Relevance of Energy Effcency Gan n Massve MIMO Wreless Network Ahmed Alzahran, Vjey Thayananthan, Muhammad Shuab Quresh Computer Scence Department, Faculty of Computng and Informaton Technology Kng Abdulazz Unversty, Jeddah 21589, Saud Araba. Abstract The massve MIMO and energy effcency (EE) analyss for the next generaton technology are the hottest topcs n wreless network research. Ths paper explans about massve MIMO wreless networks and EE for manfold channel whch s an evoluton massve MIMO. Ths research wll help to desgn and mplement a practcal system of next generaton network based on massve MIMO where effcent processng provdes EE gan. In order to approach ths research, dfferent types of manfolds are consdered wth effcent technques that depend on the rank of the channel matrx. Employng the specfc manfold that helps to analyze the rate of the feedback ncreases not only the overall performance of the MIMO system but also the EE. We studed the convergence technques used for optmzng quantzaton errors whch have nfluences wth manfold feedback. Here, we have focused on relevant areas whch are very mportant to analyze EE gan n the future massve network. Accordng to the selected results obtaned n ths research, many challenges wll be possble to make useful proposals. Keywords Massve MIMO; manfolds; EE gan; feedback; convergence; quantzaton I. INTRODUCTION Concept of basc MIMO system has been used n many applcatons for many decades but ts desgn concept used n wreless networks s growng wth next generaton technology. The EE concepts are very attractve because they are not only used for the cost reductons, but also they are very useful to ncrease the lfetme of the components used n massve MIMO wreless networks. Massve MIMO wreless networks and communcaton systems are mplemented wth a large number of antennas n mult-channel envronments [1]. In ths, channel used n massve MIMO should be mantaned because EE gan depends on the dynamc and statstc behavor of the channel. If the channel state nformaton (CSI) s consdered, the feedback employed n the recever should be optmzed to mprove EE performance. The optmal feedback desgn usng approprate manfolds and massve MIMO can be analyzed through energy-effcent algorthms depended on the channel matrx, whch needs a manfold to mprove the rank and dmenson of the covarance matrx [3], [4]. Complexty s a serous concern for massve MIMO because the dmenson of the matrx s nfluenced drectly. The novelty of ths research s manfold feedback desgned for massve MIMO system. Regardng the EE mprovement based on massve MIMO, analyzng the key observatons of massve MIMO such as feedback and few relevant parameters are useful n ths research. As a practcal matter, however, ths EE exctement s tempered by the feasblty of makng perfect and global CSI avalable at all the termnals of a massve MIMO network. It s very dffcult and often mpossble to provde such a perfect CSI because of rapd channel varatons and power ncreasng dmensonalty of channels. In the massve MIMO scheme, the uncertanty of channel estmates even at the recever, and lmted avalablty of communcaton resources to send nformaton back from the recever to other termnals n a network. Thus, t s crtcal to developng technques for provdng lmted CSI wth reasonable EE to the transmtters through the feedback used massve MIMO scheme [9]. Ths lmted CSI at the transmtters helps sgnfcantly to boost the capabltes of current wreless technologes. When consderng a sngle user communcaton and a pont-to-pont lnk n the massve MIMO scheme, utlzaton of antennas s unavodable. Thus, the transmtter and recever needs and antennas respectvely. The practcal problem of the conventonal recever s always a bg ssue n the desgn. Here, manfold technques provde bg mprovements when desgn of the feedback s effcent. Overhead problem and EE s ncreased wth a total number of antennas used n the transmtter of massve MIMO [6]. The geodesc and chordal dstances consdered n the manfold of dynamc channel should be approprate to make effcent calculatons. The optmzed wth dmensons of the manfold whch MIMO channel needs to reduce the rank of the channel matrx, power and complexty. A geodesc, whch s a non-lnear curve of MIMO channel, holds a dstance between any two ponts located on the curve assumed as a surface of any manfolds [2]. Ths small curve magned on the manfold of the channel s a straght lne. Also these two ponts are very close to each other n the Eucldean space. Sngular value decomposton (SVD) of the matrx and egenvectors assocated to ths matrx are necessary steps to calculate the performance of massve MIMO systems. These steps and calculatons n MIMO need to be mproved through the approprate optmzaton technques [8]. Lnear channel model based on SVD wth optmzaton wll enhance the EE n an open and closed loop of MIMO system. The sectons and sub-sectons n the paper are categorzed as follows. Secton II provdes basc nformaton of MIMO and desgn that enhances the EE. Secton III ntroduces the massve MIMO wth feedback and types of manfolds. In Secton IV, 351 P a g e
