prof. rose qingyang hu ieee communications society...

MU-MIMO, NOMA and D2D in 5G/IoT Wireless Systems

Prof. Rose Qingyang HuIEEE Communications Society Distinguished Lecturer

Communications Network Innovation (CNI) LabDepartment of Electrical and Computer Engineering

Utah State UniversityLogan, UT, USA

November 09, 2016IEEE ComSoc Orange County

Motivation and Objective

D2D/NOMA/MU-MIMO/mmWave for 5G and IoT

I NOMA can support more simultaneous connections, which is suitable to address thechallenges related to massive connectivity.

I A NOMA system is interference limited, i.e., the achievable data rates for someusers will be quite small, which is applicable to many applications related to theInternet of Things (IoT).

I One of the goals of 5G is to support up to 50 billion devices, the massiveconnections put challenges to current communication systems. However, allowingpart of the devices directly communicate with each other (the so called D2D) canhelp achieve potential gains.

I D2D transmitter and receiver are close to each other, which allows lower powertransmission. This is important in today’s small size battery-driven devices

I D2D users can share the same spectrum with cellular users with careful interferencecoordination mechanisms. Thus the overall system spectrum efficiency can beenhanced

I mmWave frequency band provides a desirable choice for short range low powerwearable device communications and high bandwidth

I etc.

Prof. Rose Qingyang Hu IEEE Communications Society Distinguished LecturerMU-MIMO, NOMA and D2D in 5G/IoT Wireless Systems

Presentation Topics

I NOMA and beamforming in downlink cellular network with underlay D2D

I Distance based power control for D2D communications in uplink cellular network

I Uplink NOMA using near-far effect and fractional power control

I Blockage and coverage study in mmWave based relay system


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications

A NOMA and MU-MIMO Supported Cellular Network withUnderlay D2D Communications


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications System Model

System Model

We consider a downlink MU-MIMO cellular network that jointly supports NOMA andD2D underlaid users as shown in Fig. 1.The BS has N antennas with power PMBS . M cellular users (CUs) are randomly deployed,each equipped with one antenna. Furthermore, a total number of P underlaid D2D users(DUs) are also randomly deployed.

...

......

,NK

CU

,1NCU

Beam N

MBS

1w

1,1

CU

1,K

CU

1Beam

Nw

N Antennas...

CUs

2D DTX

2D D RX

2 1D D Link

2 2D D Link

2D D Link P

1,1h

2,2h

,p ph

Figure 1: System Model



System Model

For beam n, NOMA allows a set of Φn = {u(n, 1), u(n, 2), . . . , u(n,K)} CUs to bescheduled on the same radio resource simultaneously, K ≥ 2. We use u(n, k) to denotethe CU that is served by beam n with NOMA sequence k in that beam. Assume xn is thetransmitted signal in the n-th beam, and according to NOMA, xn is a superimposedsignal of a total K users in beam n,

xn =K∑

k=1

√λu(n,k)Pnsu(n,k). (1)

...

......

,NK

CU

,1NCU

Beam N

MBS

1w

1,1

CU

1,K

CU

1Beam

Nw

N Antennas...

CUs

2D DTX

2D D RX

2 1D D Link

2 2D D Link

2D D Link P

1,1h

2,2h

,p ph



System Model

In the above equation, E(|su(n,k)|2) = 1, E(.) is the expectation function. λu(n,k) is the

fraction of the allocated power to user u(n, k),∑K

k=1 λu(n,k) = 1. Pn is the totaltransmitted power for beam n. The total transmission power of a BS is equallypartitioned among N beams, i.e., Pn = PMBS

N, where PMBS is the total BS transmission

power.At the MBS, a precoding scheme is applied to support MU-MIMO. We denote theprecoding matrix as W, which consists of N vectors, i.e.,

W = [w1,w2, . . . ,wN ], (2)

where wn ∈ CN×1 is the beamforming vector of the n-th beam.



System Model

The received signals at u(n, k) and DU p can be respectively expressed as

yu(n,k) = hu(n,k)

N∑n=1

wnxn +P∑

p=1

√PDhp,u(n,k)sp + nu(n,k) (3)

yDUp =P∑

p′=1

√PDhp′,ps

′p + hp

N∑n=1

wnxn + np, (4)

where sp is the transmitted signal of DU p. We also have E(|sp|2) = 1. PD is thetransmission power of DUs. hu(n,k) and hp are the channel gains for downlink CU u(n, k)and for DU p, respectively. hp,u(n,k) is the channel gain between DU p and CU u(n, k),and similarly hp′,p is the channel gain between the transmitter of DU p′ and the receiverof DU p. We assume the channel information is perfectly know at the BS. nu(n,k) and npare i.i.d. additive white Gaussian noise at CU u(n, k) and DU p, respectively.nu(n,k), np ∼ CN (0, 1).


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications NOMA with SIC and Problem Formulation

SIC process

1 Within a NOMA group, CU with a weaker channel is normally allocated a higherdownlink transmission power to ensure QoS.

2 UEs with strong channel gain can always decode the weaker UE’s message thensubtract from the composite signal.

3 The decoding process will continue until the UE get its desired signal. This is calledsuccessive interference cancellation (SIC).



Without loss of generality, we assume |hu(n,1)| ≤ |hu(n,2)| ≤ . . . ≤ |hu(n,K)|. Since thedecoding order follows the ascending order of channel gains, CU j will decode CU imessage, if i < j . SIC then removes the decoded message from its observation. CU itreats signals from CUs with index j > i as interference. Assuming perfect interferencecancellation, we can rewrite (3) as

yu(n,k) = hu(n,k)wn

√λu(n,k)Pnsu(n,k) + hu(n,k)wn

K∑k′=1,k′ 6=k

√λu(n,k′)Pnsu(n,k′)

+hu(n,k)

N∑n′=1,n′ 6=n

wn′

K∑k′=1

√λu(n′,k′)Pn′su(n′,k′) +

P∑p=1

√PDhp,u(n,k)sp + nu(n,k)(5)

where the second term on the right side is the interference from users in the sameNOMA group. The third term represents inter-beam interference.


