Numerical Optimization Based Efficient Beam Switching ... - IEEE Xplore

2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Wireless Communication Systems (WCS)

Numerical Optimization Based Efficient Beam Switching for 60GHz Millimeter-wave Communications Bin Li, Zheng Zhou, Haijun Zhang

A. Nallanathan

Beijing University of Posts and Telecommunications Beijing, China 100876 Email: [email protected]

Institute of Telecommunications King’s College London London, WC2R2LS, United Kingdom Email: [email protected]

Abstract—Beam-forming training (or beam-steering) in the 60GHz millimeter-wave system is formulated as a numerical optimization problem. Although numerical search is of special promise to this problem, as the objective function (i.e, the signalto-noise ratio) involves many local optimums, search failures cannot be avoided due to the greedy essence of classical Rosenbrock method. In order to address the great challenge, we develop an appealing direct numerical algorithm inspired by a probabilistic search mechanic. In contrast to classical schemes, numerical probes leading to reward improvement are always accepted, while search moves towards worse solution are permitted with a probability that is associated with an external temperature parameter. In order to enhance search performance of discrete space and exclude the exhaustive search-based neighbor exploitation, we further design a promising two-level annealing schedule. With the new probabilistic framework, the permission of movements to worse solutions is progressively restricted, which is controlled by two iterative parameters respectively corresponding to pattern probe and pattern move processes. Consequently, it may basically escape from local optimums. We then apply the new numerical search to 60GHz beam-switching. Experimental simulations validate this developed beam-switching scheme.

I.

I NTRODUCTION

The bandwidth demanding wireless personal area networks (WPANs) operating in 60GHz millimeter-wave frequency band have being gradually coming into picture [1][2], which is stimulated by the wireless reform of Gbps transmissions as well as a massive amount of unlicensed spectrum available at this frequency band. The first 60GHz WLAN/WPANs standardization is developed by the IEEE 802.15 WPANs millimeterwave alternative PHY Task Group (TG) 3c, which aims to a mandatory data rate 1.6Gbps and an optional transmission mode up to 3Gbps [3][4]. Recently, the contributions from the IEEE 802.11 TG ad further make 60GHz communication as an appealing spectral reuse candidate for wireless local area networks (WLANs) in a dual-band paradigm (i.e. 5GHz and 60GHz)[5]. It is no doubt that, for high-speed 60GHz wireless transmissions, an efficient beam-forming (BF) training or beamswitching is not only of significant to reduce protocol overhead (i.e. the number of preambles), but also is meaningful to minify power consumptions of 60GHz communications [6]. Relying on an exhaustive search, unfortunately, the existing popular two-stage scheme requires remarkable protocol overhead [4][5].

978-1-4673-2815-9/13/$31.00 ©2013 IEEE

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In order to develop an efficient BF training for 60GHz communications, from an appealing numerical optimization perspective, we formulate beam-switching as a discrete-space search problem. Within the two dimensional search space consisting of two pattern indexes from the prescribed beam codebook, it try to identify the optimal Tx-Rx beam-pair maximizing the receiving signal-to-noise ratio (SNR) by using as less protocol overhead (and energy) as possible. When the derivatives of reward function (i.e. the receiving SNR) are available as in most applications, the conjugate gradient can be utilized to solve this problem effectively. If the analytic objective function cannot be obtained as in the formulated beam-switching problem, the classical Rosenbrock numerical method may be properly employed. However, the encountered objective function (i.e., the receiving SNR) is non-smoothness and contains numerous local optimums, hence Rosenbrock search may be driven into local areas, leading to search failures [7]. We present an efficient BF training technique in the investigation, and the main contributions may be two-fold: (1) To overcome the defects of classical numerical search, we firstly introduce a simulated annealing (SA) mechanic to Rosenbrock method, and design a promising numerical optimization algorithm. By analogous to the physical annealing process [8], during the new numerical search, rather than only permitting the search moves to better solutions, the search probes toward worse rewards are also accepted with a probability [9]. The turbulence probability is specified by a timevarying parameter. In order to improve the performance of probabilistic search in finite-space and avoid locally exhaustive search, we further design a new two-level parameter adaptation scheme. With this promising numerical framework, the local optimums can be basically avoided by the new numerical method. (2) By formulating 60GHz BF training as a numerical optimization problem, we present an efficient beam-switching scheme based on the designed numerical algorithm. This new numerical scheme can implicitly exploit local gradient information of the involved objective function, resulting in constructive search moves. Owing to the integrated probabilistic turbulence mechanic and the enhanced search ability, the proposed algorithm may basically ignore local optimums, and the complete success of beam-search can be achieved.

