being solved by a distributed max-k-cut (MkC)-based algorithm in Section IV. In contrast to the suboptimal resource allocation algorithm proposed in [23], we consider the user association problem for multiple SBS’s based on intra-SBS interference minimization. Finally, we cast the non-convex problem as a rank-constrained differ-ence of two convex functions (D.C.) programming problem to solve the precoding and power allocation in Section V.

In summary, the main contributions of this work are summarized as follows:

• We first propose a novel distributed MkC-based

al-gorithm for user association using practical wireless channel models. Furthermore, the performance bounds of the proposed algorithm are derived;

• Furthermore, joint precoding and power allocation is proposed using the rank-constrained D.C. programming technique. More specifically, the original non-convex op-timization problem is formulated as a rank-constrained D.C. programming problem before an iterative algorithm is devised to maximize the weighted sum-rate (WSR) with QoS constraints for each UE. The convergence of the proposed iterative algorithm is proven.

The rest of this paper is organized as follows. First, an introduction to the D.C. programming techniques and the MkC problem is provided in Section II. Next, the MEC sys-tem model is presented in Section III before an MkC-based algorithm is developed for user association in Section IV. After that, an iterative joint precoding and power allocation algorithm using the rank-constrained D.C. programming tech-niques is established in Section V followed by the derivation of the performance bound of the proposed iterative algorithm in Section VI. Finally, extensive computer simulation results are presented in Section VII.

Notation: Uppercase boldface and lowercase boldface let-ters are used to denote matrices and vectors, respectively. IN

represents the identity matrix with size N × N . AT and AH are the transpose and conjugate transpose of A, respectively. [a]i denotes the i-th element of vector a. In addition, kAk

stands for the `2 norm of A while |A| denotes the absolute

TABLE I

SUMMARY OF KEY NOTATIONS.

Symbol Description

Ak,n The entry of A representing the belonging of the n-th user

Vi The i-th vertex

K The number of SBS’s

a(φ, θ) Array response vector with azimuth angle φ and elevation angle φ

NR The number of antennas in the receiver

NT The number of antennas in the transmitter

wk,u Analog beamforming vector employed by the u-th UE of the

k-th SBS

Hk,u The u-th UE’s channel model under the k-th SBS

fk,u Digital beamforming vector for the u-th user of the k-th SBS

Fk Digital precoding matrix for UEs under the k-th SBS

vk,u analog beamforming vector for the u-th user of the k-th SBS

Vk Analog precoding matrix for UEs under the k-th SBS

p The set for all users’ power allocation vector Sk The maximal number of users for the k-th SBS

Ωku,j The sum of the weights of the edges from a vertex u in the Set k to all the vertices in Set j

ωku,jq The weight between two vertices

NkNk The partition set for the k-th SBS with size |Nk| = Nk

¯

Fu The reformulated digital precoder to release non-convex rank

constraint

F The set of digital precoder in the rank-constrained problem gu The effective array gain of theu-th UE of the k-th SBS

τk,u The weight of rate for the u-th UE of the k-th SBS

Pk Transmit power constraint for the k-th SBS

U(m) _{Eigenvectors corresponding to the ¯N −1 smallest eigenvalues}

of ¯Fu(m)

Furthermore, rank(A) and trace(A) represent the rank and trace of A, respectively. A  0 represents that A is a positive semi-definite matrix. Finally, ∇f (A) represents the gradient of function f (A).

Symbol: Table I summarizes the key symbols applied in this paper.

II. PRELIMINARYKNOWLEDGE FORD.C. PROGRAMMING ANDMkC PROBLEM

A. Review of D.C. Programming

In this section, a brief review of the D.C. programming is provided. In general, the D.C. programming problem has the following form:

minimize

x∈Rn f0(x) − g0(x) (1)

subject to fi(x) − gi(x) ≤ 0, i = 1, · · · , M.

where the functions fi: Rn → R and gi: Rn → R for i =

0, 1, · · · , M are convex.

Clearly, the optimization problem in Equation (1) is not necessarily convex. As a result, it is non-trivial to find the optimal solution. To solve the D.C. programming problem, the convex-concave procedure (CCP) algorithm is well re-garded as one of the most successful algorithms among many proposed solutions [24]. The CCP algorithm iteratively ap-proximates the original problem with a convexified problem

by linearizing gi, for i = 0, 1, · · · , M , with its first-order

Taylor expansions. More specifically, the objective function in the (m+1)-th iteration of the CCP algorithm is formulated as

minimize f0(x) − g0(x(m)) − h∇g0(x(m)), x − x(m)i (2)

where x(m) represents the state at the m-th iteration. Since Equation (2) is convex, it can be straightforwardly solved by most convex optimization software packages [25]. Furthermore, by taking advantage of the convex property, the (m + 1)-th solution is always better than the m-th solution, which guarantees the convergence of the iterative algorithm stated in Equation (2). The detailed CCP algorithm can be found in [26].

B. Review of Capacitated MkC Problem

Fig. 3. Illustration of an MkC problem in a graph |V| = 8, |E| = 10 and k = 3. The maximal solution of this MkC problem is 6 + 5 + 5 = 16.

For the MkC problem, we are given a weighted graph H = (V, E ) consisting of a vertex set and an edge set denoted by V and E , respectively. The goal is to partition V into k non-empty sets in such a way that the sum of the weights of edges wijbetween different partitions is maximized as shown

in Fig. 3. It is worth noting that the partition is not unique in general. Some MkC-related problems are summarized as follows:

• MC: A special case of MkC when k = 2 [27].

• Conventional MkC: Just divide V vertices into k disjoint non-empty partitions without additional constraints [28].

• Max Steiner k-cut: Each partition must include at least one vertex from a given set T = {t1, t2, · · · , tl} ∈ V,

where l ≥ k [29].

• MkC with given sizes: The partitions V1, V2, · · · , Vk

must satisfy |Vi| = si with a given set {s1, s2, · · · , sk},

for all 1 ≤ i ≤ k [30].