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications Problem Formulation

Problem Formulation

The design objective is to maximize the total system sum throughput from both CUs andDUs. To this end, we need to determine 1) the NOMA set of each beam, i.e., Φn; 2) thepower allocation factor λu(n,k) for each user k in the NOMA set of beam n; and 3) theprecoding vector wn. Therefore, the problem can be formulated as follows.

maxΦn,wn,λu(n,k)

N∑n=1

K∑k=1

f (E{γu(n,k)}) +P∑

p=1

f (E{γDUp}) (12)

subject toK∑

k=1

λu(n,k) = 1, n = 1, 2, . . . ,N, (13)

f (E{γu(n,k)}) > R0, ∀k 6= K , (14)

wn ∈ CN×1. (15)

Constraint (13) is the summation of user power in one beam. Constraint (14) sets alower rate limit for users that experience SIC interference in NOMA to ensure good userexperience. f (E{γ}) is used to calculate Shannon capacity,

f (E{γ}) = log(1 + E{γ}). (16)


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications Precoding and User Grouping Algorithm

The optimization problem is a non-convex NP-hard problem that needs to determineΦn,wn, λu(n,k) jointly.To make this problem feasible to solve, we seek a heuristic solution by decomposing theoriginal problem into two sub-problems. We first develop different precoding methods,which aim to suppress either the inter-beam interference among CUs or the interferencefrom CUs to DUs. Based on the precoding matrices, we further define a user groupingand power allocation algorithm for NOMA.



First ZF Precoding

In this scheme, we first select one user from each beam and then generate thebeamforming matrix based on N selected users. Specifically, users with the largestchannel gain in each beam are selected. The channel gain vector for these N selectedCUs are denote as H = [hu(1,K), hu(2,K) . . . hu(N,K)]. The zero-forcing beamforming vectoris calculated based on:

hu(n,K)wm = 0, if m 6= n. (17)

Thus, wm should lie in the null space of Hn. Here, Hn is defined as

Hn = [hu(1,K), . . . , hu(n−1,K), hu(n+1,K), . . . , hu(N,K)], (18)

which consists of downlink channel vectors for CUs from all beams except from beam n.



Second ZF Precoding

The first ZF based method helps reduce inter-beam interference IUu(n,K) = 0 in (6). Sincewe aim to maximize the total sum rate in the system, the total throughput from DUscontributes to the total throughput as well. Therefore, the second precoding methodhelps reduce the interference between CUs and DUs, i.e.,

∑Nn=1 Pn|hpwn|2 = 0 in (10).

Hence we should set hpwn = 0, for all n. Or equivalently,

wn = null(HD), (19)

where HD = [h1, . . . , hP ], and null(.) is the null space or kernel of a matrix.


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications Power Allocation User Selection Algorithm

User Selection

Criteria

I NOMA would prefer to group users with greater channel differences.

I Precoding matrix W is designed to minimize inter-beam interference or CU to DUinterference.

I NOMA groups users with highly correlated channels so that using the precodingmatrix generated by the representative CU in each beam can achieve a smallinter-beam or CU-DU interference

Therefore, the criteria for NOMA user grouping is to choose CUs with highly correlatedchannels but with big channel gain differences in each beam. For simplicity, we setK = 2, which means each NOMA group consists of 2 users. In each NOMA pair, wedenote the user with a weaker channel gain as the first user while the stronger one as thesecond user.



Optimal Power Allocation

For the first ZF scheme, the bemforming matrix is designed based on the null space ofthe second users in all N beams, second users will not receive any inter-beaminterference. Thus the SINR is

γu(n,2) =λu(n,2)Pn|hu(n,2)|2

IDu(n,2) + σ2n

. (20)

The first users, on the other hand, will receive non-zero inter-beam interference as theprecoded signals from other beams will have components projected into the first usersignal space. The SINR is expressed as

γu(n,1)=(1− λu(n,2))Pn|hu(n,1)wn|2

|hu(n,1)wn|2λu(n,2)Pn + IDu(n,1) + IUu(n,1) + σ2n. (21)



Optimal Power Allocation

The optimal power allocation factor λu(n,2) is yet to be solved. Based on the optimizationproblem proposed in the previous section, we form a new problem that aims to maximizethe sum capacity in each beam.

maxλu(n,2)

2∑k=1

f (E{γu(n,k)}) (22)

subject to0 < λu(n,2) < 1, (23)

f (E{γu(n,1)}) ≥ R0. (24)

The problem defined above is convex with respect to λu(n,2) and its KKT conditions aregiven as follows.

∂

(∑2k=1 f (E{γu(n,k)})

)∂λ∗u(n,2)

=µ

∂

(R0 − f (E{γu(n,1)})

)∂λ∗u(n,2)

, (25)

R0 − f (E{γu(n,1)})|λ∗u(n,2)≤ 0, (26)

µ ≥ 0, (27)

µ

(R0 − f (E{γu(n,1)})|λ∗

u(n,2)

)= 0. (28)



Equation (25) is the stationarity condition and µ is KKT multiplier, (26) is the primalfeasibility, (27) is dual feasibility and (28) is the complementary slackness. Solving for(25), we can get

λ∗u(n,2) =

(ID2 + 1)

((ID1 + 1 + Σ)H2 − (1 + µ)H1

)H1H2ρ(µ− ID2)

, (29)

where, ρ = Pn/σ2n is the transmit SNR, H2 = |hu(n,2)|2, H1 = |hu(n,1)wn|2 is the channel

gain for user 2 and user 1, ID1 = IDu(n,1)/σ2n, ID2 = IDu(n,2)/σ

2n is the interference-to-noise

ratio of user 1 and user 2, respectively. Σ = IUu(n,1)/σ2n is the inter-beam

interference-to-noise ratio.Clearly, µ 6= 0. Otherwise, λ∗u(n,2) < 0 cannot satisfy (23). Therefore, we can solve (28)for the optimal λ∗u(n,2).

