Mutual Coupling Calibration for Multiuser Massive MIMO ... - IEEE Xplore

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 1, JANUARY 2016

Mutual Coupling Calibration for Multiuser Massive MIMO Systems Hao Wei, Dongming Wang, Member, IEEE, Huiling Zhu, Member, IEEE, Jiangzhou Wang, Senior Member, IEEE, Shaohui Sun, and Xiaohu You, Fellow, IEEE

Abstract—Massive multiple-input multiple-output (MIMO) is a promising technique to greatly increase the spectral efficiency and may be adopted by the next generation mobile communication systems. Base stations (BSs) equipped with large-scale antennas can serve multiple users simultaneously by exploiting the downlink precoding in time division duplex (TDD) mode. However, channel state information (CSI) of uplink transmissions cannot be simply used for downlink precoding, because the gain mismatches of the transceiver radio frequency (RF) circuits disable the channel reciprocity. In this paper, we focus on antenna calibration for massive MIMO systems with maximal ratio transmit (MRT) precoding to solve the channel nonreciprocity problem. A new calibration method, called mutual coupling calibration, is proposed by using the effect of mutual coupling between adjacent antennas. By exploiting this method, the BS can perform the calibration without extra hardware circuit and users’ involvement. We also build up the model of calibration error and derive the closed-form expressions of the ergodic sum-rates for evaluating the impact of calibration error on system performance. Simulation results verify the high calibration accuracy of the proposed method and show the significant improvement of system performance by performing antenna calibration. Index Terms—Antenna calibration, mutual coupling, channel reciprocity, massive MIMO.

I. I NTRODUCTION

M

ULTIPLE-ANTENNA technology, also named multiple-input multiple-output (MIMO), has been used in wireless communications. A MIMO system can provide diversity gain and spatial multiplexing gain by transmitting the signal through multiple antennas [1]. In multiuser MIMO (MU-MIMO) systems, the performance is improved further by exploiting the downlink precoding at the base station (BS) with

Manuscript received November 18, 2014; revised May 20, 2015; accepted August 25, 2015. Date of publication September 3, 2015; date of current version January 7, 2016. This work was supported in part by the National Basic Research Program of China (973 Program 2013CB336600), in part by the Natural Science Foundation of China (NSFC) under Grant 61221002 and Grant 61271205, in part by China High-Tech 863 Program under Grant 2014AA01A706, and in part by the Colleges and Universities in Jiangsu Province Plans to Graduate Research and Innovation KYLX15_0075. The associate editor coordinating the review of this paper and approving it for publication was Dr. Ryan J Pirkl. H. Wei, D. Wang, and X. You are with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China (e-mail: weihaoseu.edu.cn; wangdmseu.edu.cn; [email protected]). H. Zhu and J. Wang are with the School of Engineering and Digital Arts, University of Kent, Canterbury CT2 7NT, U.K. (e-mail: [email protected]; [email protected]). S. Sun is with the State Key Laboratory of Wireless Mobile Communications, Beijing 100191, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TWC.2015.2476467

the knowledge of downlink channel state information (CSI) [2]. Hence, it is very important for a BS to obtain the downlink CSI accurately. As an innovative scaling-up, a large number of antennas are equipped at the BS, known as massive MIMO technique [3]–[5]. By exploitation of excess spatial degrees of freedom, massive MIMO can greatly improve the spectral efficiency and energy efficiency, and it has become a promising technique for the next generation of wireless communication systems [6]. For frequency division duplex (FDD) systems, the BS transmits the pilot symbols to the user equipment (UE), then the UE estimates downlink CSI and feeds it back to the BS [7]–[9]. Since the numbers of both the downlink pilots and the channel responses each UE must estimate are proportional to the number of antennas at the BS, the overhead of the downlink pilots and the feedback of downlink CSI becomes unacceptable in the massive MIMO systems [6]. On the other hand, time division duplex (TDD) is more suitable for the communication scheme in massive MIMO systems, thanks to the channel reciprocity. Based on the electromagnetic theory, transmission signals experience the same fading in the downlink and uplink channels if the time interval is less than the channel coherence time [10]. Thus, the BS can estimate CSI for both uplink and downlink channels through uplink pilots. However, in practice, the whole channel is made up of not only the wireless propagation channel, but also the transceiver radio frequency (RF) circuits at both sides of the link [11]. Normally, RF circuits consist of the antennas, RF mixers, filters, analog to digital (A/D) converters, power amplifier, etc., and are highly related to the temperature and humidity of the environment [12]. Although the wireless propagation channel is reciprocal, the RF gains of transceiver circuits for each antenna are usually not symmetric. The mismatches disable the reciprocity of the whole channel. Therefore, antenna calibration should be performed to keep reciprocity for TDD systems [13]. Recently, antenna calibration has attracted much attention. Since the RF gain of each antenna can be considered as constant in hours or even days [14]–[16], the antenna calibration needs to be performed only once within a long time. There are two types of calibration methods. The first type is the hardware-circuit calibration method. By introducing extra calibration circuits, the BS exploits the directional couplers and multiple switches to connect the transmit circuits of each antenna with the receive circuits of other antennas, and the self-transmitted signals are used as the calibration signals [14]. The transceiver of each antenna can also be connected with one of the other antennas by attenuators and multiple switches. The BS selects one

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WEI et al.: MUTUAL COUPLING CALIBRATION FOR MULTIUSER MASSIVE MIMO SYSTEMS

