Design of Orthogonal Uplink Pilot Sequences for TDD Massive MIMO under Pilot Contamination

Transcription

1 Journal of Counications Vol., No., January 07 Design of Orthogonal Uplink Pilot Sequences for TDD Massive MIMO under Pilot Containation Sajjad Ali, Zhe Chen, and Fuliang Yin School of Inforation and Counication Engineering, Dalian University of Technology, Dalian 603, China Eail: {zhechen, Abstract Massive MIMO has been acknowledged as a proising technology to counter the deand for higher data capacity for wireless networks in 00 and beyond. owever, each Base Station (BS) requires good enough knowledge of Channel State Inforation (CSI) on both the uplink and the downlink as assive MIMO relies on spatial ultiplexing. In Tie Division Duplex (TDD) assive MIMO systes, this CSI is acquired using channel reciprocity. owever, the use of nonorthogonal uplink pilot sequence due to liited coherence tie leads to pilot containation in TDD assive MIMO systes that results in inter-cell interference in the downlink data transission. This paper proposes a design of orthogonal uplink pilot sequences for ulti-cell TDD assive MIMO systes. We propose to use Zadoff-Chu Pilot Sequences (ZCPS) and eliinate pilot containation during channel estiation process. In the proposed design, each BS is assigned with a specific orthogonal code and the set of ZCPS is ultiplied eleent-wise at each BS with BS-specific orthogonal code to generate orthogonality aong pilot sequences across neighboring cells. The proposed design eliinates pilot containation during channel estiation process thus achieves significant su-rate gains as verified by the siulation results. Index Ters Massive MIMO, channel state inforation, pilot containation, Zadoff-Chu, orthogonal codes I. INTRODUCTION The assive MIMO is a proising technology for the Fifth Generation (5G) cellular networks due to its unprecedented high spectral efficiency []-[3]. owever, the perforance of assive MIMO systes depends critically on the precision of the Channel State Inforation (CSI), regardless whether the CSI is used for the uplink reception or for the downlink transission [4], [5]. This CSI can be obtained either using Frequency- Division Duplex (FDD) or Tie-Division Duplex (TDD). In FDD assive MIMO systes, the CSI is estiated by the Mobile Stations (MSs) and signaled back to the Base Station (BS). Thus the CSI signaling overhead scales linearly with the nuber of antennas deployed at the BS that shows the use of large antenna arrays ipractical. Manuscript received October 7, 06; revised January, 07. This work was supported by National Natural Science Foundation of China (Nos. 6707, 670), National igh Technology Research and Developent Progra (863 Progra) of China (No. 05AA06306), Major Projects in iaoning Province Science and Technology Innovation (No ), and Fundaental Research Funds for the Central Universities of China (No. DUT3AB06). Corresponding author eail: flyin@ ail.dlut.edu.cn. doi:0.70/jc owever, in TDD assive MIMO systes, the CSI is obtained at the BS using the uplink pilot training that will be used for the downlink transission, by exploiting reciprocity between the uplink and the downlink channels. Furtherore, in TDD assive MIMO systes, the signaling overhead iposed by the acquisition of the uplink CSI scales linearly with the nuber of MSs, which is typically uch lower than the nuber of antennas deployed at the BS [6], [7]. owever, the accuracy of the CSI obtained and thus the attainable syste perforance depends on having perfectly orthogonal uplink pilot sequences allocated to the different MSs across the network. Orthogonal uplink pilot sequences ay only be assured for the MSs roaing within the sae cell, but not for those scattered across the different cells, because of liited channel coherence tie [8], [9]. The worst-case scenario is associated with the ulti-cell systes relying on the pilot reuse factor of one when all cells use the sae set of orthogonal pilot sequences at the sae tie. Then the pilot sequences for different MSs are correlated, the estiated CSI of an MS is containated by the CSI of neighboring MSs that results in inter-cell interference. This detriental