An Efficient Hybrid Beamforming Design for Massive MIMO Receive Systems via SINR Maximization Based on an Improved Bat Algorithm
Mohammed A. Almagboul, Feng Shu, Yaolu Qin, Xiaobo Zhou, Jin Wang, Yuwen Qian, Kingsley Jun Zou
aa r X i v : . [ c s . I T ] N ov An Efficient Hybrid Beamforming Design forMassive MIMO Receive Systems via SINRMaximization Based on an Improved Bat Algorithm
Mohammed A. Almagboul, Feng Shu, Yaolu Qin, Xiaobo Zhou, Jin Wang, Yuwen Qian, and Kingsley Jun Zou
Abstract —Hybrid analog and digital (HAD) beamforming hasbeen recently receiving considerable deserved attention for apractical implementation on the large-scale antenna systems.As compared to full digital beamforming, partial-connectedHAD beamforming can significantly reduce the hardware cost,complexity, and power consumption. In this paper, in orderto mitigate the jamming along with lowering the hardwarecomplexity and cost by reducing the number of RF chainsneeded, a novel hybrid analog and digital receive beamformerbased on an improved bat algorithm (I-BA) and the phase-only is proposed. Our proposed beamformer is compared withrobust adaptive beamformers (RABs) methods proposed by us,which are considered in the digital beamforming part. Theevolutionary optimization algorithm is proposed since most of theRAB methods are sensitive to the DOA mismatch, and dependingon the complex weights, resulting in an expensive receiver. In theanalog part, analog phase alignment by linear searching (APALS)with a sufficiently fine grid of points is employed to optimize theanalog beamformer matrix. The performance of the proposedI-BA is revealed using MATLAB simulation and compared withBA, and Particle swarm optimization (PSO) algorithms, whichshows a better performance in terms of convergence speed,stability, and the ability to jump from the local minima.
Index Terms —Wireless Communication, Beamforming, Inter-ference Suppression, SINR.
I. I
NTRODUCTION
Although the initial applications of adaptive beamformingwere in military areas such as sonar and radar, its use in civil-ian applications like mobile communications, ultrasonics, andseismology also gained great popularity today [1]. Adaptivebeamforming has well-known advantages like enhancing thesystem capacity and reduce the interference by steering theantenna array main beam pattern toward the desired signal,while steer the nulls toward the interference signals directions;this can be accomplished by constantly updating the totalbeamforming weights in a hybrid system. Due to the mul-tiplicity and diversity of the sources of interference resulting
Mohammed A. Almagboul, Feng Shu, Yaolu Qin, Xiaobo Zhou, Jin Wang,Yuwen Qian, and Kingsley Jun Zou are with School of Electronic and OpticalEngineering, Nanjing University of Science and Technology, Nanjing, 210094,China.Mohammed A. Almagboul is also with the Electronic Engineering Depart-ment at Sudan Technological University, Khartoum, Sudan, and the Com-munication Engineering Department, AlMughtaribeen University, Khartoum,Sudan.Feng Shu is also with the College of Computer and Information Sciences,Fujian Agriculture and Forestry University, Fuzhou 350002, China, and theCollege of Physics and Information, Fuzhou University, Fuzhou 350116,China. from the wide spread of wireless devices, the employmentof hybrid adaptive beamforming in smart transportation andunmanned aerial vehicles (UAVs) will be one of the mostimportant techniques that can be used to avoid the risk ofthe undesired interference and jamming signals [2], whereas,with the potential widespread use of UAVs in the near futurein many civilian applications, they face a highly criticalthreat using a relatively easy method i.e., drone jammers,particularly when used for goods delivery, where criminalscan use jammers to obtain goods or obtain the UAV itself.On the other hand, reducing the UAV payload and powerconsumption are considered one of the most important designgoals. Therefore, the use of the hybrid system is very desirable,where it allows us to reduce the number of RF chains in thesystem compared to a fully digital beamforming design. Thereare a number of algorithms and ways to design the adaptivebeamforming; an algorithm that has high convergence speed,low computation, low complexity, and better performance issurely needed.The immense hardware cost and power consumption formassive multiple-input multiple-output (MIMO) systems dueto the large number of RF chains required for a singlereceiver unit is considered one of the most design challenges.Particularly, in the classic massive MIMO system each antennais connected to one RF chain, resulting in a remarkably highhardware cost, complexity, and power consumption, wherethe RF chain includes power-avid components like amplifiersand analog-to-digital converter (ADC) [3]. Consequently, theuse of the hybrid analog and digital (HAD) beamformingreceived great interest from researchers, due to promisingpractical implementation in the massive MIMO systems for5G communications [4], where it requires fewer numbers ofRF chains as compared to a fully digital beamforming design[5, 6]. Moreover, HAD beamforming combines the accuracyand speedy features of digital beamforming which compensatethe reduction of RF chains, and the inexpensive characteristicof analog beamforming [7, 8].Nature-inspired metaheuristic optimization algorithms arewidely used recently to cope the restrictions of the con-ventional adaptive optimization algorithms based on error-derivative methods in terms of inflexibility, getting stuck in alocal minima, and the need of accurate knowledge of directionsof arrival (DOAs) of jamming signals, like linearly constrainedminimum variance (LCMV), and minimum variance distor-tionless response (MVDR) [7, 9, 10]. The application of thesemetaheuristic algorithms in the array pattern synthesis in order RF chain . . . . . .. . . . . . (cid:2207) (cid:4666) (cid:1866) (cid:4667) (cid:1840) (cid:1844)(cid:1832) (cid:1839) Analog
