Spatial Lobes Division Based Low Complexity Hybrid Precoding and Diversity Combining for mmWave IoT Systems
IIEEE INTERNET OF THINGS JOURNAL, VOL. , NO. , 2018 1
Spatial Lobes Division Based Low ComplexityHybrid Precoding and Diversity Combining formmWave IoT Systems
Yun Chen, Da Chen, Yuan Tian, and Tao Jiang,
Senior Member, IEEE
Abstract —This paper focuses on the design of low complexityhybrid analog/digital precoding and diversity combining in mil-limeter wave (mmWave) Internet of things (IoT) systems. Firstly,by exploiting the sparseness property of the mmWave in theangular domain, we propose a spatial lobes division (SLD) togroup the total paths of the mmWave channel into several spatiallobes, where the paths in each spatial lobe form a low-ranksub-channel. Secondly, based on the SLD operation, we proposea low complexity hybrid precoding scheme, named HYP-SLD.Specifically, for each low-rank sub-channel, we formulate thehybrid precoding design as a sparse reconstruction problem andseparately maximizes the spectral efficiency. Finally, we furtherpropose a maximum ratio combining based diversity combiningscheme, named HYP-SLD-MRC, to improve the bit error rate(BER) performance of mmWave IoT systems. Simulation resultsdemonstrate that, the proposed HYP-SLD scheme significantlyreduces the complexity of the classic orthogonal matching pursuit(OMP) scheme. Moreover, the proposed HYP-SLD-MRC schemeachieves great improvement in BER performance compared withthe fully digital precoding scheme.
Index Terms —IoT, millimeter wave communication, hybridprecoding, low complexity, diversity combining.
I. I
NTRODUCTION T HE wireless data traffic of Internet of things (IoT) isexpected to grow exponentially in the next few years,since the number of access devices in IoT will face explosivegrowth [1]. Millimeter wave (mmWave) technology, which isone of the most important technologies for IoT, can greatlyalleviate the above traffic pressure due to the abundant spec-trum resources and large bandwidth [2]. Moreover, the smallwavelength of mmWave signals enables the deployment oflarge antenna arrays into small space of IoT devices [3].By now, the 60 GHz mmWave communication protocolshave been introduced in IEEE 802.11ad and 802.11ay [4],[5]. However, owing to the high carrier frequency, mmWave
Manuscript received September 7, 2018; revised November 3, 2018; ac-cepted November 6, 2018; Date of publication ...; date of current version ...This work was supported in part by the National Science Foundation of Chinawith Grant numbers 61771216, 61631015 and 61729101, Fundamental Re-search Funds for the Central Universities with Grant number 2015ZDTD012,China Scholarship Council (CSC), and the National Science Foundation ofChina with Grant 61601191. (
Corresponding author: Tao Jiang. )Y. Chen, D. Chen, Y. Tian, and T. Jiang are with Wuhan National Laboratoryfor Optoelectronics, School of Electronic Information and Communications,Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: chen [email protected]; [email protected]; yuan [email protected];[email protected]).Copyright (c) 2012 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected]. signals experience severe attenuation, which makes mmWaveface many challenges when applied to the IoT [6]. As anotherpromising technology for IoT and 5G, massive multiple-inputmultiple-output (MIMO) could generate high precoding gainsto compensate for the high path loss of mmWave throughthe precoding technology [7]–[10]. Therefore, it is of greatsignificance to study precoding schemes in mmWave IoTsystems [11].There are three main candidate precoding schemes, i.e.,fully digital precoding, analog precoding and hybrid pre-coding. The fully digital precoding is widely employed inthe classic MIMO communication system, which demandsradio frequency (RF) chains comparable in number to theantennas [12], [13]. Though multiple data streams could betransmitted simultaneously, the prohibitive energy consump-tion of these RF chains makes the fully digital precodingimpractical for the mmWave IoT system [14]. In the analogprecoding architecture, all the antennas share a single RF chain[15]. Using the phase shifters, analog precoding could obtainhigh precoding gains with low power consumption, but hasto tolerate some performance loss. To circumvent the aboveproblems, the hybrid precoding has been proposed, wherea high-dimensional analog precoder is followed by a low-dimensional digital precoder [16]–[20]. Between the analogand digital precoders, the number of the RF chains is muchless than the number of antennas. The hybrid precoding couldachieve similar performance as the digital precoding withmuch lower power consumption therefore it is more attractiveto mmWave IoT systems.There are many papers devote to the design of the hybridprecoding schemes [17], [21]–[24]. The hybrid precodingarchitecture was first proposed for mmWave communicationsin [17]. According to the sparse structure of the mmWavechannel, an orthogonal matching pursuit (OMP) base schemewas proposed. This scheme firstly models the spectral effi-ciency optimization problem as a sparse reconstruction prob-lem. Then, it selects the analog precoding vectors from theset of array response vectors and constructs the digital pre-coding matrix by the least square. Though the OMP schemecould achieve good spectral efficiency, it contains singularvalue decomposition (SVD) and inverse operations of highdimensional matrices, which lead to high computational com-plexity. Therefore, many recent hybrid precoding literaturesfocus on reducing the complexity of the hybrid precoding.In [21], the authors proposed four methods to achieve dif-ferent tradeoffs between the performance and complexity for a r X i v : . [ c s . I T ] N ov IEEE INTERNET OF THINGS JOURNAL, VOL. , NO. , 2018 single user hybrid precoding. In [22], [23], the array-of-subarrays architecture was considered to reduce the computingcomplexity in which each RF chain is only collected withpartial antennas. In [24], the beamspace schemes were alsoproposed to obtain low-complexity hybrid precoding matrices,which transformed high-dimensional matrix operations intolow-dimensional beamspace matrix operations. Moreover, theangular domain signal processing methods were also proposedfor mmWave communications, which utilize array signal pro-cessing technologies to provide reliable design [25], [26].To the best of our knowledge, all above methods werebased on the clustered channel model and did not fully utilizethe sparseness property in angular domain of the mmWave.According to [27]–[29], the angles of the arrive/departure(AOAs/AODs) of the paths in the mmWave channel could begrouped in several separated spatial lobes (SLs). For pathsin different spatial lobes, their AOAs/AODs are sufficientlyseparable, while the AOAs/AODs of the paths in one spatiallobe are relatively close. This sparseness property in theangular domain leads to the possibility to divide the mmWavechannel approximately orthogonally, which could be utilizedto reduce the complexity of the hybrid precoding and improvethe system performance.In this paper, we propose a low complexity hybrid pre-coding scheme and a diversity combining scheme for themmWave IoT systems. By exploiting the sparseness propertyin angular domain of the mmWave, we firstly carry out aspatial lobes division (SLD) operation to group the totalpaths into several spatial lobes. SLD operation reconstructsthe clustered mmWave channel into equivalent spatial lobeschannel which consists of several approximately