• Capacitated MkC: Given a set {s1, s2, · · · , sk}, the

partitions V1, V2, · · · , Vk must satisfy |Vi| ≤ si [31].

Since the inherent NP-hardness, the capacitated MkC can only find a locally optimal solution in polynomial time. A binary edge formulation (i.e. wij= 0, 1) is proposed in [32],

where the integer variable xij for i, j ∈ V is defined as:

xij =

(

1 if i and j are in the same partition,

Thereby the MkC problem is formulated as the following integer linear programming (ILP) formulation [33]:

maximize X i,j∈V,i<j ωij(1 − xij) (4a) subject to xih+ xhj− xij ≤ 1, ∀i, j, h ∈ V, (4b) X i,j∈Q,i>j xij ≥ 1, ∀Q ⊆ V, |Q| = k + 1, (4c) xij ∈ {0, 1}, ∀i, j ∈ V, (4d)

where constraints (4b) and (4c) are the triangle and clique inequalities respectively. Triangle inequality implies the log-ical conditions that if xih = 1 and xhj = 1 hold, then by

transitivity the value of xij should be 1 as well, meaning

vertices i and j are in the same partition. Constraint (4c) imposes that at least two from every subset of k + 1 vertices have to be in the same partition. Constraints (4b) and (4c) imply that there are at most k partitions.

III. SYSTEM MODEL AND PROBLEM FORMULATION

A. MEC System Model

We consider an MEC system of K SBS’s serving N UEs as shown in Fig. 1. We denote by N = {1, 2, · · · , N } the UE index set while Nk = {1, 2, · · · , Nk} stands for the

UE index set for UEs served by the k-th SBS. Furthermore, we assume that each SBS can serve maximal Sk users, i.e.,

Nk ≤ Sk for k = 1, 2, · · · , K. The set of k is denoted by

K = {1, 2, · · · , K}.

Assuming that each UE can attach to only one SBS, we define A(n) = k to denote that the n-th UE is attached to the k-th SBS. Using A(n), we further define a UE-SBS association matrix denoted by A of dimension K × N . The entry of A is given by : Ak,n= ( 1 if A(n) = k, 0 otherwise, (5) for k ∈ K and n ∈ N .

B. Downlink Transmission Model

As shown in Fig. 4, the SBS’s are equipped with mmWave MU-MIMO systems, each with NRF RF chains and NT

antennas aiming to transmit Nk data streams to Nk of N

receivers with NRreceive antennas. Furthermore, we assume

that SBS’s operate in orthogonal channels. As a result, inter-SBS interference is not considered in the sequel.

Following the same design commonly implemented in the literature [34], only one data stream is designated to each scheduled receiver. We use sk ∈ CNk to denote the data to

be transmitted with EsksHk = 1

NkINk.

Without loss of generality, we focus our following dis-cussions on the k-th SBS. The hybrid precoding system first multiplies sk with the digital precoding matrix Fk =

[fk,1, fk,2, · · · , fk,Nk] with fk,u ∈ C

NRF×1 _{being the}

dig-ital beamforming vector for the u-th UE. After that, the output signal is multiplied by the analog precoding matrix

Vk = [vk,1, vk,2, · · · , vk,NRF] with vk,u ∈ C

NT×NRF_{. The}

resulting precoded signal xk of length NT can be expressed

as

xk = Vk· Fk· sk = Vk

X

n∈N

Ak,nfk,nsk,n. (6)

The precoded signal xk is then broadcast to Nk UEs. The

signal received by the u-th UE associated with the k-th SBS is given by [35]

yk,u= Hk,uxk+ nk,u

= Hk,uVkfk,usk,u

+ Hk,uVk X n∈N n6=u Ak,nfk,nsk,n | {z } Intra-SBS Interference +nk,u, (7)

where Hk,u ∈ CNR×NT is the MIMO channel matrix

between the k-th SBS and its u-th UE, and nk,u is the

complex additive white Gaussian noise with zero mean and variance equal to σ_k,u2 .

Assuming that UEs under consideration are all low-cost terminals with analog-only decoding, the decoded signal according to sk,u is given by

ˆ

sk,u= wHk,uHk,uVkfk,usk,u+ wHk,un˜k,u, (8)

where wk,u of length NRis the analog beamforming vector

employed by the u-th UE of the k-th SBS with the power constraint of kwk,uk2= 1 and

˜ nk,u= Hk,uVk X n∈N n6=u Ak,nfk,nsk,n+ nk,u. (9)

Note that the first term in Equation (8) stands for the desired signal while the second termn˜k,u is the sum of the receiver

noise and interference from other UEs in the same SBS network.

C. Channel Model

It has been shown that the mmWave wireless channel can be well modeled by the Saleh-Valenzuela model [15]. We assume that the channel state information (CSI) is perfectly known. Following the same technique proposed in [34], each scatter is assumed to contribute only one propagation path. As a result, the u-th UE’s channel model under the k-th SBS can be modeled as Hk,u= s NTNR Lk,u Lk,u X l=1 αk,u,l× aR(φrk,u,l, θ r k,u,l) · a H T(φ t k,u,l, θ t k,u,l), (10)

where Lk,u is the number of scatters of the u-th UE’s

channel. Furthermore, αk,u,l is the complex path gain with

zero mean whilenθr

Digital Precoder Analog Precoder x Analog Decoder Transmitter The 1-st User User Beam Scheduling Analog Decoder The u-th User

User Data Stream

Fig. 4. Block diagram of the hybrid precoding system under consideration.

W × Q considered in this work, the array response vector a is represented by

a(φ, θ) =√1 W Q

h

1, ejκd(sin φ sin θ+cos θ),

· · · , ejκd((P −1) sin φ sin θ+(Q−1) cos θ)iT_{, (11)}

where κ = 2π_λ is the wavenumber and d is the distance between two adjacent antennas.