2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Wireless Communication Systems (WCS)

Simulation results demonstrate the advantages of the suggested beam-switching scheme over the other existing schemes, which may provide great promise to 60GHz millimeter-wave communications. The rest of this paper is outlined as follows. The next section will give a detailed beam-switching system model. Subsequently, the numerical optimization based beam-switching scheme is developed in Section 3. In Section 4, numerical simulation and performance evaluation are presented. Finally, we conclude this investigation in Section 5. II.

B EAM - FORMING IN 60GH Z COMMUNICATIONS

A. Codebook Based Beam Forming In 60GHz communications, a feasible way to generate beams is to simply shift the radio-frequency (RF) phases [35][10]. As is reported by [10], the beam codebook is usually defined by an N × K matrix, W(N, K), which is specified by the elements number N and the desired number of beams K. Each column of W corresponds to the phase rotations of elements, which can generate a specific beam pattern. For 60GHz WPANs, the (n, k)th elements of W(N, K) is given by: (N,K)

wn,k with

( fn,k = f loor

= j fn,k

(1)

n × mod (k + K/4, K) K/4

Targeting the reduced protocol overhead and energy consumption, a two-stage beam-switching scheme has recently been adopted by the undergoing 60GHz standardizations, i.e. IEEE 802.15.3c and 802.11ad [4][5], which can be substantially divided into the sector level search (SLS) and the normal beam search. (1)

′

(sector)

(1)

(sector)

Let Nt = Nt and Nr = Nr be the number of sector beams (i.e., sector-level codebook size) of (beam) transceiver and receiver, respectively, while Nt = 2Nt (beam) and Nr = 2Nr be the number of the normal beams (i.e. beam-level codebook size) of the transceiver and receiver, respectively. Usually, the number of normal beams (2) corresponding to one sector can be determined by Nt = (beam) (sector) (2) (beam) (sector) Nt /Nt and Nr = Nr /Nr . Thus, the total number of preambles, with which the search complexity of the two-step scheme can be measured [12], is given by: (1)

(2)

× Nr(1) + Nt × Nr(2) (5) [ ( )2 ] (1) (1) = Nt × Nr(1) 1 + 4Nt Nr / Nt × Nr(1)

N3c = Nt (2)

For elaboration simplicity, we employ the 1-D uniform spaced antenna array in the following analysis. Given the pattern codebook W, the array factor corresponding to the kth beam steering vector can be written by: Aθ,k (θ′ ) =

C. Prevous Works

)

Here, f loor(x) denotes the biggest integer smaller than or equal to x, while mod(x, y) refers to the modular operation on x with respect to y. Practically, K and M should meet the constraint K = 2M [10].

N −1 ∑

where L is the number of paths (or clusters) and Kl is number of sub-paths of the lth cluster. αk,l = |αk,l |exp(jϕk,l ) corresponds to the complex channel gain of the kth sub-path of the lth cluster, with i.i.d random phase ϕk,l distributed over U [0, 2π), τk,l is the time delay, θk,l and ϕk,l are the angle of arrival (AoA) and angle of departure, respectively [11].