orthogonalsub-channels. Then, based on the SLD operation, we proposea low complexity hybrid precoding scheme, named HYP-SLD,which formulates the hybrid precoding design as a set of sparsereconstruction problems. For each sub-channel, the HYP-SLDscheme provides a decoupling solution to the design of theanalog and digital precoding matrices. Finally, we further pro-pose a maximum ratio combining based diversity combiningscheme, named HYP-SLD-MRC. For data streams in eachsub-channel, the HYP-SLD-MRC scheme adds data streamsweighted by the corresponding signal-to-noise ratios (SNR)together for reducing the bit error rate (BER) of IoT. Themain contributions of this paper are summarized as follows. • We fully utilize the sparseness property in the angulardomain of the mmWave to design the low complexity hy-brid precoding scheme. The complexity of the proposedHYP-SLD scheme is proportional to the number of pathsin one spatial lobe (sub-channel). Compared with theOMP scheme, the reduction of computational complexityis more than in a mmWave IoT system where thetransmitter has 64 antennas and 16 RF chains, and thereceiver has 32 antennas and 8 RF chains. • Through a simple linear summation operation, the pro-posed HYP-SLD-MRC scheme maximizes the outputSNR for each sub-channel. Therefore, the BER perfor-mance is greatly improved compared with the fully digitalprecoding scheme. Moreover, since the HYP-SLD-MRCscheme deals with each sub-channel rather than the total signals for the mmWave IoT systems, the multiplexinggains could also be obtained.Simulation results demonstrate that the proposed HYP-SLD achieves near-optimal spectral efficiency and BER per-formances. Moreover, the proposed HYP-SLD-MRC schemeachieves great improvement in BER performance comparedwith the fully digital precoding scheme.The rest of the paper is organized as follows. In SectionII, the system model, channel model and the problem for-mulation are presented. The characteristics of spatial lobes,the equivalent spatial lobes channel and the low complexityhybrid precoding strategy are demonstrated in Section III.In Section IV, the diversity combining scheme is proposed.The simulation results are presented in Section V. Finally, weconclude this paper in Section VI.We use the following notations in this paper: a is a scalar, a is a vector, A is a matrix and A is a set. A ( i ) is the i th column of A and (cid:107) A (cid:107) F is the Frobenius norm of A . A T , A ∗ , A − denote the transpose, conjugate transpose andinverse of A respectively. diag( A ) is a vector that consistsof diagonal elements of A and blkdiag( A , B ) is the blockdiagonal concatenation of A and B . [ A | B ] is the horizontalconcatenation. | a | is the modulus of a . I N denotes a N × N identity matrix. O ( N ) means the order is N . CN ( a , A ) is acomplex Gaussian vector with mean a and covariance matrix A . E [ A ] is the expectation of A .II. S YSTEM M ODEL , C
HANNEL M ODEL AND P ROBLEM F ORMULATION
A. System Model
The hybrid precoding structure we consider in mmWave IoTsystems is shown in Fig. 1. The transmitter and receiver of IoTdevices are equipped with N t and N r antennas, respectively.The number of the RF chains at the transmitter and the receiverare respectively denoted as N tRF and N rRF , which are subjectto the constrains N s ≤ N tRF ≤ N t and N s ≤ N rRF ≤ N r ,where N s denotes the number of the data streams.At the transmitter, N tRF × N s baseband precoding matrix F BB followed by an N t × N tRF analog precoding matrix F RF transforms N s data streams to N t antennas. Setting F T = F RF F BB , the discrete-time transmitted signal vector could bewritten as X = F T s , (1)where s is the N s × symbol vector with E [ ss ∗ ] = N s I N s . Inthis system, F RF is implemented by phase shifters, which hasconstant amplitude constraint (cid:16) F ( i )RF F ( i ) ∗ RF (cid:17) l,l = 1 /N t , where ( · ) l,l denotes the l th diagonal element of a matrix. In addition,the total power constrain is enforced by (cid:107) F RF F BB (cid:107) F = N s .We adopt a narrowband block-fading channel model asshown in [17], which yields the received signal as r = √ ρ HF T s + n , (2)where H is the N r × N t mmWave channel matrix, ρ is theaverage received power, and n ∼ CN (0 , σ n ) is the additivewhite Gaussian noise vector. HEN et al. : SLD BASED LOW COMPLEXITY HYP AND DIVERSITY COMBINING FOR MMWAVE IOT SYSTEMS 3
Digital Baseband Precoder BB F s N RF ChainRF Chain tRF N RF F s N t N r N Digital Baseband Combiner
RF ChainRF Chain rRF N BB W RF W N Fig. 1. Block diagram of the hybrid precoding structure in mmWave IoT systems.
After being combined at the receiver, the received signal is y = √ ρ W ∗ T HF T s + W ∗ T n , (3)where W T = W RF W BB , W RF is the N r × N rRF RF combin-ing matrix which should satisfy (cid:16) W ( i )RF W ( i ) ∗ RF (cid:17) l,l = 1 /N r and W BB is the N rRF × N s baseband digital combining matrix. B. Channel Model
The mmWave signals have higher free-space pathloss thanlower frequency signals and are sensitive to blockages, whichlead to limited spatial scattering. Therefore, the clusteredchannel model is usually used to represent the mmWavechannel [28], which could be expressed as H = (cid:114) N t N r M N M (cid:88) m =1 N (cid:88) n =1 α m,n a r ( θ r m,n ) a t ( θ t m,n ) ∗ , (4)where M is the number of clusters and each cluster contributes N propagation paths, α m,n denotes the complex gain of the n th path in the m th cluster, θ rm,n ∈ [0 , π ] and θ tm,n ∈ [0 , π ] are the AOA and AOD, respectively. By adopting uniformlinear arrays (ULAs), the antenna array response vectors a r ( θ r m,n ) and a t ( θ t m,n ) at the transmitter and the receiver couldbe written as a t ( θ t m,n ) = 1 √ N t (cid:104) , e j (2 π/λ ) dsin ( θ t m,n ) , ..., e j ( N t − π/λ ) dsin ( θ t m,n ) (cid:105) T , (5)and a r ( θ r m,n ) = 1 √ N r (cid:104) , e j (2 π/λ ) dsin ( θ r m,n ) , ..., e j ( N r − π/λ ) dsin ( θ r m,n ) (cid:105) T , (6)respectively, where λ is the wavelength of the signal, d = λ/ denotes the aperture domain sample spacing. For convenient,we rewrite the channel in a more compact form as H = A r diag( α ) A t ∗ , (7)where α = (cid:113) N t N r MN [ α , α , ..., α MN ] T contains the complexgains of all paths, and the matrices A r = (cid:2) a r ( θ r1 , ) , a r ( θ r1 , ) , ..., a r ( θ r1 ,N ) , ..., a r ( θ r M,N ) (cid:3) (8) and A t = (cid:2) a t ( θ t1 , ) , a t ( θ t1 , ) , ..., a t ( θ t1 ,N ) , ..., a t ( θ t M,N ) (cid:3) (9)contain the array response vectors. Inspired by (7), we couldfind that the number of the paths is the upper bound of therank of the mmWave channel matrix. C. Problem Formulation