antenna as the reference antenna and measures the calibration coefficients between the reference antenna and the other antennas [17]. In some cases, the hardware-circuit calibration method is still used for massive MIMO systems [18], [19]. The second type of calibration methods is the signal-space calibration method. Contrarily to the methods relying on the hardware circuits, the calibration procedure takes place entirely in the signal space. In [12], total least squares based calibration was proposed for MU-MIMO systems. However, this method is based on exchanging the calibration signals between the transmitter and the receiver, which is infeasible for massive MIMO systems because of the heavy feedback. According to the analysis and simulations in [20], [21], we only need to perform calibration at the transmitter since the RF mismatches of the UE have a negligible impact on the system performance. Then, more feasible calibration methods: the dot-division method [22] and the on-the-air method [16], [13], were presented for coordinated multi-point (CoMP) systems. One or several calibration supporters (can also be UEs) with good channel condition are chosen to estimate and feedback the downlink CSI to the BS. From the above, the calibration accuracy of hardware-circuit calibration method highly depends on the RF circuits [14], [17]. In massive MIMO systems, the calibration hardware circuits will become very complex and expensive, since a huge number of directional couplers and dividers are required to be introduced. Furthermore, the calibration circuits may bring extra non-reciprocity, because the channel doesn’t contain the calibration circuits when the BS communicates with the UEs [17]. The calibration accuracy of the dot-division method [22] and the on-the-air method [16] mainly depends on the channel quality between the BS and the UE which feedbacks the downlink CSI. However, both these calibration methods are infeasible for the massive MIMO systems due to large increase of feedback overhead. Actually, UEs are much desirable to be not involved in the calibration procedure. Thus, to exclude UEs from the calibration procedure, the self-calibration method was proposed in [21] for each BS in CoMP systems. By exploiting the statistics of the ambiguity factors between uplink and downlink channels, an innovative precoding technique called robust signal-to-leakage-plus-noise ratio (RSLNR) precoding was presented to improve the performance of CoMP systems [23], [24]. Extending the self-calibration method to massive MIMO systems, a novel calibration method, referred to as Argos method, was presented in [15]. Instead of the feedback from UEs, the Argos method only involves the antennas of the BS and exchanges the calibration pilot signals with a reference antenna. However, the Argos method is very sensitive to the placement of the reference antenna, and the system performance cannot keep stable unless all the other antennas have very good signal-to-noise ratio (SNR) to the reference antenna. So far, most calibration methods are presented for the zero forcing (ZF) precoding, of which the processing complexity is high due to the pseudo-inverse calculation of the channel matrix [25]. Maximal ratio transmit (MRT), also called conjugate beamforming, is a simple linear precoding technique and suitable for massive MIMO systems because of its high feasibility [3], [25]. To the best knowledge of the authors, there have been no calibration methods for MRT precoding. Thus,

607

in this paper, we focus on the antenna calibration for massive MIMO systems with MRT precoding and investigate the impact of RF mismatches at both the BS and the UEs on the system performance. When hundreds of antennas are deployed at the BS, the distance between adjacent antennas becomes small, generally less than half a wavelength [4]. When two antennas are near each other, whether one and/or both are transmitting or receiving, some of the energy that is primarily intended for one antenna ends up at the other. This electromagnetic interaction between the antennas in an antenna array is called mutual coupling [26]. The less the distance between the two antennas, the stronger the mutual coupling effect becomes [27]. The inherent mutual coupling in an antenna array was utilized to calibrate and predict the radiation patterns of a phased array [28]. Hence, we use the effect of mutual coupling to define the channel between the co-located BS’s antennas, which was not investigated in [15], [21]. Then, we propose a new calibration method which is called mutual coupling calibration. By utilizing the strong mutual coupling between adjacent antennas, the BS can perform antenna calibration without extra hardware circuits and UEs’ involvement and overcome the instability of the Argos method. Furthermore, we build up the model of calibration error which is caused by thermal noise, and derive the closed-form expressions of the ergodic sum-rates for evaluating the impact of calibration error on system performance. The rest of this paper is organized as follows. Firstly, the general model of RF gain is given for multiuser massive MIMO system, and the impact of RF mismatches on system performance is investigated in Section II. Secondly, in Section III, a new calibration method called mutual coupling calibration is proposed for MRT precoding, the model of calibration error is built up and the closed-form expressions of the ergodic sum-rates are derived for evaluating the impact of calibration error on system performance. Then, simulation results and discussions are presented in Section IV. Finally, conclusions are summarized in Section V. The notation adopted in this paper conforms to the following convention. Vectors are denoted in lower case bold: x. Matrices are upper case bold: A. I M denotes the identity matrix of M × M. (·)∗ , (·)T and (·)H represent conjugate, transpose, and Hermitian transpose, respectively. Tr ( A) is the trace of A. The operator E (·) denotes expectation. N μ, σ 2 stands for normal distribution with mean μ and variance σ 2 . U (a, b) stands for uniform distribution on the interval [a, b]. II. S YSTEM M ODEL AND F UNDAMENTALS In this section, the downlink transmission of a massive MIMO system with MRT precoding is considered. The impact of RF mismatches at both the BS and the UEs on the system performance is investigated. A. System Model There is one BS with M antennas in the central of the cell, which serves K single-antenna UEs. M K is assumed for the massive MIMO systems. In practice, the whole channel consists of not only the wireless propagation channel, but also the

608


Fig. 1. System model of the RF mismatches.

transceiver RF circuits of antennas at both sides of the link, which is depicted in Fig. 1. As shown in Fig. 1, each antenna of the BS and the UE has a transmit RF and a receive RF module. C BS,t and C BS,r denote transmit and receive RF matrix of the BS, respectively. C UE,t and C UE,r denote transmit and receive RF matrix of the UE, respectively. All of these matrices are diagonal. Define C BS,t = diag tBS,1 , . . . , tBS,m , . . . , tBS,M , C BS,r = diag rBS,1 , . . . , rBS,m , . . . , rBS,M , C UE,t = diag tUE,1 , . . . , tUE,k , . . . , tUE,K , C UE,r = diag rUE,1 , . . . , rUE,k , . . . , rUE,K ,

(1) (2) (3) (4)

where tBS,m , rBS,m (m = 1, . . . , M) and tUE,k , rUE,k (k = 1, . . . , K ) are the RF gains characterized as follows t tBS,m = tBS,m eιφBS,m , r rBS,m = rBS,m eιφBS,m , t tUE,k = tUE,k eιφUE,k , r rUE,k = rUE,k eιφUE,k .

G UL = C BS,r H T C UE,t G DL = C UE,r H C BS,t .

(5) (6) (7) (8)

Here, the amplitudes of the RF gains are assumed to be of lognormal distribution [20], [21], and the phases are assumed to be of uniform distribution [20], [21], [29]. Therefore, we have the following notations: 2 t ln tBS,m ∼ N 0, δBS,t , φBS,m ∼ U −θBS,t , θBS,t , 2 r ln rBS,m ∼ N 0, δBS,r , φBS,m ∼ U −θBS,r , θBS,r , 2 t ln tUE,k ∼ N 0, δUE,t , φUE,k ∼ U −θUE,t , θUE,t , 2 r ln rUE,k ∼ N 0, δUE,r , φUE,k ∼ U −θUE,r , θUE,r . Considering RF gains, we characterize the uplink and downlink channel matrices as T G UL = C BS,r R1/2 r H C UE,t

G DL = C UE,r H R1/2 t C BS,t ,

where H ∈ C K ×M represents the small-scale channel matrix, and each element h i j (i = 1, . . . , K ; j = 1, . . . , M) is a zero mean circularly symmetric complex Gaussian random variable of variance 1/2 per dimension, that is h i j ∼ CN (0, 1). Rt and Rr denote the transmit and receive spatial correlation matrices at the BS, respectively. The spatial correlation at the UE is not considered, since only one antenna at each UE and the distance between arbitrary two UEs is usually far enough. It is known that, both the wireless propagation channel and the spatial correlation obey the principle of reciprocity, that is 1/2 T T . Thus, in order to focus on Rt = RTr and H R1/2 t = Rr H the RF mismatches and for ease of exposition, we ignore the spatial correlation to perform analysis for uncorrelated channel matrices. Then, (9) is simplified as

(9)

(10)

From (10), it can be seen that, due to the RF mismatches, the whole channel is obviously not reciprocal, i.e. G DL = G TUL .