effect is known as pilot containation that constitutes a uch ore severe ipairent copared to the effect of additive white Gaussian noise (AWGN). Therefore, pilot containation fors a perforance bottleneck in assive MIMO counication systes [6], [7], [0]. A nuber of schees have been proposed in the literature to eliinate the pilot containation fro the TDD assive MIMO systes [5], [6], [9], [], []. Reference [5] and [] proposed tie-shifted pilots with a finite and an infinite nuber of BS antennas, respectively. owever, tie-shifted pilot schee entails a central controller for anaging the tie-shifting of the pilot-intervals in all of the cells in order to protect their orthogonality across different cells, which becoes a challenge for growing nuber of users and cells. Siilarly, [6] consisted of an aalga of downlink and uplink training phases, which are capable of eliinating pilot containation at the cost of requiring a uch longer training duration than the conventional siultaneous uplink training. More specifically, the schee of [6] consists of ( 3) training phases for an -cell syste. Therefore, it requires that the coherence interval of the channel is no less than ( 3), where is the length of the training sequences, which is assued to be equal to 07 Journal of Counications 40

2 Journal of Counications Vol., No., January 07 the nuber of users per cell. Whereas [9] and [] proposed iniu ean-square error (MMSE) based precoding and scheduling ethods, respectively. In [9], the precoding atrix at one BS is designed to iniize the su of the squared error of its own users and interference to the users in all other cells. The distributed single-cell precoding ethod is shown to provide better perforance than traditional single-cell zero-forcing precoding. owever, this schee [9] needs the knowledge of second-order statistics of all the uplink channels. Although, a BS estiates only its in-cell channels, not the interfering channels fro the adjacent cells. Therefore, it is ipractical to presue that the BS can obtain the second-order statistics of all the uplink channels without estiating the. Whereas, [] presented the pilot scheduling under two MMSE criteria, and proposed a low coplexity pilot scheduling algorith otivated by the channel angle of arrival nonoverlapping condition. owever, this proposed scheduling algorith entails the knowledge of angles of arrival (AOAs) of all the users, which is unrealistic to know in a practical environent. Along with aforeentioned schees and extensive pilot containation eliination literature has not focused on uplink pilot sequence design or selection features and such contributions are liited in the literature, e.g., [3] and [4], where uplink pilot sequences in neighboring cells are treated as noise. Anzhong et al. [3] proposed to phase shift a given Zadoff-Chu (ZC) sequence [5] aong ultiple cells and calculate the required phase shift to be used in each cell. ien et al. [4] proposed a greedy sequence assignent algorith, where the sequences are allowed to take rando values and are not chosen fro a predefined set of sequences. This akes a practical ipleentation rather challenging, as the coplete sequences need to be transitted fro the BS to the respective users. Jae Won et al. [6] treat the intercell pilot interference proble with ZC sequences and find subsets of such sequences that iniize inter-cell pilot interference. Their approach treats sequences in neighboring cells as noise as well and assues that pilots of each user occupy all available subcarriers, aking the used fraework not suitable for the TDD assive MIMO systes. Because in TDD assive MIMO syste only a liited portion of the coherence interval can be used for the uplink training. Different fro [3], [4] and [6], [7] and [8] proposed a user capacity-achieving pilot sequence design together with power allocation for downlink transission in a single- and ulti-cell ultiuser assive MIMO syste, respectively. Both schees [7] and [8], proposed to generate pilot sequences and the corresponding power allocation schee to satisfy the signal-to-interference-plus-noise ratio (SINR) requireents of all the users in the syste, not considering the