The target of designing the hybrid precoding matrices isto maximize the spectral efficiency of mmWave IoT systemsachieved with Gaussian signalling over the mmWave channel[30], where the spectral efficiency is given by R = log (cid:16)(cid:12)(cid:12)(cid:12) I N s + ρN s R − n W ∗ BB W ∗ RF HF RF F BB × F ∗ BB F ∗ RF H ∗ W RF W BB (cid:12)(cid:12)(cid:12)(cid:17) , (10)where R n = σ W ∗ BB W ∗ RF W RF W BB is the noise covariancematrix. As shown in [17], the design of precoding matrices andcombining matrices could be separated. The only differenceis that the combining matrices do not have an extra powerconstraint. Therefore, we mainly focus on the design ofthe precoding matrices at the transmitter and the combiningmatrices at the receiver could be obtained similarly. Thecorresponding target of designing the precoding matrices couldbe simplified to maximize the mutual information, which isgiven by I t ( F RF , F BB ) = log (cid:16)(cid:12)(cid:12)(cid:12) I + ρN s σ n HF RF F BB × F ∗ BB F ∗ RF H ∗ (cid:12)(cid:12)(cid:12)(cid:17) . (11)However, directly designing the precoding matrices to maxi-mize (11) is very non-trivial. Through mathematical derivation,the hybrid precoding design problem could be formulated asan equivalent sparse reconstruction problem which is aimedto minimize the Euclidean distance between the product ofthe analog and digital precoding matrices and the optimal un-constrained precoding matrix [17]. The sparse reconstructionproblem could be formulated as ( F optRF , F optBB ) = arg min F BB , F RF (cid:107) F opt − F RF F BB (cid:107) F , s . t . F RF ∈ F RF , (cid:107) F RF F BB (cid:107) F = N s , (12) IEEE INTERNET OF THINGS JOURNAL, VOL. , NO. , 2018 where F opt is the optimal unconstrained precoding matrixwhich could be obtained from the SVD of the mmWavechannel H and F RF is the set of the feasible RF precodersinduced by the constant amplitude constraint. Note that, sincethe feasibility constraint on the RF precoding matrix is non-convex, it is very difficult to find a global optimal solution. Inthe design of our hybrid precoding scheme, we mainly exploitthe sparseness property of the mmWave in the angular domainto find a low complexity near-optimal solution.III. P ROPOSED L OW C OMPLEXITY H YBRID P RECODING A LGORITHM B ASED ON S PATIAL L OBES D IVISION
In this section, we firstly demonstrate the characteristicof spatial lobes of the mmWave channel. Then, we proposethe SLD operation which reconstructs the mmWave channelinto the equivalent spatial lobes channel. Based on the SLDoperation, the low complexity hybrid precoding strategy isdemonstrated in detail. Finally, we compare the complexity ofthe proposed hybrid precoding scheme with the OMP scheme.
A. The Spatial Lobes Characteristics of mmWave
Recently, the mmWave channel was adequately measured byNYU WIRELESS which confirmed that the mmWave could beutilized in the 5G cellular networks [27]–[29]. The polar plotof 28 GHz mmWave channel [27] is shown in Fig. 2. At thereceiver, there are five dominated spatial lobes with azimuthangle spreads, which confirms that the mmWave channels alsohave sparseness property in angular domain. In the traditional3GPP and WINNER II channel models, which are widelyused in LTE, the paths in one time cluster are assumed toarrive at a same angular spread. Whereas the measurementresults by NYU WIRELESS indicate that there are somedifferences between the time cluster and the spatial lobe, whichare summarized as follow. • The paths in one spatial lobe could come from morethan one time cluster. Each spatial lobe represents a mainAOA/AOD at which groups of multiple path components(MPCs) arrive/depart over a contiguous range of anglesover several hundreds of nanoseconds [29]. • A cluster may contain multipath components which travelclose in time but arrive/depart from many angle lobedirections [28]. • The number of spatial lobes is independent of the numberof time clusters [28].The above differences indicate that the AOAs/AODs ofpaths in different time clusters may be close to each other.Therefore, we could not handle different time clusters sepa-rately. In contrast, the angles of paths in different spatial lobesare sufficiently separable, which prompts us to reconstruct themmWave channel from the spatia lobes perspective and furtherto reduce the complexity of the hybrid precoding.By exploiting the above characteristics of the spatial lobesand considering a relatively large number of antennas areusually employed in mmWave IoT systems, we make a rea-sonable assumption that the paths in different spatial lobesare approximately orthogonal since the AOAs/AODs of thesepaths are sufficiently separable. Therefore, the paths in the
Fig. 2. The polar plot of mmWave channel measured in Manhattan at 28GHz [27]. mmWave channel could be divided into several approximatelyorthogonal groups. An example of the angular domain distri-bution for the propagation paths considered in this paper isshown in Fig. 3, where there are four spatial lobes and eachspatial lobe contains two subpaths. (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) SubpathSpatial lobe
Orthogonal
Fig. 3. An example of the angular domain paths in the mmWave channel,where there are four spatial lobes and each spatial lobe contains two subpaths.
B. SLD Operation and the Equivalent Spatial Lobes Channel
As we could see, the clustered mmWave channel (4) ismade of multiple propagation paths. Therefore, grouping thepaths means dividing the channel. Based on the sparsenessproperty of the mmWave in the angular domain, the SLDoperation groups the total paths into several spatial lobes andreconstruct the mmWave channel (4) into the equivalent spatiallobe channel. Note that, the number of groups and the numberof paths in each group are the number of spatial lobes and thenumber of sub-paths in each spatial lobe, respectively.The equivalent spatial lobes channel could be written as H sl = (cid:114) N t N r P Q P (cid:80) p =1 Q p (cid:80) q =1 α p,q a r ( θ r p,q ) a t ( θ t p,q ) ∗ = H + H + ... + H P , (13) HEN et al. : SLD BASED LOW COMPLEXITY HYP AND DIVERSITY COMBINING FOR MMWAVE IOT SYSTEMS 5 where H i = (cid:114) N t N r P Q Q p (cid:80) q =1 α i,q a r ( θ r i,q ) a t ( θ t i,q ) ∗ , i = 1 , , ..., P represents the i th sub-channel which contains the paths in the i th spatial lobe for both transmitter and receiver, P is thenumber of spatial lobes, and Q p is the number of subpathsin the p th spatial lobe. According to [22, Section II-A] and[23, Section V-A], the maximum number of the spatial lobesis 5 and the mean angles of the spatial lobes are uniformlydistributed between and π , while the angles (AOAs/AODs)of the paths in one spatial lobe are randomly distributed withinthe range of the spatial lobe. Since the paths in different spatiallobes are approximately orthogonal, these sub-channels couldbe treated as approximately orthogonal to each other. Theexpression form of (13) is similar as the cluster channel model(4) and could be regarded as a reconstruction of (4). Therefore,we make H = H sl in the rest of the paper. We could also write(13) in a more compact expression as H = A r diag( α ) A t ∗ , (14)where A r = (cid:2) a r ( θ r1 , ) , a r ( θ r1 , ) , ..., a r ( θ r1 ,Q ) , ..., a r ( θ r P,Q P ) (cid:3) and A t = (cid:2) a t ( θ t1 , ) , a t ( θ t1 , ) , ..., a t ( θ t1 ,Q ) , ..., a t ( θ t P,Q P ) (cid:3) .Accoding to the spatial lobe property, the above two antennaarray response matrices could be divided into several parts as A t = (cid:2) A t1 , A t2 , ... A t P (cid:3) , (15) A r = (cid:2) A r1 , A r2 , ... A r P (cid:3) , (16)where A t i = (cid:2) a t ( θ t i, ) , a t ( θ t i, ) , ..., a t ( θ t i,Q i ) (cid:3) , i = 1 , , ..., P (17)and A r i = (cid:2) a r ( θ r i, ) , a r ( θ r i, ) , ..., a r ( θ r i,Q i ) (cid:3) , i = 1 , , ..., P (18)contain the antenna array response vectors of the i th sub-channel. According to (14)-(18), it could be obtained that Q is the upper bound of the rank of the sub-channel. Therefore,we actually divide the mmWave channel into several low-rankapproximately orthogonal sub-channels. C. Hybrid Precoding Based on Spatial Lobes Division
In this subsection, we present a low complexity hybridprecoding scheme based on the SLD operation. In the designof the hybrid precoding, a principle of maximizing the usageof the channel is adopted, that is we keep the number of thedata streams equal to the number of the total paths.