D. Analog Precoding

We firstly design the analog precoding schemes on both UEs and SBS’s. The power constraints of analog precoders can be formulated by

|[wk,u]i|2= 1/NR, i = 1, 2, · · · , NR;

|[vk,u]i|2= 1/NT, i = 1, 2, · · · , NT. (12)

It is well-known that distinct array response vectors are asymptotically orthogonal as the number of antennas in an antenna array goes to infinity [36], i.e.

lim N →+∞a H_(φt k,u, θ t k,u) · a(φ t `,v, θ t `,v) = δ(k − `)δ(u − v). (13) However, since the infinite number of antennas is not practical, the residual interference must be taken into consid-eration for the analog precoding design. Recalling the channel model in Equation (10), we can asymptotically orthogonalize

the transmitted signals by optimizing the design of wk,u and

vk,u with given user association:

{w∗k,u, v∗k,u} = arg max ˜

wk,u, ˜vk,u

Mk

X

u=1

log2(1 + SINR ( ˜wk,u, ˜vk,u))

(14) subject to v˜k,u∈ Btk,u,

˜

wk,u∈ Brk,u,

where Bt_k,u and Br_k,u are the array response vectors for the SBS and UE denoted by Bk,ut =aT(φtk,u,1, θ t k,u,1), · · · , aT(φtk,u,Lu, θ t k,u,Lu) , Bk,ur =aR(φrk,u,1, θ r k,u,1), · · · , aR(φrk,u,Lu, θ r k,u,Lu) . (15)

The analog precoders are selected from the array response vectors by taking advantage of the perfect CSI.

Furthermore, SINR ( ˜wk,u, ˜vk,u) is given by

SINR ( ˜wk,u, ˜vk,u) =

| ˜wH

k,uHk,uv˜k,u|2

X n∈N ,n6=u Ak,n| ˜wk,uH Hk,uv˜k,n|2+ 1 γ , (16) where γ = _{N σ}P2

u is the SNR for each user. In deriving the

results above, we have assumed fk,ufk,uH ≈ Ik. As a result,

the optimal analog precoders at both transmitter and receiver can be straightforwardly found by exhaustively searching in the feasible sets of Bt

k,u and B r

E. Problem Formulation

For notational simplicity, we denote by gH

k,u the effective

array gain of the u-th UE with

gk,uH = wHk,uHk,uVk. (17)

Then, the channel capacity of the u-th UE under the k-th SBS is given by

Rk,u= log2 1 +

pk,u|gk,uH fk,u|2

P

i∈NAk,npk,i|g

H

k,ufk,i|2+ σk,u2

! .

(18) Subsequently, the system WSR can be formulated as

Rtot= K X k=1 Nk X u=1

τk,uRk,u(pk, Fk, A), (19)

where τk = [τk,1, τk,2, · · · , τk,Nk] with

PNk

u=1τk,u = Nk

is the vector containing the corresponding weights for UEs while pk = [pk,1, pk,2, · · · , pk,Nk] with

PNk

u=1pk,u ≤ Pk is

the vector containing the transmit power of the k-th SBS. We further denote by p = [p1, · · · , pK] the vector containing all

users’ power allocation.

Finally, the optimal design of user scheduling and hybrid precoding matrices, as well as power allocation can be formulated as

P1: maximize

p,F ,A Rtot(p, F , A) (20)

subject to C1: kVkfk,uk2= 1, ∀u ∈ Nk, ∀k ∈ K,

C2:

Nk

X

u=1

pk,u ≤ Pk, ∀k ∈ K,

C3: Rk,u≥ λk,u, ∀u ∈ Nk, ∀k ∈ K,

C4: N X n=1 Ak,n≤ Sk, ∀k ∈ K, C5: K X k=1 Ak,n= 1, ∀n ∈ N .

where C1 ensures that each RF chain is of unit power.

The total transmit power is limited by Pk as shown in C2

while C3 ensures that the QoS for the u-th UE of the

k-th SBS wik-th a minimum data rate of λk,u. In addition, in

constraints C4 and C5, the number of UEs served by one

SBS is constrained while one UE can only be attached to one SBS for transmission.

Since the problem P1 is highly non-convex, it is

analyt-ically intractable to derive a closed-form solution to P1. In

Section IV, we first formulate the UE association problem as a capacitated MkC problem, which can be solved by a distributed local-search algorithm. After that, a general rank-constrained D.C. programming technique is developed in Section V to solve the local optimal digital precoder and power allocation by approximating the problem in each iteration as a standard convex optimization problem.

IV. MAX-k-CUTPROBLEM FORUSERASSOCIATION

In the sequel, the user allocation is designed to minimize the interference caused by the side lobe of beamformers based on the proposed capacitated MkC algorithm before the performance bounds are derived.

Since the antenna number is finite in practice, the residual interference must be considered in the analog precoding de-sign. Recalling the channel model presented in Equation (10), we can asymptotically orthogonalize the transmitted signals by optimizing the design of wu and vu:

P2: maximize ˜ A K X k Nk X u=1

log₂(1 + SINR ( ˜wk,u, ˜vk,u))

(21) subject to X n∈N Ak,n≤ Sk, ∀k ∈ K; X k∈K Ak,n= 1, ∀n ∈ N .

A. A Distributed Local-Search Algorithm

Fig. 5. The weight of two vertices (UEs).

As exhibited in [37], the user association problem is NP-hard since the number of possible combinations between UEs and SBS’s is QK

j=1

N −Pj−1

k=0Nk

Nj
, where we set N0 = 0.

