IEEE ICC 2016 - Next-Generation Networking and Internet Symposium
Energy Efficiency of Resource Scheduling for Non-Orthogonal Multiple Access (NOMA) Wireless Network Fang Fang† , Haijun Zhang‡§ , Julian Cheng† , Victor C.M. Leung‡
† School
of Engineering, The University of British Columbia, Kelowna, BC, Canada of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC, Canada § National Mobile Communications Research Laboratory, Southeast University, Nanjing, China. Email: †
[email protected], ‡
[email protected], †
[email protected], ‡
[email protected]
‡ Department
Abstract—Non-orthogonal multiple access (NOMA) is a promising technique for the fifth generation mobile communication due to its high spectrum efficiency. By applying superposition coding and successive interference cancellation techniques, multiple users can be multiplexed on the same subchannel in NOMA systems. Previous works focus on subchannel and power allocation to maximize the sum rate; however, the energy-efficient resource allocation problem has not been studied for NOMA systems. In this paper, we aim to optimize subchannel assignment and power allocation to maximize the energy efficiency for the downlink NOMA network. Assuming perfect knowledge of the channel state information at base station, we propose lowcomplexity suboptimal algorithms which include subchannel assignment and power allocation for subchannel users. In the power allocation scheme, difference of convex functions programming approach is exploited to transform and approximate the original optimal problem into a convex optimization problem. Simulation results show that our proposed algorithms yield much better improvements than orthogonal frequency division multiple in terms of sum rate and energy efficiency.
I. I NTRODUCTION In the fourth generation mobile communication systems such as long-term evolution (LTE) and LTE-Advanced, orthogonal frequency division multiple access (OFDMA) has been widely adopted to achieve higher data rate. The demand for mobile traffic data volume is expected to be 500-1,000 times larger in 2020 than that in 2010. To further meet overwhelming requirement of data rates, various new techniques have been proposed in recent years, and these techniques include interleave division multiple access [2], low density spreading, and non-orthogonal multiple access (NOMA) [3]. Among them, by applying superposition coding (SC) and successive interference cancellation (SIC) techniques at the receiver, NOMA is well considered as a promising candidate for the next generation mobile communication systems. Resource allocation has been investigated in OFDM and NOMA systems [4]–[8]. The author in [4] proposed a near optimal cooperative Nash bargaining resource allocation strategy for OFDMA networks. In [5], the basic concept of NOMA was introduced, and the cell-edge user throughput performance improvement was presented based on the systemlevel simulations. In [6], by using fractional transmit power
978-1-4799-6664-6/16/$31.00 ©2016 IEEE
allocation (FTPA) among users and equal power allocation across subchannels, system-level performance was compared for a NOMA system and an OFDMA system. In [7], a greedy subchannel and power allocation algorithm was proposed for OFDMA based on NOMA systems. A cooperative NOMA transmission scheme with fixed choices of power allocation coefficients was proposed in [8]. Although some works have been done for resource allocation in NOMA systems, these papers mainly focused on sum rate maximization. However, energy consumption of wireless networks has been rapidly increasing. Therefore, saving more energy based on transmitting a fix amount of symbols, which can be measured by energy efficiency, is an important and practical consideration [9]. To the best of the authors’ knowledge, the resource allocation problem that maximizes the system energy efficiency has not been studied yet for the NOMA systems. In this paper, we focus on the energy efficienct resource allocation in downlink NOMA networks and use bits per Joule to measure the energy efficiency performance of the system. By formulating subchannel and power allocation problem for downlink NOMA network as an energy efficiency optimization problem, the difference of convex (DC) programming is utilized to achieve the maximum energy efficiency of the system. The rest of the paper is organized as follows. Section II presents the NOMA system model and formulates our optimization problem. In Section III, we propose algorithms to maximize energy efficiency of the system. Performance of the proposed algorithms is evaluated in Section IV by simulations. Finally, Section V concludes the paper. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION We consider a downlink of NOMA network. By applying SIC at the receiver of user terminals (UTs), a base station (BS) transmits its signals to M user terminals through N subchannels. We denote m as index for the mth mobile user where m ∈ {1, 2, · · · , M } and denote n as index for the nth subchannel where n ∈ {1, 2, · · · , N }. In this cell, M users are uniformly distributed in a circular region with radius R. The total bandwidth of the system, BW , is equally divided into N subchannels where the bandwidth of each subchannel is
Bsc = BW/N . Let Mn ∈ {M1 , M2 , · · · , MN } be the number of users allocated on the subchannel n (SCn ) and the power allocated to user m (U Tm ) through SCn is denoted by pm,n . Then the subchannel and BS power constraints can be given M N n pi,n = pn and pn = Ps , where pn and Ps are by
lower CRNN [5], i.e., for any two user Mi and Mj share the same SCn with the CRNNs |Hi,n | ≥ |Hj,n |, we always set pi,n < pj,n to obtain higher sum rate. This assumption is widely used in the NOMA scheme [6]. Consider that Mn users are allocated on SCn with CRNNs order
the allocated power on SCn and the total transmitted power of the BS, respectively. In NOMA systems, we assume that the BS has full knowledge of the channel state information. According to the NOMA protocol [5], multiple users can be allocated to the same subchannel with SC and SIC techniques. Blocking fading channel is considered in the system model, where the channel fading of each subchannel remains the same within a subchannel, but it varies independently across different subchannels.
