[雙語(yǔ)翻譯]嵌入式系統(tǒng)開(kāi)發(fā)外文翻譯--大規(guī)模多小區(qū)tdd系統(tǒng)的導(dǎo)頻協(xié)調(diào)（英文）

1、Pilot Coordination for Large-Scale Multi-Cell TDD SystemsDavid Neumann, Andreas Gr¨ undinger, Michael Joham, and Wolfgang Utschick Associate Institute for Signal Processing, Technische Universit¨ at M¨ unc

2、hen, 80290 Munich, Germany {d.neumann,gruendinger,joham,utschick}@tum.deAbstract—Pilot contamination limits the performance of a multi-cell time division duplex system with a large number of base station antennas. We stu

3、dy the potential benefits of coordination during the training phase and we propose efficient algorithms for practical systems. Our derivations are based on results from asymptotic analysis and the practical relevance is

4、demonstrated by simulations with realistic system parameters.I. INTRODUCTIONRecently, there has been an increasing interest in cellular networks with a large number of base station antennas. This so called massive MIMO c

5、oncept promises high gains with very simple signal processing methods [1], [2]. The high number of antennas makes channel estimation and feedback very costly in a frequency division duplex (FDD) system. Thus, most works

6、on this topic assume time division duplex (TDD) systems, where the estimation of the channel takes place in an uplink training phase [1], [3]–[5]. That is, the resources spent on pilots depend on the number of served use

7、rs, but not on the number of antennas at the base station. For the very high antenna gains in these systems, the performance is severely degraded by channel estimation errors due to inter-cell interference in the trainin

8、g phase, so called pilot contamination. It can be shown that this interference ultimately limits the performance for uncoordinated base sta- tions with a very high number of antennas and with favorable propagation condit

9、ions, i.e., independently distributed channel coefficients for each antenna [1], [3], [6]–[9]. A few methods have been proposed to tackle the contamination issue in the uncoordinated case [4], [9]–[11]. In this work, we

10、study the coordination of pilots in the uplink training phase. Previous work on this subject has been done in [12], where a straightforward greedy algorithm is proposed, based on the channel estimation error as perfor- m

11、ance metric. This approach is based on a specific spatial channel model that leads to low rank channel covariance matrices. In contrast to this work, we use results from the asymptotic analyses in [3] and [5] to formulat

12、e a combinatorial network utility maximization (NUM) problem with respect to the coordination strategy. Thus, our approach can handle arbitrary covariance matrices and we can show an improved performance even when the co

13、variance matrices are scaled identities. We analyze possible benefits from pilot coordination by an optimal algorithm based on exhaustive enumeration and provide efficient algorithms for training coordination in practica

14、l systems.II. SYSTEM MODELWe consider a cellular network with L base stations, where each base station has M transmit antennas and serves K single antenna users. The number of base station antennas is significantly large

15、r than the number of simultaneously served users per base station, i.e., K ? M. We further assume that the communication system is in TDD mode and that channel reciprocity holds. We consider a block fading channel model.

16、 Let hijk ∈ CMdenote the vector of complex channel gains from user k in cell j to all antennas of base station i in one coherence block. These vectors are pairwise statistically independent and each vector channel is Gau

17、ssian distributed with zero mean and covariance matrix Rijk ∈ CM×M. For ease of notation, we collect the channel vectors of all K users in cell j to the base station i as columns of the matrix Hij. Let ρtr denote th

18、e effective training SNR and Ttr the number of available pilot symbols, i.e., the available number of orthog- onal pilot sequences. Under the assumptions that the training takes place simultaneously in all cells and the

19、reception is synchronized, the received training signals at base station i are given byWi = √ρtrL ?j=1 HijDj + Ni ∈ CM×Ttr (1)where the orthonormal rows of Dj ∈ CK×Ttr contain the pilot sequences for all K user

20、s in cell j and the entries of Ni are assumed to be i.i.d. complex Gaussian distributed with zero mean and unit variance.III. CHANNEL ESTIMATIONIf we reuse the same pilot sequences in all cells, i.e., Dj = ¯ D ?j, a

21、nd correlate the received training signals with the pilots, we obtain the estimate due to ¯ DH ¯ D = I,Yi = Wi 1 √ρtr ¯ DH =L ?j=1 Hij + 1 √ρtr ? Ni (2)at base station i, that coincides with the least squa