rigorousness of pilot containation. Furtherore, pilot sequence design of [7] and [8] is based on the rules of the Generalized Welch-Bound- Equality (GWBE) sequence design. Different fro [7] and [8], in this work the proposed pilot sequence design uses ZC sequence and eliinates pilot containation during channel estiation process. Given the above background, this paper proposes an efficient and practical pilot containation eliination schee for ulti-cell TDD assive MIMO systes. The proposed design of orthogonal uplink pilot sequences uses ZC pilot sequences (ZCPS) as uplink pilot sequences, which reain orthogonal within a cell due to their constant aplitude and zero autocorrelation (CAZAC) property (i.e., the correlation of a ZC sequence of any length with the circularly shifted version of itself is zero for non-zero shifts). The perfect circular autocorrelation property allows ultiple orthogonal sequences to be generated fro a ZC sequence. In fact, if the periodic autocorrelation of a ZC sequence provides a single peak at the zero lag, the periodic correlation of the sae sequence against its cyclic shifted replica provides a peak at a lag CS, where CS is the nuber of saples of the cyclic shift. This creates a zero-correlation zone (ZCZ) between the two sequences [5]. To ake pilot sequences orthogonal across the network, the orthogonal codes are used. Before rando access, a set of ZCPS is ultiplied eleent-wise with BS-specific orthogonal code row at each BS that will ake ZCPS orthogonal across the network. The proposed schee will eliinate pilot containation during channel estiation process. Furtherore, the proposed schee uses conventional siultaneous uplink pilot training and does not require any prior knowledge regarding either the MIMO channels or MS inforation. The reaining sections of this paper are organized as follows. The ulti-cell TDD assive MIMO syste odel, uplink training and pilot containation proble are presented in Section II. Section III describes orthogonal codes, ZC sequences, proposed design of orthogonal ZCPS, eliinating pilot containation during channel estiation process, downlink transission, and achievable throughput rates. Section IV presents siulation and result discussions. Finally, soe conclusions are given in Section V. Notations: The notations used in this paper are as follows. The boldface variables denote the atrices or vectors. The transpose and the eritian transpose are denoted diag{ d} by T (.) and (.), respectively. A sybolizes a diagonal atrix with diagonal entries equal to the coponents of vector d and indicates eleent-wise ultiplication. The trace and inverse operations are denoted by tr. and., respectively. The two-nor, expectation, and variance are sybolized as.,. and var., respectively. II. MUTI-CE TDD SYSTEM MODE Consider a cellular network coposed of hexagonal cells, tagged by l,,...,, where the BS of each cell contains an array of A antennas and serves U single- 07 Journal of Counications 4

3 Journal of Counications Vol., No., January 07 [b] z ru. In the BS of the q-th cell, the zru, then z ru antenna MSs, where ipliedly A >> U. All the BSs and MSs are synchronized and TDD operation is eployed to estiate the CSI at the BS. Unity frequency reuse (UFR) is eployed and ZCPS will be orthogonal within a cell due to their CAZAC property. The average powers during transission at each BS and MS are dl and up, signal received during uplink training phase at the a-th antenna of the q-th BS is, [9], [0] U y qa () where v qa is the i.i.d. AWGN with zero ean and unit variance. et independent and identically distributed (i.i.d.) zero-ean, circularly syetric coplex Gaussian distribution ℂ (0,) and known to nobody, and rqu is a positive Vq [ vq Yq [y q y q... y qa ] A, vq... vqa ] A. All cells eploy the sae set of U uplink pilot sequences, represented by satisfying constraint Z [z z... zu ] U constant and supposed to be known to everybody. This ulti-cell odel is illustrated in Fig., where the hrqua Z Z I, Dlq diag{[ lq variable odel fast fading that presued to be a constant for a duration of T sybols and can be defined as [4], [6] hlq lq hlqu ( l ) D hlqua up lqu hlqua zlu v qa l u