Energy Efficiency Optimization of Generalized Spatial Modulation with Sub-Connected Hybrid Precoding
Kai Chen, Jing Yang, Xiaohu Ge, Yonghui Li, Lin Tian, Jinglin Shi
aa r X i v : . [ ee ss . SP ] J a n Energy Efficiency Optimization of GeneralizedSpatial Modulation with Sub-Connected HybridPrecoding
Kai Chen † , Jing Yang † , Xiaohu Ge †∗ , Yonghui Li ‡ , Lin Tian § , Jinglin Shi §¶† School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, Hubei,China ‡ School of Electrical and Information Engineering, University of Sydney, Sydney, Australia § Beijing Key Laboratory of Mobile Computing and Pervasive Devices, Institute of Computing Technology, ChineseAcademy of Sciences, China ¶ University of Chinese Academy of Sciences , Chinae-mail: [email protected]
Abstract —Energy efficiency (EE) optimization of millime-ter wave (mm-Wave) massive multiple-input multiple-output(MIMO) systems is emerging as an important challenge for thefifth generation (5G) mobile communication systems. However,the power of radio frequency (RF) chains increases sharply due tothe high carrier frequency in mm-Wave massive MIMO systems.To overcome this issue, a new energy efficiency optimizationsolution is proposed based on the structure of the generalizedspatial modulation (GSM) and sub-connected hybrid precoding(HP). Moreover, the computation power of mm-Wave massiveMIMO systems is considered for optimizing the EE. Simulationresults indicate that the EE of the GSM-HP scheme outperformsthe full digital precoding (FDP) scheme in the mm-Wave massiveMIMO scene, and 88% computation power can be saved by theproposed GSM-HP scheme.
Index Terms —energy efficiency, generalized spatial modula-tion, millimeter wave, massive MIMO
I. I
NTRODUCTION
Millimeter wave (mm-Wave) communication and massivemultiple-input multiple-output (MIMO) are two key tech-nologies in the fifth generation (5G) mobile communicationsystems [1]. Despite the fact that the mm-Wave technologycan enable high-rate communication, fast attenuation and shortcommunication distance will limit the performance of mm-Wave communication systems [2]. Fortunately, massive MIMOtechnology can provide high beamforming gain, which canconcentrate the transmission energy in a certain direction andovercome the attenuation problem of mm-Wave transmission[3] [4].Although the 5G mm-Wave massive MIMO systems canincrease the spectrum efficiency, the large number of RFchains in the massive MIMO systems will consume hugeenergy and restrict the improvement of the EE [5] [6]. Toreduce the energy consumption of RF chains, hybrid precoding(HP) technology is proposed to lessen the number of RFchains in the massive MIMO systems [7] [8].There are twotypical hybrid precoding structures currently, i.e. the sub-connected structure and the fully-connected structure. The sub- connected array adopts the structure that each RF chain ismerely connected to part of the antennas through a phaseshifter. In this way, system complexity is reduced at the costof the antenna gain, which is more valuable for improving theEE.Generalized spatial modulation (GSM) is another technol-ogy that has shown promise in reducing the number of RFchains. By utilizing the additional spatial dimension, GSM canimprove the EE of massive MIMO system while guaranteeingthe spectral efficiency [9]. The input data streams in GSMare divided into two parts, one part is the amplitude-phasemodulation (APM) domain data streams for the traditionalN-order symbol modulation, and the other part is the space-domain data stream for the antenna selection [10] [11]. GSMtakes the index of activated antennas as spatial symbols thatexploit degree of spatial freedom without introducing any RFchains. Therefore, combining GSM with mm-Wave massiveMIMO system can effectively reduce the power consumptionand hardware complexity.Most of the studies regarding the EE of cellular networksignore the computation power of the base station or simplyset it to a constant value [12] [13] [14] [15]. But [16] pointsout that the computation power of the massive MIMO systemwill consume more than 50% energy at the base station, andthe optimization of computation power plays a major role inthe improvement of the EE for 5G cellular networks. In thispaper, we study the EE of the system combining GSM with HPtechnology in the mm-Wave scene, and the computation poweris considered in the analysis. The EE is analyzed with respectto the number of active users, RF chains, and antennas pergroup via simulations. Note that the GSM-HP system was firstproposed in [17], in which spectral efficiency was studied. Tothe best of our knowledge, this paper is the first to research theEE of the GSM-HP system in the mm-Wave massive MIMOscene.The remainder of this paper is organized as follows. Thesystem model of the GSM with sub-connected HP scheme isescribed in Section II. Section III analyzes the EE of thesystem. In Section IV, simulation results are provided, andSection V concludes this paper.II. S
YSTEM M ODEL
In this paper, we analyze the EE of the GSM with sub-connected HP scheme. The block diagram is given in Fig. 1,where a mm-Wave massive MIMO system with N T transmitantennas and K single-antenna users is considered. Fig. 1. System model of the GSM with sub-array HP scheme.