22、res (LS) estimate of the channels Hii, since the noise at the base station antennas is white. Because of the orthonormal rows in ¯ D, the transformed noise matrix ? Ni = N ¯ DH still has i.i.d entries with zero

23、 mean and unit variance. We note that, even if we reuse the same pilot sequences in each cell, the assignment of the pilots to the users influencesγul ik =? 1M tr(Φik,ik) ?21ρulM 1 M tr(Φik,ik) + 1 M ?j,m 1 M tr(RijmΦik,

24、ik) + ?(j,m)∈Kµ(i,k) (j,m)?=(i,k) | 1M tr(Φik,jm)|2 . (8)γdl ik = ρik 1M tr(Φik,ik)1ρdlM + 1 M ?j,m ρjm tr(RjikΦjm,jm)/ tr(Φjm,jm) + ? j?=i m:µ(i,k)=µ(j,m) ρjm 1M |tr(Φjm,ik)|2/ tr(Φjm,jm) (9)VI. ALGORITHM

25、SA. Exhaustive EnumerationTo get an idea of the potential benefits of coordination, we solve the NUM problem in (10) optimally by exhaustive enumeration of all possible pilot assignments. For one cell, the number of poss

26、ible assignments isK?1 ?k=0 (Ttr ? k) = Ttr!(Ttr ? K)!. (11)Note that we can fix the assignment of one cell without affect- ing the performance. The total number of possible assignments is thus ? Ttr!(Ttr ? K)!?L?1 . (12

27、)For larger systems, the enumeration of all possible assignments quickly becomes computationally intractable. Thus, we need efficient algorithms to manage the training coordination.B. Degradation Based Greedy AssignmentT

28、he first greedy algorithm we introduce is based on a degradation measure as proposed in [13]. At each iteration of the algorithm, we have a set of users which are already assigned to pilots and a set of free users which

29、still have to be assigned. Initially, the users in one cell are assigned randomly, while all other users are free. The first step in each iteration is to calculate the utilities that result from adding each of the free u

30、sers to the set of assigned users for each possible pilot. Then for each user calculate the degradation, i.e., amount of utility that is lost, when the user only gets the second best pilot. The user which has the highest

31、 degradation, i.e., the user which is most sensitive to the current assignment, is then assigned to its best pilot. To calculate the utilities for the assigned users the utility function has to be separable, i.e.,U(r) =

32、?(i,k) Uik(rik). (13)Each of the assigned users is in one of the sets K1, . . . , KTtr and the partial utility is given by? U(K1, . . . , KTtr) = ?(i,k)∈?p KpUik(rik) (14)where the rates rik are calculated using the assi

33、gnments Kp.Formally we have the following steps. Let F denote the set of unassigned users. For each unassigned user (i, k) ∈ F Calculate the optimal pilotp? ik = arg max p∈Pi ? U(K1, . . . , Kp ∪ {(i, k)}, . . . , KTtr)

34、(15)and degradation measuredik = ? U(K1, . . . , Kp? ik ∪ {(i, k)}, . . . , KTtr)? arg max p∈Pi,p?=p? ik? U(K1, . . . , Kp ∪ {(i, k)}, . . . , KTtr) (16)where Pi denotes the set of still available pilots in cell i. The s

35、elected user is then given by(i?, k?) = arg max (i,k)∈F dik (17)and is assigned to its optimal pilotKp? i?,k? ← Kp? i?,k? ∪ {(i?, k?)} (18)Pi? ← Pi?\{p? i?,k?} (19)F ← F\(i?, k?). (20)These steps are repeated until all u

36、sers are assigned, i.e., F = ?.C. Variance Based Greedy AssignmentThe degradation based greedy algorithm still needs a lot of SINR evaluations for each assignment. To further reduce complexity, we propose another greedy

37、algorithm, where we use a heuristic to select the most sensitive user in a given iteration. Namely, we select the unassigned user with the worst average channel condition since this user is most likely to be affected by

38、inter-cell interference. Thus, we avoid the costly selection process of the degradation based algorithm and only have to search for the optimal pilot for the selected user.D. Position Based AssignmentAnother possible coo

39、rdination strategy is based on the observation that, with a simple geometric path-loss model, weak users generate a large amount of interference in neigh- boring cells, while strong users generate a small amount of inter

40、ference. This motivates a coordination strategy which is only based on the positions of the users and that can be applied in each cell separately. Let us first assume we have Tp = K, a one dimensional Wyner network where