Large-scale Multi-user Distributed Antenna System for 5G Wireless Communications Dongming Wang, Zhenling Zhao, Yuqi Huang, Hao Wei, Xiangyang Wang, Xiaohu You National Mobile Communications Research Lab., Southeast University, China;
[email protected] Abstract—In this paper, we study the large-scale multi-user distributed antenna system (DAS) for hot-spot coverage in the future 5G wireless network. Firstly, the multi-user system model of large-scale DAS is introduced and a simple random pilot reuse scheme is presented to reduce the overhead of pilot. Then, the sum-rate of system is derived, and its asymptotical performance is studied when the number of antennas goes to infinity. Moreover, an attractive method for large-scale DAS using matrix sparsification is presented to simplify the signal processing, which is of great significance for the future research. Finally, we study the detection bit error ratio (BER) and area spectral efficiency of large-scale DAS.
I. I NTRODUCTION Distributed antenna system (DAS) is a promising way to greatly improve the spectral efficiency. In DAS, all of the remote antenna units (RAUs) are connected to the baseband processing unit (BPU) by fiber or cable, and then powerful joint processing can be done at BPU. For hot-spot coverage, when large number of RAUs are deployed, the advantages of both massive MIMO and ultra-dense network can be exploited. Therefore, large-scale DAS is a very promising technique for 5G system, especially for indoor [1] or outdoor hotspot coverage [2]. Recently, both theoretical and experimental results show that large scale DAS can provide very large spectral efficiency [3], [4]. In this paper, we demonstrate the system design of largescale DAS. Firstly, we study the channel state information acquisition by using pilot reuse. Then, we derive the sum-rate of the system. We also propose a simple scheme which can use the sparsity of the channel matrix to reduce the complexity of the joint processing. Finally, we evaluate the BER of MMSE and Belief-Propagation (BP) algorithms, and also the area spectral efficiency (ASE) of large-scale DAS with limited pilot resources for outdoor hot-spot coverage. II. S YSTEM M ODEL OF THE U PLINK M ULTI -U SER DAS In this section, we firstly introduce the concept of pilot reuse and then give the system model of large-scale DAS with channel estimation. A. Channel Model and Pilot Reuse In this paper, we consider a single cell system with M RAUs, which are connected to a BPU through fiber or cable. Each RAU is equipped with N antennas, and K users with single antenna are served in the cell. For large-scale DAS, both M and K are very large. To reduce the overhead of the pilot resource, we consider pilot
reuse. We assume that the K users are divided into L groups. In each group, the users use Kpilot orthogonal pilot sequences for uplink transmission [5]. Without loss of generality, we assume that K = Kpilot × L, where both Kpilot and L are integers. Pilot reuse is an efficient way to use the pilot resource in large-scale DAS. The idea of pilot reuse is that if the users with the same pilot sequence are separated by a large distance, the pilot contamination will be not large. In this paper, for simplicity, we consider random pilot reuse, that is, each user in a group randomly selects a different pilot sequence from the Kpilot orthogonal pilot sequences. Using the pilot reuse scheme, the received pilot signal at BPU can be expressed as YP =
L
Gl SP + NP ,
(1)
l=1
where SP is a Kpilot × Kpilot pilot matrix, YP represents a M N × Kpilot received pilot signal matrix, Gl is the M N × Kpilot channel matrix from the Kpilot users of the lth group to the M RAUs, and NP is M N × Kpilot Gaussian noise matrix and each element is independently and identically distributed (i.i.d) zero mean circularly symmetric complex Gaussian (ZMCSCG) with variance γP . Similar to [6], we assume the orthogonal pilot matrix SP =IKpilot . In this paper, we consider a simple channel model in [7], [8]. For the l-th group, the k-th (k = 1, . . . , Kpilot ) column of Gl can be modelled by 1
2 hl,k , gl,k = Λl,k
(2)
where λl,m,k cd−α l,m,k , Λl,k diag [λl,1,k , · · · , λl,M,k ], T T Λl,k Λl,k ⊗ IN , hl,k = hT , · · · , h . Here, λl,m,k l,1,k l,M,k and dl,m,k are the large scale fading and the distance between the k-th user of the l-th group to the m-th RAU, respectively. c is the path loss at the reference distance, and α is the pass loss exponent, generally between 3.0 and 5.0. hl,m,k stands for the N × 1 small scale fading channel vector from the k-th user of the l-th group to the m-th RAU and each entry follows i.i.d ZMCSCG with unit variance.