The input of the system includes 1 space-domain datastream and N S = K APM-domain data streams. The N S APM-domain data streams are then transmitted to the base-band precoder to generate N RF RF-domain symbols. Sincethe sub-connected hybrid precoding structure is adopted, wedivide the N T transmit antennas into N M antenna groups,and each group consists of N K antennas, which satisfies N T = N M N K . According to the principle of GSM, it isrequired that N S ≤ N RF < N M . Therefore, the space-domaindate stream can control the switches to distribute the outputsignals of RF chains to N RF out of the N M antenna groups,while the remaining ( N M − N RF ) antenna groups will not beactivated during the signal transmission period.The number of available spatial modulation schemes issymbolized by M ≥ . Each spatial modulation scheme isdetermined by the space-domain data stream, M can thus beexpressed as: M = 2 log N M N RF , (1)where ( (cid:5)(cid:5) ) denotes the binomial coefficient and ⌊ (cid:5) ⌋ denotes thefloor operation. We let C m ∈ C N T × N RF represent the m -thspatial modulation matrix with ≤ m ≤ M . Due to the spacelimitation, the explanation for the spatial modulation matrixis omitted here, and more technical details can be found in[17]. Finally, the received signal vector y ∈ C K × is given asfollows when the m -th spatial modulation scheme is selected: y = H H AC m D m x + n , (2)where A ∈ C N T × N T represents the RF precoding matrix, and D m ∈ C N RF × N S represents the baseband precoding matrixwhen the m -th spatial modulation matrix is selected. Limitedby the total transmitting power P max of the base station, theprecoding matrix is required to satisfy: k AC m D m k F = P max , (3)where k (cid:5) k F denotes the Frobenius norm of the matrix.We let x = [ x , . . . , x k , . . . , x N S ] T symbolize the N S APM-domain data streams, where x k obeys a complex Gaus-sian distribution with 0-mean and 1-variance, and n =[ n , . . . , n k , . . . , n K ] T symbolize the additive white Gaussiannoise (AWGN), where n k obeys a complex Gaussian distribu-tion with 0-mean and σ N -variance. [ (cid:5) ] T denotes the transposi-tion. H H ∈ C K × N T is the mm-Wave massive MIMO channelmatrix, and h Hk ∈ C × N T represents the channel matrix of the k -th user. Obviously, H H = [ h , . . . , h k , . . . , h K ] H , where [ (cid:5) ] H denotes the conjugate transposition. Due to the high-path-losspropagation characteristic in free space, the spatial selectionand scattering of mm-Wave are limited. Meanwhile, the large-scale antenna array structure of the mm-Wave transceiverleads to high correlation of the antenna, and the number ofpropagation paths of mm-Wave is much smaller than that oftransmission antennas. Therefore, it is not accurate to modelthe mm-Wave channel with the statistical fading distributionthat used in conventional MIMO analysis in a sparse scatteringenvironment. In this paper, we adopt the geometric channelmodel with a finite scattering and multipath to characterizethe mm-Wave MIMO channel [18]. The channel matrix of the k -th user is given as: h k = s N T β k N ray N ray X i =1 ρ ki u ( ψ i , ϑ i ) , (4)where N ray represents the number of multipath betweenusers and the base station, and N T represents the numberof transmission antennas. β k = ζ/l γ k is the large-scale fadingcoefficient between the base station and the k -th user, where ζ obeys a lognormal distribution