From (5), it is noted that although such a two-stage beamswitching can reduce the number of preamble transmissions, the search complexity still has a order of O(Nt × Nr ) ∼ O(N 2 ). In other words, with the further increasing of antenna elements, the required overhead and consumed energy may still easily become unaffordable. III.

N UMERICAL O PTIMIZATION BASED B EAM - FORMING

where d denotes the spacing distance between two adjacent elements, and λ is the wavelength. The normal direction of antenna array with respect to x-axis is denoted by θ, which is related with the random gesture of array and remains perpendicular to the orientation of linear array elements, with the codebook index of k. θ′ accounts for signal arrival direction with respect to x-axis.

In this investigation, we will treat 60GHz beam-switching as a global optimization problem in 2-D plane formed by (p, q). In contrast to existing schemes, a much competitive way is thereby to search through the 2-D beam-indexes plane within a numerical framework, in which each search could contribute to the final solution. The reward function (the receiving SNR) is denoted by f (p, q), and the objective is to identify the best beam-pair maximizing this reward. In practice, the global optimum is unimodal around the best beam-pair (popt , qopt ). Notice that, however there may exist many local optimums.

B. Channel Modeling

A. Problem Formulation

wn,k ej2πn(d/λ)cos(θ−θ )

(3)

n=0

Given the typical short-range indoor scenes, wireless propagations in 60GHz WPANs may exhibit the intensive multipath phenomenon. The popular channel model is generally based on the modified Saleh-Valenzuela (S-V) indoor modeling [11], with the channel impulse response (CIR) given by:

SN R =

h(t, θ, ϕ) = α0,0 δ(θ − α0,0 )δ(ϕ − ϕ0,0 )δ(t − τ0,0 )+ Kl L−1 ∑∑

αk,l δ(θ − αk,l )δ(ϕ − ϕk,l )δ(t − τk,l ),

It is obvious that integration on both time (i.e. time of arrival, ToA) and angle (i.e. AoA) produces the total received signal power. Thus, the SNR in receiver is expressed as: L−1 l −1 ∑ K∑ 1 2 × |αk,l Ap,ϕ (ϕk,l )Aq,φ (φk,l )| σn2

(6)

l=0 k=0

(4)

l=1 k=1

595

where Ap,ϕ (ϕk,l ) denotes the array gain of receiving beam with the index of p in the direction of (k, l)th path, Aq,φ (φk,l )

2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Wireless Communication Systems (WCS)

denotes the array gain of transceiving beam with the index of q in the direction of (k, l)th path. σn2 represents the power of additive while Gaussian noise (AWGN), which is assumed to be independent of the used beam-pair. As is noted from (6), the reward function is only related with the adopted beam-pair (p, q), and hence we represent it by f (p, q) = SN R(p, q). Traditionally, with the term ‘optimal beam-forming’ the beam steering vector w should be dynamically adjusted according to the provided CSI. However, such a priori information usually requires a dedicated feedback channel and also consumes considerable power, which greatly excites the codebook based BF. Accordingly, given the well-designed beam steering vectors W, BF actually aims to select the best beam-pair (popt , qopt ) from the predefined codebook, with the objective of maximizing the receiving SNR in (6). (popt , qopt ) = max SN R(p, q), (p,q)

p = 0, 1, . . . , K − 1; q = 0, 1, . . . , K − 1 (7) For the above formulated beam-forming problem based on the unconstrained numerical optimization, it is noted that the single agent essence of this problem, i.e., each reward value can only be derived from one single experiment, basically excludes the other popular biological optimization techniques, such as genetic algorithm (GA) and particle swarm optimization (PSO), which should rely on multi-agents conducting their search. B. Rosenbrock Search As the considered analytic reward function is practically unavailable, Rosenbrock numerical search may be of particular interest to the formulated beam-switching problem. Rosenbrock search essentially includes two phases, that is, probe moving and pattern moving [7]. 1) Probe Moving: Firstly, probe moving along the n orthogonal directions is performed. Then, the new start point and potential descent direction will be discovered. In our analysis, n = 2 for the 1-D antenna array. The initial solution is denoted by s(1) = [p(1) , q (1) ]. The initial move steps, corresponding to two search directions, are denoted by ξ1 and ξ2 , respectively. The magnification factor of move steps is µ > 1 and the shrinkage factor is ν ∈ (−1, 0). The initial direction d(1) and d(2) is given by: d(1) = (1, 0)T , d(2) = (0, 1)T