B. Channel Estimation of Large-scale DAS The received pilot signal of the k-th user can be obtained as follow gi,k + nP,k , (3) yP,k = gl,k +
978-1-4799-8088-8/15/$31.00 ©2015 IEEE
i=l
where yP,k and nP,k are the k-th column of YP and NP , respectively. Then we can obtain the MMSE estimation [3] 1
where Qk
ˆk, g ˆl,k = Λl,k Qk2 h (4) L −1 1 ˆ k Q 2 yP,k . It = Λi,k + γP IM N , h k i=1
ˆ k ∼ CN (0, IM N ) and it represents the is noticed that h Rayleigh fading part of the estimated channels. Therefore, the covariance matrix of the channel estimation error vector ˆl,k can be expressed by [3] g ˜l,k = gl,k − g ˜l,k ) = Λl,k − Λl,k Qk Λl,k . cov (˜ gl,k , g
(5)
It should be noted that for a given k, the estimates g ˆl,k ˆ k is not depend on l, are correlated for each l. But since h it allows us to make a connection of each g ˆl,k . Define the following matrices ˜l = g ˆl = g ˆl,Kpilot ˜l,Kpilot ˆl,1 · · · g ˜l,1 · · · g G G ˜= G ˆ= G ˆL ˜L ˜1 · · · G ˆ1 · · · G G G The ideal channel matrix G can be expressed as ˆ + G. ˜ G=G ˆ the relationThen, at BPU, with the channel estimation G, ship between transmitted signal and received vector can be modelled by ˆ + Gs ˜ + n, y = Gs (6) y denotes the received signal vector at BPU, s = where T T · · · s , and sl is the Kpilot × 1 transmitted signal sT 1 L vector of the users in the l-th group, and n is the M N × 1 complex additive white Gaussian noise vector with covariance
matrix of E nnH = γD IM N . III. S UM - RATE A NALYSIS OF L ARGE - SCALE DAS WITH P ILOT R EUSE According to [6], [9], the MMSE joint detection with channel estimation can be expressed as
−1 ˆG ˆH + Σ ˆH G y, (7) sˆ = G where Σ is the covariance matrix of interference and noise, and it can be calculated by Σ=
L
˜lG ˜H E G + γD IM N . l
where the second equation is obtained by the following matrix identity det (I + AB) = det (I + BA) . We use the strong law of large number to give the sum-rate analysis for M → ∞. Theorem 1: As M → ∞, CˆLB obeys CˆLB − a.s. CˆLB,inf − −−−−− → 0, where M N →∞
Kpilot
CˆLB,inf =
log2 det (Ξk + IL ),
Furthermore, we can obtain from (5) that (9)
k=1
For the knowability of channel estimation matrix ˆ1, · · · , G ˆ L and the received vector y, the uncertainty G of transmitted signal s is determined by the covariance matrix
(11)
k=1
Δ ξi,l,k = Tr Qk Λi,k Σ−1 Λl,k , ⎤ ⎡ ξ1,1,k · · · ξ1,L,k ⎥ ⎢ .. .. .. Ξk = ⎣ ⎦. . . . ξL,1,k
···
(12) (13)
ξL,L,k