Beamformer (cid:2162) (cid:1844)(cid:1832)
Digital Beamformer (cid:2188) (cid:1830) (cid:2016) (cid:883)
The received interference signals . . . (cid:1871) (cid:1856) (cid:4666) (cid:1872) (cid:4667) RF chain (cid:1876) (cid:883) (cid:4666) (cid:1872) (cid:4667) (cid:1876) (cid:1840) (cid:4666) (cid:1872) (cid:4667) The received desired signal (cid:2016) (cid:1856) (cid:2016) (cid:1837) (cid:1861) (cid:883) (cid:4666) (cid:1872) (cid:4667) (cid:1861) (cid:1837) (cid:4666) (cid:1872) (cid:4667) (cid:1876)(cid:3556) (cid:883) (cid:4666) (cid:1872) (cid:4667) (cid:1876)(cid:3556) (cid:1838) (cid:4666) (cid:1872) (cid:4667) (cid:1876) (cid:883) (cid:4666) (cid:1866) (cid:4667) (cid:1876) (cid:1838) (cid:4666) (cid:1866) (cid:4667)
Fig. 1. Partial-connected hybrid analog and digital BF structure at the receiver to provide SLL minimization and steering the nulls in thedesired interference directions has received great interest fromresearchers recently due to its flexibility, and being able to dealwith non-convex and non-differentiable optimization problems[9-13]. Genetic algorithm (GA) [14] is one of the ancient andwell-known nature-inspired metaheuristic techniques, wherehas been used early for synthesizing pattern of antenna arrays[15]. Particle swarm optimization (PSO) [16] is another widelyknown evolutionary algorithm; It is faster, efficient, easierto implement, and has a capability of solving linear andnonlinear optimization problems. PSO is used extensively forthe designing of antenna arrays [17, 18]. A lot of other Meta-heuristic optimization algorithms also successfully employedin antenna arrays synthesizing applications [12, 19-21], suchas the Ant-Lion optimization (ALO) technique introducedin [22], Grey Wolf Optimizer (GWO) [23], The cat swarmoptimization (CSO) [24], ant colony optimization (ACO) [25],Invasive Weed Optimization (IWO) [26], simulated annealing(SA) [27], Whale Optimization Algorithm (WOA) [28], andothers.The Bat Algorithm (BA) is an evolutionary swarm intel-ligence algorithm initiated by Yang in 2010 [29], inspiredfrom the nature behavior of bats, which use echolocation bychanging pulse rates of emission and loudness to detect preyand avert obstacles. A number of researchers have used Batalgorithm for linear antenna array (LAA) to steer nulls andminimize sidelobe level (SLL). Tong and Truong [10] provedthat the Bat algorithm can outperform the accelerated particleswarm optimization (APSO) and GA in terms of adaptivenull-steering, sidelobe suppression, and computation time inarray pattern nulling synthesis using phase-only control. In[30] again they utilize BA in order to minimize SLL andto place nulls in the desired directions using amplitude-onlycontrol, and proved that the BA based beamformer is moreeffective and faster as compared to GA and APSO. In [31]BA based beamformer using complex weight (amplitude andphase) compared with APSO shows faster convergence andhigher efficiency. However, all above researches and a lot ofother researches using different nature-inspired optimizationalgorithms mainly concentrate on the full digital beamformerinstead of hybrid analog and digital system. To best of our knowledge, very few employments of these algorithms inhybrid analog and digital beamformer were carried out [32-36]. In [34, 35] the authors proposed a phase-only hybridanalog and digital beamforming based on GA with the aim ofminimizing the transmit power under signal-to-interference-plus-noise ratio (SINR) constraints. Based on the ParticleSwarm Ant Colony Optimization (PSACO) algorithm, in [36]a partial-connected hybrid precoding structure for widebandMassive MIMO systems is proposed in order to realize excel-lent energy and spectral efficiency. In [33] a joint precoding inthe multiuser MIMO system with the objective of maximizingthe capacity is carried out with a genetic algorithm (GA).Furthermore, the authors in [32] proposed two hybrid digitaland analog beamformers based on PSO and manifold opti-mization (MO) in order of maximizing capacity. However, allthese research activities mostly focusing on a transmitter notreceiver. The authors in [37] proposed a transmitter/receiverbased on OFDM, random subcarrier selection (RSCS), and di-rectional modulation (DM) for secure messages transmission.In general, the proposed beamformers concentrating mainlyon the transmitter, and the objective issues such as capacitymaximization, secrecy rate maximization [38], maximizingsignal-to-leakage-and-noise ratio (Max-SLNR) per user [39,40], and transmit power minimization, while often neglectingthe robustness. Some research activities provide improvementson BA to avoid the weaknesses of the algorithm being trappedin the local minima or yielded unstable results [41-43]. Thispaper focuses on an efficient interference suppression at thereceiver using partial-connected HAD beamforming structurevia maximizing SINR in the case of the presence and absenceof DOA mismatches. The main contributions of this paper aresummarized as follows:1) Present an Improved-BA and analyze its special proper-ties and excellent features in terms of adaptive beamform-ing. The main distinctions between the Improved-BA andthe BA are the bats ′ compensation for Doppler effects inechoes, and the possibility of selecting different habitats;this makes the algorithm further imitating the bats ′ be-haviors and thus improves the stability and efficiency.2) An efficient partial-connected HAD receive beamformerbased on Improved-BA is proposed, which highly reduces the cost and complexity, maximizing SINR and steeringthe nulls in the directions of interferences.3) To guarantee high efficiency and robustness of our de-sign, we first optimize the digital baseband beamform-ers’ vector by means of closed-form solution using ro-bust adaptive beamforming methods, namely diagonal-loading (DL) technique [44], and spatial matched filter(SMF), which control both amplitude and phase (complexweights). Moreover, we propose an efficient I-BA opti-mization algorithm to optimize the digital beamformervector by controlling only the phase, resulting in an inex-pensive and easy-to-implement receiver. Thereafter, ana-log beamformer’s weights vectors are optimized throughanalog phase alignment (APA) by linear search (LS) usinga sufficiently fine grid of points in the whole DOAs range.The performance of the proposed algorithm is comparedwith BA, and PSO evolutionary algorithms, which showsbetter ability to jump from the local minima, fasterconvergence speed, and relatively high stability. Further-more, the proposed hybrid beamformer I-BA-APALS iscompared with other proposed hybrid beamformers DL-APALS and SMF-APALS, in addition to the conventionalfully digital standard capon beamformer (SCB), and DLtechniques, in terms of SINR obtained, robustness, andnulls depth for a given SNR of the desired and interfer-ence signals, which showed better performance comparedto others.The rest of this work is structured as follows: in the following,our system model of partial-connected hybrid analog anddigital beamformer is defined. In section III the problemformulated. Thereafter, basic BA and proposed Improved-BAare described, and the results discussed in Section IV, and Vrespectively. Finally, conclusions are given in Section VI. Notation : Capital X , boldface small x , and small x lettersare used to represent matrices, vectors, and scalars, respec-tively. Notations ( · ) T and ( · ) H denote transpose and conjugatetranspose of a matrix, respectively. | x | denotes the magnitudeof a complex number x , while E {·} denotes the expectationoperation. II. S YSTEM MODEL
Assume an N-elements partial-connected HAD beamformerstructure at the receiver. Its block diagram is shown in Fig. 1,which used to reduce the hardware cost and energy consump-tion with somewhat less performance. In this structure, thereceiver is chosen to be equipped with N isotropic antennasdivided into L subsets of antenna arrays, and each subsetcontains M antenna elements, where the number of RF chains N RF chosen to be less than the number of antenna elements N RF ≤ N . Each subset of antenna array elements connectedto only one RF chain. The antenna elements are followed bya phase shifters that feed the RF chains. In Fig. 1, hybridBF receives one desired signal s d ( t ) e j π f c t with an angleof arrival (AOA) θ d , and K interference signals i k ( t ) e j π f c t with different angles of arrival θ k ( k = , ..., K ) . The receivedsignals x m ( t ) of the lth sub-array at the input of each mth element ( m = , ..., M ) includes the desired narrow band signal, the interference narrow band signals, and an additive Gaussiannoise v ( t ) with zero mean and variance σ n . Therefore, the lth sub-array output ˜ x l ( t ) can be represented as follows,˜ x l ( t ) = M − ∑ m = s d ( t ) e j π f c (cid:16) t − (cid:16) τ d − (( l − ) M + m − ) dc sin θ d (cid:17) − α l , m π fc (cid:17) + K ∑ k = M − ∑ m = i k ( t ) e j π f c (cid:16) t − (cid:16) τ k − (( l − ) M + m − ) dc sin θ k (cid:17) − α l , m π fc (cid:17) + v l ( t ) (1)where, d is the spacing between adjacent antenna array ele-ments assumed throughout this paper to be 0 . λ , τ d and τ k arethe propagation delays from the desired signal emitter and kthinterference signal emitter, respectively, to a reference pointwhich is assumed to be the first element on the array, and c isthe speed of light. Eq. (1) includes the phase difference α l , m for the mth phase shifter of the analog beamformer in the lth sub-array. After the analog beamformer, the signal ˜ x l ( t ) passes through the L RF chains which include ADCs anddown converters, resulting the following baseband signal ina matrix-vector notation for all L subsets, x ( n ) = F HRF A s ( n ) + v ( n ) , (2)where F RF = diag ( f , ..., f l , . . ., f L ) f l = √ M (cid:2) exp (cid:0) j α , l (cid:1) , exp (cid:0) j α , l (cid:1) , . . ., exp (cid:0) j α M , l (cid:1) (cid:3) T (3)A matrix F RF is the N × L phase shift matrix, s ( n ) = [ s d ( n ) , i ( n ) , . . . , i K ( n )] T , v ( n ) = [ v ( n ) , v ( n ) , . . . , v L ( n )] T is an additive white Gaussian noise (AWGN), and A is N × ( K + ) matrix of steering vectors a ( θ ) , A = [ a ( θ d ) , a ( θ ) , . . . , a ( θ K )] , (4)where the column vector a ( θ ) is called an array manifoldwhich can be given by, a ( θ ) = h , e j π sin θ , . . . , e j π ( N − ) sin θ i T (5)After the digital beamformer, f D ∈ C N RF × , Eq. (3) becomes, y ( n ) = f HD F HRF A s ( n ) + f HD v ( n ) (6)Through the digital beamforming vector f D we can control theamplitude, phase, or both. f D = (cid:2) a e j α , a e j α , . . . , a L e j α L (cid:3) T (7)III. P ROBLEM FORMULATION FOR