B. Impact of RF Mismatches on the System Performance For clarity of analysis, estimation error is ignored for uplink CSI. Then, by MRT precoding, the overall downlink signals at the UEs are written as y = βmis G DL G ∗UL x + n = βmis C UE,r H C BS,t C ∗BS,r H H C ∗UE,t x + n

(11)

where βmis =

1 Tr G TUL G ∗UL

(12)

is a scaling factor to satisfy the transmit power constraint. y = [y1 , . . . , y K ]T is the discrete-time received signal vector, x = transmitted to each UE with [x1 , . . . , x K ]T is the signal vector the power constraint E xk xk∗ = P. n is the complex additive white Gaussian noise (AWGN) vector, in which the elements are independent and identically distributed (i.i.d.) complex


Gaussian random variables with zero mean and variance σn2 . The received signal of the kth UE is given by yk = βmisrUE,k hk C BS,t C ∗BS,r hH k tUE,k x k + βmisrUE,k

K

hk C BS,t C ∗BS,r hiH tUE,i xi + n k , (13)

609

where ρ = P/σn2 . At high SNR, since noise is ignored, (17) can be simplified as tUE,k 2 sinc2 θBS,t sinc2 θBS,r mis · . (18) γk = M · 2 2 K eδBS,t +δBS,r tUE,i 2 i=1,i=k

i=1,i=k

where hk = [h k1 , . . . , h km , . . . h k M ] is the kth row-vector of channel matrix H. When the number of BS antennas is large i.e. M → ∞, the column vectors of H are asymptotically orthogonal. Thus, from [3], [30], we have 1 a.s. 1 * hk C BS,r C *BS,r hH Tr C − → C BS,r k BS,r M M 1 1 a.s. * hk C BS,t C *BS,r hH Tr C − → C BS,t k BS,r M M 1 a.s. hk C BS,t C *BS,r hiH −→ 0, (k = i) M 2 1 a.s. 1 Tr C BS,t C *BS,t C BS,r C *BS,r , hk C BS,t C *BS,r hiH −→ M M (14) (k = i) ,

K

E R mis = E Rkmis = K · E Rkmis ,

and the ergodic rate of the kth UE is E Rkmis = E log 1 + γkmis ⎡ ⎛ ⎢ ⎜ ⎢ ⎜ ⎜ = E⎢ ⎢log ⎜1 + M · ⎣ ⎝

2 2 = E rBS,m = e2δBS,r ,

tUE,k 2 K

tUE,i 2 ⎞⎤

⎟⎥ sinc2 θtBS sinc2 θrBS ⎟⎥ ⎟⎥ . · 2 +δ 2 ⎟⎥ δBS,t BS,r ⎠⎦ e

1 Tr C BS,r C *BS,r M 1 Tr C BS,t C *BS,r lim M→∞ M ∗ = E tBS,m rBS,m = E tBS,m E rBS,m 2 2 = eδBS,t + δBS,r sinc2 θBS,t sinc2 θBS,r ,

M→∞

(19)

k=1

i=1,i=k

where lim

Then, the ergodic sum-rates of all UEs with RF mismatches are given by

(20)

For simplicity of analysis, approximations are made for ergodic sum-rates in the high SNR regime. Since ln (1 + e x ) is a convex function and using Jensen’s inequality [31] E log 1 + eln x ≥ log 1 + eE[ln x] ,

1 Tr C BS,t C *BS,t C BS,r C *BS,r M→∞ M 2 2 = E tBS,m rBS,m 2 2 = E tBS,m E rBS,m lim

we have E Rkmis

= e2δBS,t + 2δBS,r . 2

Thus, one obtains βmis

2

=

(15)

1 2

M · e2δBS,r ·

K tUE,k 2

.

(16)

k=1

Then, the signal-to-interference-plus-noise-ratio (SINR) of the kth UE with RF mismatches is γkmis

=

rUE,k 2 ρ K tUE,i 2

K i=1,i=k

2 tUE,i 2 e2δBS,t +1

eδBS,t +δBS,r ⎧ ⎡ ⎛ ⎞⎤⎫⎤ K ⎬ ⎨

2 2 tUE,i ⎠⎦ ⎦ − E ⎣ln ⎝ · exp E ln tUE,k ⎭ ⎩ i=1,i=k sinc2 θtBS sinc2 θrBS = log 1 + M · 2 2 eδBS,t +δBS,r ⎧ ⎞⎤⎫⎤ ⎡ ⎛ K ⎬ ⎨

2 tUE,i ⎠⎦ ⎦ . · exp −E ⎣ln ⎝ ⎭ ⎩ 2

2

i=1,i=k

rUE,k 2 2 −δ 2 2 tUE,k 2 eδBS,t BS,r sinc2 θ Mρ BS,t sinc θBS,r K tUE,i 2 i=1

≥ log 1 + M ·

sinc2 θtBS sinc2 θrBS

(21)

,

i=1

(17)

Note that a sum of several log-normal random variables can be approximated by a log-normal random variable, which is called the Fenton-Wilkinson method [32]. Defining ⎞ ⎛ K

2 tUE,i ⎠, (22) X = log ⎝ i=1,i=k

610


is the lower bound of the ergodic sum-rates in the case of an ideal RF circuit at high SNR, which means that ideal ideal ideal C ideal BS,t = C BS,r = I M , C UE,t = C UE,r = I K .

(27)

And

+ mis 2 2

RBS = K · log e · δBS,t + δBS,r , − log sinc2 θtBS sinc2 θrBS %. $ 2 e4δUE,t − 1 mis 2

RUE = K · log e · 2δUE,t − 0.5 log +1 K −1 (28)

are the system performance losses due to the RF mismatches at 2 the BS and the UEs respectively. In the condition of small δUE,t and large K , we can further obtain Fig. 2. Monte Carlo simulations and log-normal approximation to the PDF of the sum of (K − 1) log-normal random variables. The amplitude variance of RF mismatch at the UE is 1 dB, 2 dB and 3 dB respectively.

we can approximate X as a normal random variable with mean μ X given by % $ 2 e4δUE,t − 1 2 +1 . μ X = log (K − 1) + log e · 2δUE,t − 0.5 log K −1 (23) Generally, the variance of amplitude of RF gain is not large, usually 0.5 dB∼3 dB [20], [22]. Fig. 2 shows the numerical approximation to the probability density function (PDF) with mean and variance computed by the Fenton-Wilkinson method, as well as the empirically generated PDF by Monte Carlo simulations. It can be seen that the approximations have good accuracy. Moreover, the approximation is quite accurate with small amplitude variance of RF mismatch. Therefore, substituting (23) into (21), a lower bound of the ergodic sum-rates is given by ⎡ ⎢ sinc2 θtBS sinc2 θrBS M mis = K · log ⎢ E R 2 2 ⎣1 + K − 1 · LB1 eδBS,t +δBS,r & e