study of feedback and bref convergence technques for EE gan are gven. Results and analyss of ths research based on Pn-manfold and Stefel manfold are tabulated and dscussed wth necessary graphs n Secton V. Overall conclusons, and further work are summarzed n Secton VI. II. DESIGN OF MIMO Accordng to [18], the desgn of transmtter and recever are analyzed for MIMO system. The desgn of the transmtter allows us to ncrease the EE and rate wth same transmsson power. It means that t requres less transmsson energy for hgher data rate. MIMO system requres more energy than SISO because crcut and sgnal processng for MIMO requre large energy consumpton. A. Basc MIMO The basc MIMO contans transmtter and recever wth multple transmttng and recevng antennas, respectvely. In MIMO system model, the parameters of the precodng, nput, channel, nose and output are used to form a mathematcal model. In ths system (1), followng dmensons are used,,,, and. In order to calculate the EE gan for fxed and varable rate of MIMO system, statstc power requrements of the nternal components and dynamc power of communcaton channels are requred. If total data n s transmtted through MIMO wth same transmsson power Pt and data rate R, the transmsson energy can be calculated as npt Et (2) R Matrces nfluenced to the channel are vared wth the tme, external nose and other envronmental changes. So, desgn of basc MIMO and ts channel matrces should be able to handle all stuatons wth low energy consumptons. Spectral and EE lmts of sngle and multple lnks that handle n dfferent envronmental condtons can also be desgned n massve MIMO [15]. B. Applcaton of MIMO Applcatons of MIMO are many, but they can be categorzed nto three dfferent approaches they are coordnated MIMO, massve MIMO and mllmeter wave MIMO. In network MIMO, coordnated MIMO s used for whch EE nfluences wth mprovement of spectral effcency and specfc coordnaton [14], [17]. Massve MIMO s ncreasng wth a number of users and base statons where EE ncreases wth a number of antennas [5]. Mllmeter wave MIMO may be consdered n the 5G development. Accordng to the research [10], the manfolds can be used n all energy savng applcatons nvolved wth non-lnear channel models. C. Basc MIMO wth Manfolds The manfolds can be used n the feedback of the basc MIMO. Wthn the recever, manfolds are employed to optmze the EE and power whch ncreases the overall (1) performance. Here, energy s analyzed wth feedback optmzaton usng Stefel manfolds. In feedback, all avalable manfolds are consdered to ncrease the overall performance of basc MIMO [12]. In order to optmze the energy performance, the Stefel manfold can be used n MIMO, channel estmatons and some specfc modulatons schemes. D. Desgn of Energy Effcent MIMO wth Manfolds Energy effcent MIMO can be desgned from varous ways they are such as reducng complexty durng the processng and effcent energy managements. The complexty of MIMO depends on the algorthms used n the communcaton path durng the processng. To ncrease the EE, propertes of the manfold such as rank reducton, optmzaton can be used dynamcally. III. DESIGN OF MASSIVE MIMO Massve MIMO s desgned wth a large number of antennas whch may be ether fxed or varable sze. Gan of each antenna s also consdered wth szes of antennas (gan s proportonal to the area of the antenna). When employng the energy effcent components used n the massve MIMO system, the overall lfetme ncreases. The overall EE gan depends on the desgn dedcated for partcular applcatons. When more features and servces are nvolved n a partcular applcaton, energy consumpton wll ncrease but best EE can be acheved wth optmum desgn. It s also of nterest to study structured quantzaton codebooks for feedback that helps us to desgn massve MIMO wth low decodng complexty. A. Massve MIMO wth Feedback The desgn concept of feedback used n the massve MIMO s same as basc MIMO. Here, the sze of the channel matrx s very large for the feedback that carres CSI to the base staton (BS). Processng of passng CSI through the feedback needs energy whch depends on the number of antennas used n BS. When ncreasng the number of antennas at BS, progress of feedback changes to handle the CSI. Here, energy consumpton s proportonal to the sze reducton whch s possble wth matrx technques employed n feedback. Regardng the EE analyss, followng types are studed. 