respectively. The propagation vector connecting the a-th BS antenna of the q-th cell and the u-th user of the r-th / cell is hrqua rqu, where hrqua is a rando variable with j lqua j cos( lqua) e, e ( l ) D cos( lqua ), j j e lqua e ( l ) D cos( lquat ) j lquat j e..., e () lq... lqu ]}, and hlq A. hlqua Then, we have Yq up Dlq lq Z Vq (3) l where t is the nuber of i.i.d paths, lquat is the phase of After the q-th BS receives the signal Yq, the channel the path and it is a rando variable uniforly distributed in [0, ), D is the antenna spacing at the BS, is the qq is estiated with the MMSE estiator [9], [0] wavelength of the carrier, and lquat 0, is a rando ˆ MMSE D I ZD Z Y Z q qq up qq up lq l (4) up Dqq I up Dlq Yq Z l angle of arrival (AOA). Whereas rqu invariable odel path-loss and shadow fading that change slowly over space [], [], [0]. A. Uplink Training At the start of every coherence interval, all the MSs in the network synchronously transit their uplink pilot sequences, which are the colun vectors with length. B. Pilot Containation u u Cell q Cell r st-cell rth-cell / hrqua. rqu u u-th user qth-cell u Fig.. The connectivity odel between the a-th antenna of the q-th cell and u-th user of the r-th cell in a TDD M-MIMO Syste. Define Uplink pilot Pilot containation z ru as the uplink pilot sequence transitted by the u-th user in the r-th cell and it is denoted by T It is obvious fro (4) that the q-th BS estiates the desired channel qq by correlating the received signal z ru z... z, where z z is the pilot sequence eleent, and without loss of generality, assue [] ru [] ru [ ] ru 07 Journal of Counications th-cell Fig.. The pilot containation proble. [b ] ru Yq with the known pilot sequence. Since all cells 4

4 Journal of Counications Vol., No., January 07 eploy the sae set of pilot sequences, which is the worst case scenario, therefore, this Channel Estiate (CE) is severely polluted by the MSs of adjacent cells, which are allocated sae pilot sequences. This is so-called pilot containation and is illustrated in Fig.. Thus, (4) of MMSE CE can be siplified as ˆ MMSE I qq Dqq DlqDqq up l / Dqq qq Dlqlq Vq Z l q, l up fourth ter The fourth ter of (5) shows the severity of the pilot containation utilation that result in a considerable estiation error. III. PROPOSED PIOT CONTAMINATION EIMINATION SCEME As shown in Section II-B, the CE relying on the uplink pilot sequences suffers fro pilot containation and the existing schees [3], [5], [6], [9], [] and [] either require relatively large training duration or require prior knowledge regarding either the MIMO channels or MS inforation. Fortunately, the nuber of cells is liited copared to the nuber of MSs, therefore it is possible to allocate distinct orthogonal code rows to the BSs. These BS-specific orthogonal code rows can be exploited to eliinate pilot containation during CE process. Before discussing the proposed schee in detail, let us briefly explain the orthogonal codes and ZC sequences, respectively. A. Orthogonal Codes The orthogonal codes such as Orthogonal Variable Spreading Factor (OVSF) and Walsh-adaard codes can be used in the proposed design [], []. The code rows of these two orthogonal codes are utually orthogonal; hence eleent-wise ultiplication of code rows with ZCPS will ake ZCPS orthogonal across the network. Specifically, OVSF codes were first coenced for 3G systes to aintain the orthogonality aong different uplink channels in a wireless counication syste []. An 8-by-8 orthogonal atrix can be given as, (5) O 8 (6) where each row of the atrix can be represented as O 8,w, where w indicates the row nuber. B. Zadoff-Chu Sequences The ZC sequences are a category of polyphase sequences defined as [5], [3] n z z( n) exp( jπ ), n 0,,..., P (7) P where P (even) is the length of the sequence and,,, P is the root index of the sequence. ZCs of any length possess an ideal or perfect periodic autocorrelation property (i.e., the correlation with the circularly shifted version of itself is zero for any non-zero shifts) P P n0 T z n z n (8) where is the shift or correlation lag, and P P. C. Orthogonal ZCPS The proposed pilot containation eliination schee ultiplies ZCPS