⎤

2 4δUE,t

·

−1 K −1 2

e2δUE,t

+ 1⎥ ⎥. ⎦

(24)

log (1 + x) > log (x) , we obtain another lower bound of the ergodic sum-rates as ideal mis mis E R mis = RLB − RBS − RUE , (25) LB2

' ideal RLB

= K · log

(

M K −1

)* (26)

(29)

From the analysis above, the RF mismatches at both the BS and the UEs give rise to the system performance loss. For the BS, both amplitude and phase mismatches result in the performance degradation. However, for the UE, only the amplitude mismatch cause the performance decrement, and the sum-rates decrease 2 is small. Hence, it is strongly suggested to slightly if the δUE,t perform antenna calibration at the BS. III. M UTUAL C OUPLING C ALIBRATION M ETHOD In this section, we present a new calibration method for MRT precoding, which is called mutual coupling calibration. By utilizing the strong mutual coupling between adjacent antennas, the BS can perform antenna calibration without extra hardware circuits and UEs’ involvement. We also build up the model of the calibration error and analyse its impact on the system performance. A. Mutual Coupling Calibration Method for MRT Precoding The objective of antenna calibration is to eliminate nonreciprocity caused by the RF mismatches at the BS. From (11), if we can obtain a calibration matrix C cal to satisfy C BS,t C cal C ∗BS,r = αcal I M ,

Furthermore, using the inequality

where

mis 2

RUE ≈ K · log e · 2δUE,t .

(30)

which is equal to the identity matrix multiplied by a scalar, then we can eliminate the effect of RF mismatches at the BS. The dimensional layout of the 256-antennas array at the BS is shown in Fig. 3, where the antennas are mounted on a hexagonal grid [28]. All the antennas are assumed to be thin dipoles, with length l = 0.5λ, where λ is the wavelength, diameter a = 0.005λ and load impedance Z L = 50 . When the distance between any adjacent antennas d = 0.5λ, the self-impedance of each antenna is Z A = 73 + j42.5 , and the mutual-impedance between pairs of adjacent antennas is Z M = −21.27 − j31.19 [26]. The effect of mutual coupling is dependent on Z A , Z M , and Z L [26], [27], which can be used to carry out the antenna calibration.


611

where n i (i = 1, 2, 3, 4) is the complex AWGN. Ignoring the thermal noise, the accurate calibration coefficients between Au and Av for MRT precoding can be obtained through Am and are calculated as tu ru∗ (tu Z Crm ) (tm Z Cru )∗ αu,v = = , (34a) tvrv∗ (tv Z Crm ) (tm Z Crv )∗ tvrv∗ (tv Z Crm ) (tm Z Crv )∗ = . (34b) αv,u = tu ru∗ (tu Z Crm ) (tm Z Cru )∗ If there are other antennas adjacent to both Au and Av except for Am , multiple calibration coefficients between Au and Av can be averaged to obtain a more precise one for improving the calibration accuracy. Then, the iterative calibration method to obtain the calibration coefficients for all antennas is described as Algorithm 1. Algorithm 1 Iterative Calibration Method Initialization: Let 0 ∈ C M×M ficient matrix, ⎡ (0) 1 α1,2 ⎢ (0) ⎢ α2,1 1 ⎢ ⎢ .. .. ⎢ . . ⎢ 0 = ⎢ (0) (0) ⎢ α f,1 α f,2 ⎢ . .. ⎢ . . ⎣ . (0) (0) α M,1 α M,2

Fig. 3. 256-antennas array layout which is mounted on a hexagonal grid.

be the initial calibration coef(0)

... α1,M (0) ... α2,M .. . . .. . . . (0) ... 1 α f,M .. . . .. . . . ... 1

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

The diagonal elements of 0 are 1. The subscript of calibration coefficient denotes the sequence number of the antenna, which is the number of antennas sorted by taking the rows of the matrix as a priority in antennas array shown in Fig. 3. If a pair of antennas are not adjacent, their (0) calibration coefficients are zero, for example, α1,M = 0 and (0)

Fig. 4. Au , Av and Am are three adjacent antennas in hexagonal antennas array at the BS, which just become the three vertices of an equilateral triangle. Curved arrows represent the effect of the mutual coupling between adjacent antennas.

The effect of mutual coupling among three antennas is illustrated in Fig. 4. tu , ru , tv , rv , tm , rm denote the three transmit and receive RF gains, respectively. Z u,m , Z m,u , Z v,m and Z m,v are the factors of mutual coupling, and we can obtain the equal relation Z u,m = Z m,u = Z v,m = Z m,v = Z C according to [28] because the distances between any two of these three antennas are equal. Assuming these three antennas transmit signals with unit power sequentially, the received signal at Au from Am is yu = tm Z Cru + n 1 ,

(31)

the received signal at Av from Am is yv = tm Z Crv + n 2 ,

(32)

and the received signals at Am from Au and Av are written as ym,1 = tu Z Crm + n 3 ,

(33a)

ym,2 = tv Z Crm + n 4 ,

(33b)

α M,1 = 0. Iteration: Choose the f th antenna as the reference antenna, and i denotes the time of iteration. Then, the iteration begins. In (i) th iteration, given i−1 , the elements of i can be obtained as (i) αu,v =

= where

M 1

(i)

ηu,v

m=1

M 1

(i)

ηu,v

(i−1) (i−1) αu,m αm,v

(i) ξu,v,m

m=1

(i) ηu,v

is the number of non-zero elements in (i) (i) (i) ξ (i) u,v = ξu,v,1 , . . . , ξu,v,m , . . . , ξu,v,M ,

(i)

(i−1) (i−1)

where ξu,v,m = αu,m αm,v . When all the elements of i are non-zero, the iteration ends. That means the calibration coefficients between arbitrary two antennas have already been obtained. Ending: Choose the f th row in i to generate the calibration matrix C cal = diag α f,1 , α f,2 , . . . , α f,M .