SINR
MAXIMIZATION
The input observation vector x ( t ) , can be formulated for allsub-arrays as, x ( t ) = a ( θ d ) s d ( t ) + K ∑ k = a ( θ k ) i k ( t ) + v ( t )= a ( θ d ) s d ( t ) + A i i ( t ) + v ( t )= x s ( t ) + x i ( t ) + v ( t ) , (8) where A i matrix constitutes of all steering vectors of in-terference signals, and i ( t ) = [ i ( t ) , i ( t ) , . . . , i K ( t )] T . Inthis work, we assume that all the signals are zero mean, andindependent. Multiplying these signals by analog and digitalbeamformer weights and adding them together resulting in thefollowing output, y ( n ) = f HD F H RF ( x s ( n ) + x i ( n )) + f HD v ( n ) (9)The correlation matrix estimation can be composed from thesignal and noise samples at n time intervals, which is givenby, P T = E (cid:8) s d ( n ) s Hd ( n ) (cid:9) + K ∑ k = E (cid:8) i k ( n ) i Hk ( n ) (cid:9) + E (cid:8) v ( n ) v H ( n ) (cid:9) = P d + P i + P v , (10)where P d represents the desired signal self-correlation matrix,while P i , and P v represent the undesired interferences plusnoise input signals self-correlation matrices respectively. TheSINR is given by dividing the power of the desired signal bythe sum of powers of all interference and noise signals. Thus,the hybrid system output power for the signal of interest canbe given by, σ s = E n(cid:12)(cid:12) f HD F HRF x s ( n ) (cid:12)(cid:12) o = E n(cid:12)(cid:12) f HD F HRF a ( θ d ) s d ( n ) (cid:12)(cid:12) o = P d f HD F HRF a ( θ d ) a H ( θ d ) F RF f D (11)In the same context, we can derive the hybrid system outputpower for the unwanted signals as follows, σ i = f HD F HRF A i P i A Hi F RF f D (12) σ v = P v f HD f D (13)Therefore, the SINR is defined as, SINR = σ s σ i + σ v = P d f HD F HRF a ( θ d ) a H ( θ d ) F RF f D f HD F HRF A i P i A Hi F RF f D + P v f HD f D (14)Since v l ( n ) is an uncorrelated noise signal with zero meanand variance σ , we get P v = σ I . Without loss of generality,assume P i = I , where I is an identity matrix with appropriatesize, Eq. (14) can be rewritten as follows, SINR = P d (cid:12)(cid:12) f HD F HRF a ( θ d ) (cid:12)(cid:12) f HD F HRF A i A Hi F RF f D + σ f HD f D (15)Our goal is to maximize SINR. However, evolutionary algo-rithms usually looking for the minima, thus, the cost function(CF) can be given by the inverse of SINR as follows, minimize CF = f HD F HRF A i A Hi F RF f D + σ f HD f D P d (cid:12)(cid:12) f HD F HRF a ( θ d ) (cid:12)(cid:12) s . t . f HD F HRF a ( θ d ) = f HD F HRF a ( θ d ) = f D f HD F HRF R i + n F RF f D s . t . f HD F HRF a ( θ d ) = , (17)where R i + n = K ∑ k = P k a ( θ k ) a H ( θ k ) + P v (18) A. Design of the digital weight vector
If the actual covariance matrix, R i + n , are well known, Prob-lem (17) can be solved using Lagrange’s multiplier techniqueas, f D = R − i + n F HRF a ( θ d )( F HRF a ( θ d )) H R − i + n F HRF a ( θ d ) (19)Here, to calculate f D we use the initial value of F RF , that makesthe array main beam steers towards the direction of the desiredsignal. Since f HD F HRF a ( θ d ) =
1, the optimization problem (17)is equivalent to the following one,min f D f HD F HRF R i + n F RF f D + P d (cid:12)(cid:12) f HD F HRF a ( θ d ) (cid:12)(cid:12) s . t . f HD F HRF a ( θ d ) = f D f HD F HRF ˆ RF RF f D s . t . f HD F HRF a ( θ d ) = , (21)where ˆ R is the estimated array covariance matrix, since atypical information about different signals may not be possible.ˆ R = Q Q ∑ q = x ( q ) x H ( q ) , (22)where Q is the snapshot size. Therefore, we get f D by solving(21) same like the solution of problem (17) using Lagrange’smultiplier as, f D = ˆ R − F HRF a ( θ d )( F HRF a ( θ d )) H ˆ R − F HRF a ( θ d ) (23)As Q increases, ˆ R will converge to the true covariance matrix.However, the convergence of the Standard Capon Beamformer(SCB) is so slow. To resolve this problem, a widely used diag-onal loading method has been used in order to improve SCBperformance. The diagonal loading technique can improve theperformance of SCB by adding to the covariance matrix anidentity matrix scaled by a real weight called diagonal loadinglevel [44]. Assume ξ is the proposed diagonal loading level,the new digital beamformer vector can be given by, f D = (cid:0) ˆ R + ξ I (cid:1) − F HRF a ( θ d )( F HRF a ( θ d )) H (cid:0) ˆ R + ξ I (cid:1) − F HRF a ( θ d ) (24)The diagonal loading level ξ has a considerable effect onthe performance of SCB; therefore, several methods have been proposed to optimize the diagonal loading level. One of themost effective and simple methods is the spatial matched filter(SMF) method [45]. The loading level of SMF is given by, ξ SMF = Q k ˆ a ( θ d ) X k = ˆ a H ( θ d ) ˆ R x ˆ a ( θ d ) , (25)where ˆ a ( θ d ) = a ( θ d ) k a ( θ d ) k is the normalized steering vector, andˆ R x = Q xx H is the estimation covariance matrix of the receivedsignal.Although the above-presented complex weights’ methodsand other similar methods are very impressive mathematicallyand fast; however, it requires an expensive receiver makingthem impractical. Moreover, these algorithms get trapped inlocal minima. Consequently, we propose an efficient meta-heuristic optimization algorithm in order to optimize thedigital beamformer weights using only the phase, where asshown in Eq. (7), digital beamformer vector can be adjustedusing amplitude only (i. e., a , a ,..., a K ), phase only (i. e., e j α , e j α , . . . , e j α K ), or complex. B. Design of the analog weight vectors