eleent-wise with the BS-specific orthogonal code rows. This eleent-wise ultiplication will ake ZCPS orthogonal across the network. The proposed schee takes the length of ZCPS as the ultiple of two i.e. P, where. Furtherore, the rows of the orthogonal codes can be re-used in a siilar pattern as that of the frequency reuse pattern in wireless counication systes. A ZC sequence of length P with root index, can be given as n z z( n) exp( jπ ), n 0,,..., (9) Then the set of cyclically shifted ZCPS of z can be represented as z ( ), where ( ). ere, we consider a seven cell syste; therefore, each BS of the seven-cell cluster can be assigned to a distinct orthogonal code row fro the O 8 atrix. Then, each of these assigned orthogonal code rows is ultiplied eleent-wise with the set of cyclically-shifted ZCPS at each BS of the seven cell syste as given below, refer to Fig. 3. c z ( ) O e, 8, w z ( n) z ( n ) O ( n ), n 0,,..., e, 8, w (0) where * denotes the eleent-wise ultiplication, e,,...,7 represents the nuber of the BS in the seven cell syste. This eleent-wise ultiplication will ake c,, c,,..., c 7, a set of sequences utually 07 Journal of Counications 43

5 Journal of Counications Vol., No., January 07 orthogonal to each other. This is fro the fact that zz where z is an eleent of ZC sequence. This assertion is proved as follows. since we have X c, k c, k ( ) 8,0 ( ) 8, z O z O z( ) z( ) O 8,0 O 8, O8,0 O 8, 0 X 0 () ence, proposed orthogonal ZCPS design can eliinate pilot containation fro TDD assive MIMO systes. Next section will show that the proposed orthogonal ZCPS design can eliinate pilot containation during channel estiation process. st -cell c z O, ( ) 8, 3 Uplink pilot Pilot containation Fig. 3. Orthogonal ZCPS. c z O q, ( ) 8,3 qth-cell c z O r, ( ) 8,4 4 rth-cell c z O, ( ) 8, 7th-cell D. Eliinating Pilot Containation During CE Process Consider the scenario of the seven-cell cluster; refer to Fig. 3, where each cell has one user that transits its uplink training sequence. Then, the uplink training signal received at the q-th BS can be given as U y h c v () qa up lqu lqua q qa l u After receiving the uplink training signal y qa, the q-th BS will estiate the channel h qq3a with the MMSE estiator. The MMSE estiate of the channel h qq3a is U MMSE qq3a up qq3 up q lqu q q q l u hˆ I c c y c (3) hˆ MMSE qq3a U upqq3 I up lqu l u qq3hqq 3a v qacq up (4) Using atrix inversion lea ( ) ( ) I A I I A A, (4) can be further siplified as hˆ x up qq3 U x MMSE up qq3l l u h lqu v c qq3 qq3l x ql q up (5) Dropping user and antenna subscripts, then (5) can be rewritten as MMSE up qq qq qq hqq x q q q up hˆ q up lq l where. vc (6) Fro (6), it is obvious that the MMSE estiation of the channel h qq3a, after ipleenting the proposed schee, are clean fro the pilot containation. E. Downlink Transission After estiating the uplink CE using the proposed schee, the BSs can acquire the downlink CE by exploiting the channel reciprocity of the TDD protocol. Consider that the inforation sybols transitted by the BS of the q-th cell to its users are bq [ bq bq... b qu ] and the AU linear precoding atrix is E ( ˆ ) T q qq, where denotes a particular linear precoding ethod perfored at the BS and Ĥqq are the MMSE CE. Then, Eb q q is the transission precoding (TP) vector transitted by the q-th BS. Furtherore, consider that the inforation sybols b q and precoding ethod (.) satisfy b q 0, b b I tr EE q q, which iply that the average power constraint at the BS is satisfied [], [6]. The signal vector received by the users of the q-th cell is q dl qq qq q q q q q and F D E b W, ( U vector) (7) where W q is the i.i.d. AWGN with zero ean and unit variance. Therefore, the signal received by the u-th user can be given as 07 Journal of Counications 44

