A Novel Channel Estimation Algorithm for 3GPP LTE Downlink System Using Joint Time-Frequency Two-Dimensional Iterative Wiener Filter
Jinfeng Hou, Jian Liu
School of Communication and Information Engineering University of Electronic Science and Technology of China (UESTC) Chengdu 611731, China Email: houjinfeng@gmail.com, liuj@uestc.edu.cn
Abstract—The channel estimation algorithms are employed in 3GPP Long Term Evolution (LTE) downlink system to assist the coherent demodulation of Orthogonal Frequency Division Multiplexing (OFDM) symbols. Based on the comparison of several exiting different channel estimation algorithms, we propose a joint time-frequency two-dimensional iterative Wiener filter (IWF) channel estimation algorithm for 3GPP LTE downlink system. In this scheme, we first apply the linear minimum mean square error (LMMSE) algorithm based on singular value decomposition (SVD) for IWF in frequency domain, and then the values after the first filtering in frequency domain are used to achieve the second IWF in time domain. Comparing to the conventional algorithms, the channel estimation algorithm proposed by this paper brings up lower bit error rate (BER) and adds little computational complexity.

I. I NTRODUCTION In December 2004, the Third Generation Partnership Program (3GPP) members started a feasibility study on the enhancement of the Universal Terrestrial Radio Access (UTRA) in the aim of continuing the long time frame competitiveness of the 3G Universal Mobile Telecommunications System (UMTS) technology beyond High Speed Packet Access (HSPA). This project is called Long Term Evolution (LTE) [1]. Using Orthogonal Frequency Division Multiple Access (OFDMA) on the air interface as multiple access technology for the downlink, 3GPP LTE takes place of Code Division Multiple Access (CDMA) which is applied to UMTS for a long time. At the same time, 3GPP LTE uses multipleinput multiple-output (MIMO) technology as well as adaptive technology to enhance the data rate and system performance, which makes the air interface transmission capacity reach over 100Mbit/s on the downlink. 3GPP LTE, favored by the most telecommunication operators from the whole world, has been generally recognized as the internationally powerful mobile communication system to support of the world telecommunications industry in 2010 to 2020. Orthogonal Frequency Division Multiplexing (OFDM) has been applied in the physical layer of 3GPP LTE downlink system due to its high data rate transmission and high bandwidth efficiency to mitigate the inter symbol interference (ISI) in a
This work is supported by National Natural Science Foundation of China (No. 60932002), Fundamental Research Funds for the Central Universities (No. ZYGX2009J005).

severe multi-path fading channel [1]. A dynamic estimation and tracking of the fading channel at the receiver is necessary before the coherent demodulation of OFDM symbols since the radio channel is frequency selective and time-varying for wideband mobile communication systems [2]. In wideband mobile channels, the pilot-based signal correction scheme has been proven a feasible method for OFDM systems. When pilot-symbol-aided channel estimation is employed, pilot symbols, known by both the transmitter and the receiver, are sent in predefined locations. By processing the received signal at these positions, the receiver can estimate the whole channel response for each OFDM symbol. The pilot-symbol-aided channel estimation algorithms for 3GPP LTE downlink system can be based on Least Square (LS) or Minimum Mean Square Error (MMSE) [3] in the mobile communication environment. The two algorithms mentioned above are used to estimate channel in frequency domain. LS algorithm is the simpler algorithm, which dose not need channel information; MMSE algorithm uses the correlation between subcarriers and channel statistic information, which has better estimation performance and is widely used in OFDM channel estimation. In this paper, we present a novel channel estimation algorithm for 3GPP LTE downlink system, called joint timefrequency two-dimensional iterative Wiener filter (IWF) algorithm, which is based on linear minimum mean square error (LMMSE) estimation. In this algorithm, the LMMSE algorithm is used for IWF in frequency domain firstly, and then the values after the first filtering in frequency domain are used to achieve the second IWF in time domain. The performance of the estimator is evaluated using 3GPP LTE parameters, showing that the proposed algorithm effectively improves the bit error rate (BER) performance which is even closer to the ideal channel estimation compared with the conventional algorithms. The computational complexity of the LMMSE estimator can be reduced by using an approximated LMMSE estimator with optimal rank reduction by singular value decomposition (SVD) [4]. Thus, the algorithm proposed by this paper brings little computational complexity. The rest of this paper is organized as follows. In section II, the 3GPP LTE downlink system model is described. In section III, available channel estimation algorithms and timefrequency two-dimensional IWF algorithm for LTE downlink