Lemma 1: (from [31]). Each left and right singular vectorscorresponding to non-zero eigenvalues of the matrix channelconverge in chordal distance to the array response vectorswhen the number of the total paths ( L ) in the channel ismuch less than the number of antennas at both transmitterand receiver, i.e., L = o ( N t ) and L = o ( N r ) .Lemma 1 demonstrates that the array response vectorsare approximate orthogonal with each other and the channelrepresentation (14) “converges” to the SVD of H for largenumber of the antennas. Corollary 1:
When L (cid:28) min ( N t , N r ) , the left and rightsingular matrices of the total channel matrix H consist of the left and right singular vectors from the sub-channels,respectively. Proof:
For the i th sub-channel, we have H i = A r i diag( α i ) A t i ∗ = U i Σ i V ∗ i . (19)According to (15) and (16), the total array response matricesconsist of the array response matrices for each sub-channel.In the meantime, according to Lemma 1, we could concludethat left and right singular vectors corresponding to the Q largest singular values in U i and V ∗ i converge in chordaldistance to the responding array response vectors in A r i and A t i , respectively.Since the left and right singular matrices are the optimalunconstrained fully digital precoding matrices, Corollary 1indicates that, the design of the precoding matrix for the totalchannel matrix could be divided into the precoding designfor each sub-channel when L (cid:28) min ( N t , N r ) . Note thatthe angles of antenna response vectors for different spatiallobes are sufficiently separable, which makes the “inter-lobes”interference very small. Thus, even the antenna responsevectors are not orthogonal to each other for the antennasarray of practical size, we could still divide the total hybridprecoding problem into several subproblems, each of which isonly designed for one sub-channel.Therefore, for the i th spatial lobe or sub-channel, theoptimization problem could be formulated as ( F optRF i , F optBB i ) = arg min F BB i , F RF i (cid:13)(cid:13) F opt i − F RF i F BB i (cid:13)(cid:13) F , s . t . F RF i ∈ F RF , (cid:107) F RF i F BB i (cid:107) F = N s A i (cid:30) P (cid:80) i =1 A i , (20)where F opt i = V i (: , Q i ) is the optimal referenceprecoding matrix, F RF i and F BB i are the analog precodingmatrix and digital precoding matrix for the i th sub-channel,respectively. F RF = (cid:83) i =1 , ,...,P F RF i is the set of the feasibleRF precoders and F RF i is the feasible set of RF precoder forthe i th sub-channel. A i is the total power in the i th spatiallobe and we assume equal power distribution in this paper.Note that, since the number of paths Q i in each sub-channelis very small, i.e., Q i (cid:28) min( N t , N r ) , the sub-channel couldbe considered to be in a very poor scattering environment.Inspired by Lemma 1, in the proposed hybrid precodingscheme, we set the antenna array response matrices A t i and A r i as the reference matrices F res , rather than the fully digitalprecoding matrix obtained by high-dimensional SVD, for the i th sub-channel. However, for arrays of practical sizes, onlysetting A t i and A r i as the reference precoding matrices maycause many performance losses. Therefore, we further performa digital precoding design at the baseband. In summary, inour hybrid precoding scheme, we decouple the solution ofthe optimization problem (20) into analog and digital phases,where the target of the analog precoding is to find the constantamplitude vectors which are closest to each entry of the F res in the l norm sense, and the digital precoding is aimed toremove the interference and perform power allocation to these IEEE INTERNET OF THINGS JOURNAL, VOL. , NO. , 2018 vectors. We demonstrate the design of the analog and digitalprecoding matrices in detail as follows.