λ∗u(n,2) =ρH1 + ID1 + 1 + Σ

2R0ρH1− ID1 + 1 + Σ

ρH1. (30)

λ∗u(n,1) = 1− λ∗u(n,2). (31)


A NOMA and MU-MIMO Supported Cellular Network with Underlay D2DCommunications Simulation results

Simulation Results

We present the performance results from simulation. The coverage area of MBS is acircle with a radius of 500 m. The number of transmit antennas is N = 3. The totalnumbers of CUs and DUs are M = [8, 16, 32, 60, 90] and P = 2 respectively. M varies inorder to study the multi-user diversity effect. The distance with each DU pair is fixed at30 m. PMBS and PD are set to 30 Watt and 1 Watt, respectively.For comparison purpose, instead of using NOMA in each beam, we apply a traditionalTDMA scheme here to support these 2 users in each beam. Specifically, we allocate anequal number of time slots to 2 TDMA users. The scheme is also referred as ”NaiveTDMA”.

RTDMA =1

2

(log(1 + γ1) + log(1 + γ2)

). (32)



Fig. 2 presents the system capacity of two proposed ZF precoding methods as thenumber of users grows, the results are scaled over the highest achievable rate. Here weset R0 = 0.5 b/s/Hz.

15 30 45 60 75 9010

20

30

40

50

60

70

80

90

100

Number of CUs

Sys

tem

Thr

ough

put (

%)

NOMA, ZF1Naive TDMA, ZF1NOMA, ZF2Naive TDMA, ZF2

Figure 2: System capacity of two proposed ZF precoding methods vs. Naive TDMA as thenumber of user grows (R0 = 0.5 b/s/Hz).



1 NOMA outperforms naive TDMA in both precoding schemes when the number ofCUs is large. However, when the number is small, limited CUs can be chosen toperform NOMA, thus, the performance gain is not obvious, even worse than TDMA.

2 ZF2 leads to a higher overall system throughput than ZF1. With ZF2, DUsexperience a much lower interference than with ZF1.

3 The system benefits more from NOMA+MU-MIMO due to a higher multiuserdiversity gain.

15 30 45 60 75 9010

20

30

40

50

60

70

80

90

100

Number of CUs

Sys

tem

Thr

ough

put (

%)

NOMA, ZF1Naive TDMA, ZF1NOMA, ZF2Naive TDMA, ZF2



In Fig. 3, the throughput of CUs is calculated. ZF1 has a much better performance thanZF2 since ZF1 precoding eliminates inter-beam interference for CUs while ZF2 aims toeliminate interference from CUs to DUs. But if we combine results from both Fig. 2 andFig. 3, we can see that the overall throughput is higher with ZF2 since DUs areconfigured with a very good channel setting so that they contribute to overall throughputsignificantly.

15 30 45 60 75 900

10

20

30

40

50

60

70

80

90

100

Number of CUs

CU

s T

hrou

ghpu

t (%

)

CUs with NOMA, ZF1CUs with Naive TDMA, ZF1CUs with NOMA, ZF2CUs with Naive TDMA, ZF2

Figure 3: CUs capacity of two proposed ZF precoding methods vs. Naive TDMA as the numberof user grows (R0 = 0.5 b/s/Hz).


D2D Communication Underlay in Uplink Cellular Networks with Distance BasedPower Control

D2D Communication Underlay in Uplink Cellular Networks withDistance Based Power Control


D2D Communication Underlay in Uplink Cellular Networks with Distance BasedPower Control System Model

System Model

In this paper we consider a multi-cell uplink cellular network with underlaid D2Dcommunications, as shown in figure below. We assume that CUEs are uniformlydistributed in each cell and DUEs follows a PPP distribution.

CUE

D2D pair

Signal

Interference

Figure 4: System ModelProf. Rose Qingyang Hu IEEE Communications Society Distinguished LecturerMU-MIMO, NOMA and D2D in 5G/IoT Wireless Systems

D2D Communication Underlay in Uplink Cellular Networks with Distance BasedPower Control System Model

Power Control

For CUE

Denoted as r the distance from a typical CUE to its associated BS, the uplink transmitpower can be expressed as Pc = rα, where α > 2 is pathloss exponent

For DUE

Denote the distance from a typical DUE to its associated BS as D. The transmit powerof DUE is Pd = ηDα, where η is a control parameter. The value of η should be verysmall to avoid generating excessive interference to cellular links and other D2D links.


D2D Communication Underlay in Uplink Cellular Networks with Distance BasedPower Control Coverage Probability

CUE Coverage Probability

The interference to CUE is composed of interference from CUEs in other cells and allDUEs. We assume all interfering CUE form a PPP and their transmit power are i.i.d. Toanalyze the interference from DUEs, we further partition the interfering DUEs into twogroups, i.e., same cell DUEs and other cell DUEs. The SINR and coverage probability forCUE can be expressed as

SINRc =hr−αPc

δ2 + Ic + I ind + I outd

. (33)

P[SINRc > T ] = P[h > T (δ2 + Ic + I ind + I outd )]

= LIc (T )LI ind

(T )LI outd

(T ). (34)

LIc (S), LI ind

(S), and LI outd

(S) are the Laplace transform of random variable Ic , I ind and I outd

evaluated at S , respectively.



CUE Coverage Probability

By taking some reasonable approximations, we can get the close form expression forcoverage probability of CUEs

LIc (S) = exp(− πλb(SE[Pc ])

2α(π

2− atan(

R2

(SE[Pc ])2α

))). (35)

E[Pc ] =2Rα

2 + α. (36)

LI ind

(S) = exp(− 2πλd

SηR2

2(1 + Sη)

). (37)

LI outd

(S) = SE[Pd ]R2−α

α− 2, E[Pd ] =

2ηRα

α + 2(38)



DUE Coverage Probability

The interference (from other DUEs and all CUEs) to a DUE is dependent on the distancefrom it to the associated BS. We made some assumptions in the analysis. Numericalresults show that our analytical result can very well provide a tight upper bound for theDUE coverage probability. The SINR and coverage probability of DUE can be expressedas

SINRd =hPdd

−α

δ2 + Ic + Id(39)

P[SINRd > T ] =

∫ R

0

P[h >Tdα

Dαη(δ2 + Ic + Id)|D]fD(D)dD. (40)

P[h >Tdα

Dαη(δ2 + Ic + Id)|D] = LIc (

Tdα

Dαη)LId (

Tdα

Dαη). (41)



DUE Coverage Probability

After some appropriate approximation, we can get the close form expression for coverageprobability of DUE

P[SINRd > T ] =1

R2

(x exp(

A

x)− AEi (

A

x))∣∣∣∣R2

1

. (42)

A = − π

sinc( 2α

)

(Tdαη

) 2α(λbE[P

2αc ] + λdE[P

2αd ]). (43)

E[P2αd ] =

η2αR2

2,E[P

2αc ] =

R2

2.