According to the unitary constraint, the cost function givenin (16) can further be simplified as, minimize F RF CF = f HD F HRF A i A Hi F RF f D + σ f HD f D P d s . t . f HD F HRF a ( θ d ) = , (26)where f D is given by (24), therefore, the second term inthe numerator and the denominator are constant, thus, theoptimization problem in (26) can be reformulated as, minimize θ CF = (cid:12)(cid:12) f HD F HRF A i (cid:12)(cid:12) s . t . f HD F HRF a ( θ d ) = , (27)where θ is the searching angle in the range − π ≤ θ ≤ π ,which will be used to construct F RF , where, as shown in Eq.(3), the matrix F RF can be built using the corresponding phaseof the mth antenna of subarray l , α m , l . α m , l = πλ (( l − ) M + m + ) dsin θ (28)By adjusting the value of θ in (28), we can minimize thecost function in (27). This can be done using APALS withsufficiently fine grid of points in the above defined range of θ . To perform linear fine searching, we will use small enoughsearching step size ∆θ , where the range of θ is divided into N step sub-periods or points. Therefore, the angle θ in (28) isselected from the set, Θ ∈ (cid:8) − π , − π + ∆θ , . . . ., π (cid:9) .IV. P ROPOSED EVOLUTIONARY OPTIMIZATIONALGORITHM
Evolutionary optimization algorithms are also known asmeta-heuristic algorithms such as GA, PSO, and BA algo-rithms have become recently popular and very efficient thatcan easily solve many hard optimization problems. In thispaper, these algorithms have been proposed to design HADbeamforming by optimizing f D weight vector in order ofmaximizing the SINR. A. Bat algorithm
The BA is inspired from the advanced echolocation capa-bility of bats used to sense distance in order to avoid barrierand detect prey. It is a promising optimization algorithm thatcharacterized by robustness, accuracy, and fast convergencecompared to its predecessors such as genetic algorithm andPSO. In BA, bats fly randomly at position x ti with velocity v ti ,loudness A ti , frequency f i in a range [ f min , f max ] , and the pulserate of emission r ti in the range of [0, 1]. The new solutionsare obtained by updating the positions and velocities for thegroup of microbats at time step t which can be given by: f i = f min + ( f max − f min ) β (29) v ti = v t − i + (cid:0) x ti − x ∗ (cid:1) f (30) x ti = x t − i + v ti , (31)where β ∈ [ , ] is a random vector drawn from a uniformdistribution. x ∗ is the current global best location (solution)which is located after comparing all the solutions among allthe N microbats. f min and f max are chosen depending on thedomain size of the interested problem. When one solution ischosen from the current best solutions in local search, a newsolution for each microbat is produced locally utilizing randomwalk as: x new = x old + ε A t , (32)where ε ∈ [ , ] is a random number, A t is the averageloudness of all the microbats at time step t . Moreover, asiteration progress, the loudness A i and the rate r i of emissionpulse can be updated by, A t + i = α A ti , r t + i = r i [ − exp ( − γ t ) , (33)where α and γ are constants ( < α < , γ > ) which canbe tuned experimentally. After the iterations completed, theglobal best x ∗ will be found and used as the optimal result[46]. We summarize the basic steps of BA in algorithm 1. B. Improved bat algorithm
BA received a number of improvements attempts in recentyears in order to address the algorithm’s shortcomings suchas unstable results and being trapped in the local minima [41-43]. In this paper, we adopt the novel BA (NBA) proposed byXian-Bing Meng et al. [42]. In addition, more refinement hasbeen made in order to improve stability by tuning the inertiaweight using random variables to help the algorithm easilyskip out of the local minima [41]. The NBA algorithm differsfrom the classic BA in the following points,1) In classic BA, the bats search for their food in one habitat,while in NBA they can do that in different habitats.2) No consideration for the Doppler effects in BA, whilstall bats can compensate for Doppler effects in echoesaccording to the closeness of their targets.3) In NBA, the bats have quantum behavior instead ofmechanical behavior, so that a bat can access any positionin the entire search area with a specific probability.The bats ′ habitat selection depends on a stochastic decision,if a uniform random number R ∈ [ , ] is less than the Algorithm 1: proposed Hybrid Beamformer Based on BA Input: Initializing the bat population x i , v i , f i , A i , r i , thenumber of iterations N, the population size n, boundslimits Lb, Ub, and the desired and interferences angles θ d , θ j . for (i < Max number of iterations) do Find the current best solutions by updating velocitiesand locations, and adjusting frequency, Eqs.