To cope with this obstacle, a heuristic algorithm is proposed by exploiting the interference minimization. The intra-SBS interference minimization problem is formulated as

minimize A K X k=1 Nk X u=1 X n∈N n6=u Ak,n|wHk,uHk,uvk,n|2. (22)

Equation (22) to maximize the inter-SBS interference as follows: maximize A Itot= K X k6=j k,j=1 Nk X u=1 X n∈N n6=u Ak,n|wHk,uHk,uvj,n|2. (23)

Thus, as shown in Fig. 5, the counterpart weight between two vertices (UEs) is given by

ωku,jq =

(

0, if j = k,

|wH

k,uHk,uvj,q|2, otherwise.

(24)

In this way, the problem in Equation (24) can be trans-formed as an MkC problem, which can be solved using a distributed local-search algorithm. We can regard an SBS net-work as one “cut”. To maximize the inter-SBS interference, we propose a local-search algorithm to solve the problem P2.

We first denote by Ωku,j the sum of the weights of the edges

from a vertex u in Set k to all the vertices in Set j. Ωku,j

takes the following form:

Ωku,j =

Nj

X

q=1

ωku,jq. (25)

A distributed local-search algorithm for the capacitated MkC problem [32] is given as follows:

1) Initialization: Partition the UEs into K sets, N1, N2, · · · , NK before randomly initializing

P

nAk,n≤ Sk, i.e., Nk ≤ Sk for k = 1, 2, · · · , K.

2) Iterative Step: Determine if there is an association pair q in Set j and u in Set k for which

NkΩku,k+ NjΩjq,j > NkΩjq,k+ NjΩku,j. (26)

If such a pair exists, we reassign the q-th UE to the k-th SBS while the u-th UE to the j-th SBS.

3) Termination: Stop the iteration when all pairs violate Equation (26), i.e.,

NkΩku,k+ NjΩjq,j ≤ NkΩjq,k+ NjΩku,j. (27)

for all k, j ∈ K and u ∈ Nk, q ∈ Nj.

The computational complexity of the local-search algo-rithm can be analyzed as follows: In each iteration, one UE needs to examine at most N − 1 times to check if any pair satisfies Equation (26). Thus, the local-search algorithm has computational complexity of the order of O(N2).

Since no central coordinators are assumed in the search algorithm proposed above, the proposed iterative algorithm can be executed in a distributed manner. In the MEC system, we consider a fully coordinated scenario where the SBS’s collaborate to address the user association problem. SBS’s are able to share with each other the CSI of UEs. Since the inter-SBS interference can be eliminated by the orthogonal channels, we can optimize the user association using the proposed local-search algorithm by maximizing the inter-SBS interference.

B. Worst-Case Analysis

The theorem below characterizes the performance lower bound of the distributed local-search algorithm for all K ≥ 2. We define Ils= K X k=1 Nk X u=1 Ωku,k. (28)

where Ils is the solution given by the local-search algorithm.

Theorem 1. Assuming that the maximal value of a MkC problem isImax. The solution obtained using the local-search

algorithm has a value no smaller than1 −_K1 of the optimal solution value, i.e.,

Ils

Imax

≥ 1 − 1

K. (29)

Proof. See Appendix A.

Since it is non-trivial to analytically evaluate Equation (28), we will use computer simulation to confirm the effectiveness of our proposed association algorithm in Section VII.

V. PROPOSEDITERATIVEALGORITHM FOR

RANK-CONSTRAINEDD.C. PROBLEM

In this section, we will derive the optimal digital precoder and power allocation at each SBS for a given association matrix A and a set of analog precoders. Without loss of gen-erality, we focus the following discussion on the k-th group while omitting the subscript k for presentational simplicity. In addition, we set the number of UEs attached to each SBS to ¯N while the maximum total transmit power P0.

Then, the optimal design of the precoding matrices as well as power allocation can be formulated as

P3: maximize p,F Rtot(p, F ) (30) subject to C1: kV fuk2= 1, u = 0, 1, · · · , ¯N , C2: ¯ N X u=1 pu≤ P0, C3: Ru≥ λu, u = 0, 1, · · · , ¯N .

Since the tasks of precoding design and power allocation are highly coupled, we will propose a joint optimization algorithm to maximize the WSR in this section.

A. Rank-constrained D.C. problem

It can be easily seen that the challenge in solving P3 is

the non-convexity of Rtot(p, F ). To cope with this problem,

we first express the digital precoder as ¯

Fu= pufufuH, (31)

with constraints rank( ¯Fu) ≤ 1 and ¯Fu 0.

Furthermore, the constraints C1 and C2 in P3 can be

It is worth noting that the optimal digital precoder f_u∗is the eigenvector corresponding to the only non-zero eigenvalue p∗_u of optimal ¯F_u∗, where p∗_uis the optimal power allocation [38]. The variable pu is designed to ensure that C1 in P3 is

satisfied.

Substituting Equation (31) into Equation (18), we have

Ru( ¯Fu) = log2   1 + gH uF¯ugu PN¯ i=1 i6=u gH uF¯igu+ σ2u    = log₂   ¯ N X i=1 g_uHF¯igu+ σ2u   − log₂    ¯ N X i=1 i6=u gH_uF¯igu+ σ2u   . (33)

Thereby, P3 can be reformulated as a D.C. problem with

a rank constraint: P4: maximize ¯ F f (F ) − g(F ) (34) subject to C1: ¯ N X u=1 VHF¯uV ≤ P0, C2: Ru≥ λu, u = 1, 2, · · · , ¯N , C3: ¯Fu 0, u = 1, 2, · · · , ¯N , C4: rank( ¯Fu) ≤ 1, u = 1, 2, · · · , ¯N , where F = [ ¯F1, ¯F2, · · · , ¯FN¯] and f (F ) = ¯ N X u=1 τulog2   ¯ N X i=1 gH_uF¯igu+ σu2  , (35) g(F ) = ¯ N X u=1 τulog2    ¯ N X i=1 i6=u gH_uF¯igu+ σu2   . (36)