612


In Algorithm 1, the effect of mutual coupling is used to define the channel between the co-located BS’s antennas, which was not investigated in the Argos method [15]. In the initialization of the algorithm, only the calibration coefficients between adjacent antennas are calculated, since the mutual coupling between neighbor antennas is much stronger than the apart one [27]. Then, through several iterations, the calibration coefficient between arbitrary antenna and the reference antenna can be obtained by averaging a few calibration coefficients, because one antenna can establish the relationship with the reference antenna by several different calibration paths. From Algorithm 1, when the calibration coefficients between arbitrary two antennas are obtained, the iteration ends. Thus, √ M . The the time of iterations is on the order of O log Argos method is of low complexity, since it directly calculates the calibration coefficients without iterations. However, when the distance between one antenna and the reference antenna is far away, the coefficients may be very small due to the weak mutual coupling, which yields an ill-behaved estimation that degrades the system performance. Therefore, by our proposed mutual coupling method, the BS can perform antenna calibration without extra hardware circuits and the UEs’ involvement and overcomes the instability of the Argos method with a modest increase of the complexity. Note that, besides MRT precoding, the proposed mutual coupling calibration method can also be used for ZF precoding. According to [15], [33], when the BS exploits ZF precoding, the calibration matrix C cal was supposed to satisfy C BS,t C cal = αcal C BS,r .

(35)

phase mismatches of RF gains are eliminated, the amplitude mismatches of RF gains still exist, which also result in the performance degradation. Therefore, it is very important to design the calibration method for MRT precoding, which is the focus of our paper. B. Impact of Calibration Error on System Performance From the analysis above, a new calibration method was presented for MRT precoding. However, the calibration error has negative impact on the system performance due to the thermal noise in the calculation of the calibration coefficients. It is assumed that the complex AWGN is i.i.d. complex Gaussian / random variable with zero mean and variance σc2 = 1 ρcal , where ρcal is the calibration SNR. Then, the calibration coefficient is given by (tu Z Crm + n 1 ) (tm Z Cru + n 2 )∗ (tv Z Crm + n 3 ) (tm Z Crv + n 4 )∗ = αu,v εu,v ,

αˆ u,v =

where εu,v =

tu Z C r v rv /tv = , tv Z C r u ru /tu tv Z C r u ru /tu = = . tu Z C r v rv /tv

αv,u

1+

εu,v ≈ =

(38b)

2 σε,1 =

As shown in (39), the calibration coefficients for ZF precoding cannot be simply used for MRT precoding. Although the

1+ 1+

1 tm∗ ru∗ 1 tm∗ rv∗

1 ∗ Z C∗ n 3 1 ∗ Z C∗ n 4

+ +

1 tu r m 1 tv r m

(41)

1 ZC n1 1 ZC n2

1 + n ε,1 , 1 + n ε,2

(42)

με,1 = με,2 = 0 and the variance

(39)

1 1 1 ∗ Z C n 1 + tu ru∗ tm∗ rm |Z C |2 n 1 n 3 1 1 1 ∗ Z C n 2 + tv rv∗ tm∗ rm |Z C |2 n 2 n 4

where n ε,1 and n ε,2 are i.i.d. complex Gaussian random variables with the mean

(38a)

Then, according to (38a) and (38b), taking the calibration coefficients between adjacent antennas as the initialization of Algorithm 1, the finial calibration coefficients for ZF precoding can be obtained through iteration. Comparing (30) with (35), it can be seen that the aim of calibration for ZF precoding is different from MRT precoding. If we substitute the calibration matrix of (35) into (30), one obtains C BS,t C cal C ∗BS,r = αcal C BS,r C ∗BS,r .

m u

(36) (37)

Thus, different from (34a) and (34b), the accurate calibration coefficients between Au and Av for ZF precoding can be obtained as αu,v =

1 ∗ 1 Z C∗ n 3 + tu rm 1 1 ∗ 1 tm∗ rv∗ Z C∗ n 4 + tv rm

1 + t ∗1r ∗

is the calibration error when the calibration coefficient between the uth antenna and the vth antenna is calculated through the mth antenna. When calibration SNR is high, εu,v can be approximated by

Then, the antennas Au and Av transmit and receive calibration signals between each other, and the received signals are yu = tv Z Cru + n 1 , yv = tu Z Crv + n 2 .

(40)

2 σε,2 =

(

1

|t |2 |r |2 ( m u 1 |tm |2 |rv |2

+ +

1

(43) )

1

|tu |2 |rm |2 |Z C |2 ) 1 1 |tv |2 |rm |2

|Z C |2

σc2 σc2 .

(44)

Proposition 1: For complex variables α=

1 + n1 = |α| eιθ 1 + n2

(45)

and α1 = 1 + n 1 = |α1 | eιθ1 α2 = 1 + n 2 = |α2 | eιθ2 ,

(46)

where n 1 and n 2 are zero mean circularly symmetric complex Gaussian random variables, n 1 ∼ CN 0, 2σ12 and


/ / n 2 ∼ CN 0, 2σ22 . When 1 2σ12 and 1 2σ22 are very large (e.g. 1), the distribution is approximately log-normal of |α| distributed as ln |α| ∼ N 0, σ 2 . The PDF is given by 2 1 − (ln z) e 2σ 2 , f (z) = √ 2π σ z

z > 0,

(47)

where σ 2 = σ12 + σ22 . And the distribution of θ is approx imately Gaussian distributed as θ ∼ N 0, σ 2 . The PDF is written as −θ 2 1 e 2σ 2 , f (θ ) = √ 2π σ

−∞ < θ ≤ ∞.

(48)

Proof: See Appendix A. From Proposition 1 and (42), it can be seen that the obeys log-normal distribuamplitude of εu,v approximately tion ln εu,v ∼ N 0, σε2u,v and the phase of εu,v approx imately obeys Gaussian distribution εu,v ∼ N 0, σε2u,v , 0 2 + σ2 2. where σε2u,v = σε,1 ε,2 From Algorithm 1, the calibration efficient between two antennas which are not adjacent is calculated by multiplying the calibration efficient of other antennas. For example, the calibration error of the calibration efficient between Au and Av is written as (i) εu,v =

M 1

(i) ηu,v

(i−1) (i−1) εu,m εm,v .