Lemma 2:
For the selected vectors of different sub-channels,there is no overlap between the corresponding feasible sets F RF i , i = 1 , , ..., P . Proof:
Define the beam coverage of the i th spatial lobeas CV ( SL i ) = (cid:91) j =1 , ,...,Q CV (cid:0) a ( θ t i,j ) (cid:1) , i = 1 , , ..., P, (21) where CV (cid:0) a ( θ t i,j ) (cid:1) is the beam coverage of the steeringvectors in the i th spatial lobe (sub-channel). For the ULAconsidered in this paper, the half-power beam width of thearray is approximately equal to ◦ /N [32], where N isthe number of antennas, i.e., length ( CV (cid:0) a ( θ t i,j ) (cid:1) ) = 102 ◦ /N ( length ( CV ( . )) represents the beam width of CV ( . ) ). There-fore, we have ◦ N ≤ length ( CV ( SL i )) ≤ Q i ◦ N . (22)As shown in Fig. 3, the AOAs and AODs in different spatiallobes are sufficiently separable. When the angle interval (cid:52) θ between the mean angles of different spatial lobes satisfies (cid:52) θ > Q i ◦ N , (23)there will be no overlap between different spatial lobes.Moreover, since the angles of CV ( F RF i ) could not exceedthe range of the i th spatial lobe, we have CV ( F RF i ) ⊆ CV ( SL i ) . (24)Therefore, there will be no overlap between the differentfeasible sets.Lemma 2 indicates that the selected vectors for differentsub-channel cause small interference with each other and thetotal feasible set F RF could be simply divided into P partsfor each sub-channel to select the vectors in parallel. Actually,this is why we assume that the paths in different spatial lobesare approximately orthogonal with each other in section III.A.Therefore, (20) could be simplified as ( F optRF i , F optBB i ) = arg min F BB i , F RF i (cid:13)(cid:13) F opt i − F RF i F BB i (cid:13)(cid:13) F , s . t . F RF i ∈ F RF i , (cid:107) F RF i F BB i (cid:107) F = N s A i (cid:30) P (cid:80) i =1 A i , (25)In the analog precoding phase, to make the precodingscheme more practical for the limited feedback system, feasi-ble sets are quantized with limited b bits [33]. The quantizedcandidate matrix for the transmitter is A quantt = (cid:104) a quantt ( θ ) , a quantt ( θ ) , ..., a quantt ( θ b ) (cid:105) , (26)where the entries of A quantt are a quantt ( θ i ) = 1 √ N t (cid:104) , e jπ sin( π ( i − b ) , ..., e j ( N t − π sin( π ( i − b ) (cid:105) T . (27) Note that, the quantization candidate matrix divides theangular domain space into b parts uniformity, and could befurther divided into P spatial lobes parts as A quantt = (cid:104) A quantt1 , A quantt2 , ..., A quantt P (cid:105) . (28)Given the quantization matrices, the remaining operationsin the analog precoding phase are to find the vectors formthe quantization matrices which are closest to each entry ofthe F res in the l norm sense. This is equivalent to findthe vectors along which the reference matrix F res has themaximum projection. We only introduce the analog precodingdesign at the transmitter, while the analog precoding matrix atthe receiver could be obtained in the same way. The correlationmatrix is Ψ = A quant ∗ t i F res . (29)The power distributed in each direction could be calculated as k = diag( ΨΨ ∗ ) . (30)Then, we select the position indexes of the Q i largest values in k , and obtain the corresponding vectors from the quantizationmatrices. Once a vector has been selected, the value of thecorresponding location in k is set to be zero to eliminate theeffects of the vector. According to (29) and (30), the analogprecoding matrix for the i th sub-channel could be obtained as F RF i = [ F RF i , F RF i , ..., F RF iQi ] , i = 1 , , ..., P, (31)where F RF ij represents the selected vectors steering at the j th paths in the i th sub-channel. After the analog precodingmatrices for all sub-channels are obtained, the final analogprecoding matrix at the transmitter could be determined by F RF = [ F RF , F RF , ..., F RF P ] . (32)Note that, since the selected vectors F RF ij are not orthogonal-ized, we only need to find these vectors to steer at the pathsand leave the orthogonalization process to the digital precodingphase. In the similar way, the analog precoding matrix at thereceiver could be obtained as W RF = [ W RF , W RF , ..., W RF P ] . (33)After the analog precoding phase, we obtain the effectivelow-dimensional channel as H eq = W ∗ RF HF RF = [ W RF , W RF , ..., W RF P ] ∗ H [ F RF , F RF , ..., F RF P ]= W ∗ RF HF RF , W ∗ RF HF RF , . . . , W ∗ RF HF RF P W ∗ RF HF RF , W ∗ RF HF RF , . . . , W ∗ RF HF RF P ... ... . . . ... W ∗ RF P HF RF , W ∗ RF P HF RF , . . . , W ∗ RF P HF RF P = (cid:101) H , (cid:101) H , . . . , (cid:101) H P (cid:101) H , (cid:101) H , . . . , (cid:101) H P ... ... . . . ... (cid:101) H P1 , (cid:101) H P2 , . . . , (cid:101) H P P , (34)where (cid:101) H ij ∈ C Q i × Q j are called as effective sub-channels.According to (14), we could find that W RF i and F RF i areone by one correspondence for the i th sub-channel. Therefore, HEN et al. : SLD BASED LOW COMPLEXITY HYP AND DIVERSITY COMBINING FOR MMWAVE IOT SYSTEMS 7
Algorithm 1
Hybrid Precoding Based on Spatial Lobes Divi-sion (HYP-SLD)
Input: A t , A r , A quantt , A quantr Output: F RF , F BB , W RF , W BB for i ≤ P do F res = A ti Ψ = A quant ∗ t i F res for j ≤ Q i do k ← argmax l =1 ,..., Q diag( ΨΨ ∗ ) F RF i = (cid:104) F RF i (cid:12)(cid:12)(cid:12) A quant( k )t i (cid:105) Eliminate the effect of the selected vector diag( ΨΨ ∗ )( l ) = 0 end for end for F RF ← [ F RF , F RF , ..., F RF P ] We could obtain W RF in the same way W RF = [ W RF , W RF , ..., W RF P ] H eq = W ∗ RF HF RF for i ≤ P do Compute the SVD of W ∗ RF i HF RF i from H eq W ∗ RF i HF RF i = U ii Σ ii V ∗ ii F BB i = V ii , W BB i = U ii end for F BB = blkdiag( F BB , F BB , ..., F BB P ) W BB = blkdiag( W BB , W BB , ..., W BB P ) F BB = √ N s F BB (cid:107) F RF F BB (cid:107) F only the diagonal effective sub-channels make sense, and (34)could be rewritten as (cid:101) H eq = (cid:101) H . . . (cid:101) H P P , (35)where (cid:101) H ii contains the paths whose AODs and AOAs belongto the i th spatial lobe. Lemma 3:
The left and right singular matrices of theeffective channel (cid:101) H eq could be directly obtained by applyingSVD for each effective sub-channel (cid:101) H ii , i = 1 , , ..., P . Proof:
For each effective sub-channel, we have (cid:101) H ii = (cid:101) U ii (cid:101) Σ ii (cid:101) V ∗ ii , i = 1 , , ..., P, (36)where (cid:101) U ii and (cid:101) V ii are the left and right singular matricesof H ii and Σ ii is a diagonal matrix with the singular valuesarranged in decreasing order. Therefore, the effective channel(35) could be written as (cid:101) H eq = (cid:101) U (cid:101) Σ (cid:101) V ∗ . . . (cid:101) U P P (cid:101) Σ P P (cid:101) V ∗ P P = (cid:101) U (cid:101) Σ (cid:101) V ∗ , (37)where (cid:101) U = (cid:101) U . . . (cid:101) U P P , (38) (cid:101) Σ = (cid:101) Σ . . . (cid:101) Σ P P , (39) (cid:101) V = (cid:101) V . . . (cid:101) V P P . (40)Since (cid:101) U ii and (cid:101) V ii are unitary matrices and (cid:101) Σ ii is a diagonalmatrix of non-negative elements, (cid:101) U (cid:101) Σ (cid:101) V ∗ is a singular valuedecomposition of the channel (cid:101) H eq .Note that, since there is no constant magnitude constrainsin the digital precoding phase, the digital precoding matricescould be directly obtained by applying SVD. According toLemma 3, the digital precoding matrices for the transmitterand receiver could be easily determined as F BB = (cid:101) V , W BB = (cid:101) U . (41)Finally, the precoding matrices are normalized to satisfy thepower constrains at the transmitter. The proposed scheme isdescribed in detail in Algorithm 1 . D. Computational Complexity Analysis
In this subsection, we briefly analyze the complexity ofproposed HYP-SLD hybrid precoding scheme. To simplify theexpression, we assume Q = Q = ... = Q P in this subsection.Compared with the OMP scheme, the reduction in complexityis mainly reflected in the following aspects.