Next, we propose to transform the QoS constraint C2into

a convex constraint as follows:

g_uHF¯ugu+ (1 − 2λu)    ¯ N X i=1 i6=u gH_uF¯igu+ σ2u   ≥ 0. (37) In the following, we devise an iterative algorithm to solve P4 as a standard D.C. programming problem by first

ignoring C4. More specifically, the optimal F∗ is obtained

by iteratively solving ¯Fu for u = 1, 2, · · · , ¯N . Similar to the

procedures in [26], the iterative algorithm gives the optimal ¯

Fu(m+1)at the m-th iteration by solving the following convex

problem (See Appendix B):

maximize ¯ Fu f ( ¯Fu) − g( ¯Fu(m)) − h5g( ¯F (m) u ), ¯Fu− ¯Fu(m)i (38) subject to C1, C2, C3 in P4,

where h·i denotes the inner product of two matrices, i.e., hA, Bi = trace(AT_{B). The gradient of g( ¯F}(m)_{) can be}

computed as 5g( ¯Fu(m)) = ¯ N X j=1 j6=u wj/ ln 2 PN¯ i=1 i6=j gH uF¯igu+ σj2 gjgjH. (39)

It is worth noting that h5g( ¯Fu(m)), ¯Fu− ¯F (m)

u i is a real value

since 5g( ¯Fu(m)) and ¯Fu− ¯F (m)

u are both Hermitian.

B. The General RCOP

To solve P4, we will first introduce a rank constrained

op-timization problem (RCOP). Inspired by RCOP, we will then propose an iterative algorithm to solve P4 by formulating a

convex optimization problem in each iteration.

We now consider the rank constraint C4 in P4. A general

RCOP to optimize a convex objective subject to a set of convex and rank constraints can be formulated as follows:

P5: minimize

X f (X) (40)

subject to X  0; X ∈ C; rank(X) ≤ r,

where f (X) is a convex function, C is the set of given convex constraints and X ∈ CN × ˜˜ N is a general positive semidefinite matrix.

As shown in [39], RCOP can be solved by an iterative method to gradually approach the constrained rank. In the m-th iteration, we solve the following semidefinite program-ming (SDP) problem: minimize X(m+1)_,e(m) f (X (m+1)_{) + we}(m+1) ₍₄₁₎ subject to X(m+1) 0, X(m+1)∈ C, e(m+1)IN −r˜ − U (n)H_X(m+1)_U(m)_{ 0,} e(m+1)≤ e(m)_,

where w > 0 is the weighting factor. Using the eigenvalue de-composition (EVD), U(m) _{∈ C}N ×( ˜˜ N −r) _{is the orthonormal}

eigenvectors corresponding to the ˜N − r smallest eigenvalues of X(m)_{solved in the previous iteration. In the first iteration}

where m = 0, e(0) _{is the ( ˜N − r)-th smallest eigenvalue of}

X(0) that can be obtained by

minimize

X(0)

f (X(0)) (42)

subject to X(0)  0; X(0) ∈ C,

C. Iterative Algorithm forP4

It is straightforward to prove that Equation (38) is a concave optimization problem as shown in Section V-A. By combining P4 and P5, an iterative algorithm for the

rank-constrained D.C. programming problem is derived. The optimal g( ¯F(m+1)) in the m-th iteration is given by solving the following convex problem:

P6: minimize ¯ Fu,e(m+1) t( ¯Fu, e(m+1)) (43) subject to C1: ¯ N X u=1 VHF¯uV ≤ ¯N , C2: Ru≥ λu, u = 1, 2, · · · , ¯N , C3: ¯Fu 0, C4: e(m+1)IN −1¯ − U(m)HF¯uU(m) 0, C5: e(m+1)≤ e(m),

where U(m)_{is the eigenvectors corresponding to the ¯N − 1}

smallest eigenvalues of ¯Fu(m) and t( ¯Fu, e(m+1)) has the

following form:

t( ¯Fu, e(m+1)) (44)

=g( ¯F_u(m)) + h∇g( ¯F_u(m)), ¯Fu− ¯Fu(m)i − f ( ¯Fu) + we(m+1).

P6 is indeed a standard convex optimization problem that

can be solved via available convex software packages, such as CVX [25]. C1ensures the total power constraint and C2

guar-antees the QoS constraint for each UE. Furthermore, C3, C4

and C5 are the constraints followed from Equation (41) in

which we set r = 1. The proposed iterative algorithm is summarized in Algorithm 1. In each iteration, we solve a D.C. programming problem and update the optimal ¯Fu∗(m). If

the WSR t(m)can no longer be improved, the digital precoder ¯

Fu+1 of the (u + 1)-th UE is then optimized successively in

the same manner.

Finally, we analyze the computational complexity of the proposed rank-constrained D.C. programming algorithm. In each iteration, an SDP problem is derived as shown in P6.

The existing SDP solver based on the interior point method has computational complexity of the order of O(N_k4) as

¯

Fu ∈ CNk×Nk [39]. Furthermore, the EVD conducted in

each iteration has computational complexity of the order of O(N3

k). As a result, the complexity of the proposed algorithm

is of the order of O(N4

k) in each iteration.

D. Convergence Analysis

In the following, we provide the convergence analysis of the proposed iterative algorithm for solving the rank-constrained D.C. programming problem.