(49)

m=1

Thus, the calibration error is the cumulative product of several calibration error variables, and the distribution of calibration error variable does not change in iterations. Then, the calibration matrix after calibration is given by (50) Cˆ cal = diag αˆ f,1 , αˆ f,2 , . . . , αˆ f,M ,

For simplicity, we make an assumption that (N −1) are i.i.d. random variables, εp ( p = 1, . . . M) with amplitude and phase obeying the distributions (N −1) (N −1) ∼ N 0, σε2 , where ln ε p ∼ N 0, σε2 and ε p the variance 2 2 e2δBS,t +2δBS,r 2 2 σε = τ f · E σεu,v = 2τ f (54) |Z C |2 ρcal due to several iterations, where τ f ∈ R+ is a scalar number which depends on the antenna array layout and the position of the reference antenna. Therefore, we have / −1) σε2 2 = e E ε(N , (55) p / 2 −1) = e−σε 2 . E ε(N (56) p Under this assumption, the calibration error factor εm (m = 1, 2, . . . , M) can be considered as i.i.d. random variables. Then, one obtains ⎤ ⎡ M M

1 1 (N −1) −1) ⎦ ε(N E εp E [εm ] = E ⎣ = p M M p=1

=

1 M

M

(N )

αˆ f,m = α f,m ε f,m

m = 1, 2, . . . , M

(51)

(N )

where ε f,m is the calibration error and N is the total number of (N )

iterations. In the last iteration step, the calibration error ε f,m can be seen approximately to be averaged by M calibration error variables, which is written as (N )

ε f,m

p=1

and E |εm |2 ⎡⎛

⎞⎛ ⎞∗ ⎤ M M

1 1 −1) ⎠ ⎝ −1) ⎠ ⎦ = E ⎣⎝ ε(N ε(N p p M M p=1 p=1 ⎤ ⎡ M M M 1 ⎣ (N −1) 2 (N −1) (N −1) ∗ ⎦ = 2E εq εp ε p + M

(52)

p=1

After many operations of cumulative product, addition and (N −1) average, ε f,m, p ( p = 1, . . . M) are supposed to be independent (N −1) εp

−1) ε(N f,m, p

and

(N ) ε f,m

and εm , respectively. Then, we have εm =

M 1 (N −1) εp . M p=1

q=1,q= p

p=1

1 2 = 2 M · e2σε + M (M − 1) M 2 e2σε − 1 . (58) =1+ M Then, considering the calibration error, the overall received signals at the UE are

=

M 1 (N −1) = ε f,m, p . M

(57)

p=1

y = βcal G DL Cˆ cal G ∗UL x + n = βcal C UE,r H C BS,t Cˆ cal C ∗

M 1 (N −1) (N −1) = ε f, p ε p,m M

on f and m. Thus, for brevity, we abbreviate

p=1

−1) −1) = 1, E ε(N · E ε(N p p

p=1

and

as

613

H ∗ BS,r H C UE,t x αcal βcal C UE,r HH H C ∗UE,t x + n,

+n

where = diag (ε1 , ε2 , . . . , ε M ), and

1 . βcal = ∗ Tr G T Cˆ Cˆ cal G ∗ UL

cal

(59)

(60)

UL

The received signal of the kth UE is yk = αcal βcalrUE,k hk hH k tUE,k x k

(53)

+ αcal βcalrUE,k

K

i=1,i=k

hk hiH tUE,i xi + n k .

(61)

614


Thus, similar to the approximation (15), the SINR of the kth UE in the presence of calibration error is rUE,k 2 2 |E [εm ]|2 2 tUE,k 2 e−2δBS,t |αcal | Mρ K E |εm |2 tUE,i 2 γkcal =

i=1

rUE,k 2 2 |αcal | ρ K tUE,i 2

K i=1,i=k

2 tUE,i 2 e−2δBS,t +1

. (62)

At high SNR, =M·

perf_cal

RLB

ideal mis = RLB − RUE .

(69)

It is shown that the impact of RF mismatches at the BS can be entirely eliminated with the perfect calibration. However, performance loss still exists because of the RF mismatches at the UE. Fortunately, this loss should be very small when the RF 2 is small. circuits at the UEs are of good quality and δUE,t

i=1

γkcal

is the difference between the perfect calibration and the calibration with noise. We can see that the performance loss caused by the calibration error is inversely proportional to calibration SNR and increases with the amplitude variance of RF mismatches at the BS. From (67) and (68), we have

tUE,k 2 · ω, K tUE,i 2

(63) IV. S IMULATION R ESULTS

i=1,i=k

0 where ω = |E [εm ]| E |εm |2 is the impact factor of calibration error on the system performance. According to (57) and (58), the impact factor is given by ⎡ ⎤−1 $ % 2 2 e2δBS,t +2δBS,r ⎢ exp 2τ f − 1⎥ ⎢ ⎥ |Z C |2 ρcal ⎢ ⎥ ω = ⎢1 + ⎥ , 0 < ω < 1. ⎢ ⎥ M ⎣ ⎦ 2

(64) From (64), it can be seen that ω is related to the amplitude variance of RF mismatches at the BS, the calibration SNR and the factor of mutual coupling. If the amplitude mismatches are per2 2 = δBS,r = 0, and only the phase fectly eliminated, that is δBS,t mismatches are presented, then we have ⎡ ⎤−1 1 exp 2τ f −1 2ρ |Z | C cal ⎦ . ω = ⎣1 + (65) M Thus, although ω is independent of the phase range of RF mismatches at the BS, there still exists performance loss duo to the calibration error caused by the phase mismatches. Considering the case of perfect calibration, which is equivalent to ρcal → ∞, we obtain lim ω = 1.

(66)

ρcal →∞

That means the calibration error vanishes and has no impact on the system performance. Henceforth, compared with (25), (26) and (28), the lower bound on ergodic sum-rates with calibration error is written as cal ideal mis RLB = RLB − RUE − R cal_err ,

In this section, system simulations have been carried to to investigate the impact of RF mismatches on the system performance and verify the proposed calibration method. The simulation parameters are set as follows. The number of antennas at the BS is 256, and the 16-by-16 dimensional layout is shown in Fig. 3. There are 12 single-antenna UEs served by the BS. As the iterative method is shown in Algorithm 1, the fact that calibration coefficients are a product of measurements indicates that some considerations should be given to the choice of the reference antenna’s location. In order to minimize the cumulative calibration error, we assume the reference antenna to be in the centre of the 16-by-16 antenna array. Thus, through many heuristic attempts, we set τ f = 32 prudently for (54) in the simulation. A. Impact of Amplitude Mismatch of RF Gain In order to evaluate how much and how RF mismatches have impact on the system performance, we present results for amplitude mismatches and phase mismatches separately. Firstly, the impact of amplitude mismatches on the system performance is investigated. For effective discussion, we define a parameter, normalized ergodic sum-rates, which is the ratio of the ergodic sum-rates with RF mismatches and the ergodic sum-rates in the ideal case. Fig. 5 shows the relation between normalized ergodic sumrates and amplitude variance for ρ = 15 dB. It can be seen that ergodic sum-rates decrease linearly with increasing amplitude variance both at the BS and at the UEs. The impact of amplitude mismatches at the BS is greater than that at the UEs, which is consistent with the theoretical result (28). Moreover, when amplitude variance is 3 dB both at the BS and at the UE, the loss of system capacity is almost 20%.