1) Perfect or lmted CSI s avalable at the transmtter 2) Perfect or lmted feedback channel 3) Lnear precodng based on CSI The energy of the feedback channel s the rato of the power used n the feedback and the data rate on the feedback channel as gven (2). Here, sum of the source codng rate s also n whch feedback channel uses the optmzaton. In ths paper, a low-rate, Zero-Delay, error-free feedback channel from the recever to the transmtter are basc assumptons. It means that the recever s assumed to have perfect channel knowledge. Here, achevng EE n massve MIMO s a bg challenge. In partcular, challenges of feedback employed n massve MIMO are expected to compute from geometrc parameters lke dmenson, coordnates, geodesc dstance, manfold volume and ball volumes for varous types of manfolds defned through equalty or nequalty constrants on traces and equalty or nequalty constrants on ranks of the matrces. 352 P a g e
Usng these parameters, we can analyze the EE performance of sphere packng quantzaton codebooks and random quantzaton codebooks over those manfolds. Our objectve n ths project would be to use those parameters to desgn spectrally effcent MIMO systems wth quantzed covarance feedback [6], [7] that ncreases the EE. B. Types of Manfolds wth Feedback In the recent research papers, manfolds are consdered wth latest MIMO schemes that use the energy effcent feedback desgned wth followng manfold technques. Grassmannan: The specal structure of the Grassmann manfold that affects the capacty of the overall MIMO system ncludng massve MIMO. Here, EE depends on the rank and dmenson of the channel matrx obtaned from the massve MIMO and used for manfold technque. Some useful nformaton about Grassmannan manfold and ts quantzaton bounds, whch affect the capacty and EE n feedback desgn, are studed from [10]. Remannan: In a complete Remannan vew, dstance between the two selected ponts along the geodesc curve should be optmzed. Geodesc curves and optmzed dstances around the manfold are what channel matrx expects to mnmze the dmenson and ncreases the smoothness of the curve used around the manfold. Mnmzng dmenson helps us to ncrease the EE n feedback desgn. Pn-manfold: The covarance matrx s computed from the current channel used between the transmtter and recever antennas [7]. The covarance matrx s represented by a pont on the surface of any 3D objects called as Pn-manfold. The EE of feedback depends on the number of bts used n the codebook, whch s a representaton of quantzaton created from Pnmanfolds [7]. Stefel manfold: Accordng to [8], [13], Stefel manfold provdes better optmzaton wth quck convergence. Emplyng ths Stefel manfold technque, matrce obtaned from Stefel manfold enhances the recever optmzaton of the basc and massve MIMO system. Regardng the EE concept, better optmzaton and quck convergence helps to analyze ths research. Also, Stefel manfold are useful for desgnng energyeffcent feedback. C. Massve MIMO and EE Gan Many research papers show that MIMO provdes EE gan when MIMO system holds more antennas. There are many optons whch control the energy performance. They depend on how many antennas are n acton at the tme n ether base staton or user termnals (moble staton) and qualty whch s optmzaton of channel. We can analyze how optmzaton enhances the EE gan n massve MIMO developments whch are wreless networks merged wth latest MIMO technology such as manfold and quantzaton nfluenced wth feedback. Defnton: Spectral effcency s proportonal to the emtted power. So, changes of the EE depend on the power used n MIMO channels. EE = Spectral /power (3) Regardng the terms used n (3), unts of EE, spectral and power of massve MIMO are n (bts/joule), (bts/channel), (Joule/channel), respectvely. As mentoned n [7], sets of postve sem-defnte matrces are consdered to dentfy the Pn-manfold wth varous trace and ranks, whch optmze the overall problems n the massve MIMO system. General Pn-manfolds can be wrtten as: ( ( ( (4) In trace nequaltes Tr(Q), power controls the EE whch provdes effcency of the overall massve MIMO system. Fndng matrx Q s approprate for achevng the goal of ths research. Ths matrx Q satsfes the