with 0-mean and 9.2 dB-variance and l k represents the distance between the k -th userand the base station. γ is the path loss factor and is set as4.6 in this paper [19]. ρ ki is the complex gain of the k -thuser on the i -th multipath, which is considered as the small-scale fading coefficient. Furthermore, ρ ki is an independent andidentically-distributed random variable for each k (1 , . . . , K ) and i (1 , . . . , N ray ) . ψ i and ϑ i represent the azimuth and ele-vation angle of the i -th multipath between users and the basestation from the antenna array of the base station, respectively.Compared with other antenna structures, the two-dimensionalplanar antenna array is smaller in size and less complex tomake the most of the angle information of the signal, whichis more suitable for a mm-Wave massive MIMO system.Therefore, we employ the planar antenna array structure in thispaper. The array response u ( ψ i , ϑ i ) corresponding to azimuthangle ψ i and elevation angle ϑ i is formulated as follows: ( ψ i , ϑ i ) = 1 √ N T [1 , . . . , exp j πλ d ( l sin( ψ i ) sin( ϑ i )+ r cos( ϑ i )) , ..., exp j πλ d (( L −
1) sin( ψ i ) sin( ϑ i )+( R −
1) cos( ϑ i ))] T , (5)where λ represents the carrier wavelength and d = λ/ represents the inter-element spacing. Besides, ≤ l ≤ ( L − and ≤ r ≤ ( R − are the row and column of antenna array,and the size of the antenna array is N T = LR .III. E NERGY E FFICIENCY O PTIMIZATION
In this paper, the energy efficiency η EE of mm-Wave massiveMIMO systems is expressed as [20] η EE = R total P total , (6)where R total is the wireless channel capacity of mm-Wavemassive MIMO systems, and P total is the total power of mm-Wave massive MIMO systems. A. Wireless Channel Capacity
According to the system model in Section II, the receivedsignal of the k -th user is given as y k = h Hk AC m D m x + n k . (7)The spectral efficiency R k of single-user GSM is calculatedby the mutual information between x , m and y k , i.e. R k = I ( y k ; x , m ) . (8)Since m is a discrete channel input, the mutual informationabove cannot be expressed in a closed form, which bringsgreat inconvenience to the performance analysis. In [17], anapproximate closed-form expression of spectral efficiency isprovided: R k = log M σ N − M M X n =1 log M X t =1 (cid:12)(cid:12)(cid:12)X k,n + X k,t (cid:12)(cid:12)(cid:12) − ! , (9)where P k,n symbolizes the conditional covariance matrix of y k when the n -th spatial modulation matrix is chosen. P k,n is given as follows: X k,n , σ N + h Hk AC n d n,k d Hn,k C Hn A H h k . (10)Based on the spectrum efficiency of the k -th user, the totalchannel capacity can be expressed as R total = B K X k =1 R k , (11)where B represents the bandwidth.A reasonable hybrid precoding algorithm can achieve thesame system performance as the optimal full-digital precoding (FDP) [21].Therefore, to simplify the analysis, we assume theperformance of HP consistent with full-digital zero-forcingprecoding when calculating the channel capacity. B. Power Consumption
As mentioned in Section I, the computation power cannotbe ignored or set to a constant in the mm-Wave massiveMIMO scene. Similar to [22], we divide the total power ofthe base station into three parts, including transmission power,computation power and the fixed power: P total = P transmission + P computation + P fix . (12)The detailed power consumption is modeled below basedon the system introduced in Section II.