(67) B. Impact of Phase Mismatch of RF Gain

where perf_cal

R cal_err = RLB

cal − RLB ( ⎡ exp 2τ f ⎢ 1 + = K · log ⎢ ⎣

e

2 +2δ 2 2δBS,t BS,r

|Z C |2 ρcal

M

) −1

⎤ ⎥ ⎥ (68) ⎦

Fig. 6 shows the relation between normalized ergodic sumrates and phase range for ρ = 15 dB. With the increase of phase range at the BS, ergodic sum-rates decrease sharply. When the phase range is π/2 at the BS, the capacity loss is 50%, which is very huge. On the other hand, the phase range at the UEs has no impact on system performance, which is consistent with


Fig. 5. Normalized ergodic sum-rates without calibration versus the amplitude variance of RF mismatches.

615

Fig. 7. Ergodic sum-rates versus ρcal with the MRT calibration coefficients and ZF calibration coefficients, respectively.

for perfect calibration. That means R cal_err reduces to zero, which can be seen in (68). Besides, the number of iterations is only 4, which is very small compared with the large number of the antennas. On the other hand, for comparison, the performance of ZF calibration coefficients is also illustrated in Fig. 7, since the proposed mutual coupling calibration method can also be used for ZF precoding. The ZF calibration coefficients are obtained from (35). As shown in Fig. 7, it can be seen that the ergodic sum-rates increase initially with ZF calibration coefficients, but approach a limit lower than the one with MRT calibration coefficients. According to (28) and (39), although the phase mismatches of RF gains are eliminated, the amplitude mismatches of RF gains still exist, which also result in the performance degradation. Thus, compared with ZF calibration coefficients, our proposed calibration method is shown to be more effective for MRT precoding. Fig. 6. Normalized ergodic sum-rates without calibration versus the phase range of RF mismatches.

the theoretical result (28). Thus, from Fig. 5 and Fig. 6, we can draw the conclusion that the RF mismatches at the BS are the major factor degrading system performance and it is essential for antenna calibration at the BS. C. Impact of ρcal on the Calibration Performance It is assumed that RF gain matches perfectly at the UEs. Thus, we focus on the RF mismatches at the BS and study the impact of calibration error. Given the amplitude variance 2 2 = δBS,r = 2 dB and the phase range θtBS = θrBS = π/4, δBS,t the impact on system performance is illustrated in Fig. 7. It can be seen that, by the proposed mutual coupling calibration method for MRT precoding, the ergodic sum-rates increase with the increment of ρcal . When ρcal is large enough, such as greater than 15 dB, the ergodic sum-rates approach a limit

D. Impact of Amplitude Variance and Phase Range with Calibration Error The impact of amplitude and phase mismatches at the BS on system performance is shown in Fig. 8(a) and Fig. 8(b), respectively. According to Fig. 7, we set ρcal = 15 dB, where ergodic sum-rates almost achieve the performance with perfect calibration. For comparison, the performance of RSLNR precoding is also depicted, which is able to adaptively control the cooperation level among the coordinated BSs by exploiting the statistics of the calibration error factors [23], [24]. Note that, the MRT calibration coefficients cannot be used for RSLNR, since the principles of these two precodings are different. Fortunately, the ZF calibration coefficients obtained by (35) are suitable for RSLNR precoding. From Fig. 8(a), it can be seen that ergodic sum-rates of both MRT precoding and RSLNR precoding decrease gradually with increment of amplitude variance. That means the amplitude mismatches of RF gains at the BS still degrade the performance, although the calibration has been

616


of the transceiver RF circuits, the whole communication channel actually is not reciprocal, and the uplink CSI cannot be simply used for downlink precoding. It is shown that the RF mismatches at the BS are the major factor degrading the system performance. Thus, it is very necessary to perform calibration at the BS, while there is no need to calibrate at the UE. By exploiting the proposed method, BS can perform the calibration efficiently without extra hardware circuits and users’ involvement. Furthermore, after calibration, the amplitude variance of RF mismatches still causes slight performance loss. However, the phase range of RF mismatches has no impact on the system performance. A PPENDIX A P ROOFS OF P ROPOSITION 1 A. Amplitude Approximation From (45) and (46), we can see that the distribution of |α1 | is Rician, and the PDF is given by $ % x 2 +1 x − 2σ 2 x 1 I0 f (x) = 2 e , x ≥ 0, (A.1) σ1 σ12 where 1 I0 (x) = 2π

1

2π

e x cos ϕ dϕ

0

is the modified Bessel function of the first kind with degree zero. As known, the PDF of the Nakagami distribution is f (x) =

Fig. 8. The impact of amplitude and phase mismatches at the BS on system performance with calibration error.

performed. From Fig. 8(b), it can be seen that, after calibration, the ergodic sum-rates of both MRT precoding and RSLNR precoding keep constant with the phase range. It means that the calibration error is not related to the dynamic range of phase mismatches of RF gains at the BS. After calibration, the phase range has no impact on the system performance, which is consistent with the theoretical results (65) and (68). V. C ONCLUSIONS In this paper, we proposed a new antenna calibration method named mutual coupling calibration by using the effect of mutual coupling between adjacent antennas for downlink MRT precoding in massive MIMO systems. Due to the gain mismatches

2m m x 2m−1 − mx 2 e , (m) m

m≥

1 , 2

(A.2)

where m is the fading parameter, and = 1 + 2σ12 is the total power of both the direct path and the other / scattered paths. According to [34], substituting m = (K + 1)2 (2K + 1) into (A.2), the Nakagami distribution can be approximated by the / Rician distribution. The parameter K = 1 2σ12 is the ratio between the power in the direct path and the power in the other scattered paths. Moreover, the Nakagami distribution with large value m is similar to the log-normal distribution with the PDF [35], [36] f (x) = √

1 2π σ1 x

2

e

− (ln x)2 2σ1

,

x > 0.

(A.3)

/ When K = 1 2σ12 is very large (i.e. 1), m=

K2 K (K + 1)2 ≈ = 2K + 1 2K 2

is also very large. Thus, in this situation, the Rician distribution can be approximated by the log-normal distribution from the / analysis above. Similarly, when 1 2σ22 is very large (e.g. 1), the distribution of |α2 | can also be approximated by the lognormal distribution with the PDF f (y) = √

1 2π σ2 y

2

e

− (ln y)2 2σ2

,

y > 0.