capacty requrements on the feedback channel. In MIMO applcatons, CSI controls the functons of recever components, whch are optmzaton, equalzaton and detecton. In ths research, the feedback lnk needs better and quck convergence that helps to analyze the EE gan. IV. FEEDBACK AND CONVERGENCE FOR EE GAIN The novelty of feedback desgned from manfolds s dependent on the quck convergence. When energy-effcent MIMO and ts feedback desgn wth a sutable manfold are consdered, fast convergence can be acheved [8]. So, massve MIMO system can be analyzed wth feedback and ts convergence. Two types of convergence technques used n [8] are useful to analyze the EE gan n ths research. They are conjugate gradent (CG) and Newton methods whch provde convergence. If massve MIMO systems acheve quck convergence, the performance of EE gan wll change. As shown n Fg. 1, massve MIMO has feedback channel that holds the manfold and convergence technques. MIMO s also consdered wth the same confguraton, but the matrx of the manfold should be larger than expected. Here, rank reducton of the covarance and manfold matrces should be very useful because error performance could be mproved [19]. Fg. 1. Massve MIMO Transmtter/Recever wth feedback. 353 P a g e
Most of the applcatons use the MIMO system wth feedback, whch needs best EE technques because many challenges depend on approprate feedback desgns. Here, overall performance of the feedback channel depends on the quantzaton and mnmum MSE, whch needs some form of optmzaton. The capacty requrements of the feedback channel depends on the dynamc channel matrcs form the manfolds. An effcent quantzaton of CSI also provdes an enhancement n channel capacty. In order to analyze the EE wth massve MIMO applcatons, studyng CSI controls the functons of recever components, whch are optmzaton, equalzaton, detecton, etc. s mportant. In order to mplement a perfect or lmted CSI, the feedback channel should have better optmzaton technque wth quck convergng parameters. There are other components such as lnear precodng based on CSI, whch needs compatble optmzaton technques. In order to optmze the feedback for EE gan, some practcal problems are mportant. They are such as the quantzed feedback model and quantzaton codebook desgn. Optmzaton of the quantzaton nfluences wth these problems, and t uses Stefel manfold technques to mnmze the problems. Followng equaton can be used for characterzng the performance when quantzed feedback [7] s n an actve. D( w) E max v H 2 H 1 (5) w Here, D(w) s the dstorton measurement, when feedback channel uses the optmzaton technques. In (5), w s the projecton codebook and value s the largest value of the. A. Feedback Analyss wth EE Gan Effcency of recevers and EE gan of massve MIMO depend on the performance of the feedback. In ths analyss, there are few assumptons on rank that depends on the channel matrx nfluenced wth nose and envronments. Practcal lmts of antennas used n massve MIMO are drectly nvolved wth envronmental condtons. The capacty of the feedback lnk also ncreases lnearly wth the number of transmt antennas [6], [11]. The key problem here s to fnd algorthms to map frequency doman channel estmates to feedback bts and then from feedback bts to the covarance matrces for all the carrers smultaneously [16]. The MSE and ts convergence behavor are consdered n the feedback analyss, whch transfer the CSI from the recever to the transmtter. Accordng to [8], convergence of the MSE proved that rank reducton controls the convergng tme whch ncreases the EE n massve MIMO system. B. Impact of MSE n EE Gan The MSE calculatons provde the necessary nformaton to acheve the EE gan through CG algorthm. Convergence behavour of massve MIMO system depends on the followng equaton: MSE j ( j) 2 e R (1 ) (6) 2 (0) R e In (6), MSE shows the -th symbol and j-th teraton when massve MIMO system converges. The represents the egenvalues. Accordng to [18], convergence behavor depends on the covarance matrx. Convergence rate s the sgnfcant concept n ths research because t provdes necessary nformaton to analyze the EE. It has some nfluences wth R where propertes of egenvalues take place. As a conventonal technque, CG method s studed. Optmzaton wth mnmzng MSE on the Stefel Manfold s descrbed n [8]. The Stefel manfold s the set of p- tuples of orthonormal vectors (7) or equvalently C nk T Vn, k { Q C Q Q Ik} (7) Where s the dentty matrx. In Stefel manfold, Q s full column rank matrx whch has unque soluton. Accordng to [13], Stefel manfold can be employed