1) Transmission Power:
Transmission power consists ofpower consumed by amplifiers, radio frequency and switches.The amplifier power P PA is expressed as P PA = 1 α k AC m D m k F = P max α , (13)where α stands for the efficiency of the amplifier.The RF power includes the power of RF chains and phaseshifters in the RF precoding. Considering that there are only N RF out of N M antenna groups chosen to work in the GSMsystem, hence the number of working antennas is N RF N K ,which is equal to that of phase shifters. With P RF per chain symbolizing the power of each RF chain and P per shifter sym-bolizing the power of each phase shifter, the RF power isformulated as: P RF = N RF P RF per chain + N RF N K P per shifter . (14)Switches are required to select the antenna groups in thespatial modulation structure, the switch power can thus beexpressed as P switch = N RF P per switch . (15)According to (13) (14) (15), we then obtain the transmissionpower: P transmission = P max α + N RF P RF per chain + N RF N K P per shifter + N RF P per switch . (16)
2) Computation Power:
Computation power is composedof all the power consumed by the base station for calcula-tion, including channel estimation, channel coding, and linearprocessing.The channel estimation is processed within a stable coherentblock, therefore, the channel estimation power is expressed asthe product of the number of coherent blocks unit time ν block and the energy consumption per channel estimation κ , i.e. P CE = ν block κ, (17)where ν block is calculated by the coherence time T c and thecoherence bandwidth B c , i.e. block = BB c T c . (18) κ in (17) is given as κ = γ CE L BS , (19)where γ CE represents the floating-point operations needed perchannel estimation and L BS represents computation efficiency(in Gigaflops/Watt) of the base station. Assuming that thepilot-based channel estimation method is adopted, then N T pilot sequences will be received at the base station. The lengthof each pilot sequence is τ K , where τ ≥ denotes thefactor that enables the pilots to be orthogonal. The base stationestimates the channel according to the product of the pilot andpilot sequences with the length of τ K [23], γ CE can thus beformulated as γ CE = 2 τ N T K . (20)According to (18) (19) (20), we obtain channel estimationpower: P CE = BB c T c τ N T K L BS . (21)Channel coding power is proportional to the informationrate, which is written as P CD = P COD R total = P COD B K X k =1 R k , (22)where P COD represents the efficiency of channel coding (inWatt per bit/s).In this paper, linear processing includes baseband precodingand solution of the precoding matrix. The power of basebandprecoding is expressed as: P BB = B γL BS , (23)where γ represents the floating-point operations per basebandprecoding. The product of the baseband precoding matrix( N RF × N S ) and the data stream matrix ( N S × ) requires N RF N S floating-point operations [24]. Considering that thebaseband signal is in the complex domain, we modify thefloating-point operations as γ = 8 N RF N S . (24)According to (23) (24), the power of baseband precoding isgiven by P BB = B N RF N S L BS . (25)The solution of the precoding matrix is carried out everttime channel estimation is processed, the power consumed bythe solution of the precoding matrix can thus be expressed as the product of the number of coherent blocks unit time ν block and the energy consumption per solution operation κ precoding : P LP C = ν block κ precoding , (26)where κ precoding can be expressed as the ratio of floating-pointoperations required to perform a solution of the precodingmatrix to the computation efficiency of the base station, i.e. κ precoding = γ precoding L BS . (27)The power consumed by the solution operation of theprecoding matrix can then be concluded as: P LP C = BB c T c γ precoding L BS . (28)According to (25) (28), we obtain the linear processingpower: P LP = B N T N S L BS + BB c T c γ precoding L BS . (29)Moreover, according to (21)(22)(29), the computation powercan be expressed as: P computation = BB c T c τ N T K L BS + P COD B K X k =1 R k + B N T N S L BS + BB c T c γ precoding L BS . (30)
3) Fixed Power:
Other power, such as cooling, voltageconversion loss, etc., is set to the fixed power P fix .Finally, by submitting (16) and (30) into (12), the totalpower of the base station is given as follows: P total = P max α + N RF P RF per chain + N RF N K P per shifter + N RF P per switch + BB c T c τ N T K L BS + P COD R total + B N RF N S L BS + BB c T c γ precoding L BS + P fix . (31)IV. S IMULATION R ESULTS