(29)-(31). if (rand > r i ) then Select a solution among the best solutions. Generating a local solution around the selectedbest solution. end if ((rand < A i )) and f ( x i ) < f ( x ∗ ) then Updating new solution. Increasing r i and reducing A i . end Ranking the bats and find the current best x ∗ i = i + end Output: global best, and the beamforming weights.threshold of the selection P ∈ [ , ] , bats will choose thequantum behavior instead of mechanical. In quantum behavior,bats can search in a wide range of habitats. If a food has beenfound in one of these habitats, others would come to it assoon as discovered. Thus, the positions of the bats can berepresented as, x t + i j = g tj + θ ∗ (cid:12)(cid:12)(cid:12) m tj − x ti j (cid:12)(cid:12)(cid:12) ∗ ln (cid:16) u ij (cid:17) , i f rand j () < P , g tj − θ ∗ (cid:12)(cid:12)(cid:12) m tj − x ti j (cid:12)(cid:12)(cid:12) ∗ ln (cid:16) u ij (cid:17) , otherwise , (34)where x ti j is the N bats’ positions in a D-dimensional space, i ∈ [ , . . ., N ] , j ∈ [ , . . ., D ] . θ is the contraction -expansioncoefficient, m tj is the mean of the individual’s best positionin a D-dimensional space at time step t , and u i j is uniformlydistributed in the range between 0 and 1. On the other side,with mechanical behavior of bats the frequency can changedue to the relative motion between the bat and the prey, so as,it must rely on the bats ′ compensation rates for the Dopplereffect. When the bat, prey, or both move away from each otherthe frequency decreased, and increased in the vice versa case.The new mathematical model can be represented as follows, f i = f min + ( f max − f min ) ∗ rand ( , ) (35) f , i , j = (cid:16) c + v ti , j (cid:17) c + v ti , j ∗ f i , j ∗ + C i ∗ (cid:16) g tj − x ti , j (cid:17)(cid:12)(cid:12)(cid:12) g tj − x ti , j (cid:12)(cid:12)(cid:12) + ε (36) v t + i , j = w ∗ v ti , j + ( g tj − x ti , j ) ∗ f i , j (37) x t + i , j = x ti , j + v ti , j , (38)where, C is a positive number represents the compensationrates, ε is the smallest constant number in computer used toavoid zero-division error, c is the speed of signal in the air( c = m / s ), and w is an inertia weight parameter that can Algorithm 2: proposed Hybrid Beamformer Based onImproved-BA Input: Initializing the bat population, the number ofiterations N, the population size n, bounds limits Lb, Ub,the desired and interferences angles θ d , θ j , theparameters of original BA, α , γ , f min , f max , A o , r o ,the parameters of IBA P , C , θ , G , σ . for (i < Max number of iterations) do if (rand ( , ) < P) then Generating new solutions using Eq. (34). else Generating new solutions using Eqs. (35)-(39). end if (rand > r i ) then Generating a local solution around the selectedbest solution using Eqs. (40)-(42). end Select a solution among the best solutions. Updating new solutions, the loudness and pulseemission rate using Eq. (33). Ranking the bats and find the current best g t . if the current best does not improve in G time step then Re-initialize the loudness A i and set temporarypulse rates r i as a uniform random numberbetween [0.85, 0.9]. end i = i + end Output: global best, and the beamforming weights.be adjusted in order to improve the stability of the algorithmby quickly jump out of the local minima, which is given by, w = µ min + ( µ max − µ min ) ∗ rand () + σ × randn () , (39)where, µ min , µ max are the minimum and maximum factor ofthe stochastic inertia weight, respectively. rand () , randn () arethe random number between 0 and 1, and random number ofstandard normal distribution, respectively. σ is the deviationbetween the stochastic inertia weight and its mean. With regardto local search, since it is required that the bat approachingthe prey silently as possible, bats would decrease the loudnessand increase the rate of the pulse emission. In addition, theloudness created by other bats in the vicinity should be alsotaken into consideration. The local generation new position foreach bat can be represented as follows, i f ( randn ( , ) > r i ) (40) x t + i , j = g tj ∗ (cid:0) + randn (cid:0) , σ (cid:1)(cid:1) (41) σ = (cid:12)(cid:12) A ti − A tmean (cid:12)(cid:12) + ε , (42)where randn ( , σ ) is a Gaussian distribution with 0 meanand variance σ . A tmean is the average loudness of all bats attime step t . Based on the above description, the basic stepsare summarized in algorithm 2. TABLE IP
ARAMETERS USED FOR DIFFERENT ALGORITHMS
Algorithm parametersPSO f min = , f max = , w ∈ [ . , . ] , C = . , C = . α = γ = . , f min = , f max = , A o ∈ [ , ] , r o ∈ [ , ] .Improved-BA α = γ = . , f min = , f max = . , A o ∈ [ , ] , r o ∈ [ , ] , G = , P ∈ [ . , . ] , C ∈ [ . , . ] , θ ∈ [ . , ] , µ min = . , µ max = . , σ = . -15 -10 -5 0 5 10 15 SNR of desired signal in dB -505101520253035 S I NR i n d B SCB [47]DL [44]DL - APALSSMF - APALSI-BA - APALSoptimal SINR
Fig. 2. SINR comparison of DL techniques and proposed Improved-BA inthe absence of mismatch, N=32, and Q=128, the number of population = 40for proposed algorithm
V. S
IMULATION RESULTS