n the feedback channel of the basc and massve MIMO system where dmensons of matrces could be controlled through ths manfold. The space of orthonormal matrces, whch s rectangular wth k < n have assocated n defnton 1. The C used n (7) s representng the complex feld of Stefel manfold. Defnton 1: The defnton of complex Stefel manfold s defned as C 2 n, k, j / (8) j Y V Y k n In (8), k/n s a constant value on the man dagonal of the matrx, whch s a pont on the manfold. Defnton 2: The complex dmenson of the Stefel manfold can be defned that t s the sum of the dmenson of skew-hermtan matrces and the dmenson of ( matrces. C nk, dm V k( n k) 0.5 k( k 1) (9) Sgnal-to-nterference-plus-nose rato (SINR) and a number of antennas from massve MIMO decde the teratons whch take more energy. ( ( ( (10) In (10), P, s the receved power for each transmttng symbol and the nose power. ( ( ( (11) Equaton (11) can be used to calculate the convergence behavor of MSE, whch s an error nfluenced wth dmenson of the covarance matrx and ts rank. 354 P a g e
Capacty bts/s/hz Rate (IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, C. Impact of Quantzaton n EE Gan As far as ths research s concerned, quantzaton plays the man role n the desgn of feedback. The convergence and MSE calculatons are characterzng the feedback through the correct quantzaton. The mpact of quantzaton gets changed through the manfolds because t depends on the channel model of massve MIMO. 7.06 7.05 7.04 Nt=100, Nr=40 Nt=200, Nr=60 Massve MIMO system wth PN-manfold V. RESULTS AND ANALYSIS Massve MIMO schemes wth Pn-manfold and Stefel manfolds can provde better EE through the capacty. In order to ncrease the manfold channel performance, selected confguratons of massve MIMO schemes are consdered to analyze the results. To reduce the rank and dmenson, Stefel manfold can be employed n the feedback channel of the MIMO scheme. Pn-manfolds can be used n the MIMO channel through the feedback lnk where quantzaton technque s appled to characterze channels mathematcally. As shown n Fg. 2, feedback capacty for massve MIMO scheme s ncreased wth antennas, whch are n transmttng termnal. Total of antennas from both transmttng and recevng termnals s also mportant for overall capacty wth SNR. Table I shows the convergence of MSE n massve MIMO schemes. Accordng to [8], Stefel manfold s appled n both the CG and Newton methods. 450 400 350 300 250 200 150 100 50 Massve MIMO 0-10 -5 0 5 10 15 20 SNR n db Fg. 2. Feedback capacty for massve MIMO scheme. TABLE I. Stefel Manfold CG Nt = 100, Nr = 40 Nt = 200, Nr = 60 Capacty for massve MIMO CONVERGENCE OF MSE Newton 7.03 7.02 7.01 7 50 100 150 200 Number of feedback bts Fg. 3. Rate wth feedback bts. Feedback data can be ether sent through the Addtve Whte Gaussan Nose (AWGN) channel or MIMO channel. Quantzaton s one of the recommended areas n ths research. Feedback and quantzaton n the manfold recever of MIMO system where each element obtaned from Stefel manfold s quantzed wth dfferent rate and tested. Computng mnmum egenvectors assocated wth egen values s one of the advantages when Stefel manfold s employed n quantzaton development. Fg. 3 shows the rate aganst feedback bts for massve MIMO scheme, whch s the new step used to reduce the rank of large matrces employed n the channel matrces. VI. CONCLUSION AND FURTHER WORK In ths research paper, we have noted the EE analyss for massve MIMO wreless network for next generaton technology wth manfold and convergences technques used n feedback and quantzaton. Manfolds are ntroduced to mnmze the dmensons of large matrces created dynamcally from the massve MIMO. In partcular, Pn-manfold s more attractve to ncrease the EE gan than the other manfolds because t has more optons that are dynamcally applcable durng the operatons. From the theoretcal analyss usng convergences technques, quantzed feedback can be desgned wth the Stefel manfold technque whch ncreases not only the channel capacty, but also the EE gan n the massve MIMO system. In the future research, we wll contnue the EE gan analyss wth more results whch prove the drect comparson between the EE and manfolds. Also, we can nvestgate the problem of achevable throughput and EE under complex envronments. ACKNOWLEDGMENT The work was funded by the Deanshp of Scentfc Research (DSR), Kng Abdulazz Unversty, Jeddah, under grant No (611-011-D1434). The authors, therefore, acknowledge wth thanks DSR techncal and fnancal support. 355 P a g e
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