6 Journal of Counications Vol., No., January 07 Fqu U k where E q and (8) dlqqu h qqu hqqu... hqqua eqkbqk wqk e qk is the k-th colun of the precoding atrix w qk is the k-th eleent of W q. F. Achievable Throughput Rates In order to show the effectiveness of the proposed schee and the advantages of eradicating the pilot containation, the lower bound of the achievable downlink throughput rate is derived using atched filter (MF) precoding given by [9] ˆ qq Eq ˆ qq (9) et g h h... h e, then qk dl qqu qqu qqu qqua qk (8) can be rewritten as U Fqu gqkbqk wqk k gqk bqk gqk gqk bqk wqk In (0), the effective noise is defined as wqk gqk gqk bqk wqk Now, (0) can be written in the failiar for Fqu gqk bqk wqk (0) () () where b qk, F qs, gqk and w qk are the input, output, known channel and additive noise, respectively. Now the achievable downlink throughput rate for () is [6], [9] R qk g qk log var g IV. SIMUATION AND RESUT DISCUSSIONS qk (3) To verify the effectiveness of the proposed schee, soe siulation results are presented. These siulations are based on a ulti-cell TDD M-MIMO syste and siulation paraeters are listed in Table I. The AOAs lquat of all paths are the i.i.d Gaussian rando variables with ean AOA 90 and standard deviation AOA 90. The achievable downlink throughput rate of the proposed schee, given in (3), is evaluated by (6) of MMSE CE. Pilot-assisted CE represents the sophisticated cobination of downlink training and scheduled uplink training to eradicate the pilot containation proposed in [6]. The MMSE CE with aligned pilots, proposed in [], represents the estiator that depends on all the MSs of all the cells siultaneously transitting their uplink pilot sequences those occupy OFDM sybol lengths for its uplink training. The MMSE CE with the staggered pilot sequences represents the estiator, in which the MSs roaing in different cells transit their uplink pilot sequences at non-overlapping instances proposed in []. The su-rate perforances of staggered pilots of [] are evaluated using appendix given in [6]. The achievable downlink su-rate perforance versus different network paraeters is evaluated for the proposed schee and copared with those of [6] and []. TABE I: VAUES OF PARAMETERS FOR SIMUATION Paraeter Sybol Value Nuber of cells 7 Nuber of users per cell U 4 Nuber of antennas at each A BS 50 Average uplink transit up 0dB power Average downlink transit power dl 0dB Direct gain qqu Cross gain lqu where l q 0.3 Pilot length 8 Frequency re-use factor Mean of AOAs AOA 90 Standard deviation of AOAs Antenna spacing AOA Nuber of paths t 50 The achievable downlink su-rate versus cross gain perforance of different schees is illustrated in Fig. 4. When the cross gain increases, the su-rate of all the schees decrease. We can observe fro Fig. 4 that the su-rate perforances of the pilot assisted CE and MMSE with aligned pilots fall drastically fro 3 bps/z to.8 bps/z and 8. bps/z to 0.6 bps/z, respectively, as the cross gain increases. Whereas the su-rate of the proposed schee with MMSE CE estiator drops fro 3 bps/z to bps/z, which is a drop of only 9 bps/z copared with the falls of 0. bps/z and 7.5 bps/z of pilot assisted CE and MMSE with aligned pilots, respectively. Therefore, the perforance of the proposed estiators is far better than those of [6] and [], which authenticates the effectiveness and superiority of the proposed MPSOACO schee. The achievable downlink su-rate versus a nuber of cells perforance of different schees are illustrated in Fig. 5, where the values of the cross gain coefficients used between the q-th cell and its adjacent cells are D Journal of Counications 45

7 Journal of Counications Vol., No., January 07 lqu 0.3 and lqu 0. for 8 and 9, increases fro 5 to 30. This shows that the perforance of the proposed estiator is better than those of [6] and []. respectively. As the nuber of cells increases, the surate values of all the schees decrease. It is observed fro Fig. 5 that the su-rate values of the pilot assisted CE and MMSE CE estiator with aligned pilots decrease drastically fro bps/z to 5 bps/z and 8.3 bps/z to.6 bps/z, respectively, as the nuber of cells increases. Whereas the su-rate of the proposed schee with MMSE CE drops fro 3.5 bps/z to bps/z, which is a drop of only 0.5 bps/z copared with the decreases in the su-rate of 0. bps/z and 7.5 bps/z of pilot assisted CE and MMSE with aligned pilots, respectively. Therefore, the perforance of the proposed estiators is far better than those of [6] and []. Fig. 6. Perforance coparison of the proposed MPSOACO schee with the schees of [6] and [] for