Towards SE and EE in 5G with NOMA and Massive MIMO Technologies
aa r X i v : . [ c s . I T ] A p r Towards SE and EE in 5G with NOMA andMassive MIMO Technologies
Di Zhang ∗ , Zhenyu Zhou † , and Takuro Sato ∗∗ GITS/GITI, Waseda University, Tokyo, Japan, 169–8050Email: di [email protected], [email protected] † National Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China, 102206Email: zhenyu [email protected]
Abstract —Non-Orthogonal Multiple Access (NOMA) has beenproposed to enhance the Spectrum Efficiency (SE) and cell-edge capacity. This paper considers the massive Multi-InputMulti-Output (MIMO) with Non-Orthogonal Multiple Access(NOMA) encoding. The close-form expression of capacity ofthe massive MIMO with NOMA is given here. Apart from theprevious Successive Interference Cancellation (SIC) method, thePower Hard Limiter (PHD) is introduced here for better realityimplement.
Index Terms —Cellular networks, energy efficiency, massiveMIMO, NOMA.
I. I
NTRODUCTION
Within the background of 5G research, the EE issue wasproposed as another important elements together with theprevious SE issue. Nowadays, while studying about the SE andEE, some potential techniques were proposed, such as the mas-sive MIMO [1], mmWave [2], NOMA [3], etc. For mmWave,the main work was waiting for further spectrum resourcesallocation from ITU. For massive MIMO, some prior workshad been done based on the existing MIMO technologies, suchas the cellular zooming [4]. And thanked to this proposal,once proposed,a great deal of studies erupted in EE studies.For instance, in [5] [6], some power allocation mechanismswere proposed towards massive MIMO, but antenna selectionwas focused in those paper whereas the BS coverage area wasneglected. Although lots of studies had been done, but wenoticed that if we combine the NOMA together with massiveMIMO, by some potential techniques, we can further enhancethe EE performance. Which relied in the fact that energyconsumption and achievable total transmission rate by a certainbandwidth are two factor of EE performance.II. A
NALYSIS OF M ASSIVE
MIMO
SYSTEM WITH
NOMA
A. Capacity Analysis of NOMA with Signal Antenna
Consider that in a massive MIMO system, there are M antennas serving for a number of K user equipments (UEs).While the signal information transmitted from the antennas tothe UEs, the received K × signals can be demonstrated as: y = p P k Hx + n , (1)where H represents for the M × K channel matrix betweenthe transmit antennas and received UEs. P k denotes for the power of each signal that transmitted from antenna to receivedUEs whereas x , n represent for the transmitted signal andadditive white gaussian noises (AWGN), where the AWGN is a n ∼ C (0 , additive noises. Here √ P k x is the simultaneouslytransmitted symbol vector of the signals.The channel matrix models the independent fast fading,slow fading which is also can be expressed by the geometricattenuation and log-normal shadow fading. Thus the channelcoefficient h m,k can be demonstrated as h m,k = a m,k p β m,k where a m,k is the fast fading coefficient from the m th antennato k th UE. p β m,k models the geometric attenuation andshadowing fading coefficient, which can be demonstratedby the distance factor while ignoring the shadowing fadinginfluence and can be expressed as β m,k = d αm,k . Here the d m,k denotes the distance from antenna to the received UEwith α as the path loss factor. Without loss of generality, wesuppose that in one coverage area, the BS is located in thecenter with radius R D where UEs uniformly distributed withinthe coverage area.Take the power coefficient as γ , while adopting the non-orthogonal multiple access (NOMA) and successive interfer-ence cancellation (SIC), which will successively remove thesignal of other UEs while i < k and treat the i > k as thenoise, thus we can get the achievable data rate of k th UE as: R k = log (1 + ρ | h m,k | γ k ρ | h m,k | P Ki = k +1 γ k + 1 ) , (2)where ρ represents for the transmit SNR. Be aware that thedata rate of UE with number K is R K = log (1+ ρ | h K | γ K ) .Suppose that the channel information will determine the datarate