Input

Channel encoding

Scrambling

Modulation

Layer mapper

Precoding

Resource X element mapper

OFDM modulator

x

Wireless channel Output Channel decoding Descrambling Demodulation Layer demapper Signal detection Channel OFDM estimation Y demodulator y

Fig. 1: 3GPP LTE downlink system model

frequency

system are discussed. In section IV, the simulation environments and results are described. Finally, section V concludes the paper. II. S YSTEM D ESCRIPTION Fig. 1 displays the 3GPP LTE downlink system model used in this paper. On the transmitter side, the input bits are fed into the channel encoding block [5]; the coded bits are scrambled and modulated into complex-valued modulation symbols; these complex-valued modulation symbols are mapped onto one or multiple transmission layers on the antenna ports, precoded on each layer and mapped to resource elements for each antenna port where the reference signals are inserted; finally, these symbols of each antenna port, including data and reference signals, are modulated into complex-valued time-domain OFDM signals which will be transmitted over a wireless multi-path channel [6]. At the receiver, we assume the perfect synchronization. After OFDM demodulator, the received signal Y can be described as: Y = XH + W (1) where Y is the received signal vector, X is a matrix with the elements of the transmitted signals on its diagonal, H is a channel frequency response vector, and W is a vector of independent identically distributed (i.i.d.) complex zero-mean 2 Gaussian noise with variance σW . The noise W is assumed to be uncorrelated with the channel H. In order to recover the transmitted bits from the received signal, the channel estimation block needs to obtain an estimation of parameter H. For this purpose, reference signals are transmitted in some predefined time-frequency two-dimensional positions in the 3GPP LTE downlink system. The received signal in these locations can be written as: YP = XP HP + WP (2)

OFDM symbol subcarrier

R0

R0

R0

R0

R0

R0

R0 l 0

R0 l
6 l 0

l

6 time Fig. 2: Mapping of downlink Cell-specific reference signals (one antenna port)

use Cell-specific reference signals to give an analysis. Fig. 2 illustrates the resource elements used for reference signal transmission in a resource block on one antenna port case. The notation R0 is used to denote a resource element used for reference signal transmission on antenna port. From Fig. 2 we can see that reference symbols are transmitted in the first and fifth OFDM symbol within a slot with an even frequencydomain spacing of 6. III. C HANNEL E STIMATION A LGORITHM A. Available Channel Estimation Algorithms Given the received data YP and the transmitted reference symbols XP at reference signal positions, the LS estimation of the channel frequency response at these positions in formula (2) can be given as: ˆ HP,LS = XP −1 YP (3)

where XP , HP and WP are subsets of the corresponding matrices defined in formula (1), and the subscript (·)P denotes positions where reference signals are transmitted. In the 3GPP LTE standard, three types of downlink reference signals are defined: Cell-specific reference signals, Multicast Broadcast Single Frequency Network (MBSFN) reference signals and UE-specific reference signals [6]. In this paper we

Then by linear interpolating the channel frequency responses of reference resource elements in both time and frequency domain, we can estimate the channel transfer function values of data resource elements as shown in Fig. 2. The LS estimation of HP is susceptible to Gaussian noise. The other estimation algorithm is MMSE, whose performance is better than the LS estimation [3], which tries to

minimize the mean square error between the actual and estimated channels. The mathematical representation for MMSE estimator of the channel frequency response in frequency domain is as follows [4]: HLM M SE ( ( )−1 )−1 2 ˆ = RHHP RHP HP + σW XX H HP,LS (4)

as: ˆ (2) HP,LM M SE ( = RHP HP RHP HP + β SN R IP

)−1

ˆ (1) HP,LM M SE

(7)