(8)

Notice that, the search directions d(i) (i = 1, 2) are supposed to be orthonormal vectors. The search start during each probe round is denoted by y(1) and the terminated solution by y(n+1) . Starting from the we firstly probe along ) ( initial solution, ) ( d(1) . If we have f y(1) + ξ1 d(1) ≥ f y(1) , then this probe operation is success and let: y(2) = y(1) + ξ1 d(1)

(9)

Also, the probe step is updated by using ξ1 = µξ1 , which leads to a much large movement in the next probe round. Otherwise,

596

( ) ( ) if f y(1) + ξ1 d(1) < f y(1) , this probe operation is failed, then we set y(2) = y(1)

(10)

In fact, after several probe successes, the move step will be enlarged. So, the probe moving in current round may have already advanced rashly which easily misses the optimal solution. Thus, a backward search is adopted in the next round probe. The probe step is thereby updated by ξ1 = νξ1 . After probing along one direction d(1) , the similar probe operations will be performed on the remaining direction d(2) . Finally, the probed solution y(n+1) can be obtained and one probe round is finished. Subsequently, we begin another round of probe operation. The new start solution is set to y(1) = y(n+1) . This probe moving iteration is terminated until all the direction probes have failed. Then, after the kth iteration, the obtained new solution can be given by s(k+1) = y(n+1) . 2) Pattern Moving: A new group of orthonormal search directions will be constructed after the probe moving stage. Following the probed results, we may firstly have: s(k+1) = s(k) +

n ∑

λi d(i)

(11)

i=1

where λi denotes the accumulative moving step along the ith (i) probe direction d∑ . Further manipulations on (11) result in (i) (k+1) (k) s −s = i=1,2 λi d . It is worthy observing that, from this formulation, the direction p = s(k+1) −s(k) may give an approaching descent direction [7]. During the next probe moving, the new established directions should take this descent direction fully into account. Thus, the new search directions can be defined by:  (j) λj = 0 d n p(j) = ∑ (12) (j) λj ̸= 0  λi d i=j

By utilizing the Gram-Schmidt orthogonalization procedure, the new constructed search directions can be further orthogonalizd.  (j) j=1 p (j) j−1 (i)T (j) ∑ q = (13) q p p(j) − q(i) j ≥ 2 q(i)T q(i) i=1

The orthonormal directions can be now derived: ¯(j) = q(j) /∥q(j) ∥ d

(14)

¯(j) It is obvious that these constructed search directions d are linearly independent quantities which also keep orthogonal with each other. Then, the probe moving and direction construction will be continued alternately, until the relative change in the solution drops below a pre-specified threshold η, i.e., ∥s(k+1) − s(k) ∥ ≤ η. Notice that, a bad initiation (p(1) , q (1) ) may easily drive the search into a local optimum, resulting in the unfruitful search. As the Rosenbrock search can only converge to local optimums, the numerical search based beam switching process