As the function g( ¯Fu) is concave, its gradient ∇g( ¯Fu) is

super-gradient. Therefore, we have

g( ¯Fu) ≤ g( ¯Fu(m)) + h∇g( ¯F (m)

u ), ¯Fu− ¯Fu(m)i. (45)

Algorithm 1 Proposed Iterative Algorithm for Rank-constrained D.C. Problem

Input:

Effective channel: g1, g2, · · · , gN¯;

Random initialization of ¯Fu(0), u = 1, 2, · · · , ¯N ;

Initial information: s, s0, t( ¯Fu(0), e(0));

Initialize U(0)_{, e}(0) _{by solving Equation (42);}

Stop criterion: 1, 2. Procedures: 1: while |(s0− s)/s| ≤ 1 do 2: Update s: s = s0 3: for 0 ≤ u ≤ ¯N do 4: m = 0 5: while |(t( ¯Fu(m+1), e(m+1))−t( ¯F (m) u , e(m))| ≤ 2do 6: Obtain the optimal value t(m+1) of objective

function and ¯Fu(m+1), e(m+1) in Equation (43) 7: Update U(m) from ¯Fu(m+1) via EVD

8: Update m = m + 1 9: end while 10: end for 11: Update s0: s0= t(m+1) 12: end while 13: Outputs: F∗= [ ¯F₁∗(m), ¯F₂∗(m), · · · , ¯F_N∗(m)¯ ]. Since e(m+1) ≤ e(m) _{and ¯F}(m) u is feasible to Equa-tion (43), it follows: g( ¯F_u(m+1)) − f ( ¯F_u(m+1)) + e(m+1) (46) ≤g( ¯F_u(m)) + h5g( ¯F_u(m)), ¯Fu− ¯Fu(m)i − f ( ¯Fu) + e(m), ≤g( ¯F_u(m)) − f ( ¯F_u(m)) + e(m),

which shows that the solution ¯Fu(m+1) is always better than

or equal to the previous solution ¯Fu(m). Thus, the algorithm

must converge to a critical point.

VI. PERFORMANCEANALYSIS

In this section, we will derive the performance upper and lower bounds of the proposed scheme. We will first begin with the analog-only scheme. The expected capacity is given by

E[Rk,u] =E [log2(1 + ρ)] ,

=E "

log2 1 +

|w∗H

k,uHk,uvk,u∗ |

2

1/γ + Ik,u

!#

, (47)

where Ik,u is the received interference represented as

Ik,u= X n∈N n6=u Ak,n|w∗Hk,uHk,uvk,n∗ | 2_{. (48)}

From Equations (10) and (13), the optimal array response vectors in transmitter and receiver are denoted by [15]

w_k,u∗ = aR(φrk,u,l∗, θ_k,u,lr ∗), (49)

Proposition 1. If the optimal analog beamformers are de-signed asw∗_k,u= aR(φrk,u, θrk,u) and v∗k,u= aT(φtk,u, θtk,u),

respectively, the following inequality holds: X n∈N n6=u Ak,n|wk,u∗HHk,uvk,n∗ | 2_{≤ Z(N} k− 1)Ξ. (51)

whereΞ is a constant and Z = D2

k,uα2k,u.

Proof. See Appendix C.

Recalling Equation (47), the expected downlink capacity for each UE can be rewritten as

E[Rk,u] = E  log₂  1 + Z 1/γ + Y  , (52) where

Z = |w_k,u∗HHk,uvk,u∗ |

2_,

= D_k,u2 α2_k,u, (53)

From Equation (49), we have

Y = X n∈N n6=u Ak,n|w∗Hk,uHk,uv∗k,n| 2 = D2_k,uα2_k,u X n∈N n6=u Ak,n  v∗H_k,uv_k,n∗  2 , = Z X n∈N n6=u Ak,n  v∗Hk,uvk,n∗   2 . (54)

Proposition 2. The lower and upper bounds of the sum-rate capacity can be given by

Z ∞

0

log₂(1+x)dFX(x) ≤ E[Rk,u] ≤

Z ∞

0

log₂(1+z)dFZ(z),

(55) where FX(x) and FZ(z) are the CDF of SINR and Z,

respectively.

Proof. From Proposition 1, Y can be upper bounded by

Y ≤ Z(Nk− 1)Ξ, (56)

where 0 ≤ Ξ ≤ 1 with Ξ being the expected residual interference power between distinct beams. In our proposed system, the beams will be selected and grouped to reduce the residual interference. Clearly, Ξ = 0 if the number of antennas goes to infinity or the steering vectors of different users are strictly orthogonal. In contrast, Ξ = 1 if different UEs have same AoDs. In general, the value of Ξ can be numerically derived between 0 and 1.

Capitalizing on the Extreme Value Theory [40], we can derive the cumulative distribution function (CDF) of Z as

FZ(z) = 1 − e− z

C, (57)

where C = 2NTNR/Lk,u. By setting Ξ = 0, i.e., the

interference is totally removed, we have

E[Rk,u] ≤

Z ∞

0

log2(1 + z)dFZ(z). (58)

Finally, the CDF of the SINR lower bound can be given by

FX(x) = 1 − e

− x

Cγ(1−Ξ(Nk−1)x)_{. (59)}

The detailed derivation can be found in Appendix D. Using the CDF above, the lower bound of the sum-rate capacity can be derived as

E[Rk,u] ≥

Z ∞

0

log2(1 + x)dFX(x). (60)

It is analytically intractable to obtain a closed-form solu-tion to Equasolu-tion (58). We will show the numerical results in simulation section.

Note that the upper bound is achieved if the interference from other UEs can be eliminated completely. Furthermore, since the number of transmitter antennas is finite in practice, the analog beamforming vectors shown in Equation (14) and Equation (16) inevitably incur residual inter-user interference. Thereby, digital precoders as well as power allocation are utilized to suppress the residual interference.

VII. SIMULATIONRESULTS

In this section, we will use computer simulations to con-firm the performance of the proposed UE-SBS association and rank-constrained D.C. programming algorithms. In the simulations, we consider a system of multiple SBS’s each equipped with a 4×4 UPA (i.e., NT = 16) and N ground UEs

each equipped with a 2 × 2 UPA (i.e. NR= 4). The number

of paths in the wireless channel model is set to Lu= 4. We

model the azimuth AoAs/AoDs uniformly distributed over [0, 2π] while the elevation AoAs/AoDs uniformly distributed over [−π/2, π/2], respectively. For each computer experi-ment, we compute the average over 100 realizations.