ˆ where HP,LS is the LS estimation value of parameter HP 2 obtained from formula (3), σW is the variance of AWGN, RHHP is the crosscorrelation matrix between all subcarriers and the subcarriers with reference signals within the same OFDM symbol, RHP HP is the autocorrelation matrix of the subcarriers with reference signals within the same OFDM H symbol, and the superscript (·) )denotes Hermitian transpose. ( −1 in formula (4) with its By replacing [ term XX H the ( )−1 ] expectation E XX H , the MMSE channel estimator in frequency domain can be represented as [4]: ( )−1 ˆ LM M SE = RHH RH H + β IP ˆ H HP,LS (5) P P P SN R where β is a constant depending on the type of modulation, SN R is the average signal-to-noise ratio, and IP is the identity matrix. Then using linear interpolation algorithm in time domain, we can estimate the channel transfer function values of all data resource elements as shown in Fig. 2. From formula (5) we can see that the MMSE channel estimation algorithm requires knowledge of the channel frequency correlation and the operating SN R. Thus, it has better performance than the LS estimation algorithm. B. Joint Time-Frequency Two-dimensional IWF Channel Estimation Algorithm To improve the BER performance, while not increasing too much computational complexity, and taking into account that the 3GPP LTE downlink system inserts reference signals in both the time and frequency domain, in this paper we present a joint time-frequency two-dimensional IWF channel estimation algorithm for the system. At first, one IWF is applied in frequency domain for the OFDM symbol containing reference signals. And then, another IWF is applied in time domain for all subcarriers within multiple OFDM symbols respectively. The new algorithm will be described as follows. 1) IWF in Frequency Dimension: In the first stage, only the reference signals in the same OFDM symbol are used to obtain the estimation of the channel frequency response which can be expressed as: ˆ (1) HP,LM M SE ( = RHP HP RHP HP + )−1 (6)

The estimate of the channel frequency response after IWF ˆ (2) in the subcarriers with reference signals HP,LM M SE is then employed to obtain an estimation of the channel frequency response of all subcarriers within the same OFDM symbol. ˆ HF,LM M SE ( )−1 (8) ˆ (2) H = RHH RH H + β IP
P P P

SN R

P,LM M SE

2) IWF in Time Dimension: Assume that the estimated channel frequency responses of the nth subcarriers after the first IWF in the frequency domain can be given as: ˆ (n) HF,LM M SE [ ]T ˆ (n) ˜ (n) ˆ (n) ˜ (n) ˆ (n) ˜ (n) = H0 + W0 , · · · , Hi + Wi , · · · , HL−1 + WL−1 (9) where L is the number of the OFDM symbols with reference ˆ (n) ˜ (n) signals within each subframe. Hi and Wi are the channel frequency response and the corresponding residual noise of the nth subcarrier in the ith OFDM symbol with reference signals. After IWF based on LMMSE algorithm in the time domain for the nth subcarrier to reduce the corresponding residual noise, yields: ˜ (n) HF,LM M SE ( (n) (n) = RHP HP RHP HP +
(n) β SN R IL

)−1

ˆ (n) HF,LM M SE

(10)

where RHP HP is the autocorrelation matrix of the nth subcarrier of all OFDM symbols with reference signals within one subframe. Then we use the estimated channel frequency response after ˜ (n) IWF HF,LM M SE to estimate the channel frequency response of the nth subcarriers of all OFDM symbols within one subframe. ˆ (n) HT,LM M SE ( )−1 (11) (n) (n) ˜ (n) =R R + β IL H
HHP HP HP SN R F,LM M SE

β SN R IP

ˆ HP,LS

Then an IWF based on LMMSE algorithm is used for ˆ (1) HP,LM M SE to reduce the noise effects, which can be given

where RHHP is the crosscorrelation matrix between the nth subcarriers of all OFDM symbols and the nth subcarriers of all OFDM symbols with reference signals within one subframe. Finally, we get the channel transfer function values of all data resource elements as shown in Fig. 2. Note that there is a matrix inverse involved in the estimator both in time and frequency domain, which has high computational complexity if the number of reference signals is very large. To reduce the complexity of the estimator proposed by this paper, we adopt a low-rank approximation based on the SVD [4] of the autocorrelation matrix. The matrix inverse is decomposed as: )−1 ( β RHP HP + SN R IP ( ) (12) ( )−1 SN R SN R SN R −1 H IP − β × U Λ + β IP = β U