|H1,n | ≥ |H2,n | ≥ · · · ≥ |Hm,n | ≥ |Hm+1,n | ≥ · · · ≥ |HMn ,n | . (3) According to the SIC decoding order, User m can be successfully decoded and remove the interference symbols from users i > m. However, the interference symbol from User i < m cannot be removed and will be treated as noise by User m. Therefore, the SINR of User m with SIC at receiver can be simply written as
n=1
i=1
A. Signal Model Considering Mn users are allocated on SCn , the received signal at U Tm on SCn is ym,n =
√
pm,n hm,n sm +
Mn
√
pi,n hm,n si + zm,n
(1)
i=1,i=m
where sm and si are modulated symbols, hm,n = gm,n · P L−1 (d) is the coefficient of SCn from the BS to U Tm , and where gm,n is assumed to have Rayleigh fading channel gain, and P L−1 (d) is the path loss function between the BS and U Tm at distance d. Let zm,n ∼ CN 0, σn2 be the additive white Gaussian noise (AWGN) with zero mean and variance σn2 . In a downlink NOMA network, each subchannel can be shared by multiple users. Each U Tm on SCn receives its signals as well as interference signals from other users on the same subchannel. Therefore, without SIC at receiver, the received signal-to-interference-plus-noise ratio (SINR) of U Tm on the SCn is written by SIN Rm,n
=
pm,n |hm,n |2 M n σn2 + pi,n |hm,n |2 i=1,i=m
=
pm,n Hm,n M n 1+ pi,n Hm,n
(2)
i=1,i=m
σn2
SIN Rm,n =
(4)
i=1
Then the sum rate of U Tm on SCn can be expressed as ⎛ ⎞ ⎜ Rm,n (pm,n ) = Bsc log2 ⎜ ⎝1 +
⎟ pm,n Hm,n ⎟. ⎠ m−1 1+ pi,n Hm,n
(5)
i=1
In the rest of paper, we simply use NOMA systems to represent downlink NOMA network with SC and SIC techniques. Therefore, the overall sum rate of NOMA systems can be written as R=
Mn N
Rm,n (pm,n ) =
n=1 m=1
N
Rn (pn )
(6)
n=1
where Rn is the sum rate of subchannel n. B. Problem Formulation In this subsection, we formulate the energy-efficient subchannel assignment and power allocation as an optimization problem in the NOMA system. For energy efficient communication, it is desirable to maximize the amount of transmitted data bits with a unit energy. For each subchannel in the NOMA system, given assigned power pn on SCn and additional circuit power consumption pc , the overall energy efficiency the system can be given by
2
where = E[|zm,n | ] is the noise power on SCn and Hm,n = |hm,n |2 /σn2 represents the channel response normalized by noise (CRNN) of U Tm on SCn . In NOMA systems, SIC process is implemented at UT receiver to reduce the interference from other users on the same subchannel. The optimal decoding order for SIC is the increasing order of CRNNs. Based on this order, any user can successfully and correctly decode the signals of users whose decoding order comes before that user. Thus, the interference from the users having poorer channel condition can be cancelled and removed by the user who has better channel condition. In order to maximize the sum rate of SCn , we generally allocate higher power to the users with
pm,n Hm,n . m−1 1+ pi,n Hm,n
E=
N n=1
En =
N
Rn . p + pn n=1 c
(7)
For the downlink NOMA network, SC with SIC technique is well investigated in [10], [11]. The implementation complexity of SIC at the receiver increases with the maximum number of the users allocated on the same subchannel. In order to keep the receiver complexity comparatively low, we consider the simple case where only two users can be allocated on the same subchannel. This assumption is important because it also restricts the error propagation. In this case, given that the two users sharing SCn with CRNNs |H1,n | ≥ |H2,n |, the sum rate of SCn can be expressed as
Rn (pn ) =W1,n log2 (1 + βn pn H1,n )
(1 − βn ) pn H2,n + W2,n log2 1 + 1 + βn pn H2,n
(8)
where βn is the proportional factor of power allocation among the two users on SCn . Generally, βn is used for the user who performs SIC on SCn and βn ∈ (0, 1). The optimal power proportional factor can be decided within our proposed subchannel assignment scheme. In (8), Wi,n represents the weighted bandwith of the user i. To obtain an energy-efficient resource allocation scheme for this system, we formulate the energy efficiency optimization problem as N Rn (pn ) p + pn pn >0 n=1 c
max
βn ∈(0,1),
subject to
N
p n = Ps
(9)
(10)
n=1