In this section, the performance of Improved-BA (I-BA),DL, and DL-SMF in order to achieve maximum SINR andnulls placement in the desired directions using partial -connected HAD receive beamformer has been evaluated andcompared with other efficient fully digital conventional opti-mization algorithms, namely, SCB [47], DL technique [44].The simulation parameters used by the proposed algorithmand other evolutionary algorithms were presented in Table1. Other parameters set as: diagonal loading level ξ = θ d = o , and two interference signals arriving from angles θ k = o , − o . The SNR of the interference signals isassumed to be 15.Fig. 2 presents the output SINR versus input SNR of thedesired signal, in this examination, Q is set to be 128, and N to be 32. Fig. 2 compares RAB techniques that have beenused to optimize digital beamforming vector and the proposedevolutionary optimization algorithm that employed to optimizethe digital beamforming vector by controlling the phase only.Observing Fig. 2, we notice that our proposed evolutionaryoptimization technique has better performance compared toall other techniques. The hybrid I-BA - APALS has a bestperformance which is highly close to the optimal followed bySMF-APALS, which has a very close performance, while thetraditional SCB and DL methods have very poor performancefor higher ( SNR d ) , especially the SCB method. Fig. 3. The effects of snapshots size on the output SINR in the absenceof mismatch, N =
16, a) SINR versus
SNR d , b) Convergence characteristiccurves, the number of population = 40 Fig. 3 (a) and Fig. 4 (a) present the curves of SINR versusSNR of the desired signal ( SNR d ) for snapshots size 32 and128 using our proposed Improved-BA (I-BA) algorithm andcompared the results with DL technique and SCB when theantenna array size equal 16 and 32, respectively. The SNR ofinterference signals ( SNR i ) is chosen to be 15dB. Observingthese figures, we find that the SCB method has a very lowperformance compared with our proposed algorithm and DLtechnique as expected. The significant degradation of SCBshown in Fig. 4 (a) is because of the growing differencebetween the estimated array covariance matrix ˆ R and the truecovariance matrix as N increases. For the ( SNR d ) less than-5dB, we notice that the DL technique and our proposedalgorithm have almost the same performance, however, for TABLE IIC
OMPARISON THE RESULTS OF NULLS DEPTH FOR DIFFERENT ALGORITHMS , WHEN THE NUMBER OF ANTENNA ARRAY ELEMENTS EQUAL
AND
Q=128Algorithm Nulls Depth in dB Optimized angle ( θ ) Optimized digital beamformer phases ( α , α , α , α ) − o o SCB [47] -18.2325 -19.1922 − −
DL [44] -23.2880 -21.2294 − −
DL-APALS -36.3780 -19.9926 1.0367e-04 − SMF-APALS -36.3803 -21.9080 1.0367e-04 − I-BA-APALS -36.3947 -37.8852 1.0367e-04 0.2285, 0.2618, 0.0029, 0.0362TABLE IIIC
OMPARISON THE RESULTS OF NULLS DEPTH FOR DIFFERENT ALGORITHMS , WHEN THE NUMBER OF ANTENNA ARRAY ELEMENTS EQUAL
AND
Q=128Algorithm Nulls Depth in dB Optimized angle ( θ ) Optimized digital beamformer phases ( α , α , α , α ) − o o SCB [47] -19.3760 -24.7878 − −
DL [44] -26.2609 -22.0527 − −
DL-APALS -36.3777 -20.0879 1.0367e-04 − SMF-APALS -36.3835 -24.0793 1.0367e-04 − I-BA-APALS -36.3789 -37.9193 1.0367e-04 0.2346, 0.0091, 0.2701, 0.0445Fig. 4. The effects of snapshots size on the output SINR in the absenceof mismatch, N =
32, a) SINR versus
SNR d , b) Convergence characteristiccurves, the number of population = 40 higher values of ( SNR d ) the performance of our proposedalgorithm is significantly better than DL technique. Therefore, -80 -60 -40 -20 0 20 40 60 80 Angle in degrees -60-50-40-30-20-100 N o r m a li z ed B ea m G a i n i n d B SMF- APALSDL- APALSI-BA- APALSDL [44]SCB [47]
Fig. 5. Radiation pattern with nulls placement at − o , and 60 o , the numberof antenna array elements equal 16, Q=128 -80 -60 -40 -20 0 20 40 60 80 Angle in degrees -70-60-50-40-30-20-100 N o r m a li z ed B ea m G a i n i n d B DL- APALSSMF- APALSI-BA- APALSDL [44]SCB [47]
Fig. 6. Radiation pattern with nulls placement at − o , and 60 o , the numberof antenna array elements equal 32, Q=128 Fig. 7. Convergence characteristics curves for varying
SNR d , N , and snapshots. the population size equal 40 for all algorithms and cases, (a) N =
16, snapshots= 128,
SNR d =
0, (b) N=32, snapshots = 200,
SNR d = −
15 , (c) N =
16, snapshots = 128,
SNR i = SNR d = −
15, (d) N=32, snapshots = 200,
SNR i = SNR d =
10 20 30 40 50 60
Antenna Array Size (N) -10-505101520253035 S I NR i n d B DL method, SNRd=15dBDL method, SNRd=10dBDL method, SNRd=-5dBProposed SMF-APALS, SNRd=15dBProposed SMF-APALS, SNRd=10dBProposed SMF-APALS, SNRd=-5dB
Fig. 8. The effects of varying the number of antennas into SINR when theSNR of interference signals are fixed (
SNR i =15 dB) for different SNR d ,snapshots =128 our proposed algorithm has a better ability to minimizeinterference. On the other hand, Fig. 3 (a) and Fig. 4 (a)demonstrate the effect of the number of snapshots to the performance of different algorithms, where the performance isimproved considerably as the number of snapshots increasedfor SCB and DL techniques, whereas, there is very littleeffect on the performance of our proposed algorithm withsignificantly lower snapshots size.The optimized beamforming gains enjoined with two nullsat − o , and 60 o for a number of antenna array elements 16and 32 have been given in Fig. 5 and Fig. 6, respectively. The SNR d and SNR i are chosen to be -5dB and 15dB, respectively.The hybrid methods I-BA-APALS, SMF-APALS, and DL-APALS, in addition to the traditional techniques SCB [47]and DL [44], are used to synthesize a linear array. It can beseen obviously that the proposed I-BA-APALS algorithm hasbetter ability to mitigate the beam gain by at least -36dB atthe predefined locations of interference signals compared toother methods as shown in Table 2 and Table 3. a) Convergence characteristics: Fig. 7 shows a compar-ative convergence characteristic graphs obtained using BA,PSO, and proposed algorithm. All algorithms are used to solvethe objective function given in (27) with a different numberof antennas, snapshot size,