(n)

where U is a matrix with orthonormal columns and Λ is a diagonal matrix. For the 3GPP LTE downlink system, there are only 14 OFDM symbols in which there are 4 OFDM symbols with reference signals in each subframe, so the matrix singular value decomposition operation is relatively easy to calculate. The computational complexity of the estimator proposed by this paper is relatively low. IV. S IMULATION A ND P ERFORMANCE E VALUATION In the following, simulation results are given to demonstrate the performance of the joint time-frequency two-dimensional IWF estimator proposed in Section III for the 3GPP LTE downlink system. For the purpose, a single-user single-input single-output (SUSISO) OFDM system based on the 1.4MHz 3GPP LTE downlink physical layer parameters will be considered. The parameters for the 3GPP LTE downlink system used in the simulation are indicated in Table I. QPSK modulation scheme has been considered and Vehicular A (VehA) channel model [7] with 6 taps is employed in the simulation. We assume perfect synchronization since the aim is to observe the performance of the proposed channel estimation method. Results are presented in terms of BER as a function of the average signal-to-noise ratio (SNR). TABLE I: Simulation Paraneters
Parameters Bandwidth Channel model Data modulation Sampling frequency Subcarrier spacing Slot duration OFDM symbols per slot Antenna scheme Specifications 1.4 MHz VehA (Vehicular A) QPSK 1.92 MHz 15 KHz 0.5 ms 7 SISO
BER

10

0

10

−1

10

−2

LS MMSE Iterative Wiener Filter perfect 10
−3

0

2

4

6

8 10 SNR [dB]

12

14

16

18

Fig. 3: Comparisons of BERs for different channel estimation algorithms V. C ONCLUSIONS In this paper, we propose a joint time-frequency twodimensional IWF channel estimation algorithm for the 3GPP LTE downlink system with relatively low complexity. The proposed channel estimation algorithm is constructed by IWF based on LMMSE algorithm in both frequency and time domain, which can reduce the noise effects and improve the BER performance obviously compared with the LS estimator and MMSE estimator. Simulation results show that the proposed estimator shows better performance than both LS estimator and MMSE estimator. Finally, using a low-rank approximation estimator based on the SVD decomposition of the channel auto-correlation matrix, the complexity can be significantly reduced. R EFERENCES
[1] “Evolved Universal Terrestrial Radio Access (E-UTRA); LTE Physical Layer - General Description,” 3rd Generation Partnership Project, Tech. Spec. TS 36.201, V8.3.0, Mar. 2009. [2] A. R. S. Bahai and B. R. Saltzberg, Multi-Carrier Digital Communications: Theory and Applications of OFDM: Kluwer Academic/Plenum, 1999. [3] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O. Borjesson, “On channel estimation in OFDM systems,” in Proc. IEEE 45th Vehicular Technology Conf., Chicago, IL, Jul. 1995, pp. 815-819. [4] O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson and P. O. Borjesson, “OFDM channel estimation by singular value decomposition,” in Proc. IEEE 46th Vehicular Technology Conference, Atlanta, GA, USA, Apr. 1996, pp. 923-927. [5] “Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding,” 3rd Generation Partnership Project, Tech. Spec. TS 36.212, V8.6.0, Mar. 2009. [6] “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation,” 3rd Generation Partnership Project, Tech. Spec. TS 36.211, V8.6.0, Mar. 2009. [7] “Evolved Universal Terrestrial Radio Access (E-UTRA); Spatial channel model for Multiple Input Multiple Output (MIMO) simulations,” 3rd Generation Partnership Project, Tech. Rep. TR 25.996, V8.0.0, Dec. 2008.

The legend “LS” denotes LS channel estimation at the positions with reference signals with linear interpolation in both time and frequency domain, “MMSE” shows MMSE channel estimation in frequency domain with linear interpolation in time domain, “Iterative Wiener Filter” shows the channel estimation proposed by this paper, and “perfect” shows perfect channel knowledge for the 3GPP LTE downlink system. Fig. 3 illustrates the BER performance of channel estimation with different channel estimation algorithms for the 3GPP LTE downlink system over VehA channel. As shown in this figure, for the joint time-frequency two-dimensional iterative Wiener filter algorithm, the BER performance outperforms both LS and MMSE algorithm. Furthermore, the BER performance of proposed iterative Wiener filter algorithm is very close to the ideal estimation, but for the computational complexity, the proposed channel estimation algorithm will not increase too much.