In this section, we present the simulation results charac-terizing the EE of the considered GSM-HP system comparedwith traditional full-digital zero-forcing precoding system. Inparticular, the computation power is taken into account whencalculating EE. The simulation parameters are given in TableI. In Fig. 2, we plot the EE of GSM-HP system and FDPsystem with respect to the number of users. It can be observedthat the EE of FDP goes down as the number of usersincreases. Huge energy consumption, especially computationpower is required by more users, while the FDP systemcannot provide the corresponding capacity gain in the mm-Wave scene. The EE of GSM-HP is positively correlated withthe number of users at the first beginning, and vanishes asmore users are added, but is still superior to FDP. Spatialmodulation technology utilizes spatial freedom to increase
ABLE IS
IMULATION P ARANETERS
Parameters Values
Transmitting power P max
39 dBmPower spectral density (PSD) of noise -174 dBm/HzEfficiency of power amplifier α B
800 MHzPower per RF chain P RF per chain
45 mWCarrier frequency f c
28 GHzCoherent time T c B c
100 MHz τ L BS P COD − Watt per bit/spower per phase shifter P per shifter
15 mWpower per switch P per switch P fix N ray γ ψ i and elevation angle ϑ i [0 , π ] uniform distribution Number of Users × GSM-HP:(Nrf,Nm,Nk)=(14,16,8)FDP:(Nrf,Nm,Nk)=(14,16,8)GSM-HP:(Nrf,Nm,Nk)=(31,32,6)FDP:(Nrf,Nm,Nk)=(31,32,6) × Fig. 2. Energy efficiency VS. number of users of different schemes. channel capacity without bringing in extra power consumption.Therefore, when there are not too many users, the capacitygain provided by spatial modulation can compensate for thedecline in energy efficiency of the system. But the gain isfinite, the EE decreases as users increases furthermore.The EE against the number of RF chains is investigated inFig. 3. In this part of simulation, RF chains of the FDP schemeare required to be equal to the number of antennas, therefore,the EE of FDP is a constant value. While the EE of GSM-HPdeclines as the number of RF chains increases, indicating thatthe increasing RF chains bring in more energy consumption.Fig. 4 depicts the relationship between the EE and thenumber of antennas per group. Note that FDP does not groupthe antennas, curves of the FDP scheme show the resultsof the same number of total antennas as the correspondingGSM scheme. In Fig. 4, the EE of GSM-HP increases withthe increase in the number of antennas per group, while FDP
Number of RF Chains × GSM-HP:(K,Nm,Nk)=(3,8,16)FDP:(K,Nm,Nk)=(3,8,16)GSM-HP:(K,Nm,Nk)=(3,8,32)FDP:(K,Nm,Nk)=(3,8,32)
Fig. 3. Energy efficiency VS. number of RF chains of different schemes.
Number of Antennas per Group × GSM-HP:(K,Nrf,Nm)=(10,14,16)FDP:(K,Nrf,Nm)=(10,14,16)GSM-HP:(K,Nrf,Nm)=(10,31,32)FDP:(K,Nrf,Nm)=(10,31,32)
Fig. 4. Energy efficiency VS. number of antennas per group of differentschemes. decreases. According to the EE analysis in Section III, moreantennas per group only introduces the energy consumptionof channel estimation, solution of precoding matrices, andanalog phase shifters in GSM-HP. While the times of mm-Wave channel estimation is small, resulting in the energyconsumption of channel estimation and solution of precodingmatrices being very low. Besides, the energy consumptionof analog phase shifters can be ignored compared with thecomputation power. As a result, the increase in the numberof antennas per group does not call for excessive energyconsumption, but improves the capacity significantly, whichcontributes to higher EE.Furthermore, to have a deeper view of what effect theproposed GSM-HP scheme will have on the computationpower, we illustrate computation power versus the number ofusers in Fig. 5. As shown in Fig. 5, the computation power
Number of Users C o m pu t a t i on P o w e r( W ) FDPGSM+HP
Fig. 5. Computation power VS. number of users of different schemes( N RF , N M , N K )=(14,16,8). increases sharply for both schemes along with more users. Butthe GSM-HP scheme can economize 88% power consumptioncompared with the FDP scheme, which shows great promisein improving the EE of 5G cellular networks.V. C ONCLUSION
In this paper, we investigate the EE of the GSM withsub-array HP scheme in the mm-Wave multi-user massiveMIMO scene. The EE, considering the computation power,is modeled according to the GSM-HP system. Moreover, therelationships between the EE and the number of users, RFchains and antennas are analyzed. Simulation results showthat, combining both GSM and HP technologies can lowerthe computation power by reducing the number of RF chains.The GSM-HP scheme can improve the EE compared with thetraditional full-digital zero-forcing precoding scheme.A
CKNOWLEDGMENT