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Research Article An Improved Multicell MMSE Channel Estimation in a Massive MIMO System

Ke Li,1 Xiaoqin Song,2 M. Omair Ahmad,3 and M. N. S. Swamy3

1 College of Information Technology, Beijing Union University, Beijing 100010, China 2 College of Electronics and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 3Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada H3G IM8

Correspondence should be addressed to Ke Li; like@buu.edu.cn

Received 22 January 2014; Accepted 9 April 2014; Published 8 May 2014

Academic Editor: Kan Zheng

Copyright © 2014 Ke Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Massive MIMO is a promising technology to improve both the spectrum efficiency and the energy efficiency.The key problem that impacts the throughput of a massive MIMO system is the pilot contamination due to the nonorthogonality of the pilot sequences in different cells. Conventional channel estimation schemes cannot mitigate this problem effectively, and the computational complexity is increasingly becoming larger in views of the large number of antennas employed in a massive MIMO system. Furthermore, the channel estimation is always carried out with some ideal assumptions such as the complete knowledge of large- scale fading. In this paper, a new channel estimation scheme is proposed by utilizing interference cancellation and joint processing. Highly interfering users in neighboring cells are identified based on the estimation of large-scale fading and then included in the joint channel processing; this achieves a compromise between the effectiveness and efficiency of the channel estimation at a reasonable computational cost, and leads to an improvement in the overall system performance. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

1. Introduction

Recently, there has been a great deal of interests in MIMO systems using very large antenna arrays, namely, the massive MIMO or full dimensionMIMO (FD-MIMO) systems [1–4]. Such systems can provide a significant increase in reliability, data rate, and energy efficiency with simple signal processing [1]. When the number of base station (BS) antennas grows large, the channel vectors between the users and the BS become very large-size random vectors and under “favor- able propagation” conditions. Then, they become pairwise orthogonal. As a consequence, with simple linear processing, for example, maximum-ratio combining (MRC), or zero forcing (ZF), assuming that the BS has perfect channel state information (CSI), the interference from other users can be cancelled without consuming more time-frequency resources. This dramatically increases the spectral efficiency. Furthermore, by using a very large antenna array at BS, the transmit power can be drastically reduced.

Practically, however, the BS does not have perfect CSI. Instead, it estimates the channels as usual. Conventionally it is done by using uplink pilots. Since both the time- frequency resources allocated for pilot transmission and the channel coherence time are limited, the number of possible orthogonal pilot sequences is limited too, and hence, the pilot sequences have to be reused in neighbouring cells of cellular systems. Therefore, channel estimates obtained in a given cell get contaminated by the pilots transmitted by the users in other cells. This causes pilot contamination [5]; that is, the channel estimate at the base station in one cell becomes polluted by the pilots of the users from other cells.

Considering the importance of pilot contamination miti- gation to guarantee the good performance of massiveMIMO, many schemes, ranging from optimal pilot design and allo- cation, advanced channel estimation, to downlink precoding [5–11], have been proposed to deal with this problem.

In [10], a pilot design criterion and Chu sequence-based pilots have been proposed by exploiting the orthogonality

Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2014, Article ID 387436, 9 pages http://dx.doi.org/10.1155/2014/387436

2 International Journal of Antennas and Propagation

of the channel vectors of massive MIMO systems. Because of the proposed pilots, the channel estimate of most terminals of a cell is only interfered by partial cells rather than all the other cells, where the latter is caused by traditional pilots. As a result, pilot contamination is mitigated. It is also possible to coordinate the use of pilots or adaptively allocate the pilot sequences to different terminals in the network [8].

Multicell joint channel estimation algorithms [5, 8] or even blind techniques that circumvent the use of pilots altogether [7] may mitigate or eliminate the effects of pilot contamination. The approach in [7] exploits the asymptotic orthogonality of the channel vectors in very large MIMO systems and shows that the channel to each user can be estimated from the covariance matrix of the received signals, up to a remaining scalar multiplicative ambiguity, which can be resolved by utilizing a short training sequence.