D2D Communication Underlay in Uplink Cellular Networks with Distance BasedPower Control Numerical Evaluation

Numerical Evaluation

Under the proposed scheme the CUE coverage in the system with underlay DUEs (bluedots) is almost the same as the CUE coverage with no underlay DUEs (red dots), whichclearly shows that the existence of DUEs only has a slight impact on CUEs if distancebased power control is applied.A higher η value allows for a higher transmit power from DUEs, leading to a better DUEcoverage.

SINR (dB)-10 -5 0 5 10 15 20

Covera

ge P

robabili

ty

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1sim,uniformanasim,no d2d,uniformsim,no d2d,ppp

Figure 5: Validation of Coverage Probabilityfor CUE. Also included is evaluation of theresult by approximating the distribution ofinterfering CUEs as PPP.

SINR (dB)-10 -5 0 5 10 15 20 25 30

Covera

ge P

robabili

ty

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1sim-η=0.001ana-η=0.001sim-η=0.01ana-η=0.01

Figure 6: Validation of Coverage Probabilityfor DUE




The distance based power control scheme can effectively protect CUEs from beinginterfered by DUEs. With η = 0.001, there is barely any impact on CUEs from DUEs withpower control while at the same time about 80 percent DUEs have SINR above 0 dB.

SINR (dB)-10 -5 0 5 10 15 20

Co

ve

rag

e P

rob

ab

ility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1PC-η=0.001noPC-η=0.001PC-η=0.005noPC-η=0.005PC-η=0.01noPC-η=0.01

noD2D

Figure 7: Coverage Probability for CUE. The result for no power control cases and no D2D caseare provided to compare with our proposed scheme




SINR (dB)-10 -5 0 5 10 15 20 25 30

Covera

ge P

robabili

ty

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PC-η=0.001noPC-η=0.001PC-η=0.005noPC-η=0.005PC-η=0.01noPC-η=0.01

Figure 8: Coverage Probability for DUE. The result for no power control cases are provided tocompare with our proposed scheme


Uplink FPC with NOMA Transmission




Introduction

Compared with orthogonal multiple access (OMA), Non-orthogonal multiple access(NOMA) possesses the potential to further improve system spectrum efficiency.

Fractional power control (FPC) gives cell center and cell edge users different targetreceiving signal power levels. NOMA can exploit this difference in the received powers sothat further spectrum efficiency can be realized.

In this paper, an analytical framework on uplink NOMA with FPC is developed andperformance on the system coverage and average user achievable rate is evaluated. Theperformance study demonstrates that NOMA with FPC can bring considerable capacitygain compared to OMA with FPC.



System Model

The tagged BS under analysis is termed as BS0 and it locates at the center of a disc witha radius R. UEs associated with BS0 are uniformly distributed in the disc.

UE1 represents cell center user whose distance to BS0 is less than R1. UE2 represents celledge user whose distance to BS0 is greater than R2.

The locations of interfering UEs in other cells using the same sub-band are assumed tofollow a 2-D homogeneous Poisson Point Process (PPP) Φ with a density λ.

CUE

D2D pair

Signal

Interference

Figure 9: System ModelProf. Rose Qingyang Hu IEEE Communications Society Distinguished LecturerMU-MIMO, NOMA and D2D in 5G/IoT Wireless Systems


Denoting the transmitting distance from UEi to BS0 as ri , the pdf of r1 isfr1 (r1) = 2r1

R21, r1 ∈ (0,R1) and the pdf of r2 is fr2 (r2) = 2r2

R2−R22, r2 ∈ (R2,R).

The distance from an interfering UEj , j ∈ Φ, to its associated BS is denoted as lj and thedistance from UEj to BS0 is denoted as rj,0. It is assumed that {lj} are independent and

identically distributed (i.i.d.) and the pdf of lj is flj (lj) =2ljR2 , lj ∈ (0,R)

The channel gain from UEi to BS0 can be expressed as r−αi hi , where α > 2 is the pathloss exponent and hi ∼ exp(1) denotes Rayleigh fading gain.

With FPC on the uplink, the transmit power of UEi is expressed as Pi = rβαi , whereβ ∈ [0, 1] is a fractional power control parameter.



Introduction

Compared with orthogonal multiple access (OMA), Non-orthogonal multiple access(NOMA) possesses the potential to further improve system spectrum efficiency.

Fractional power control (FPC) gives cell center and cell edge users different targetreceiving signal power levels. NOMA can exploit this difference in the received powers sothat further spectrum efficiency can be realized.

In this paper, an analytical framework on uplink NOMA with FPC is developed andperformance on the system coverage and average user achievable rate is evaluated. Theperformance study demonstrates that NOMA with FPC can bring considerable capacitygain compared to OMA with FPC.



Denoting the transmitting distance from UEi to BS0 as ri , the pdf of r1 isfr1 (r1) = 2r1

R21, r1 ∈ (0,R1) and the pdf of r2 is fr2 (r2) = 2r2

R2−R22, r2 ∈ (R2,R).

The distance from an interfering UEj , j ∈ Φ, to its associated BS is denoted as lj and thedistance from UEj to BS0 is denoted as rj,0. It is assumed that {lj} are independent and

identically distributed (i.i.d.) and the pdf of lj is flj (lj) =2ljR2 , lj ∈ (0,R)

The channel gain from UEi to BS0 can be expressed as r−αi hi , where α > 2 is the pathloss exponent and hi ∼ exp(1) denotes Rayleigh fading gain.