Proof : The proof is the same as Theorem 2 in [6]. Theorem 1 shows that for very large M the approximation of E(CˆLB ) (averaged over the small-scale fading) can be given by CˆLB,inf . We should note that since log det (·) is a concave function on the set of Hermitian positive-definite matrices, one can verify that CˆLB,inf is also an upper bound of E(CˆLB ). IV. L OW C OMPLEXITY M ETHOD FOR L ARGE - SCALE DAS A. Channel Sparsification As we can see that joint multi-user MMSE detection can achieve the lower bound of the sum-rate. However, when both the number of RAUs and the number of users are very large, the complexity of joint processing is tremendous. For traditional DAS or traditional multi-cell cooperative MIMO systems, clustering method is employed to reduce the complexity of joint processing. However, for very large-scale DAS, the complexity of clustering is also very complex. Therefore, in this section, by exploiting the sparsity of the channel matrix of the large-scale DAS, we present a simple method to reduce the complexity of the transmission scheme. Furthermore, the method can obtain impressive performance by using the properties of the sparse matrix with low complexity. ˆ In this section, we denote the channel estimation matrix G as ˆ= g ˆj · · · g ˆK , ˆ1 · · · g G T
(8)
l=1
pilot
K ˜lG ˜H = E G (Λl,k − Λl,k Qk Λl,k ). l
of MMSE detection error. Then, we can obtain the lower bound of sum-rate as [10]
ˆ H Σ−1 G ˆ + IK , (10) Cˆ ≥ CˆLB = log2 det G
g1,j · · · gˆM N,j ] is the j-th column vector of where g ˆj = [ˆ ˆ and gˆ[N (m−1)+n],j denotes the channel estimation matrix G, the estimation of the channel parameter from the j-th user to the n-th antenna of the m-th RAU, where 1 ≤ n ≤ N , 1 ≤ m ≤ M. ˆ the best channel With the channel estimation matrix G, quality from the j-th (1 ≤ j ≤ K) user to the antenna of the RAUs is obtained by 2 2 2 g1,j | · · · gˆ[N (m−1)+n],j · · · |ˆ gM N,j | . gjmax = max |ˆ (14)
Therefore, the normalized vector of g ˆj can be written as 2 2 T |ˆ g1,j | |ˆ gM N,j | g ˘j = ··· . (15) gjmax gjmax ˘ = [˘ ˘K ]. Then, on We define a normalized matrix G g1 · · · g ˘ the sparse matrix of G ˆ is given by the basis of G, ˆ1 = G ˆ Z 1, G (16) 1 is the 0 − 1 matrix, and the element where Z 1 = z11 · · · zK 1 of zj is calculated by 1, g˘[N (m−1)+n],j ≥ 10−0.1θ 1 , z[N (m−1)+n],j = 0, g˘[N (m−1)+n],j < 10−0.1θ (17) 1 where z[N and g˘[N (m−1)+n],j are the (m−1)+n],j [N (m − 1) + n]-th element of zj1 and g ˘j , respectively. And θ is the sparse threshold in dB. Then, the sparse interference matrix is expressed as ˆ0 = G ˆ−G ˆ1. G
(18)
So we can rewrite (6) as ˆ1s + n y=G ˜,
(19) ˆ 0 s + Gs ˜ + n, with variance E n where n ˜ = G ˜n ˜H = H ˆ0 ˆ0 G G + Σ. We should note that the equivalent noise n ˜ 1 ˆ is uncorrelated to G s.
