User Selection and Power Allocation forMmWave-NOMA Networks

Jingjing Cui?, Yuanwei Liu†, Zhiguo Ding‡, Pingzhi Fan?and Arumugam Nallanathan†

? Southwest Jiaotong University, Chengdu, P. R. China† Queen Mary University of London, London, UK

‡ Lancaster University, UK

December 6th, 2017

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Outline

1 Overview and Motivation

2 MmWave-NOMA System Model

3 Proposed Solutions

4 Simulation Results

5 Conclusions

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From OMA to NOMA

1 Question: What is multiple access?2 Orthogonal multiple access (OMA): e.g., FDMA, TDMA,

CDMA, OFDMA.3 New requirements in 5G

High spectrum efficiency.Massive connectivity.

4 Non-orthogonal multiple access (NOMA): to breakorthogonality.

5 Standard and industry developments on NOMAWhitepapers for 5G: DOCOMO, METIS, NGMN, ZTE, SKTelecom, etc.LTE Release 13: a two-user downlink special case of NOMA.Next generation digital TV standard ATSC 3.0: a variationof NOMA, termed Layer Division Multiplexing (LDM).

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NOMA Basics

User m detection

User n detection

User n

Subtract user m’s signal

0

BS

User m

User m detection

Superimposed signal of User m and n

SIC

Pow

er

FrequencyUser n

User m

Time

1 Realize the multiple access in the same resource block(time/frequecy/code), but with different power levels [1].

2 Apply successive interference cancellation (SIC) at thereceiver.

[1] Y. Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan and L. Hanzo, “Non-Orthogonal Multiple Access for 5G and Beyond”,

Proceedings of the IEEE ; vol. 105, no. 12, pp. 2347-2381, Dec. 2017.

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Motivation for MmWave-NOMA Networks

1 MotivationDirectional beams in mmWave communication withlarge-scale arrays bring large antenna array gains and smallinter-beam interference.Support massive connections with high user-overloadscenarios.Meet the diversified demands of users while enhancing thespectral efficiency by using SIC techniques

2 ChallengesAccurate channel estimation and CSI feedback to the basestation (BS) induce heavy system overhead particularly inmulti-user mmWave downlink systems.The inter-beam and intra-beam interference in mmWaveNOMA systems affects the decoding order of NOMA.

[2] Z. Ding, P. Fan, and H. V. Poor, “Random beamforming in millimeterwave NOMA networks,” IEEE Access,

vol. PP, no. 99, pp. 1-1, 2017.5 / 26

MmWave-NOMA System Model

Baseband processing

...

M superposed data stream

s

...

Partial channel information feedback

K users

...

M beams

...User jerer UsUsUsUsUsererererer ererererer UsUsUsUsUsererererer jjjjjjjjjjjjjjjjjjUser j

User ker UsUsUsUsUserererer erererer kkkkkkkkkkkkkUsUsUsUsUsererererer kkkkkUser k

jjjjjjjjjjjjjjjj

w1

wM

SIC Procedure

Desired signal

detectionDesired signal

detection

Small-cell BS

1 Construct M orthogonal beams at BS in spatial domain.2 Realize NOMA transmission in each beam and apply

successive interference cancellation (SIC) at users.[3] J. Cui, Y. Liu, Z. Ding, P. Fan, and A. Nallanathan, “Optimal User Scheduling and Power Allocation forMillimeter Wave NOMA Systems,” to appear in IEEE Trans. Wireless Commun..

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Received Signal Model

1 Based on the NOMA principle, the received SINR of user k todecode user j on beam m is given by

SINRmj→k =

gmk β

mj

gmk∑π(i)>π(j) β

mi +

∑n 6=m gn

k βn + σ2 (1)

2 Note that the achievable SINR for user j on beam m can beobtained with k = j .

3 The corresponding decoding rate isRm

j→k = log2(1 + SINRmj→k), for any π(k) ≥ π(j), j , k ∈ Cm.