2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Wireless Communication Systems (WCS)

cannot be put advanced into practical use [6]. Due to the greedy essence of Rosenbrock search, even with the optimized parameters (µ, ν) the search failures are still inevitable, given the realistic objective function that involves lots of local optimums. C. Probabilistic Search In order to develop an efficient numerical optimization based BF training scheme, we should design a new numerical search by significantly enhancing the global search ability of classical direct methods while maintaining a relatively low complexity. In this section, we suggest a promising numerical method premised on a probabilistic framework. As is known, simulated annealing (SA) is a biological algorithm designed for finding the global minimum of a cost function that possesses several local minima [8]. As a generalization of the Monte-Carlo method, SA emulates the nature physical process in which the liquids freeze or metals recrystallize with a well-defined annealing process. Relying on an appealing probabilistic mechanic, SA can solve complex optimization problems with good quality. It is logical for SA to accept all state changes leading to energy (or cost) decrease. Nevertheless, it differs remarkably from classical methods (e.g. greedy search) by allowing the probabilistic acceptance of worse moves (i.e. energy increase), so that it can essentially escape from local minima in realistic applications. For the numerical beam-switching algorithm, the basic elements of SA search can be elaborated as follows. 1) Cost Function: During the considered beam-switching aiming to maximize the receiving SNR, the cost function is properly described by E(p, q) ∝ −

L−1 l −1 ∑ K∑

|αk,l Ap,ϕ (ϕk,l )Aq,φ (φk,l )|

2

(15)

l=0 k=0

2) Acceptance Criteria : The probability of transition from the current state y(i) to a new candidate state y(i+1) is specified by an acceptance probability P (E(i), E(i + 1), T ), which depends on two energy amplitudes E(i) = E(y(i) ) and E(i + 1) = E(y(i+1) ), as well as a global time-varying parameter (i.e. T ). Given the current temperature T , the probability of an increase in energy magnitude, i.e., ∆E = E(i+1)−E(i) > 0, can be given by P (E(i), E(i + 1), T ) ≃ exp(−∆E/kT )

(16)

where k is referred to as the Boltzmann’s constant [8]. It can be usually dropped directly from (16) for analysis simplicity, without affecting the search performance. When it comes to realistic optimization, SA firstly calculates the new energy E(i + 1) of the representative problem. If the energy has decreased, i.e. ∆E = E(i + 1) − E(i) < 0, the state transition (or search movement) from y(i) to y(i+1) is accepted immediately, and the system state will be changed to the new one. Otherwise, if the energy has increased, i.e. ∆E = E(i + 1) − E(i) > 0, the new state y(i+1) still may be permitted by using the probability returned by (16). The probability of accepting a worse state (i.e. E(i + 1) > E(i))

597

is given by exp(−∆E/T ), and the state transition happens if the following condition is satisfied. P (∆E, T ) ≥ γ

(17)

where γ is a random number between 0 and 1, i.e., γ ∼ U (0, 1]. From (16)-(17), it is expected that as the temperature T decreases, the probability of allowing energy increase is also reduced. If the temperature T approach zero (or small enough), then only the better moves will be accepted. 3) Temperature Schedule: The temperature parameter T is indispensable in order to control the ability of hill-climbing. At the beginning, T is initialized by a large value T0 approaching infinite, so that SA can initially wander around a broad region of search space. After a short period of movements or probes, a roughly lower (or higher) region will be discovered, and thereafter the freedom to wander should be restricted. In this analysis, we choose the initial temperature by (20) T0 = 10σ(C)

(18)

where σ(C) denotes the standard deviation of the reward function evaluated at T0 = ∞. As is indicated by [13], σ(C) and the corresponding expectation E(C) can be estimated by resorting to numerical approach. Other than a high initial temperature, a gradual reduction of temperature is also required as search proceeds. For the formulated objective function involves many local optimums, we resort to the standard geometric cooling schedule [8][9]. T (k) = T0 × κi , 0 < κ < 1

(19)