B. Low Complexity MMSE Detection and Capacity analysis Similar to Section III, joint multi-user MMSE detection is obtained by −1 H H H ˆ1 ˆ1 ˆ0 ˆ0 G ˆ1 G sˆ = G +G +Σ y. (20) G ˆ 1 , we write To fully utilize the sparsification of G H ˆ0 ˆ0 G +Σ . D = diag G
(21)
Then we redefine the detection (20) by sˆ = W H y. where
(22)
−1 H 1 ˆ1 ˆ ˆ1 W = G G G +D
So the implementation of detection will be simplified, as the matrix to be inversed is sparse [11]. According to (19) and (22), we can get the detection of sk as ⎛ ⎞ K H⎝ 1 0 ˜ + n⎠. (23) sˆk = wk g ˆk sk + g ˆk sk + g ˆj sj + Gs j=1,j=k
ˆk1 is the k-th column of where wk is the k-th column of W , g 1 ˆ G , then from (23), we can obtain the SINR of the k-th user H 1 2 w g k ˆk (24) SIN Rk = K 2 2 0 H H w H g wk g + ˆj + wk Σwk k ˆk j=1,j=k
so we get the system capacity Cˆ by Cˆ =
K
log2 (1 + SIN Rk )
(25)
k=1
After sparsification, the complexity of signal processing can be reduced greatly. Furthermore, the sparse threshold θ is updated according to the channel quality. It is obvious that the larger θ choosed, the better performance obtained, and the more complex the system will be. Therefore, we should choose θ properly to get the trade-off between performance and complexity. Moreover, the sparsity is defined to express the percentage of 0 elements of channel matrix, which is an important indicator to the complexity of system. C. Belief-Propagation(BP) detection A more promising method to exploit the sparsification of the channel matrix is BP [12], [13] algorithm, which is applied in factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI).In this case, the overall complexity of the detection is O (M N × K), and also doesn’t need matrix inversion among the detection. To apply the BP scheme with the channel sparsification method we proposed, we draw the covariance of noise as (21). As a result, it can get better performance for the system when apply the BP algorithm with sparse channel matrix in reality. V. S IMULATION R ESULTS AND A NALYSIS In this section, the performance metric of the large-scale DAS is defined, and then the theoretical results presented in the previous sections are testified through a set of Monte-Carlo simulations. A. Area Spectral Efficiency In large-scale DAS, the maximum Doppler frequency shift has restriction on the number of users which are served simultaneously in system [14]. We consider orthogonal frequency division multiplexing (OFDM) systems [15], [16] [17]. We assume that the system has the same time slot structure as long term evolution (LTE) system. There are 7 OFDM symbols in a time slot, and a resource block (RB) has 7 × 12 resource elements (REs). Similar to [14], we use one OFDM symbol for signaling in each slot. In this paper, the maximum coherence time is assumed to be 1ms (2 slots, or one subframe). Thus, the channel keeps constant over two consecutive RBs in time domain, and there are 144 REs for pilot and data transmission. Among the 144 REs, we use Kpilot REs for pilot signals. Therefore, the ratio of data resources in system is given by (ignoring the cyclic prefix overhead etc.) 144 − Kpilot . (26) η≈ 168
0
10
θ=20dB, MMSE θ=20dB, BP θ=40dB, MMSE θ=40dB, BP
−1
7000
10
6500
10
20dB
−2
BER
2
ASE(bps/HZ/km )
7500
6000
−3
10
40dB
−4
5500
10
Theoretical result M → ∞ Simulation 40dB Simulation 20dB Simulation
5000
4500 0.01
−5
10
−6
0.02
0.03 0.04 0.05 Transmitted power of users (w)
0.06
10 −50
0.07
(a) The ASE performance of Kpilot = 24.
−40
−30 −20 −10 The transmitted power of users (dBm)
Fig. 2.
0
10
The MMSE and BP detection
1
B. Simulation Results
0.995
Sparsity
0.99 Sparse threshold value 40dB Sparse threshold value 20dB 0.985
0.98
0.975
0.97 0.01
0.02
0.03 0.04 0.05 Transmitted power of users (w)
0.06
0.07
(b) The sparsity of Kpilot = 24. Fig. 1.
The ASE performance and the sparsity of Kpilot = 24.
Then, we define the average sum-rate as (bit/s/Hz)
Cˆsum = ηE CˆLB .