4 SIC condition of success: Rmj→k ≥ Rm

j→j for π(k) ≥ π(j),j , k ∈ Cm.

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Optimization Problem

1 The considered sum rate maximization problem:

maxc,β

M∑m=1

qm∑j=1

Rmj→j (2a)

s.t. Rmj→k ≥ Rm

j→j ,M∑

m=1

∑j∈Cm

βmj ≤ Ptot , (2b)

K∑k=1

cmk = qm,

M∑m=1

cmk ≤ 1, Rm

j→j ≥ R̄j , (2c)

πm ∈ Π, π(k) > π(j), j , k ∈ Cm, m ∈M. (2d)

c denotes the index set, where term cmk indicates the indicators

for user k on beam m, cmk ∈ {0, 1}.

Π denotes the set of all possible SIC decoding orders.8 / 26

Overview of Proposed Solutions

1 Difficulties:Intra-beam andinter-beam interferenceare jointly considered.The decoding order ofNOMA is affected bythe inter-beam powerallocation.Joint user schedulingand power allocation isNP-hard.

2 Solutions: Divide thecomplicated problem intosome ease of subproblems.

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Overview for Power Allocation Algorithm

Intra-beam and inter-beaminterference is jointlyconsidered.The decoding order ofNOMA is affected by theinter-beam powerallocation.Joint user scheduling andpower allocation isNP-hard.

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An example for Branch and Bound (BB) Algorithms

1 Construct a boxconstraint:

Consider atwo-dimension spacedenoted by Γ1 and Γ2.G is the feasible set. D0is the constructed initialrectangle.Point A and point Bcorrespond to theminimum and maximumboundary point in D0,respectively.

Let f be the objective function with monotonically decreasing.The optimal objective f ? belongs to the interval between f (A)and f (B).

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An Example for Branch and Bound (BB) Algorithms

2 Branch operations:Split D0 into D1 and D2along the longest edge.(A,C) and (D,B) denotethe boundary point ofD1 and D2, respectively.Calculate the upper andlower bounds over D1and D2, respectively.

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An Example for Branch and Bound (BB) Algorithms

3 Bound operations:The lower boundL = min{f (A), f (D)}.The upper boundU = min{f (C), f (B)}.Note thatU − L ≤ f (A)− f (B),the potential interval forf ? decreases.

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An Example for Branch and Bound (BB) Algorithms

4 Pruning operations:Split D1 and D2 alongits longest edge,respectively.Remove D5, which willnot affect theoptimality.

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Subproblem 1: Power Allocation Problem

1 For given the selected users and the corresponding decodingorder, the power allocation subproblem can be formulated asfollows.

minβ̃,Γ−

M∑m=1

qm∑jm=1

log2(1 + Γm

jm→jm)

(3a)

s.t.Γmjm→jm ≤

gmjmβ

mjm

gmjm∑qm

im=jm+1 βmim +

∑n 6=m gn

jmβn + σ2 , (3b)

M∑m=1

qm∑jm=1

βmjm ≤ Ptot , Rm

jm→jm ≥ R̄jm , (3c)

∑n 6=m

(gm

km gnjm − gm

jm gnkm

)βn +

(gm

km − gmjm)σ2 ≥ 0, (3d)

km > jm, jm, km ∈ Cm, m ∈M. (3e)

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Key Steps for Branch and Bound (BB) Algorithms

1 Construct box constraint sets:The objective function and the feasible set of (3) can berewritten as

U(Γ) =−M∑

m=1

qm∑jm=1

log2

(1 + Γm

jm→jm

),G =

{Γ|(3b)− (3e)

}.

The equivalent reformulation of power allocation problem is givenby

minΓ

U(Γ) s.t. Γ ∈ G. (4)

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Key Steps for Branch and Bound (BB) Algorithms

2 Construct boundfunctions:

The lower bound function:

g(Γ) =

{U(Γ), Γ ∈ G0, o.w.,

,

The upper bound function:

g(Γ) =

{U(Γ), Γ ∈ G0, o.w..