of each UE, taking ˜ γ k = P Mi = m +1 γ k , the sum rateachieved by NOMA can be expressed by: R sum = M − X m =1 log (1+ ρ | h m,k | γ k ρ | h m,k | ˜ γ k + 1 )+log (1+ ρ | h K | γ K ) , (3)thus suppose that the distance between UEs and antennasare much larger than the distance between the antennas, inaddition, on condition that the data rate request of each UE is fulfilled. The sum ergodic rate is given by: R ave = M − X m =1 Z ∞ log (1 + xργ k xρ ˜ γ k + 1 ) f | h m,k | ( x ) dx + Z ∞ log (1 + xργ K ) f | h K | ( x ) dx, (4)where f | h m,k | , f | h K | represent for the probability densityfunction (PDF) of the channel gain, which can be given as[7]: f | h m,k | ( x ) ≈ R D M X j =1 K X k =1 δ m,k e − c m,k x , (5)where δ m,k = ω m,k q − θ m,k ( R D θ m,k + R D ) c m,k with θ m,k = cos ( k − K π ) and c m,k = 1 + ( R D θ m,k + R D ) γ m,k .This can be obtained by applying the Gaussian-Chebyshevquadrature (GCQ).According to the deduction in [8], the achievable ergodicsum rate of NOMA can be given as: R ave → log ( ρ log log K ) . (6) B. Capacity Analysis of NOMA with massive MIMO
For massive MIMO system with traditional encoding meth-ods, it is proved that Minimum Mean-Square Error Detector(MMSE) can reach the maximum achievable rates in uplinkwith perfect CSI [7], whereas maximum achievable downlinkrates gained by MMSE or Regularized Zero-Forcing (RZF)[9]III. E
NERGY E FFICIENCY A NALYSIS OF M ASSIVE
MIMO
WITH
NOMAWhile solving the antenna and radio frequency (RF) chainselection problems, suppose that in each BS coverage area, thedistribution of UEs obeys the same PPP distribution and therequirements of capacity are also following the same Poissondistribution, the optimal solution can be gained by solving theproblem in one BS area of one epoch time. Thus the optimalantenna and RF chain selection problem can be written as:max P k ,P RF R ave P k + P RF , (7)subject to: C K X k =1 ( 1 η P k + P c + P RF ) ≤ P T , (8a) C K X k =1 N ak,b ≤ N abs , ∀ b, (8b) C N UEk,c ≤ K X k =1 N rfk,c ≤ N rfbs , ∀ t, (8c) C P k , P c , P RF ≥ , ∀ k. (8d)If we define a maximum weighted solution by S ∗ = max ( P k , P RF ) = P Kk =1 R ∗ k / ( P k + P RF ) ∗ the problem has feasible solutions and its optimum solution is S ∗ , then theexisting optimal solution if any, can only achieved by:max ( P k , P RF ) − S ∗ ( P k + P RF ) ∗ = K X k =1 R ∗ k − S ∗ ( P k + P RF ) ∗ = 0 , (9)and the optimal solution of max ( P k , P RF ) should be equalor smaller than S ∗ if any. Note that the RF chain powerconsumption has nothing related with the achievable capacityof one cluster although it is needed for transmission. In thiscase, while searching for the optimal solver, it will convergeto zero. Here as the general assumption, we assume that ineach step, the number of RF chain is equal to the number ofantenna in order to serving the requirement of each UE. Thusthe extreme point can be verified by the lagrange method: ∂ max ( P k , P RF ) ∂P k = ∂ R ave P k + P RF ∂P k = P k ln 2 − log ( P k N log log K )( P k + P RF ) , (10) ∂ max ( P k , P RF ) ∂ ( P k ) = ∂ R ave P k + P RF ∂ ( P k ) = − ln 2( P k ln 2) − P k log log K ln 2 ( P k + P RF ) − P k ln 2 − log ( P k N log log K )]( P k + P RF ) . (11)On condition that high SNR with limited number of UEs inone cluster, we can conclude that the second derivative shouldbe less than zero. Thus it is easily to know that the equationof power consumption P k + P RF is a affine function of P k ,and the objective is a quasi-convex function. Based on ourdeductions, this can be solved by the subgradient method,which for a given accuracy, it will search for the optimal pointthat meets the requirement of accuracy.IV. CONCLUSION
In this paper, the massive MIMO with NOMA’s achievableergodic sum rate is given. In addition, the EE performance isanalyzed here. In the following step, we will further our studywhile comparing with the previous studies and conclude theproposal.
ACKNOWLEDGEMENT
The author would like to thank Chinese Scholarship Council(CSC) for its financial support of this study under grant201306770001. R
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