With FPC on the uplink, the transmit power of UEi is expressed as Pi = rβαi , whereβ ∈ [0, 1] is a fractional power control parameter.




UE1 and UE2 form a NOMA pair with UE1 as the strong user. Based on the principle ofNOMA, SIC receiver is carried out at BS0 to decode the superimposed signal.

The post-processing signal-to-interference-plus-noise ratio (SINR) of UE1 and UE2 afterSIC can be respectively expressed as

SINR1 =h1r

(β−1)α1

h2r(β−1)α2 + I + σ2

, SINR2 =h2r

(β−1)α2

I + σ2,

where I =∑

j∈Φ gj r−αj,0 Pj denotes the inter-cell interference received at BS0. gj and Pj

are the Rayleigh fading gain of each interfering channel and the transmit power of UEj

respectively. σ2 is noise.



Coverage probability for NOMA with FPC

The coverage probability is Fi (T ) = P[SINRi > T ] and it represents the probability thatthe instantaneous SINR of UEi is greater than a certain threshold T .

By following the previous work, the coverage probability of SINR1 is evaluated as

F1(T ) = P[SINR1 > T ]

=

∫ R1

0

LI (Tr(1−β)α1 ) exp(−Tr (1−β)α

1 σ2) · Eh2,r2 [e−h2r(β−1)α2 r

(1−β)α1 T ]︸︷︷︸

Q1

2r1

R21

dr1, (44)

where LI (s) = EI [e−sI ] is the Laplace transform of random variable I evaluated on s.




The full expression of LI (s) is given by

LI (s) = EΦ,gj ,Pj

[exp(−s

∑j∈Φ

gj r−αj,0 Pj)

]= EΦ

[∏j∈Φ

Egj ,Pj [exp(−sgj r−αj,0 Pj)]]

= exp(− 2πλEg,P [

∫ ∞R

(1− exp(−sgv−αP)]

)vdv)

The last equation uses the probability generating functional (PGFL) of PPP, which statesthat E[

∏x∈Φ f (x)] = exp(−λ

∫R2 (1− f (x))dx). After approximate the expression of

integration by Taylor series, the closed form approximation of LI (s) can be derived.

LI (s) ≈ exp(

2πλN∑

n=1

2R2+nβα−nα

(nβα + 2)(nα− 2)(n − 1)!(−s)n

), (45)




Q1 can be expressed as follows:

Q1 = Er2

[ 1

1 + T(r1r2

)(1−β)α

]=

∫ R

R2

1

1 + T(r1r2

)(1−β)αfr2 (r2)dr2

=1

R2 − R22

∫ R2

R22

1

1 + T(

r(1−β)α1

x(1−β)α

2

)dx . (46)




By substituting s = Tr(1−β)α1 back into (45) and combining it with (46), one can get the

complete expression of F1(T ) as

F1(T ) =

∫ R1

r1=0

LI (Tr(1−β)α1 ) exp(−Tr (1−β)α

1 σ2)

· 1

R2 − R22

∫ R2

x=R22

1

1 + T(

r(1−β)α1

x(1−β)α

2

) 2r1

R21

dxdr1

=1

R21 (R2 − R2

2 )

∫ R21

y=0

LI (Ty(1−β)α

2 ) exp(−Ty(1−β)α

2 σ2)

·∫ R2

x=R22

1

1 + T(

yx

) (1−β)α2

dxdy . (47)




Similar to coverage probability of UE1, the coverage probability of UE2 can be derived as

F2(T ) = P[SINR2 > T ]

= Er2

[P[h2r

(β−1)α2

I + σ2> T |r2

]]=

∫ R

R2

P[h2 > Tr

(1−β)α2 (I + σ2)|r2

]fr2 (r2)dr2

=

∫ R

R2

exp(−Tr (1−β)α2 (I + σ2))

2r2

R2 − R22

dr2

=1

R2 − R22

∫ R2

R22

LI (Tx(1−β)α

2 ) exp(−Tx(1−β)α

2 σ2)dx , (48)

where LI (s) is given in (45).



Coverage probability for OMA with FPC

To make a comparison between NOMA and conventional OMA, the coverage probabilityof each UE when using OMA with FPC is also presented in this work. The number ofinterfering uplink UEs reduces to half of that NOMA case. The SINRs of UE1 and UE2

and their coverage probability are given below

SINROMA1 =

h1r(β−1)α1

12I + σ2

, SINROMA2 =

h2r(β−1)α2

12I + σ2

.

FOMA1 (T ) = P[SINROMA

1 > T ]

=1

R21

∫ R21

0

LI (T

2x

(1−β)α2 )e−

T2σ2x

(1−β)α2

dx (49)

FOMA2 (T ) = P[SINROMA

2 > T ]

=1

R2 − R22

∫ R2

R22

LI (T

2x

(1−β)α2 )e−

T2σ2x

(1−β)α2

dx (50)



Average achievable data rates

Based on the coverage probability, one can compute the average achievable rates of UE1

and UE2 for both NOMA and OMA scenarios by using Shannon capacity formula.Denoted by τi the average achievable rate of UEi when using NOMA and τi is calculatedas

τi = E[ln(1 + SINRi )]

=

∫ ∞0

P[ln(1 + SINRi ) > t]dt

=

∫ ∞0

Fi (et − 1)dt, (51)

When using OMA, UEi can only use half of the resources compared with NOMA.

τOMAi =

1

2

∫ ∞0

FOMAi (et − 1)dt. (52)



Performance Evaluation

Figures below show the comparison between the analytical results and simulation ones.One can see that with Taylor series approximation parameter N set at 1, 3, and 5, theanalytical results get closer and closer to the simulation results. N = 1 is sufficient toprovide an accurate approximation when β is less than 0.8.