(A.4)


617

Since ln |α| = ln |α1 | − ln |α2 | , the distribution of |α| can/ be approximated by the log-normal / distribution when both 1 2σ12 and 1 2σ22 are very large, and the PDF is written as 2 1 − (ln z) e 2σ 2 , f (z) = √ 2π σ z

z > 0,

(A.5)

where σ 2 = σ12 + σ22 . B. Phase Approximation Since the distribution of |α1 | is Rician, the PDF of θ1 is given by ⎧ − 12 & cos2 (θ1 ) e 2σ1 ⎨ 1 π 2 cos (θ1 ) e 2σ1 f (θ1 ) = 1+ 2π ⎩ σ1 2 ⎫ )* ' ( cos (θ1 ) ⎬ · 1 + erf , −π < θ1 ≤ π. √ ⎭ σ1 2 (A.6) As shown in (A.6), we only consider the range (−π, π ] because of the periodicity of θ1 . For analytical convenience, we relax the range of θ1 to (−∞, +∞) and the PDF is written as f (θ1 ) = 0, θ1 ∈ (−∞, −π ] ∪ (π, +∞) . (A.7) / 2 When 1 2σ1 is very large, θ1 is close to zero, and we have the approximations as follows ) ( cos (θ1 ) ≈ 1, sin (θ1 ) ≈ θ1 , erf √ σ1 2 and

( cos (θ1 ) = 1 − 2sin2

θ1 2

) ≈1−

θ12 . 2

Thus, (A.6) can be simplified as f (θ1 ) ≈ √

1 2π σ1

e

θ2 − 12 2σ1

+

e

−

1 2σ12

θ2 1 · 1e −√ 2π σ1 2

2π

θ2 − 12 2σ1

Fig. 9. Monte Carlo simulations and numerical approximation to the PDF. 1/σ12 = 1/σ22 = 10 dB.

,

where e

−

1 2σ12

≈ 0,

f (θ2 ) = √

and

f (θ1 ) = √ e 2π σ1

−

θ12 2σ12

,

−∞ < θ1 ≤ +∞.

2π σ2

e

−

θ22 2σ22

,

−∞ < θ2 ≤ +∞.

(A.9)

θ = θ1 − θ2 ,

/ is the second-order infinitesimal of θ1 . Therefore, when 1 2σ12 is very large, the distribution of θ1 can be approximated by the Gaussian distribution, and the PDF is given by 1

1

Since

θ2

θ 2 − 12 −√ · 1 e 2σ1 ≈ 0 2π σ1 2 1

/ Similarly, when 1 2σ22 is very large, the distribution of θ2 can also be approximated by the Gaussian distribution with the PDF

(A.8)

the distribution of θ can by the Gaussian dis/ / be approximated tribution when both 1 2σ12 and 1 2σ22 are very large, and the PDF is written as 2 1 − θ f (θ ) = √ e 2σ 2 , 2π σ

where σ 2 = σ12 + σ22 .

−∞ < θ2 ≤ +∞,

(A.10)

618


Fig. 9 shows the numerical approximation to the PDF and the empirically generated PDF of |α| and θ respectively by Monte Carlo simulations when 1/σ12 = 1/σ22 = 10 dB. It can be seen that the approximations are very accurate.

ACKNOWLEDGMENT We thank the reviewers for the careful reviews and suggestions which helped improve the quality of the paper.

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Hao Wei received the B.S. degree in electronic information engineering and the M.S. degree in signal and information processing from Nanjing University of Posts and Communications, Nanjing, China, in 2010 and 2013, respectively. He is currently pursuing the Ph.D. degree in information and communication engineering at the National Mobile Communications Research Laboratory, Southeast University, Nanjing, China. His research interests include massive MIMO, reciprocity calibration, and physical layer security.

Dongming Wang (M’06) received the B.S. degree from Chongqing University of Posts and Telecommunications, Chongqing, China, the M.S. degree from Nanjing University of Posts and Telecommunications, Nanjing, China, and the Ph.D. degree from the Southeast University, Nanjing, China, in 1999, 2002, and 2006, respectively. He joined the National Mobile Communications Research Laboratory, Southeast University, in 2006, where he has been an Associate Professor since 2010. His research interests include turbo detection, channel estimation, distributed antenna systems, and large-scale MIMO systems.


Huilin Zhu (M’04) received the B.S degree from Xidian Univeristy, Xi’an, China, and the Ph.D. degree from Tsinghua University, Beijing, China. She is currently a Lecturer (Assistant Professor) with the School of Engineering and Digital Arts, University of Kent, Canterbury, U.K. Her research interests include broadband wireless mobile communications, covering topics such as radio resource management, distributed antenna systems, MIMO, cooperative communications, device to device communications, and small cells and heterogeneous networks. She has participated in a number of European and industrial projects in these topics. She has served as the Publication Chair for the IEEE WCNC2013, Shanghai, Operation Chair for the IEEE ICC2015, London, U.K., and Symposium CoChair for the IEEE Globecom2015, San Diego, CA, USA. Currently, she serves as an Editor for the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY. She was the recipient of the Best Paper Award from the IEEE Globecom2011.

Jiangzhou Wang (SM’94) is currently the Chair of Telecommunications and Head of Communications Research Group, School of Engineering and Digital Arts, University of Kent, Canterbury, U.K. He has authored over 200 papers in the international journals and conferences in the areas of wireless mobile communications and has written/edited three books. His research interests include wireless multiple access techniques, massive MIMO and small-cell technologies, device to device communications in cellular networks, distributed antenna systems, and cooperative communications. He is a Fellow of the IET and was an the IEEE Distinguished Lecturer from January 2013 to December 2014. He serves/served as an Editor or Guest Editor for a number of international journals, such as the IEEE T RANSACTIONS ON C OMMUNICATIONS and the IEEE J OURNAL ON S ELECTED A REAS IN C OMMUNICATIONS . He was the Technical Program Chair of the IEEE WCNC2013 in Shanghai and the Executive Chair of the IEEE ICC2015 in London. He was the recipient of the Best Paper Award from the IEEE Globecom2012.

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Shaohui Sun received the M.S. and Ph.D. degrees in communication and information systems from Xidian University, Xi’an, China, in 1999 and 2003, respectively. From March 2003 to June 2006, he was a Postdoctoral Fellow with the China Academy of Telecommunication Technology, Beijing, China. From June 2006 to December 2010, he was with the Datang Mobile Communications Equipment Company Ltd., Beijing, China, where he led the standardization activities on the third-generation partnership project long-term evolution (3GPP LTE) time-divisions duplex mode. Since December 2010, he has been the Chief Technical Officer with the Datang Wireless Mobile Innovation Center, China Academy of Telecommunication Technology.

Xiaohu You (F’12) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Nanjing Institute of Technology, Nanjing, China, in 1982, 1985, and 1989, respectively. From 1987 to 1989, he was with Nanjing Institute of Technology as a Lecturer. From 1990 to present, he has been with the Southeast University, first as an Associate Professor and later as a Professor. His research interests include mobile communications, adaptive signal processing, and artificial neural networks with applications to communications and biomedical engineering. He is the Chief of the Technical Group of China 3G/B3G Mobile Communication R&D Project. He was the recipient of the Excellent Paper Prize from China Institute of Communications in 1987 and the Elite Outstanding Young Teacher Awards from the Southeast University, in 1990, 1991, and 1993, respectively, the 1989 Young Teacher Award of Fok Ying Tung Education Foundation, State Education Commission of China.