where the constraint (10) ensures that the power variables must satisfy the BS power constraint. Since this optimization problem is non-convex and NP-hard, it is challenging to find the global optimal solution within polynomial time. To solve this problem efficiently, in this paper, we treat subchannel allocation and subchannel power distribution separately. Assuming equal power is allocated to the subchannels, we first match subchannels to multiple users to maximize the utility and find proportional factor for multiplexed users on each subchannel.
where P F U T (m) and P F SC(n) are the preference lists of U Tm and SCn , respectively. We say U Tm prefers SCi to SCj if Hm,i > Hm,j , and it can be expressed as SCi (m) SCj (m) .
Similarly, we say SCn prefers user set qm to user set qn if the users in set qm can provide higher energy efficiency than users in set qn on SCn , and we represent this scenario as En (qm ) > En (qn ) , qm , qn ⊂ {U T1 , U T2 , · · · , U TMn } . (13) Definition 1: (Preferred Matched Pair) Given a matching M that U Tm ∈ / M(SCn ) and SCn ∈ / M(U Tm ). If En (Snew ) > En (M(SCn )) where Snew ⊆ U Tm ∪ S and S = M(SCn ), where S is the user set has been allocated on SCn . Therefore, Snew is the preferred users set for subchannel n and (U Tm , SCn ) is a preferred matched pair. Algorithm 1 Suboptimal Matching for Subchannel Allocation 1: Initialize the matched list SM atch (n) to record users matched on SCn for all the subchannels ∀n ∈ {1, 2, · · · , N }. 2: Initialize preference lists P F U T (m) and P F SC (n) for all the users ∀m ∈ {1, 2, · · · , M } and all the subchannels ∀n ∈ {1, 2, · · · , N } according to CRNNs. 3: Initialize the set of unmatched users SU nM atch to record users who has not been allocated to any subchannel. 4: while {SU nM atch } is not empty do 5: for m = 1 to M do 6: Each user sends matching request to its most preferred subchannel according to P L U T (m), n ˆ = arg
III. P ROPOSED S UBCHANNEL A LLOCATION A LGORITHM IN NOMA S YSTEMS 7: 8:
In this section, we propose a low-complexity suboptimal matching scheme for subchannel allocation (SOMSA) in the NOMA network. A. Subchannel Allocation Algorithm Description Assuming equal power is allocated on each subchannel, we propose a low-complexity subchannel-user matching algorithm, which includes the determination of proportional factor (βn ) among the multiplexed users on the same subchannel. To describe the dynamic matching between users and subchannels, we consider subchannel allocation as a two-sided matching process between the set of M users and the set of N subchannels. Considering only two users can be multiplexed on the same subchannel due to the complexity of decoding, following [5] we assume M = 2N . We say U Tm and SCn are matched with each other if U Tm is allocated on SCn . Based on the perfect channel state information, the preference lists of the users and subchannels can be denoted by
(12)
9: 10: 11:
12:
13:
14: 15: 16: 17:
T
max
n∈P F U T (m)
(Hm,n )
if |SM atch (ˆ n)| < 2 then Sub-channel n ˆ adds user m to SM atch (ˆ n), and removes user m from {SU nM atch } end if if |SM atch (ˆ n)| = 2 then a) Find power proportional factor βn for every two users in Sqm , Sqm ⊂ {Smatch (ˆ n), m} by the FTPA scheme in Section IV. A or the DC programing approach in Section IV. B. b) Subchannel n ˆ selects a set of 2 users Sqm satisfying maximum energy efficiency Enˆ (qm ) ≥ Enˆ (qn ), qm , qn ⊂ {Smatch (ˆ n), m}. c) Subchannel n ˆ sets Smatch (ˆ n) = qm , and rejects other users. Remove the allocated users from {SU nM atch }, add the unallocated user to {SU nM atch }. d) The rejected user removes subchannel from their preference lists. end if end for end while
P F U T = [P F U T (1), · · · , P F U T (m), · · · , P F U T (M )] T Algorithm 1 describes the proposed SOMSA scheme to P F SC = [P F SC(1), · · · , P F SC(n), · · · , P F SC(N )] (11) maximize the system’s energy efficiency. This algorithm in-
cludes initialization and matching procedures. In the initialization step, preferences lists of subchannels and users are decided according to the channel state information, and SM atch (n), ∀n ∈ {1, 2, · · · , N } and SU nM atch are initialized to record the allocated users on SCn and unallocated users of the system, respectively. In the matching procedure, at each round, each user sends the matching request to its most preferred subchannel. The subchannel accepts the user directly if the number of allocated users on this subchannel is less than two. For the number of the allocated users equals to 2, only the subset of users which can provide higher energy efficiency will be accepted or it will be rejected. This matching process will terminate when there is no user left to be matched. The proposed SOMSA converges to a stable matching after a limited number of iterations [12]. B. Complexity Analysis The optimal subchannel allocation scheme can only be obtained by searching over all possible combinations of users and selecting one which maximizes the system energy efficiency. If we have M users and N subchannels The sched (M = 2N