SINR Threshold (dB) -10 -5 0 5 10 15 20

Co

ve

rag

e

Pro

ba

bili

ty

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Coverage Probability of NOMA UE1 with β = 1,0.8,0.6

NOMA UE1 Simulation

NOMA UE1 Anatical Result N=1



β=0.8

β=0.6

β=1

Figure 10: Coverage probability for NOMAUE1

SINR Threshold (dB) -10 -5 0 5 10 15 20

Co

ve

rag

e

Pro

ba

bili

ty0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Coverage Probability of NOMA UE2 with β = 1,0.8,0.6

NOMA UE2 Simulation




β=1

β = 0.8β = 0.6

Figure 11: Coverage probability for NOMAUE2



Figures below compare the coverage probability of NOMA with that of OFDMA. one canobserve that the gap between the coverage probabilities of UE1 and UE2 increases as thevalue of β decreases, which indicates that a smaller value of β does make the receivedpower more distinguishable between UE1 and UE2.

SINR Threshold (dB)-10 -5 0 5 10 15 20

Co

ve

rag

e P

rob

ab

ility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Coverage Probability for β=0.8

NOMA UE1

NOMA UE2

OFDMA UE1

OFDMA UE2

Figure 12: β = 0.8

SINR Threshold (dB)-10 -5 0 5 10 15 20

Co

ve

rag

e P

rob

ab

ility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Coverage Probability for β=0.6

NOMA UE1

NOMA UE2

OFDMA UE1

OFDMA UE2

Figure 13: β = 0.6



Figure below compares the sum achievable rate between NOMA and OFDMA withdifferent β values. It can be observed that in the low SNR region, a higher β value canlead to a higher achievable sum rate. In the high SNR region, the system turns tointerference limited. β = 0.7 can support a higher achievable rate than β = 0.9.

SNR (dB)0 5 10 15 20 25 30

Ave

rag

e A

ch

ieva

ble

Ra

te

0

0.5

1

1.5

2

2.5Average Achievable Rate for β = 0.9, 0.7, 0.5

NOMA

OFDMA

β=0.9

β=0.7

β=0.5

Figure 14: Average Achievable Rate of NOMA and OFDMA, β = 0.9, 0.7, 0.5



There is an optimal value of β for average achievable rate under different SNR scenarios.Nevertheless, in uplink, it is not sufficient to determine the optimal value of β by onlyconsidering maximizing the sum rate. For instance, when SNR = 10dB, the optimalvalue of β is 1 as shown in figure. But β = 1 makes it difficult to split the compositereceived signal.

β0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ave

rag

e A

ch

ieva

ble

Ra

te

0

0.5

1

1.5

2

2.5Average Achievable for for SNR =30dB, 20dB, 10dB

NOMA

OFDMA

SNR=20dbSNR=10db

SNR=30db

Figure 15: Average Achievable Rate of NOMA and OFDMA, SNR = 30dB, 20dB, 10dB


Performance Study on Relay-Assisted Multi-hop Millimeter Wave Networks

Performance Study on Relay-Assisted Multi-hop Millimeter WaveNetworks


Performance Study on Relay-Assisted Multi-hop Millimeter Wave Networks

Millimeter Wave Communications

Motivation

I Spectrum below 5 GHz is extremely crowded

I Support skyrocketing traffic growth in 5G wireless cellular networks

I Exploring higher radio spectrum is imperative

Advantages of mmWave

I Spectrum resource is abundant

I Interference from nearby mmWave nodes can be small due to shorter transmissiondistance and the directional beamforming technique

I mmWave Communications can be more secure than radio frequency (RF)communications since the mmWave signals cannot penetrate walls and othernon-transparent objects

Challenges

I Coverage could be limited due to high pathloss

I mmWave signals are very sensitive to blockage effects compare with the lowspectrum RF signals


Performance Study on Relay-Assisted Multi-hop Millimeter Wave Networks System Model

System Model

I Downlink communication in a relay-assisted mmWave network

I Locations of mBSs, blockages, and UEs are all modeled as homogeneous Poissonpoint processes (PPP) with densities λm, λb, and λu, respectively

I Assume all mBSs, RNs, and UEs are located outdoor, which means they are notcovered by blockages

I UEs are assumed to be associated to the nearest mBS initially

I UEs experience none-line-of-site (NLOS) link can be associated to the nearby relay(RN) for a lower pathloss

I Decode-and-Forward (DF) relays are used and they are distributed as PPP with adensity λr and λr > λm

I More LOS links are expected with the assistance of RNs



System Model

NLOS LINK

LOS LINK

UE

RN

BS

BK

Figure 16: One cell of the relay-assisted mmWave network.



Blockage model

I Given a link between a UE and a mBS or a RN with distance r , the probability thatthe link has LOS is given as

P(LOS |r) = e−βr , (53)

where

β =2λi (E [L] + E [W ])

π, i ∈ {m, r}. (54)

E [L] and E [W ] are the average length and width of blockages, respectively

I The NLOS probability given a distance is simply P(NLOS |r) = 1− e−βr

I The probability of LOS decreases when the length of link increases, while theprobability of NLOS increases when the length of link increases



Pathloss model

I The pathloss in dB for a LOS link with length r can be modeled as

PLLOS [dB](r) = 20log10

(4π

λ

)+ 10αLlog10(r) + χσL . (55)

αL is the pathloss exponent of a LOS link, and χσL is LOS shadowing, which is anormal distribution in dB (lognormal distribution in linear scale) with zero mean(dB) and standard deviation σL (dB)

I For a LOS link, σL is usually small and has a small effect on the pathloss

I The pathloss in dB for a NLOS link with length r is

PLNLOS [dB](r) = 20log10

(4π

λ

)+ 10αN log10(r) + χσN , (56)

where αN is the pathloss exponent for a NLOS link, and σN is the standard deviationof shadowing for a NLOS link

I σN is usually big and has a big effect on the pathloss



Association rule

I UE is associated to the nearest mBS or RN. The pdf of the distance r between a UEand its nearest mBS or RN can be written as

friu (r) = 2πλi re−λiπr

2

, i ∈ {m, r} (57)

I When a UE experiences NLOS link to its associated BS, it can switch to the nearestRN to establish a two-hop route to the BS

I A RN is connected the BS that is closest to this RN



Directional beamforming

I At mmWave spectrum, a large number of antennas can be installed at mBSs, RNs,and UEs for directional beamforming