1) The optimal fully digital precoding is not needed inadvance . Considering that the optimal precoding matricesconverge in chordal distance to antennal response matrices forlimited scattering paths [31], we set A ti and A ri rather thanthe fully digital precoding matrices as the reference matricesfor the i th sub-channel, which could avoid SVD operation ofhigh-dimensional channel matrix.
2) The search space of the selected analog precoding vectorsis reduced . In the analog precoding phase, both the candidatematrix and the reference matrix are divided into P partsaccording to the spatial lobes. For the i th sub-channel, weonly need to select the vector from the corresponding part ofthe quantization matrix, along which the corresponding partof the reference matrix has the maximum projection.
3) The SVD in digital precoding phase is divided . Afterthe analog precoding phase, we obtain the digital domainmmWave channel H eq with P Q × P Q dimension. Since theeffective sub-channels make up a block diagonal matrix (cid:101) H eq ,we are able to handle each effective Q × Q sub-channelseparately to obtain the digital precoding matrices, which isactually implemented by performing SVD shown as (37).The computation complexities for all hybrid precodingdesign phases at the transmitter are summarized in TableI. The complexity of computing precoding matrices at boththe transmitter and the receiver doubles the number of theoperations, while the order of the overall complexity un-changed. Taking N t = 64 , N r = 32 , N tRF = 16 , N rRF = 8 , P = 4 , Q = ... = Q P = Q = 2 , b = 7 , N s = P Q = N rRF for example, we find that the reduction of the complexity ismore than compared with the OMP scheme. IEEE INTERNET OF THINGS JOURNAL, VOL. , NO. , 2018
TABLE ITHE COMPUTATIONAL COMPLEXITY FOR DIFFERENT HYBRIDPRECODING SCHEMES AT THE TRANSMITTER (cid:104)(cid:104)(cid:104)(cid:104)(cid:104)(cid:104)(cid:104)(cid:104)(cid:104)(cid:104)
Computation Scheme OMP HYP-SLD F opt O ( N N r + N ) NULLAnalog precoding matrix O (2 b N t N tRF N s ) O (2 b N t Q ) Digital precoding matrix O (( N tRF ) N t ( N tRF + N s )) O ( P Q ) IV. P
ROPOSED S PATIAL L OBES D IVERSITY C OMBINING S CHEME
HYP-SLD-MRCIn the HYP-SLD hybrid precoding scheme, the data streamsare associated with the subpaths in each spatial lobe, whichinspires us to further utilize these subpaths. As has shown in(39), the singular values matrix of (cid:101) H eq is (cid:101) Σ = (cid:101) Σ . . . (cid:101) Σ P P , (42)where (cid:101) Σ ii = (cid:101) Σ ii . . . (cid:101) Σ iiQ i , i = 1 , , ..., P, (43)contains the singular values for the i th spatial lobe and (cid:101) Σ ii ≥ (cid:101) Σ ii ≥ ... ≥ (cid:101) Σ iiQ i . It could be observed that (cid:101) Σ ii has at least one dominated singular value of the total channelmatrix H when the AOAs and AODs of different spatiallobes are sufficiently separable. Moreover, when the numberof data streams approaches the number of paths, most singularvalues including the relatively small singular values are usedto transmit signals, which causes poor BER performance.Motivated by this, we determine to design an optionaldiversity combining scheme to reduce the BER when theIoT system prefers better BER performances. Specifically, wefirstly introduce the classic maximal-ratio combining (MRC)diversity combining technique [34]. Then, a new type ofdiversity combining scheme based on MRC is proposed forthe mmWave IoT system. A. Maximal-Ratio Combining Scheme
In a SIMO system where the receiver is equipped with N antennas, the received signal vector is y mrc = h s mrc + n , (44)where h = [ h , h , ..., h N − ] T represents the channel gainvector, s mrc is the unit power signal transmitted and n isadditive white gaussian noise. MRC conducts a weightedsum across all branches (antennas) with the objective ofmaximizing SNR [34], where the weight vector is w mrc = h ∗ (cid:14) (cid:107) h (cid:107) . (45)The output signal could be obtained by ˆy mrc = w mrc y mrc . (46) LMMSE Q w output Q ˆ S ˆ y output Q Q ˆ P y ˆ P S P P w QQ PP y P y SNR w ooutoutp P w Fig. 4. The block diagram of the proposed HYP-SLD-MRC diversitycombining scheme.
Since the signal s mrc has unit average power, the instantaneousoutput SNR could be calculated by γ = | h ∗ h | σ h ∗ h = h ∗ h σ = N − (cid:80) n =0 | h n | σ = N − (cid:80) n =0 γ n , (47)where γ n is the input SNR at the n th antenna. As we can see,the output SNR is the summation of the input SNRs, whichis actually the maximum output SNR. Therefore, the outputsignal achieves better BER performance due to the increase ofthe SNR. Generally, the variable gain weighting factor w mrc could be set to be the ratio of the signal amplitude to the noisepower for the diversity path, which has been proved in [34]. B. Proposed HYP-SLD-MRC Diversity Combining Scheme
In this subsection, we demonstrate the proposed HYP-SLD-MRC diversity combining scheme shown in Fig. 4. Accordingto the singular values matrix (43), we find that each sub-channel contains at least a dominated singular value of the totalchannel. Meanwhile, since the number of subpaths satisfies Q (cid:28) min( N t , N r ) , there is no strong correlation betweenthe data streams on different subpaths. Therefore, we couldperform the diversity combining scheme in each sub-channel.At the transmitter, the signals in (1) are divided into P blocks, which is given by s = [ s , s , ..., s P ] T , (48)where s i , i = 1 , , ..., P, contains Q copies of one signaltransmitted along the i th spatial lobe (sub-channel), i.e., s i = [ s i , s i , ..., s iQ i ] T , (49)and s i = s i = ... = s iQ i . (50)The above signals are transmitted using the mmWave channelbased on the proposed HYP-SLD precoding scheme. There-fore, we associate s i with the i th sub-channel. At the receiver,linear minimum mean square error (LMMSE) demodulator HEN et al. : SLD BASED LOW COMPLEXITY HYP AND DIVERSITY COMBINING FOR MMWAVE IOT SYSTEMS 9 is utilized to demodulate the received signal y in (3). Thedemodulated signal vector could be obtained by ˆs = ( (cid:98) H ∗ (cid:98) H + σ I ) − (cid:98) H ∗ (cid:98) Hs + ( (cid:98) H ∗ (cid:98) H + σ I ) − (cid:98) H ∗ W ∗ T n = (cid:2) ˆ s , ˆ s , ..., ˆ s P (cid:3) T = (cid:2) ˆ s , ˆ s , ..., ˆ s Q , ..., ˆ s P Q P (cid:3) T , (51)where (cid:98) H = W ∗ BB W ∗ RF HF RF F BB , and ˆ s i contains Q re-ceived copies transmitted along the i th sub-channel.To maximize the output SNR for each sub-channel, weadopt the concept of MRC to combine the Q signal copies of ˆ s i , i = 1 , , ..., P . Since the power of the transmitted symbol isnormalized, the received signal amplitude after demodulationcould be written as P s = (cid:13)(cid:13)(cid:13) (cid:98) H (cid:13)(cid:13)(cid:13) F (cid:30)(cid:13)(cid:13)(cid:13) (cid:98) H ∗ (cid:98) H + σ I (cid:13)(cid:13)(cid:13) F . (52)The noise power is P n = ( (cid:98) H ∗ (cid:98) H + σ I ) − (cid:98) H ∗ W ∗ T n ∗ (( (cid:98) H ∗ (cid:98) H + σ I ) − (cid:98) H ∗ W ∗ T n ) ∗ = σ (cid:13)(cid:13)(cid:13) (cid:98) H ∗ W ∗ T (cid:13)(cid:13)(cid:13) F (cid:30)(cid:13)(cid:13)(cid:13) (cid:98) H ∗ (cid:98) H + σ I (cid:13)(cid:13)(cid:13) F . (53) Since the analog precoding matrices are selected from thequantized candidate matrices and the digital precoding matri-ces are unitary matrices, we have W ∗ T W T = I N s . (54)Therefore, (53) could be simplified as P n = σ (cid:13)(cid:13)(cid:13) (cid:98) H ∗ (cid:13)(cid:13)(cid:13) F (cid:30)(cid:13)(cid:13)(cid:13) (cid:98) H ∗ (cid:98) H + σ I (cid:13)(cid:13)(cid:13) F . (55)Then, the weight value for the total signals could be computedby (cid:98) w = P s P n = (cid:13)(cid:13)(cid:13) (cid:98) H ∗ (cid:98) H + σ I (cid:13)(cid:13)(cid:13) F σ ≈ (cid:13)(cid:13)(cid:13) (cid:98) H ∗ (cid:98) H (cid:13)(cid:13)(cid:13) F σ = (cid:13)(cid:13)(cid:13) (cid:98) H (cid:13)(cid:13)(cid:13) F σ , (56)which is actually the SNR before the LMMSE demodulation.Therefore, we set the SNRs of the Q received signal copiesbefore demodulation as the weight values and add the corre-sponding demodulated signals together, which is shown in Fig4. Each weight value could be calculated as w ij = | ˜s ij | (cid:14) | ˜n ( ij, :) | , (57)where ≤ i ≤ P, ≤ j ≤ Q i , ˜s = (cid:98) Hs , and ˜n = W ∗ T n . Thetotal weight vector is w = [ w , w ..., w P ] , (58)where w i = [ w i , w i ..., w iQ i ] , i = 1 , ..., P, represents theweight vector for the i th sub-channel and is normalized inadvance. The output signal vector is ˆ y = (cid:2) ˆ y , ˆ y , ..., ˆ y P (cid:3) T . (59)For each ˆ y i , i = 1 , , ..., P , we have ˆ y i = (cid:2) ˆ y i , ˆ y i , ..., ˆ y iQ i (cid:3) T , (60) where each ˆ y ij is the linearly combination of the demodulatedsignals, which could be calculated by ˆ y i = ˆ y i = ... = ˆ y iQ i = Q i (cid:80) j =1 w ij ˆ s ij . (61)In the proposed HYP-SLD-MRC diversity combining scheme,output SNR is maximized for each sub-channel, which couldbe easily proved by the Chebyshev inequality. For MRC,the diversity gain is proportional to the number of antennas( N ) since the output SNR is expanded by N times [35].Thus, through the proposed HYP-SLD-MRC scheme, Q timesdiversity gains could be obtained which will improve the BERperformance. Moreover, we only need to perform diversitycombining on each sub-channel, which makes the signalstransmitted along different sub-channels independent. There-fore, P times multiplexing gains could also be obtained.V. S IMULATION R ESULTS
In this section, we evaluate the performances of the pro-posed HYP-SLD hybrid precoding scheme and HYP-SLD-MRC diversity combining scheme. Both the transmitter andthe receiver of IoT devices are equipped with ULA, where N t = 64 , N tRF = 16 , N r = 32 and N rRF = 8 [17]. Ac-cording to the measurement activity in downtown Manhattanenvironment [27]–[29], the frequency of the mmWave is setto be 28 GHz and the bandwidth is set to be 100 MHz.We adopt the clustered narrow-band mmWave channel withsparsity property in the angular domain. According to the stepprocedures for generating the mmWave channel in [27], [29],we make some reasonable simplifications and set the channelparameters as follows. For P spatial lobes, the whole angulardomain is divided into P parts uniformly and the mean anglesof spatial lobes ( (cid:101) θ i , i = 1 , , ..., P ) are uniformly distributedwithin [0 , π ] , i.e., (cid:101) θ i = πP ( i − . The angle spread of eachspatial lobe is set as ∆ θ = πP to make the angles of pathsin different spatial lobes sufficiently separable and the anglesof subpaths in one spatial lobe are randomly distributed. Thegains of paths in each spatial lobe are assumed to be Rayleighdistributed and the total power of the channel is normalizedwhich satisfies E [ (cid:107) H (cid:107) F ] = N t N r . Fig. 5 compares the spectral efficiency of the proposedHYP-SLD, OMP precoding scheme and fully digital precodingscheme (marked as SVD) with different numbers of spatiallobes and subpaths, respectively. Due to the sparse character-istic of mmWave, the number of spatial lobes and subpathsare both very small, specially the maximum number of spatiallobes is 5 for 28 GHz and 73 GHz mmWave signals [28]. Itcould be observed that the proposed HYP-SLD scheme alwaysachieves similar spectral efficiency as the OMP scheme andthe fully digital precoding scheme.In Fig. 6, we compare the BER performances of HYP-SLD,OMP and the fully digital precoding schemes with differentnumbers of the subpaths and spatial lobes, respectively. Themodulation scheme is QPSK. We observe that three schemesachieve similar BER performances for different Q and P .Moreover, the BER performances for different numbers ofspatial lobes are very close. However, when the number of the -10 -8 -6 -4 -2 0 2 4 6 8 10 SNR (dB) S pe c t r a l E ff i c i en cy ( bp s / H z ) HYP-SLDOMPSVD
P=2,3,4 (a) -10 -8 -6 -4 -2 0 2 4 6 8 10
SNR (dB) S pe c t r a l E ff i c i en cy ( bp s / H z ) HYP-SLDOMPSVD
Q=1,2,3 (b)Fig. 5. Spectral efficiencies of HYP-SLD, OMP and fully digital precodingschemes with (a) different numbers of spatial lobes P and Q = 2 ; (b) differentnumbers of subpaths Q and P = 2 , where, N t = 64 , N r = 32 , N tRF =16 , N rRF = 8 , b = 7 . subpaths increases, the BER performances decreases greatly.The above phenomenon demonstrates that the number ofsubpaths has a greater impact on the BER performance.Fig. 7 shows the spectral efficiencies of different schemeswith different numbers of RF chains, where SNR = 0 dB, N s = 3 , b = 7 . We observe that when N rRF varies from 2 to10, the spectral efficiencies of HYP-SLD remain unchanged.The performance gap originates from two main aspects. 1) Weutilize the array response matrices as the reference matricesinstead of the optimal precoding matrices; 2) We only utilize N rRF = N tRF = P Q