SNR i , and SNR d . In Fig. 7 (a)and Fig. 7 (b), the number of antenna array elements are set -15 -10 -5 0 5 10 15 SNR of desired signal in dB -10-5051015202530 S I NR i n d B optimal SINRSCB [47]DL [44]DL-APALSSMF-APALSI-BA-APALS Fig. 9. Output SINR versus input SNR of the desired signal, N =
16, andQ=200, in the presence of DOA mismatches to be 16 and 32, whereas, the snapshots size are set to be128 and 200, respectively. The
SNR i is chosen to be 15, and SNR d is set to be 0 and -15, respectively. Observing thesecurves, it is shown that the BA gets local optimal solution earlyin both figures; however, our proposed algorithm has betterability to jump from local minima in both cases. AlthoughPSO has close optimal solution to I-BA in Fig. 7 (a), however,it has poor performance for higher antenna array size and weak SNR d . The comparison of average convergence curves of theproposed algorithm is illustrated in Fig. 7 (c) and Fig. 7 (d)for 20 runs, which shows a quite good stability.Fig. 8 illustrates the effect of antenna array size on theperformance of hybrid beamformer proposed by us. From Fig.8, it is shown that the performance of the proposed beam-former based on SMF-APALS is gradually improved withincreasing the number of antennas. As noticed from the curves,the different values of the received SNR of the desired signalalmost have the same impact on the performance improvementfor our proposed algorithm. On the other hand, while ourproposed algorithm showed important improvement on theperformance as antenna array size increased, DL method hasno significant impact on the performance for higher values of SNR d . b) The impact of DOA mismatches: Finally, Fig. 9 ex-amines the effect of DOA mismatch into the performanceof proposed robust adaptive methods, where, the number ofantenna array elements and snapshot size are set to be 16and 200, respectively. The maximum estimation DOA anglemismatch is chosen to be 3 o . Fig. 9 further compares theperformance of the classic SCB, and DL methods with thehybrid, I-BA-APALS, DL- APALS, and SMF- APALS pro-posed techniques in the presence of DOA mismatch, where theproposed I-BA-APALS showed better robustness performanceto the DOA mismatch followed by SMF- APALS with veryclose performance. This because the proposed I-BA-APALShas good flexibility, therefore, it has a less impact by the DOAmismatch, the number of antenna array elements, and snapshotsize. VI. C ONCLUSION
In this paper, we have proposed a hybrid beamforming sys-tem based on three hybrid adaptive beamforming techniques,namely, DL-APALS, SMF-APALS, and I-BA-APALS with theobjective of maximizing SINR. The first two methods usingonly a linear searching to obtain the optimal solution, where,the optimum digital beamformer vector is obtained by closed-form solution, and the linear searching is employed to optimizethe analog beamformer vectors. In the last hybrid scheme,we further proposed an efficient nature-inspired optimizationtechnique, that is, I-BA with aim of optimizing the digitalbeamforming vector, which gave better global optima, conver-gence speed, and stability performance as compared to BA,and PSO. With the aid of simulation and analysis, we find thatthe performance of the traditional adaptive beamformers, i.e.,SCB, and DL techniques have serious degradation when theinput SNR of the desired signal is large. By combining theDL, SMF, and I-BA methods with linear searching schemeto optimize the total beamforming vector, we got a betterperformance by I-BA-APALS in terms of output SINR, nullsdepth, and robustness against DOA mismatch followed bySMF-APALS. On the other hand, since the I-BA-APALSdepends on the phase-only as a controlling parameter; resultingin an inexpensive receiver making it convenient for practicalimplementation. This makes our proposed beamformer ap-propriate for future many applications that are likely to besusceptible to interference such as future 5G wireless cellularcommunication systems, UAVs, and intelligent transportation.VII. A
CKNOWLEDGMENTS
This work was supported in part by the National NaturalScience Foundation of China (Nos. 61771244, 61701234,61501238, 61702258, 61472190, and 61271230), in part bythe Open Research Fund of National Key Laboratory ofElectromagnetic Environment, China Research Institute of Ra-diowave Propagation (No. 201500013), in part by the JiangsuProvincial Science Foundation under Project BK20150786,in part by the Specially Appointed Professor Program inJiangsu Province, 2015, in part by the Fundamental ResearchFunds for the Central Universities under Grant 30916011205,and in part by the open research fund of National MobileCommunications Research Laboratory, Southeast University,China (Nos. 2017D04 and 2013D02).R
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