the su-rate versus the nuber of antennas. The achievable downlink su-rate versus standard deviation of AOAs perforance of different schees are illustrated in Fig. 7. We can see fro Fig. 7 that the surate perforance of all the schees is slightly changed by the standard deviation of AOAs while the su-rate values of the proposed schee are again far better than those of [6] and []. Fig. 4. Perforance coparison of the proposed MPSOACO schee with the schees of [6] and [] for the su-rate versus the cross gain. Fig. 7. Perforance coparison of the proposed MPSOACO schee with the schees of [6] and [] for the su-rate versus standard deviation of AOAs. Fig. 5. Perforance coparison of the proposed MPSOACO schee with the schees of [6] and [] for the su-rate versus the nuber of cells. V. CONCUSIONS A design of orthogonal uplink pilot sequences is proposed to eliinate pilot containation fro TDD assive MIMO systes. The proposed design uses Zadoff-Chu pilot sequences (ZCPS) and eliinates pilot containation during channel estiation process. In the proposed design, each BS is assigned with a specific orthogonal code and a set of ZCPS is ultiplied eleentwise at each BS with BS-specific orthogonal code to generate orthogonality aong pilot sequences across the neighboring cells. The proposed design uses conventional siultaneous uplink pilot training copared to the training overhead of ( 3) iposed by the pilot assisted schee of [6]. Furtherore, the proposed design The achievable downlink su-rate versus a nuber of antennas perforances of different schees are illustrated in Fig. 6. When the nuber of BS antennas increases, the su-rate of all the schees increases. It is observed fro Fig. 6 that the su-rate values of pilot assisted CE and MMSE CE with aligned pilots increase only by 7.7 bps/z and 6.5 bps/z, respectively when the nuber of antennas increases fro 5 to 30. Whereas the su-rate value of the proposed schee with MMSE CE estiator increases by 0 bps/z, which is slightly higher than those of pilot assisted CE and MMSE CE with aligned pilots, respectively, as the nuber of antennas 07 Journal of Counications 46

8 Journal of Counications Vol., No., January 07 does not require any prior knowledge regarding either the MIMO channels or MS inforation. The MF precoding is eployed for downlink transission, which is a linear precoding and siple to ipleent copared to zeroforcing precoding. Siulation results show that the surate perforance of the proposed design significantly outperfors both the pilot assisted CE and MMSE CE with aligned and staggered pilots. REFERENCES [] O. Elijah, C. Y. eow, T. A. Rahan, S. Nunoo, and S. Z. Iliya, A coprehensive survey of pilot containation in assive MIMO 5G syste, IEEE Coun. Surveys & Tutorials, vol. 8, no., pp , Second Quarter 06. [] A. Khansefid and. Minn, Achievable downlink rates of MRC and ZF precoders in assive MIMO with uplink and downlink pilot containation, IEEE Trans. on Coun., vol. 63, no., pp , Dec. 05. [3] X. Zhu, Z. Wang,. Dai, and C. Qian, Sart pilot assignent for assive MIMO, IEEE Coun. etters, vol. 9, pp , 05. [4]. u, et al., An overview of assive MIMO: Benefits and challenges, IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp , Oct. 04. [5] S. Jin, X. Wang, Z. i, K. K. Wong, Y. uang, and X. Tang, On assive MIMO zero-forcing transceiver using tie-shifted pilots, IEEE Trans. on Vehicular Technology, vol. 65, pp , 06. [6] J. Zhang, et al., Pilot containation eliination for large-scale ultiple-antenna aided OFDM systes, IEEE J. Sel. Topics on Signal Process., vol. 8, no. 5, pp , Oct. 04. [7] E. G. arsson, O. Edfors, F. Tufvesson, and T.. Marzetta, Massive MIMO for next generation wireless systes, IEEE Coun. Mag., vol. 5, no., pp , Feb. 04. [8] T. X. Vu, T. A. Vu, and T. Q. S. Quek, Successive pilot containation eliination in ultiantenna ulticell networks, IEEE Wireless Coun. etters, vol. 3, no. 6, pp , Dec. 04. [9] J. Jose, A. Ashikhin, T.. Marzetta, and S. Vishwanath, pilot containation and precoding in ulti-cell TDD systes, IEEE Trans. Wireless Coun., vol. 0, no. 8, pp , Aug. 0. [0] T.. Marzetta, Noncooperative cellular wireless with unliited nubers of base station antennas, IEEE