).
2N 2N − 2 2 uler needs to search ··· = 2 2 2 (2N )! combinations. The time complexity of exhaustive 2N )! searching is O( (2N ). In order to compare the complexity 2N of different algorithms, we take natural logarithm of the complexity. The logarithm complexity is O(ln((2N )!)−N ) = O(ln((2N )!)). By using the Stirling’s formula, ln(n!) = n ln n − n + O(ln(n)), the logarithm complexity of the exhaustive searching can be written by O(N ln N ). In the SOMSA algorithm, the complexity of the worst case is O(N 2 ). Taking natural logarithm of the complexity, the logarithm complexity is O(ln N ). Since O(ln N ) < O(N ln N ), and actual complexity of SOMSA is much less than the complexity of the worst case, and the complexity of SOMSA algorithm is much less than the optimal subchannel allocation scheme. IV. E NERGY-E FFICIENT P OWER ALLOCATION FOR S UBCHANNEL U SERS In Algorithm 1, it is required to determine the power proportional factor βn for every two subchannel users. In this section, we will fist review the existing fractional transmit power allocation scheme. Then we will propose a new energy-efficient power allocation algorithm based on DC programming. It will be shown in Section V that the proposed algorithm can result in improved energy efficiency. A. Fractional Transmit Power Allocation According to the SINR expression in (4), the transmit power allocation (TPA) to one user affects the achievable sum rate as well as the energy efficiency on each subchanel. Due to less computational complexity, FTPA is widely adopted in OFDMA systems and NOMA systems [5], [11]. In this section, we introduce FTPA to allocate different power levels among multiplexed users on each subchannel. In the FTPA
scheme, the transmit power of multiplexed U Tm in the allocated users set on SCn is allocated as per the channel gains of all the multiplexed users on that subchannel, which is given as follows −α (Hm,n ) pm,n = pn M (14) n −α (Hi,n ) i=1
where α (0 ≤ α ≤ 1) is a decay factor. In the case α = 0, it corresponds to equal power allocation among the allocated users. From (14), it is clear that when α increases, the more power is allocated to the user with poorer CRNN. Note that the same decay factor should be applied to all subchannels and transmission times. The value of α is an optimization parameter that needs to be determined via computer simulations. B. Proposed Energy-Efficient Power Allocation Algorithm Considering two users U T1 and U T2 that are to be multiplexed over SCn with CRNNs H1,n ≥ H2,n and equal weighted bandwidth W1,n , W2,n . According to the principle of SIC decoding sequences, U T1 can cancel the interfering power term of U T2 , whereas U T2 treats the symbol power U T1 as noise. The problem of finding βn to maximize energy efficiency of SCn can be formulated as (1−β )p H2,n W1,n log2 (1 + βn pn H1,n ) + W2,n log2 1 + 1+βnn pnnH2,n max . pc + pn βn ∈(0,1) (15) In order to use the DC programming approach, we can convert (15) to DC representation that can be simply written by min (q (βn ) = f (βn ) − g (βn )) (16) βn ∈(0,1)
where f (βn ) = − W2,n log2
1+pn H2,n 1+βn pn H2,n
W1,n log2 (1+βn pn H1,n ) pc +pn
and g (βn ) =
, and both terms are convex functions pc +pn with respect to βn because 2 f (βn ) > 0 and 2 g (βn ) > 0. Therefore, the DC programming approach can be used to find βn in Algorithm 2, which is shown below. Algorithm 2 Iterative, Suboptimal Solution for Subchannel Users’ Power Allocation (0) 1: Initialize k = 0. βn , set iteration number (k+1) (k) − q βn > ε do 2: while q βn 3:
4:
Define convex approximation of q (k) (βn ) as qˆ(k) (βn ) = f (βn )−g βn (k) −∂g T βn (k) βn − βn (k) (17) Solve the convex problem βn (k+1) = arg min qˆ(k) (βn ) βn ∈(0,1)
5: 6:
(18)
k ←k+1 end while
To further improve the system energy efficiency, one can also propose a novel power allocation for subchannels through
DC programming. Due to the space limitation, the details of power allocation across subchannels are omitted.