Here, i accounts for the updating iterator. As most empirical researches have shown, the decay parameter κ can be feasibly ranged in [0.1 0.99], with the better results being found in the lower range. As a compromise, however, the higher the value of κ is, the slower it will take to the decrement of temperature to the stopping criterion. D. New Numerical Algorithm for BF In practice, the simple accommodation of SA to Rosenbrock method still may easily fall into local optimums. By presenting a novel temperature schedule scheme and further properly accommodating SA mechanic into Rosenbrock method, we develop a more efficient numerical search algorithm. During this new numerical scheme, we apply the probabilistic acceptance criterion to the probe moving, and then construct the new search directions. Rather than only employing one temperature parameter as in classical SA algorithm [8], in the new method two external temperature parameters Tl and Tg are suggested, i.e., the local temperature and global temperature. These two control parameters correspond to the inner search loop (i.e. probe moving) and outer loop (i.e. pattern moving) of direct numerical algorithm, respectively. For a given outer iteration k global, we will initialize Tl = Tg during its inner iterations k local, and then update Tl = Tg × κkl local after probe moving. Subsequently, for two successive outer iterations k global + 1 and k global, we will update the global temperature by Tg (k global + 1) = Tg (k global) × κg .

2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Wireless Communication Systems (WCS)

( ) During the search process, if we have f y(1) + ξ1 d(1) ≥ ( ) f y(1) , this current probe operation is success and we will let y(2) = y(1) + ξ1 d(1) . Simultaneously, the probe step is updated by using ξ1 = µξ1 . ( ) ( ) Otherwise, if f y(1) + ξ1 d(1) < f y(1) , then this probe operation is failed. In this case, we will generate a random variable γ ∼ U [0, 1]. If the calculated acceptance probability, i.e., P = exp(∆E/Tl ), is larger than γ, we still allow this move and let y(2) = y(1) + ξ1 d(1) . Meanwhile, ξ1 is still updated by ξ1 = νξ1 . Else if P ≤ γ, the current search move will not be permitted. That is, we will let y(2) = y(1) , and notice that, probe step is now updated by ξ1 = νξ1 . After the above probabilistic acceptance, the local temperature Tl is further updated by using Tl (k local) = Tg × κkl local , and k local is then increased by 1.

Parameter Initialization Initialize k_local=1,Tl=Tg Probe Success?

local

× κkg

global

, 0 < κl , κg < 1.

Generate a random variable Magnify the probe step Yes

P is larger than

Update solution according to (9)

No

Shrink the probe step; update the Local Temperature Tl(k_local+1)=Tl(k_local) l

Magnify the probe step Update local counter k_local=k_local+1

Probe Completed?

No

Yes s(k+1)-s(k) < ?

Yes

No

Probe another direction Terminate the search process

Output the optimal beam index (popt,qopt)

Update the initial probe solution s(k+1)=y(n+1) Construct new probing direction according to (12)-(14)

(20)

Update the Global Temperature Tg(k_global+1)=Tg(k_global) g

Based on this developed new numerical algorithm, we may realize the beam switching in a much efficient way. The complete algorithm flow is also shown in Fig.1. IV.

Calculate the decrease in objective function and P

Update solution according to (9)

Once the termination condition on inner iterations has been satisfied, i.e., the probe moves of all directions failed, the new probe directions will be constructed according to (12)(14). Subsequently, the outer iterator will be updated, i.e., k global = k global + 1, and the global temperature Tg is decreased by using Tg (k global) = T0 × κkg global . Thus, the designed two-level annealing scheme can be summarized to T (k) = T0 × κkl

No

Yes

Update global counter k_global=k_global+1

E XPERIMENTS AND S IMULATIONS

Update the initial probe base point y(1)=y(n+1)