The new precoding techniques, such as pilot contami- nation precoding [11], that take into account the network structure can utilize cooperative transmission over a multi- plicity of cells—outside of the beamforming operation—to nullify, at least partially, the directed interference that results from pilot contamination. Unlike coordinated beamforming over multiple cells which requires estimates of the actual channels between the terminals and the service-arrays of the contaminating cells, the pilot-contamination precoding requires only the corresponding slow-fading coefficients.

By overviewing the abovementioned channel estimation schemes, it can be seen that, for simplicity, it is always assumed that the large-scale fading propagation (i.e., pathloss and shadow fading) is fixed and known 𝑎 𝑝𝑟𝑖𝑜𝑟𝑖, which is not the case in practice. Furthermore, the computational complexity of conventional channel estimations such as least square (LS) and minimum mean square error (MMSE) estimations, grows sharply in a massiveMIMO system, as the number of antennas is much more than that in the current multiple antennas systems. This problem is getting worse in the case of joint processing in a multicell scenario. As a countermeasure to these problems, an improved channel estimation scheme, which aims at mitigating the pilot con- tamination at an affordable expense and in a more realistic situation, is proposed in this paper.

To deal with the abovementioned problems, a new chan- nel estimation scheme is proposed by utilizing interference cancellation and joint processing. Highly interfering users in neighboring cells are identified based on the estimation of large-scale fading and then included in the joint channel processing; this achieves a compromise between the effec- tiveness and efficiency of the channel estimation and leads to an improvement in the overall system performance. Metrics of the performance evaluation of the channel estimation are defined, and finally simulation results are provided which validate the proposed scheme.

The paper is organized as follows. Section 2 gives themul- ticell massive MIMO system model and the pilot design. The conventional channel estimator and the proposed multicell joint MMSE channel estimation are presented in Section 3. Section 4 presents the simulation results and the analysis of computational complexity of the proposed scheme. Finally, Section 5 concludes this paper.

Notations. (⋅)∗, (⋅)𝑇, and (⋅)𝐻 denote the conjugate, transpose, and conjugate transpose, respectively, [⋅]

𝑖,𝑗 is the (𝑖, 𝑗)th entry

of a matrix, 𝐸{⋅} is the expectation, and ‖ ⋅ ‖ denotes the Frobenius norm.

2. Multicell Massive MIMO System Model

2.1. System Model. Here we consider a massive MIMO cellular systemwith 𝐿 hexagonal cells, as depicted in Figure 1. Each cell comprises one base station with𝑀 antennas and𝐾 single antenna users (𝐾 ≪ 𝑀, in the case of amassiveMIMO system). All the cells share the same band of frequencies. In addition, the system employs OFDM and works in time- division duplex (TDD) mode.

Let the average power (during transmission) at the base station be 𝑝

𝑓 and let the average power at each user be 𝑝

𝑟 . In

one coherence interval, the channel responses of𝑁 𝑎 symbols

are assumed to be static, which means that the channel estimate is effective only in this interval. Consequently, a total of𝑁 𝑐 symbols are used for pilots from all the terminals to BS,

and the remaining 𝑁 𝑎 − 𝑁 𝑐 symbols are used for a two-way

data transmission. Apart from that, following the model in [1], the channel responses are assumed to be constant in the frequency smooth interval, which consists of𝑁

𝑠 consecutive

subcarriers. Therefore, to estimate the channel response of one subcarrier, every terminal can transmit pilots over 𝑁

𝑠

subcarriers. In the following, channel responses of the 𝑁 𝑠

subcarriers will be estimated. As a result, the pilot length is given by 𝜏 = 𝑁

𝑐 𝑁 𝑠 , and thus up to 𝜏 terminals can transmit

pilots to BS without intracell interference. The propagation factor (channel response) between the

𝑚th base station antenna of the 𝑙th cell and the 𝑘th user of the 𝑗th