Trans. Wireless Coun., vol. 9 no., pp , Nov. 00. [] F. Fernandes, A. Ashikhin, and T.. Marzetta, Intercell interference in noncooperative TDD large scale antenna systes, IEEE J. Sel. Areas Coun., vol. 3, no., pp. 9 0, Feb. 03. []. You, X. Gao, X. G. Xia, N. Ma, and Y. Peng, Pilot reuse for assive MIMO transission over spatially correlated rayleigh fading channels, IEEE Trans. on Wireless Coun., vol. 4, pp , 05. [3] A. u, T. v,. Gao, Y. u, and E. iu, Pilot design for large-scale ulti-cell ultiuser MIMO systes, in Proc. IEEE International Conference on Counications, Budapest, 03, pp [4]. Q. Ngo, A. Ashikhin,. Yang, E. G. arsson, and T.. Marzetta, Cell-free assive MIMO: Uniforly great service for everyone, in Proc. 6th IEEE International Workshop on Signal Processing Advances in Wireless Counications, Stockhol, 05, pp [5] M. ua, M. Wang, K. W. Yang, and K. J. Zou, Analysis of the frequency offset effect on Zadoff-Chu sequence tiing perforance, IEEE Trans. on Coun., vol. 6, no., pp , Nov. 04. [6] J. W. Kang, Y. Whang,. Y. ee, and K. S. Ki, Optial pilot sequence design for ulti-cell MIMO- OFDM systes, IEEE Trans. on Wireless Coun., vol. 0, no. 0, pp , Oct. 0. [7] J. C. Shen, J. Zhang, and K. B. etaief, Downlink user capacity of assive MIMO under pilot containation, IEEE Trans. on Wireless Coun., vol. 4, no. 6, pp , June 05. [8] N. Akbar, N. Yang, P. Sadeghi, and R. A. Kennedy, Multi-cell ultiuser assive MIMO networks: User capacity analysis and pilot design, IEEE Trans. on Coun., vol. 64, no., pp , Dec. 06. [9] N. Shariati, E. Björnson, M. Bengtsson, and M. Debbah, ow-coplexity polynoial channel estiation in largescale MIMO with arbitrary statistics, IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp , Oct. 04. [0]. Yin, D. Gesbert, M. Filippou, and Y. iu, A coordinated approach to channel estiation in large-scale ultiple-antenna systes, IEEE J. Sel. Areas Coun., vol. 3, no., pp , Feb. 03. [] Y. Tseng and C. Chao, Code placeent and replaceent strategies for wideband CDMA OVSF code tree anageent, IEEE Trans. on Mobile Coput., vol., no. 4, pp , Oct.-Dec. 00. [] A. Iossifides and S. ouvros, A new aspect of Walsh- adaard coding over rayleigh fading channels, IEEE atin Aerica Trans., vol. 0, no. 3, pp , April 0. [3] B. M. Popovic, Generalized chirp-like polyphase sequences with optiu correlation properties, IEEE Trans. Inf. Theory, vol. 38, no. 4, pp , July 99. Sajjad Ali received his B.E. degree in Telecounication Engineering and the M.E. degree in Counication Systes Networks fro Mehran University of Engineering & Technology (MUET), Jashoro, Pakistan, in 007 and 0, respectively. e joined Telenor Pakistan as O&M engineer in 007. e then joined the Departent of Telecounication Engineering, MUET, as ab-ecturer in 008, and becae Assistant Professor in 0. e is currently doing his Ph.D. in Dalian University of Technology (DUT), Dalian, China. is research 07 Journal of Counications 47

9 Journal of Counications Vol., No., January 07 interests are in the field of digital signal processing and broadband wireless counications. Zhe Chen received his B.S. degree in Electronic Engineering, the M.S. degree in Signal and Inforation Processing, and the Ph.D. degree in Signal and Inforation Processing fro Dalian University of Technology (DUT), Dalian, China, in 996, 999 and 003, respectively. e joined the Departent of Electronic Engineering, DUT, as a ecture in 00, and becae an Associate Professor in 006. is research interests include digital signal processing, speech processing, iage processing, and broadband wireless counication. Fuliang Yin received his B.S. degree in Electronic Engineering and the M.S. degree in Counications and Electronic Systes fro Dalian University of Technology (DUT), Dalian, China, in 984 and 987, respectively. e joined the Departent of Electronic Engineering, DUT, as a ecturer in 987 and becae an Associate Professor in99. e has been a Professor at DUT since 994, and the Dean of the School of Electronic and Inforation Engineering of DUT fro 000 to 009. is research interests include digital signal processing, speech processing, iage processing, and broadband wireless counication. 07 Journal of Counications 48