I Antenna gain for a mBS is a function of the steering angle θ and is given as

Gm(θ) =

{Gm if |θ| ≤ θm0 otherwise

. (58)

θm is the main lobe width. The side lobe gain is ignored

I Antenna gains of UE or RN are modeled in the same way

I The combined antenna gains between a mBS and a UE, between a RN and a UE,between a mBS and a RN are GmGu, GrGu, and GmGr , respectively

I Interference from a non-serving mBS to a UE happens only when their beams aresteering at each other and PI = θmθu

4π2



Received Signal Power

I All the mBSs have the same transmit power Pm and all the RNs have the sametransmit power Pr

I Rayleigh fading (g) with zero mean is assumed for channel fading

I General downlink received signal power is P ∗ G ∗ g ∗ PL−1


Performance Study on Relay-Assisted Multi-hop Millimeter Wave Networks SNR performance in low density network

SNR performance in low density network I

I Interference is ignored and SNR is investigated in low density mmWave networks

I Given a UE served by a LOS mBS or a LOS RN, its SNR can be expressed as

SNRLOS,riu =PiGiGugiuPL

−1LOS,riu

N, i ∈ {m, r}, (59)

where riu represents the distance between a BS or a RN and a UE, giu is theRayleigh fading, PLLOS,riu is the LOS pathloss as in (55) but in linear scale, and N isthe noise power

I Given a UE served by a NLOS mBS or a NLOS RN, its SNR is similar to (59), butreplacing PLLOS,riu with the NLOS pathloss PLNLOS,riu



SNR performance in low density network II

I For a UE that is associated to its nearest mBS or RN, the probability that a LOSlink exists can be expressed as

Piu(LOS) =

∫PLOS|r fr (r)dr =

∫e−βr2πλi re

−λiπr2

dr , i ∈ {m, r} (60)

I The probability of a NLOS link is

Piu(NLOS) = 1− Piu(LOS) i ∈ {m, r} (61)

I The pdf of the distance of the LOS link is

friu ,LOS(r) =d

dr

P(riu ≤ r , LOS)

Piu(LOS)=

P(LOS |r)friu (r)

Piu(LOS), i ∈ {m, r}, (62)

where Piu(LOS) is shown in (60) and P(LOS |r) is (53)

I The pdf of the distance of the NLOS link is

friu ,NLOS(r) =P(NLOS |r)friu (r)

Piu(NLOS), i ∈ {m, r} (63)



SNR performance in low density network III

I To simplify the analysis, shadowing is not considered in the theoretical derivations

I The pathloss model can be simplified to PLLOS(r) =(

4πλ

)2rαL and

PLNLOS(r) =(

4πλ

)2rαN

I Given a UE that is associated to the nearest mBS or RN and the link is LOS, thecoverage probability for that UE can be derived as

pc,LOS,iu = Er [P(SNRLOS,riu > T )|rLOS ] = Er [P

(PiGiGugiuPL

−1LOS,riu

N> T

)|rLOS ]

= Er [P

(giu >

TNPLLOS,riu

PiGiGu

)|rLOS ] =

∫r>0

e−

TNPLLOS,riuPi Gi Gu friu ,LOS(r)dr , i ∈ {m, r},

(64)

where T is the SNR threshold for coverage

I For NLOS link, the coverage probability can be expressed as

pc,NLOS,iu = Er [P(SNRNLOS,riu > T )|rNLOS ]

=

∫r>0

e−

TNPLLOS,riuPi Gi Gu friu ,NLOS(r)dr , i ∈ {m, r} (65)



SNR performance in low density network IV

I The overall SNR distribution of a single tier mmWave network with no relays is

pSNR,m = 1− {pc,LOS,muPmu(LOS) + pc,NLOS,muPmu(NLOS)} (66)

I If a UE is connected to the BS through a RN, the overall two-hop SNR is theminimum of the two SNRs of each hop. Since the antenna gain for the link betweena RN and a mBS is much higher than the antenna gain between a RN and a UE, theSNR between a RN and a mBS is most likely greater than the SNR between a RNand a UE. To simplify the analysis, we use the RN-UE link SNR to represent theoverall two-hop SNR

I The overall SNR distribution of a UE through the nearest RN in the network is1− {pc,LOS,ruPru(LOS) + pc,NLOS,ruPru(NLOS)}

I The overall SNR distribution of a relay-assisted mmWave network can be expressedas

pSNR,r = 1− {pc,LOS,muPmu(LOS) + Pmu(NLOS)

× {pc,LOS,ruPru(LOS) + pc,NLOS,ruPru(NLOS)}} (67)


Performance Study on Relay-Assisted Multi-hop Millimeter Wave Networks SINR performance in ultra dense network

SINR performance in ultra dense network I

I In an ultra dense mmWave network, interference from other mBSs or RNs cannot beignored

I Assume there is no interference between mBS and RN and there is no interferencebetween different RNs

I For a UE associated to a mBS, only these co-channel mBSs cause interference onthe downlink. For a UE that is connected to a RN, only co-channel RNs in othercells can cause interference

I RNs in the same cell does not cause interference by properly provisioning orthogonalradio resources for the RNs in the same cell. The density of the interfering RNs is λm



SINR performance in ultra dense network II

I Given a UE served by the nearest mBS or RN and the link is LOS, its SINR can beexpressed as

SINRLOS,riu =giur−αLiu

Ii +N( 4π

λ )2

PiGiGu

, i ∈ {m, r}. (68)

Ii is the normalized interference either from other mBSs or from other RNs.

Ii = PI

∑j∈Φi

gju

(PLrju(

4πλ

)2

)−1

, i ∈ {m, r}. (69)

PI = θmθu4π2 , Φi is the set of all interfering mBSs or all interfering RNs.