(27)
In order to evaluate the performance of the large-scale DAS, we use ASE as the performance indicator, which is defined as [18] Cˆsum CˆASE = , (28) S where S is the area of the cell. TABLE I S IMULATION CONFIGURE The minimum distance between users to RAU Orthogonal Pilot (Kpilot ) K and M The number of antenna in each RAU (N ) The transmitted power of users (dBm) Path loss model (d: Km) Sparse threshold value θ (dB) Thermal noise density Noise Figure Radius of cell
2m [1 8 10 16 20 24 30 36 40 60 72] 720, 720 4 [10 12 14 16 18] 140.7 + 36.7log10(d) [20 40] -174dbm/Hz 5dB 375m
The simulation configuration is given in TABLE I. We use the simulation method provided in [18]. We firstly generate the random location of the K users. For each generated locations of the K users, we generate 500 sets of Rayleigh fading according to the channel model (4). Do this experiment for 200 iterations, we get the simulation results of ASE. For the theoretical results, we compute the ASE with CˆLB,inf for each generated locations of the K users, and after 200 iterations, we obtain the averaged ASE. In Fig.1(a), the performances of the achievable ASE are plotted against the transmitted power of users with Kpilot = 24. It is obtained that with the increment of transmitted power of users, ASE almost keeps constant, which means that it is a interference-limited system. And from the theoretical analysis, we can see that the system performance is restricted by the pilot contamination. Furthermore,we can observe that the approximation for large M is accurate, and after the channel matrix sparsification with the sparse threshold value θ= 20dB, the performance loss is about 17.6%, but the sparsity achieves about 99.5% shown in Fig.1(b), which is beneficial to joint receiver design. When the sparse threshold value θ= 40dB, the performance loss is just about 5.5% and the sparsity is 97.1%. In other words, the channel matrix has 97.1% elements are 0, so that we can use the property of sparse matrix effectively. Therefore, there is a tremendous improvement to reduce the computational complexity in large-scale DAS with the impressive performance. In Fig.1(b), the sparsity keeps constant with different transmitted power, either. Fig.2 shows the simulated BER performance of the MMSE and the FG-GAI BP algorithm with QPSK after channel sparsification. The number of FG-GAI BP iteration is 4. We observe that there is a acceptable performance loss of both MMSE and FG-GAI BP detection as expected, which strongly depend on the sparse threshold value θ. Obviously, the FGGAI BP algorithm performance is better than MMSE, and also much lower complexity when implemented in sparsed channel detection, even though both are interference limited with an error floor.
optimal orthogonal pilot number is obtained by using MonteCarlo simulation.
7500 7000 6500
ACKNOWLEDGMENT This work was supported in part by the National Basic Research Program of China (973 Program 2013CB336600), National Key Special Program No.2012ZX03003005-003, the Natural Science Foundation of China (NSFC) under grants 61221002, 61271205, and China High-Tech 863 Program under Grant No.2014AA012104.
2
ASE(bps/HZ/km )
6000 5500 5000 4500 4000
Theoretical result M → ∞ Simulation 40dB Simulation 20dB Simulation
3500 3000 2500
R EFERENCES 0
10
20 30 40 50 60 The number of orthogonal pilot Users
70
80
(a) The ASE performance versus Kpilot . 1 0.995 0.99 Sparse threshold value 20dB Sparse threshold value 40dB
Sparsity
0.985 0.98 0.975 0.97 0.965 0.96 0.955
0
10
20 30 40 50 60 The number of orthogonal pilot Users
70
80
(b) The sparsity versus Kpilot . Fig. 3.
The ASE performance and the sparsity versus Kpilot .
In Fig.3(a), the performance comparisons of the achievable ASE are plotted against Kpilot . It is observed that the ASE becomes maximal, when the number of orthogonal pilot users is about 24. Moreover, the approximation for large M is accurate with the different number of orthogonal pilot users. And with the increment of the number of the orthogonal pilot users, the performance loss becomes bigger after the channel matrix sparsification. Furthermore, although the performance in θ= 40dB is better than θ= 20dB, the complexity of joint processing will be much lower for θ= 20dB. In Fig.3(b), it is found that the sparsity of channel matrix decreases with the increment of the number of orthogonal pilot users in θ= 20dB and θ= 40dB. VI. C ONCLUSION In this paper, we present an analytical method to reduce the computational complexity for large-scale DAS. Firstly, the single-cell system model of large-scale DAS with pilot reuse is introduced. Then, the lower bound of the sum-rate is obtained with this model, and the asymptotic performance of the sumrate is analyzed for M → ∞. Moreover, an attractive method for large-scale DAS by using matrix sparsification is presented to simplify the signal processing. Simulation results show that the proposed method exhibits impressive performance and the
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