Observations:g(C/G/H) = U(C/G/H), and g(F/A/D) = U(F/A/D), forD3,D4,D6, respectively.g(G) = 0 and g(G) = 0 for D5.

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Key Steps for Branch and Bound (BB) Algorithms

Question: How to express the observations in mathematicalproblem?

3 Check the feasibility: Givena set of SINR values, testingif it is achievable isequivalent to solving thefollowing feasibility problem:

Find PA coefficientss.t. Γ ∈ G.

(5)

Observations:Problem (5) is feasible forA, D and F.One cannot find a feasiblePA coefficients for D5.

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Subproblem 2: Matching Theory for User Selection

1 Given the user power allocation coefficients, the userselection problem can be transformed into

maxc

H =M∑

m=1

qm∑j=1

Rmj→j

s.t.K∑

k=1cm

k = qm,M∑

m=1cm

k ≤ 1,

πm ∈ Π, π(k) > π(j), j , k ∈ Cm, m ∈M.

(6)

Problem (6) is a combinational problem.Exhaustive search provides an optimal approach but it surfers acumbersome computational complexity.There two objects: users and beams, which motivates usbuild a matching model.

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Subproblem 2: Matching Theory for User Selection

1 Preference lists:The preference value for the user k on beam m is theachievable rate of user k on beam m:

Hmk = log2

(1 + Γm

k

). (7)

The preference value of beam m is the sum rate of all users onbeam m:

Hm =∑

k∈ϕ(m)

log2

(1 + Γm

k

). (8)

The inter-beam interference and the intra-beam interferenceexist for each user’s rate.Users and beams compose a many-to-one matching withexternalities.

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Overview for Matching Algorithms

EDA denotes the extend deferredacceptance.The users first propose to theBSs based on its preference list.Then each BS accepts the userswith prior preferences.The goal of swap operationprocedure is to further enhancethe system sum rate.Two-sided exchange-stablematching provides the stopcriteria.

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Simulation Results

200 400 600 800 10000

2

4

6

8

10

Iteration Number

Sum

rat

e (b

its/s

/Hz)

BB: Lower boundBB: Upper bound

SNR = 5 dB

SNR = −5 dB

The proposed BBalgorithm is converged fordifferent SNR.the convergence becomeslow when the SNRincreases.

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Simulation Results

0 5 10 15 200

2

4

6

8

10

SNR (dB)

Sum

rat

e (b

its/s

/Hz)

Exhaust+BB: NOMAExhaust+BB: OMAMatching+BB: NOMAMatching+BB: OMARandom+BB: NOMARandom+BB: OMA

Matching+BB achieves agood balance between theperformance and thecomputational complexity.The application of NOMAinto mmWave can furtherimprove the spectralefficiency by appropriatepower and user selectionpolicies.

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Conclusions

The problem to maximize the sum rate for the mmWaveNOMA system by designing of user selection and powerallocation algorithms has been considered.BB technique was applied for solving the power allocationproblem optimally.For the integer optimization of the user selection, a lowcomplexity algorithm based on matching theory wasdeveloped.

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Research Opportunities and challenges for NOMA

1 MIMO-NOMA design.2 Error Propagation in SIC.3 Imperfect SIC and limited channel feedback.4 Synchronization/asynchronization design for NOMA.5 Different variants of NOMA.6 Novel coding and modulation for NOMA.7 Hybrid multiple access8 Efficient resource management for NOMA9 Security provisioning in NOMA10 Grant free NOMA design for IoT

Y. Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan and L. Hanzo, “Non-Orthogonal Multiple Access for 5G and Beyond”, Proceedings

of the IEEE ; vol. 105, no. 12, pp. 2347-2381, Dec. 2017.

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Questions?

Thanks for your attention.

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