In Fig. 6, we evaluate the total amount of residual inter-user interference that all UE’s suffer as a function of the number of groups. Specifically, we compare the performance of the distributed local-search algorithm proposed in Section IV against the greedy selection algorithm proposed in [41]. Inspection of Fig. 6 suggests that the intra-SBS interference can be suppressed by maximizing the residual inter-SBS interference.

Fig. 7 shows the total amount of residual user inter-ference as a function of the total number of users for two SBS’s. The upper and lower bounds derived in Section VI are also shown in the figure. As derived in Theorem 1, the gap between the performance upper bound and the solution obtained by the proposed algorithm is on the order of 1 −_K1 = 0.5, where K = 2 is the number of SBS’s in this simulation. The upper bound Imax is obtained by exhaustive

search.

2 3 4

The number of groups

11 11.5 12 12.5 13 13.5 14 14.5 15 Log 2 Itot N = 24, MkC N = 24, Geedy N = 36, MkC N = 36, Greedy N = 48, MkC N = 48, Greedy

Fig. 6. The effectiveness proof of local-search algorithm.

20 25 30 35 40 45

The number of users 11.5 12 12.5 13 13.5 14 14.5 15 15.5 Log 2 Itot I

max (Upper Bound)

I_ls (Proposed Local Search Algorithm) Lower Bound (Worst Case)

Fig. 7. Interference bounds for the proposed local-search algorithm for K = 2 SBS’s.

the zero-forcing scheme with global power allocation pro-posed in [26] and with uniform power allocation scheme in [15], respectively. Inspection of Fig. 8 reveals that the proposed algorithm has the best performance as compared to the conventional algorithms. More specifically, the proposed algorithm leverages a rank-constrained D.C. algorithm to jointly optimize precoding and power allocation. In contrast to the implementation of SVD in “CCP-SVD”, an iterative algorithm is proposed to satisfy the rank constraint for digital precoding design while optimizing the power allocation. The dotted and dashed curves are the upper bound and lower bound derived in Section VI, respectively.

-10 -5 0 5 10 15 SNR (dB) 0 5 10 15 20 25 30 35 40 45 50 55 Weighted Sum-Rate (bps/Hz) Proposed Algorithm CCP-SVD ZF-GloPowAll ZF-UnifPowAll Lower Bound Upper Bound

Fig. 8. Performance comparison for different algorithms in one SBS.

0 2 4 6 8 10 12 User's rate 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F(x) Proposed Algorithm CCP-SVD ZF HB Uniform Power HB

Fig. 9. CDF of WSR achieved by different algorithms with SNR = 10 dB.

Next, we examine the QoS for each UE by setting λu = 1 bps for u = 1, · · · , 12. Fig. 9 depicts the CDF of

the average UE data rate. It is evident that all UEs served by the proposed QoS-aware power allocation algorithms satisfy the minimum QoS requirement (i.e. 1 bps/Hz). Defining the outage as the average UE data rate being below the mini-mum required data rate, “Uniform Power HB” and “CCP-SVD” suffer from an outage rate of about 20% and 58%, respectively.

0 20 40 60 80 100 120 140 160 180

The number of iterations

0 5 10 15 20 25 30 35 40

Sum-rate Spectral Efficiency (bps/Hz)

-10 dB -5 dB 0 dB 5 dB 10 dB 15 dB

Fig. 10. Convergence behaviors of the proposed iterative algorithm.

-10 -5 0 5 10 15 SNR (dB) 0 20 40 60 80 100 120 Weighted Sum-Rate (bps/Hz) MkC K=2 Greedy K=2 MkC K=3 Greedy K=3

Fig. 11. Performance comparison for MkC and greedy selection for N = 24.

−10 dB to 15 dB. Fig. 10 suggests that the proposed algorithm converges monotonically within 80 iterations at all SNR values.

Finally, the comparison of MkC and greedy selection for user association is presented in Fig. 11 using N = 24 UEs served by K = 2, 3 SBS’s. Fig. 11 shows that the proposed MkC scheme outperforms the greedy selection for both K = 2, 3. Furthermore, the WSR performance improves with the increment of K since more frequency bands are

introduced.

VIII. CONCLUSION

In this paper, we have investigated an mmWave MEC system in which each user has a QoS requirement. Taking into account the hardware cost, we have proposed hybrid pre-coding techniques to reduce the number of RF chains as com-pared to the conventional fully digital precoding approaches. To suppress the intra-SBS interference, an MkC approach has been developed to solve the user association problem. Moreover, we have proposed a D.C. programming-based iterative algorithm to jointly optimize the digital precoder and power allocation for QoS-aware WSR maximization for hybrid precoding systems. To solve this coupled non-convex problem, we have proposed to cast the optimization problem as a rank-constrained D.C. programming problem before an iterative algorithm is devised by combining the conventional D.C. programming problem with RCOP. Simulation results have shown that the proposed schemes can effectively im-prove WSR while satisfying the QoS of each UE.

APPENDIXA PROOF FORTHEOREM1

Proof. Assuming the maximal value of MkC is Imax. Let

N1, N2, · · · , NK be an arbitrary solution obtained while the

value is Ils using the local-search algorithm. We can show

straightforwardly Ils= K X k=1 Nk X u=1 Ωku,k. (61)

where Ils is the solution given by the local-search algorithm.

By summing both sides of the inequalities (27) over all u ∈ Nk, q ∈ Nj, we have NkNj Nk X u=1 Ωku,k+ NkNj Nj X q=1 Ωjq,j ≤ NkNj Nj X q=1 Ωjq,k+ NkNj Nk X u=1 Ωku,j. (62) Setting Nk X u=1 Ωku,k = Γkk, Nj X q=1 Ωjq,j = Γjj, Nj X q=1 Ωjq,k= Γkq, Nk X u=1 Ωku,j = Γju, (63) we have Γkk+ Γjj ≤ Γkq+ Γju. (64)

The cut of this solution is then given by: K X k=1 K X j=1,j6=k (Γkq+ Γju) = 2Ils. (66)

The above inequality can be rewritten as

K X k=1 K X j=1,j6=k (Γkk+ Γjj) (67) = K X k=1 K X j=1,j6=k Γkk+ K X k=1 K X j=1,j6=k Γjj =(K − 1) K X k=1 Γkk+ (K − 1) K X k=1 Γjj =2(K − 1) K X k=1 Γkk.