RF chains to transmit and receive signals.Note that, the performance gaps are no more than whilethe complexity could be reduced by .Fig. 8 compares the spectral efficiencies of differentschemes with different numbers of antennas, where P = Q =2 , N s = N tRF = N rRF = 4 , b = 8 and SNR=0 dB. We observethat the proposed HYP-SLD scheme always achieves similarspectral efficiency as the fully digital precoding scheme evenfor not very large numbers of antennas (e.g., N t = N r = 16 ).In the meantime, it could be observed that when the number -40 -35 -30 -25 -20 -15 -10 -5 0 5 SNR (dB) -4 -3 -2 -1 BE R HYP-SLDOMPSVD -4 HYP-SLDOMPSVD
P=1,2,3 (a) -40 -35 -30 -25 -20 -15 -10 -5 0
SNR (dB) -3 -2 -1 BE R HYP-SLDOMPSVD
Q=1,2,3 (b)Fig. 6. BERs of HYP-SLD, OMP and fully digital precoding schemes with(a) different numbers of spatial lobes P and Q = 1 ; (b) different numbersof subpaths Q and P = 2 , where N t = 64 , N r = 32 , N tRF = 16 , N rRF =8 , b = 7 . of antennas turns very large, there are some performance gapsbetween the HYP-SLD scheme and the fully digital precodingscheme. This is because the number of quantization bits is notrelatively large enough when N t and N r become larger.Fig. 9 shows the BER performances of the HYP-SLD, OMP,fully digital and the proposed HYP-SLD-MRC diversity com-bining scheme with different numbers of data streams, where N t = 64 , N r = 32 , N tRF = 16 , N rRF = 8 , P = 4 , Q = 2 . Itcould be observed that the BER performances of the HYP-SLD, OMP, fully digital precoding schemes are almost thesame and the BER performances of HYP-SLD-MRC alwaysoutperform the fully digital precoding for different numbers ofdata streams. Moreover, the more the number of data streamsis, the more obvious the performance improvement becomes.This is because smaller singular values are used to transmitsignals when the number of data streams becomes larger. Theproposed HYP-SLD-MRC is able to transmit the signal copyalong the smallest singular value and achieves the maximumoutput SNR for each sub-channel. HEN et al. : SLD BASED LOW COMPLEXITY HYP AND DIVERSITY COMBINING FOR MMWAVE IOT SYSTEMS 11
Number of RF Chains S pe c t r a l E ff i c i en cy ( bp s / H z ) HYP−SLDOMPSVD 64x3232x32128x32
Fig. 7. Spectral efficiencies of HYP-SLD, OMP and fully digital precodingschemes with different numbers of RF chains, where N s = 3 , SNR=0 dB, N tRF = N rRF , b = 7 .
20 30 40 50 60 70 80 90 100 110 120
Number of antennas S pe c t r a l E ff i c i en cy ( bp s / H z ) HYP-SLDOMPSVD
Fig. 8. Spectral efficiencies of HYP-SLD, OMP and fully digital precodingschemes with different numbers antennas ( N t = N r ), where SNR=0 dB, P = 2 , Q i = 2 , N s = N tRF = N rRF = 4 , b = 8 . VI. C
ONCLUSIONS
In this paper, we proposed a low complexity hybrid pre-coding scheme and a diversity combining scheme in themmWave IoT system. The sparseness property in the angulardomain of the mmWave was fully utilized to design thelow complexity hybrid precoding scheme. Compared with thewidely used OMP scheme, the proposed HYP-SLD greatlyreduces the complexity. To improve the BER performance,we proposed a new type of diversity combining scheme tomaximize the output SNR for each sub-channel, which allowsthe diversity gains and the multiplexing gains to be obtained atthe same time. Simulation results have demonstrated that theproposed low complexity hybrid precoding scheme exhibitssimilar spectral efficiency and BER performances as the fullydigital precoding scheme. Moreover, the proposed HYP-SLD-MRC achieves significant improvement in BER performancecompared with the fully digital precoding scheme. Note thatthe proposed schemes only concern the single-user narrow- -40 -35 -30 -25 -20 -15 -10
SNR (dB) -4 -3 -2 -1 BE R HYP-SLDOMPSVDHYP-SLD-MRC
Ns=1Ns=6 Ns=8Ns=4
Fig. 9. BERs of HYP-SLD, OMP, HYP-SLD-MRC and the fully digitalprecoding schemes with different numbers of data streams, where N t =64 , N r = 32 , N tRF = 16 , N rRF = 8 , P = 4 , Q i = 2 , b = 7 . band system. Our future work will focus on multi-user andwide-band scenarios, where the inter-user interference anddelay are key points to design the hybrid precoding scheme.R EFERENCES[1] B. Liu, T. Jiang, Z. Wang, and Y. Cao, “Object-Oriented Network: ANamed-Data Architecture Toward the Future Internet,”
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Yun Chen received the B.S. degree from HuazhongUniversity of Science and Technology, Wuhan, P. R.China, in 2016, where he is currently pursuing thePh.D degree with Wuhan National Laboratory forOptoelectronics and School of Electronic Informa-tion and Communications. Since 2018, he has beena Visiting Student with the School of Electronics andComputer Science, University of Southampton, U.K.His current research interests include millimeterwave communications, massive MIMO and FBMC.
Da Chen received the B.S. and Ph.D. degrees fromHuazhong University of Science and Technology,Wuhan, P. R. China, in 2009 and 2015, respectively.From Sep. 2012 to Aug. 2013, he was a visitingscholar at Northwestern University, USA. From Sep.2013 to Sep. 2014, he was a visiting scholar atUniversity of Delaware, USA. He is currently anAssistant Professor with the School of ElectronicsInformation and Communications, Huazhong Uni-versity of Science and Technology, Wuhan, P. R.China. He is serving as an Associate Editor forChina Communications. His current research interests include various areasin wireless communications, such as OFDM and FBMC systems.
Yuan Tian received the B.S. and M.S. degreesfrom China University of Geosciences, Wuhan, P.R. China, in 2012 and 2015, respectively. Sheis currently working towards the Ph.D. degree atHuazhong University of Science and Technology,Wuhan. Her current research interests include var-ious areas in wireless communications, especiallyfor FBMC systems with emphasis on prototype filterdesign.