In this section, we will evaluate the performance of our suggested beam-switching algorithm. For analysis convenience, a 1-D uniform spaced antenna array is used during the following simulations and discussions. The beam codebook specified by the IEEE 802.15.3c TG is adopted in all the numerical experiments [10]. Channel condition is supposed to be quasistatic. The CM1 channel model regulated by IEEE 802.15.3c TG is used [11]. Except for a strong LOS component with a relative gain ∆K=24dB, the first-order NLOS MPCs are also considered. The number of NLOS clusters is L = 5, and the AoAs of NLOS MPCs (i.e. ϕk,l ) follow the zero-mean Laplacian distribution with a standard deviation of σϕ =20. For the new numerical search, the involving parameters are configured as follows: χ = 2.2, µ = 1.5, ν = −0.7, η1 = 0.1, η2 = 1, η = 1, κg = 0.90, κl = 0.85. In Fig.2, we have shown the search results of 100 independent realizations. In contrast to the greedy Rosenbrock method, the new numerical algorithm can generally discover the global optimum. Due to the specified termination mechanic of the new numerical search, the output solutions are sometimes near-optimal, in the sense that the outcome SNR is slightly smaller than the expected SNR by 0-2dB. It is clearly seen that the optimal (or near-optimal) Tx-Rx beam-pair has been identified via the designed numerical algorithm. The required search steps have been plotted in Fig.3. It is evaluated from the averaging on 100 independent realizations that the expected search steps are about 65.

598

Fig. 1.

Algorithm flow of the designed new numerical search method.

Without loss of generality, in the experiments the Tx and Rx antenna elements are both set to N , with the prescribed sector number of N (1) . Compared to the complete exhaustive search, from (5) the search complexity reduction is essentially attributed to the sector-level pre-search by introducing an 2 asymptotic factor N (1) . For different values of N (1) , the search complexity has been shown by Fig.4. As expected, there may exist an optimal sector number for different antennas, which may complicate the protocol flow to some extent in order to minimize the search steps. Meanwhile, notice that the accumulated steps still follow the complexity tendency of O(N 2 ). With the further increasing of elements, the search complexity may become uncontrollable, accompanying protocol overhead and energy consumption. The search complexity of our suggested scheme, which is based on the new numerical search, is also potted in Fig.4. Firstly, it is noted that, as the elements increase, the search complexity is gently increased, which is in contrast to the sharp growing of the IEEE.802.15.3c scheme. In particular, for the new scheme, the required steps are about 65 when N is 32. In comparison, the two-stage search scheme needs 128 times of preamble transmissions. When N =64, the two-stage search

2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Wireless Communication Systems (WCS)

29 (1)

IEEE 802.15.3c:N =2 (1)

IEEE 802.15.3c:N =4

28

(1)

IEEE 802.15.3c:N =6 Proposed scheme: average

27 3

10 Searching complexity

Received SNR

26

25

24

23

2

10

22 Searched SNR Target SNR Average searched SNR Average target SNR

21

20

10

20

30

40 50 60 Realization index

70

80

90

1

10

100

Fig. 2. The achieved reward by using new search algorithm. Notice that the number of antenna elements N is set to 32.

Fig. 4.

10

15

20

25

30 35 40 45 Antenna elements number

50

55

60

Performance evaluation of the presented beam-switching scheme.

400

R EFERENCES 350

[1]

300

Search steps

250

[2] 200

150

[3] 100

50

0

[4] 0

10

20

30

40 50 60 Realization index

70

80

90

100

The accumulated search steps of 100 independent algorithm Fig. 3. realizations. Notice that the number of antenna elements N is set to 32.

may even need 320 times. Apparently such a search complexity may greatly consume overhead and power. Nevertheless, the required search steps of our proposed algorithm, in the case of 64 elements, are only 125, which hence may show remarkable advantage over the other existing methods. V.

C ONCLUSION

[5]

[6]

[7] [8] [9]

In this paper, we present an efficient BF training algorithm for the emerging 60GHz millimeter-wave communications within an appealing optimization framework. In order to overcome the defects of traditional greedy numerical search, a more promising numerical optimization algorithm inspired by a probabilistic turbulence mechanic is further suggested. By designing a novel two-level temperature adaptation method, the developed numerical search may basically escape from local optimums. Experimental simulations validate our suggested beam-switching algorithm, which is superior to the existing BE training schemes. ACKNOWLEDGMENT

[10]

[11]

[12]

[13]

This work was supported by NSFC (61271180, 60972079, 60902046) and the ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2011-C1090-1111-0007).

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