than NOMA-FTPA-EQ. NOMA-DC-EQ achieves 12% more than OFDMA schems in terms of energy efficiency.
V. S IMULATION R ESULTS
VI. C ONCLUSION
In this section, simulation results are presented to evaluate the performance of the proposed resource allocation algorithms for NOMA systems. In the simulations, we consider one base station and the user terminals are uniformly distributed in the circle range with radius of 500 m. We set the minimum distance between users to be 40 m, and the minimum distance from users to BS is 50 m. The bandwidth is 5 MHz. Let M users be randomly distributed in the cell. In NOMA systems, to reduce demodulating complexity of the SIC receiver, we consider each subchannel can be allocated by two users. In OFDMA schemes, each user can only be assigned to one subchannel. In the simulations, we compare our proposed algorithms of resource allocation for NOMA systems with OFDMA systems. For the subchannel power distribution, we compare our proposed suboptimal algorithm with equal power allocation scheme based on our proposed subchannel allocation scheme. For simulations, we set BS’s peak power, Ps to 41 dBm and circuit power consumption pc = 1 W. B The maximum number of users is 60 and σn2 = N N0 , where N0 = −174 dBm/Hz is the AWGN power spectral density. For simplicity, in this paper, we consider each user has the same weighted bandwidth (W1,n = W2,n = BW/N ).
In this paper, we proposed energy-efficient resource allocation algorithms for downlink NOMA wireless networks, including subchannel assignment and power allocation among multiplexed users. By formulating subchannel allocation problem as a two-sided matching problem, we proposed SOMSA algorithm to achieve maximum energy efficiency of the system, which includes power assignment for the multiplexed users on each subchannel. In the power allocation for subchannels users, since the objective function is non-convex, DC programming was utilized to find a successive convex approximation. Thus a suboptimal power distribution over subchannel users was obtained by iteratively solving the convex subproblems. Through extensive simulations, the performance of the proposed algorithms for resource allocation was compared with the OFDMA system. It was shown that the energy efficiency of the NOMA system is much higher than the OFDMA scheme, and the proposed power allocation algorithm also outperforms the FTPA scheme. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (61471025), and the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (No. 2016D07).
7
5
x 10
R EFERENCES
Energy efficiency of system (bits/Joule)
4.5 4 3.5 3 2.5 2
NOMA−DC−DC Pc=1w NOMA−DC−EQ Pc=1w OFDMA NOMA−FTPA−EQ Pc=1w
1.5 1 10
15
20
25
30 35 40 Number of users per BS
45
50
55
60
Fig. 1. Energy efficiency of the system vs. BS power.
In Fig. 1, the performance of energy efficiency versus number of users M . In the simulation environment, we set difference tolerance ε = 0.01, the number of users M is from 10 to 60, and the bandwidth is 5 MHz. Fig. 1 shows that the energy efficiency increases as the number of users grows. FTPA among multiplexed users with equal subchannel power scheme is compared with our proposed algorithms (NOMA-DC-EQ) and OFDMA scheme. We also consider DC programming to allocate power across subchannels (NOMADC-DC) which performs the best among those schemes. When user number is 20, the energy efficiency of NOMA-DC-DC is 35% more than that of the OFDMA scheme and 30% more
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