PLrju = PLLOS,rju 1 (P(LOS |r)) + PLNLOS,rju 1 (P(NLOS |r)) . (70)

1(x) is a Bernoulli random variable with parameter x

I Given a typical UE served by the nearest mBS or RN and the link is NLOS, theSINR is similar to (68), but replacing αL with αN



SINR performance in ultra dense network III

I Given a typical UE served by the nearest mBS or RN and the link is LOS, thecoverage probability when considering interference can also be derived as

pc,I ,LOS,iu = Er [P(SINRLOS,riu > T )|rLOS ] = Er [P

giur−αLiu

I +N( 4π

λ )2

PiGiGu

> T

|rLOS ]

= Er [P

(giu > T (I +

N(

4πλ

)2

PiGiGu)rαL

iu

)|rLOS ]

=

∫r>0

e−

TN( 4πλ )2

rαLiu

Pi Gi Gu LI (TrαLiu )friu ,LOS(r)dr , i ∈ {m, r}, (71)

where LI (TrαLiu ) is the Laplace transform of random variable I evaluated at TrαL

iu ,and LI (Tr

αL) can be written as

LI (TrαL) = LΦILOS

(TrαL)LΦINLOS(TrαL) = e−2πλm

∫∞r (1−1/(1+TrαLPI v

−αL ))e−βv vdv

× e−2πλm∫∞r (1−1/(1+TrαLPI v

−αN ))(1−e−βv )vdv (72)



SINR performance in ultra dense network IV

I Given a typical UE served by the nearest mBS or RN and the link is NLOS, thecoverage probability with considering interference can be expressed as

pc,I ,NLOS,iu = Er [P(SINRNLOS,riu > T )|rNLOS ]

=

∫r>0

e−

TN( 4πλ )2

rαNiu

Pi Gi Gu LI (TrαNiu )friu ,NLOS(r)dr , i ∈ {m, r}, (73)

where LI (TrαN ) is similar to LI (Tr

αL) in (72), but replacing TrαL with TrαN



SINR performance in ultra dense network V

I The overall SINR distribution of a single tier mmWave network with no relays canbe expressed as

pSINR,m = 1− {pc,I ,LOS,muPmu(LOS)

+ pc,I ,NLOS,muPmu(NLOS)}, (74)

where pc,I ,LOS,mu and pc,I ,NLOS,mu are from (71) and (73), respectively. Pmu(LOS)and Pmu(NLOS) are from (60) and (61), respectively

I The overall coverage of a relay-assisted mmWave network can be expressed as

pSINR,r = 1− {pc,I ,LOS,muPmu(LOS) + Pmu(NLOS)

× {pc,I ,LOS,ruPru(LOS) + pc,I ,NLOS,ruPru(NLOS)}} (75)


Performance Study on Relay-Assisted Multi-hop Millimeter Wave Networks Numerical Results

Numerical Results - System Setup

mmWave BSs and RNs are assumed to operate at 28 GHz.

Table 1: Simulation Parameter Settings

Notation ValuePm, Pr 27 dBmGm, Gr 30 dBiGu 5 dBi

θm, θr , θu 10o

αLOS 2.1αNLOS 3.4σLOS 3.6 dBσNLOS 9.7 dB

Thermal noise -174 dB per HzNoise figure 7 dB

BW 1 GHz



Results of low density network I

−20 0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR Threshold (dB)

Pro

babi

lity

No relayWith relays

Figure 17: SNR performance comparison between the single tier mmWave network with no relaysand the relay-assisted mmWave network.

I λm = 1π1002 = 3.1831× 10−5, λb = 100× λm, λr = 10× λm, and λu = 200× λm

I Blockages are assumed to be squares with E [L] = E [W ] = 2 m

I Pmu(LOS) = 0.52 and Pru(LOS) = 0.8

I The performance of the network with RNs is much better than the performance ofthe network without RNs



Results of low density network II

−20 0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR Threshold (dB)

Pro

babi

lity

Theoretical resultSimulation result

Figure 18: Theoretical and simulation SNR curves of the relay-assisted network.



Results of low density network III

−20 0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR Threshold (dB)

Pro

babi

lity

No RN, λb = 50λ

m

With RNs, λb = 50λ

m

No RN, λb = 100λ

m


m

No RN, λb = 200λ

m


m

Figure 19: SNR comparison between the relay-assisted network and the single tier network withdifferent blockage density.

I Without RNs, the SNR performance degrades significantly when the blockagedensity increases

I With RNs, when the blockages increase, the number of LOS links decreases in amuch slower pace

I Adding RNs into the mmWave network can significantly improve the overall systemcoverage and SNR performance, as well as greatly enhance the system robustnessagainst blockages



Results of low density network IV

−20 0 20 40 60 800

0.2

0.4

0.6

0.8

1

SNR Threshold (dB)

Pro

babi

lity

No relayWith relays, λ

r = 5λ

m

With relays, λr = 10λ

m


m


m

Figure 20: SNR comparison among relay-assisted network with different RN density.

I SNR performance improves when the RN density increases

I Increasing RN density from 0 to 5λm provides a notable performance improvement

I Further increasing the number of RNs does not seem to improve the coverageobviously because the probability of LOS does not increase linearly with the RNdensity

I The density of RNs needs to be optimally selected so that the system can strike agood balance between overall performance improvement and economical costs



Results of ultra dense network I

−20 0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR Threshold (dB)

Pro

babi

lity

No relayWith relays

Figure 21: SINR performance comparison between no relay network and relay-assisted network.

I λm = 1π202 = 7.9577× 10−4, λb = 50× λm, λr = 10× λm, and λu = 200× λm

I Blockages are assumed to be squares with E [L] = E [W ] = 1 m

I Pmu(LOS) = 0.4502 and Pru(LOS) = 0.7609

I The performance of the network with RNs is much better than the performance ofthe network without RNs



Results of ultra dense network II

−20 0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR Threshold (dB)

Pro

babi

lity

Theoretical resultSimulation result

Figure 22: Theoretical and simulation SINR curves of relay-assisted network.



conclusions

I NOMA and MU-MIMO can greatly improve spectrum efficiency when propercooperation (precoding) and NOMA power are selected.

I Interference from D2D underlay cellular system may be significantly reduced throughpower control and beam-forming.

I NOMA, D2D, MU-MIMO are considered promising technologies for future 5G/IoTsystems.

=



Thank You !


prof. rose qingyang hu ieee communications society...

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