Recalling Equation (66), we have

(K − 1)

K

X

k=1

Γkk≤ Ils. (68)

Since the optimal solution can contain all edges, we obtain

Imax≤ (K − 1) K X k=1 Γkk+ Ils ≤ Ils+ Ils K − 1, (69) or equivalently Ils Imax ≥ 1 − 1 K. (70)

Thus, the theorem is proved.

APPENDIXB PROOF FOREQUATION(38)

Proof. Suppose f (p) is a concave function on a convex neighborhood C and differentiable at p. Then, for every y ∈ C, we have the following inequality based on the definition of concavity:

f ((1 − λ)p + λy), =f (p + λ(y − p)) ,

≥f (p) + λ (f (y) − f (p)) , (71) where 0 < λ ≤ 1.

Rearranging the terms and dividing both sides by λ, we have

f (p + λ(y − p)) − f (p)

λ ≥ f (y) − f (p). (72)

Letting λ → 0, it can be shown that the left hand side of Inequality (72) converges to f0(p) · (y − p). Finally, we have Equation (38) as follows:

f (p) + f0(p) · (y − p) ≥ f (y). (73)

APPENDIXC PROOF FORPROPOSITION1

Proof. Recalling Equation (52), the SINR can be represented as

X = Z

1/γ + Y. (74)

To derive the CDF of SINR, we have to first calculate the CDF of Y , which can be represented as

Y =ZE   Nk X i=1,i6=u  v_k,u∗Hv∗_k,i  2  , ≈Z(Nk− 1)E h v_k,u∗Hv∗_k,i 2i , (75a) ≤Z(Nk− 1)Ξ (75b)

where we have assumed that the variance of |v∗H_k,uv∗

k,i|

2

for ∀i ∈ Nk is small by recalling the Equation (13) in

Equation (75a). Equation (75b) is the average interference over all i.i.d UEs. Finally, the inequality of Equation (75b) comes from the effectiveness of association algorithm.

As the AoDs and AoAs are i.i.d for UPA antennas, the expectation can be calculated as

E h v_k,u∗Hv∗_k,i 2i₄ = Ξ = 1 4π2_N2 T Z 2π 0 Z 2π 0

|B(θk,u, θk,i, φk,u, φk,i)| 2

dθk,udφk,i,

(76)

where B(·) is given by

B(θk,u, θk,i, φk,u, φk,i)

= Q−1 X q=0 P −1 X p=0

exp [jκd [p (sin φk,usin θk,u− sin φk,isin θk,i)

+q (cos θk,u− cos θk,i)]] ,

=(1 − e

jκdn(sin φk,usin θk,u−sin φk,isin θk,i)₎P

1 − ejκdn(sin φk,usin θk,u−sin φj,isin θj,i)

×(1 − e

jκdn(cos θk,u−cos θj,i)₎Q

1 − ejκdn(cos θk,u−cos θj,i) . (77)

As shown in Fig. 12, the value of Ξ can be numerically estimated. As the number of antenna increases, the value of Ξ decreases gradually, which confirms Equation (13).

APPENDIXD

DERIVATION FOREQUATION(59)

Since αk,u,l has the distribution of X2(2), the CDF of Z

can be derived in a straightforward manner [42]:

FZ(z) = 1 − e− z

2 4 6 8 10 12 14 16 18 20

The number of antennas

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Fig. 12. The value of Ξ for different number of transmitter antennas.

For a given CDF of Z in Equation (57), the CDF of SINR can be computed as FX(x) = P (X ≤ x) = P  _Z 1/γ + Z( ¯N − 1)Ξ ≤ x  , = P  Z ≤ x γ(1 − x( ¯N − 1)Ξ)  , = 1 − e−Cγ(1−Ξ( ¯xN −1)x)_{, (79)}

where we have γ > 0 in the derivation above.

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Guanchong Niu received his bachelor degree in Physics from Jilin University, China in 2014. He is currently pursing his Ph.D. degree at the Chinese University of Hong Kong, Shenzhen (CUHKSZ). He was an intern at the Bell Labs, France between January to March 2020, developing indoor local-ization systems. His current research interests in-clude the millimeter wave(mmWave) and multiple-input multiple-output (MIMO)systems for the next-generation wireless communications and robotics.

Qi Cao received his bachelor degree in Electronic Communication Engineering from University of Liverpool in 2013, M.S. degree in Communications and Signal Processing from Imperial College in 2014 and the Ph.D. degree in School of Information and Control Engineering of China University of Mining and Technology in 2018, respectively. He joined the Chinese University of Hong Kong, Shen-zhen as postdoctoral research associate in 2019. His current research interests include MIMO wireless communications, machine learning and artificial intelligent (AI)-driven network optimization.

Man-On Pun received his BEng. degree in Elec-tronic Engineering from the Chinese University of Hong Kong (CUHK) in 1996, the MEng. degree in Computer Science from University of Tsukuba, Japan in 1999 and the Ph.D. degree in Electrical Engineering from University of Southern Califor-nia (USC) in Los Angeles, U.S.A in 2006, respec-tively. He was a postdoctoral research associate at Princeton University from 2006 to 2008.

Currently, he is an associate professor at the School of Science and Engineering, the Chinese University of Hong Kong, Shenzhen (CUHKSZ). Prior to joining CUHKSZ in 2015, he held research positions at Huawei (USA), Mitsubishi Electric Research Labs (MERL) in Boston and Sony in Tokyo, Japan. Prof. Pun’s research interests include AI Internet of Things (AIoT) and applications of machine learning in communications and satellite remote sensing.