Low-Cost Channel Estimation Algorithm for DRM Receiver

Journal of Communications Vol. 10, No. 6, June 2015

Ming Yan1 and Cheng Yan2 1GxSOC Research Institute, Communication University of China, Beijing 100024, China 2Beijing University of Posts and Telecommunications, Beijing 100876, China Email: [email protected]; [email protected]

Abstract—In this paper, we consider a digital radio mondiale estimation are separated in each dimension, and (DRM) system using orthogonal frequency division techniques including linear interpolation, windowed multiplexing (OFDM) with coherent detection at the receiver. Discrete Fourier Transform (DFT) and Wiener filter The DRM pilots are two-dimensional distribution, linear interpolation are used for estimating each dimension [5]. interpolation and Wiener filter interpolation respectively used in Work in [6] gives an OFDM transmission scheme that is the time and frequency domain as the channel estimation algorithm. We propose a low-complexity improved Wiener suitable for medium frequency and high frequency filter coefficient algorithm to estimate the OFDM channels. Our channels based DRM digital AM broadcasting. proposed algorithm differs from traditional algorithms in two Other previous work includes [7] which provides a ways. Firstly, we divide the DRM pilots into n groups to pilot design to minimize the coherence of the dictionary estimate the channel responses of corresponding OFDM sub- matrix used for sparse recovery in OFDM radio system. carriers (instead of exploiting the whole pilot at the same time Reference [8] introduces a comparative performance in traditional algorithms). Secondly, we utilize the uniform evaluation of the sampling frequency synchronization distribution characteristic of the DRM pilots to reduce the method that eliminates the initial sampling frequency number of Wiener filter coefficients, and this effectively leads offset to reduce the overall synchronization time in DRM to a reduction in computation complexity. In addition, receivers, and gives a new DRM synchronization method simulation results are also presented to gain further insights. to satisfy the advanced synchronization performance Index Terms—Channel estimation, digital radio mondiale, requirements of DRM receivers. wiener filter, OFDM Although the problem of channel estimation for DRM has been widely explored, there is still possibility for a better estimator which can further reduce the I. INTRODUCTION computations and hardware resources. In this paper, we Digital radio mondiale (DRM) is a digital audio propose a low-complexity improved Wiener filter broadcasting technology that can deliver sound quality coefficient algorithm. The proposed algorithm differs comparable to Frequency Modulation (FM) systems, from traditional algorithms in two ways. Firstly, we while working over the traditional Amplitude Modulation divide the DRM pilots into n groups to estimate the (AM) frequency bands, i.e., below 30MHz [1]. DRM channel responses of the corresponding OFDM sub- utilizes orthogonal frequency division multiplexing carriers, whereas the traditional algorithm exploits the (OFDM) transmission technique with coherent whole pilots at the same time. Secondly, since DRM demodulation at the receiver. It is well known that pilots follow a uniform distribution, the number of the channel estimation is critical for coherent detection. Wiener filter coefficients can be greatly reduced. This Known channel estimation algorithms in the literature can effectively leads to a reduction in computation be categorized into two frameworks. The first framework complexity. is decision-directed estimation (DDE) [2] and the second This paper is organized as follows. The transmission framework is pilot-based estimation (PE) [3]. characteristics of DRM is introduced in Section II. In As the DRM transmitted symbol is comprised of pilots, Section III, we describe the interpolation algorithms for PE is adopted in the DRM system. Due to the two- channel estimation. In Section IV, we propose the Wiener dimensional (2-D) pilot model, the optimal channel filter coefficient algorithm for the purpose of channel estimator is the 2-D Wiener filter based on the minimum estimation. Simulation results can be found in Section V mean squared error (MMSE) criterion [4]. However, the and Section VI concludes the paper. computational complexity is too high for practical implementation. To reduce complexity, the 2-D channel II. TRANSMISSION CHARACTERISTICS OF DRM

A. Transmission Frame Structure of DRM Manuscript received January 22, 2015; revised June 23, 2015. This work was supported by the Science Research Fund of the State DRM system includes three different types of data Administration of Radio Film and Television in China under Grant No. channels, namely, the Main Service Channel (MSC), the GDT1221. Corresponding author email: [email protected]. Fast Access Channel (FAC) and the Service Description doi:10.12720/jcm.10.6.423-428 Channel (SDC). The transmitted signal is organized in

transmission superframes, where each transmission interpolation algorithms, namely, linear interpolation, superframe consists of three transmission frames. As wiener filter and windowed DFT. In the next subsections, shown in Fig. 1, the pilot cells, which are located in the we will describe the operation of each interpolation transmission signal, consist of frequency pilots, timing algorithm in detail. pilots and gain pilots. Channel estimation mainly utilizes A. Linear Interpolation the gain pilots. The simplest implementation is the linear interpolation, which can be implemented in both time and frequency domain. The channel response for lth symbol at the

kp th subcarrier can be calculated by (5). Hˆ (,)(,) k l Hˆ k l ˆ ˆ p p1 p p H(,)(,)() kp l H k p l p  l  l p (5) llpp1 

B. Wiener Filter Based on mean square error criterion, the 2-D wiener Fig. 1. Time-frequency location of FAC and SDC signals filter interpolation is wildly used for 2-D channel estimation. The Wiener-Hopf equation can be derived by B. The Channel Models of DRM orthogonality principle in [10]-[12]. We consider a typical multi-path fading channel where E{ H ( k , l ) Hˆ * ( k , l )}  the channel can be realized by a wide-sense stationary pp , uncorrelated scattering (WSSUS) model according to the  E{ H ( k , l ) Hˆ * ( k , l )}  kp,, l p k, l p p p p  DRM standard as follows, {,}klp p k, l

l {,}klp p  k, l (6) h()()() ti c i t t i (1) i 1 where k l donates pilot index in frequency and time p , p where i is the attenuation of the i-th path,  i is the delay domain respectively, kl,, is tap coefficients of wiener of the i-th path, and cti () can be described by a complex- p p k, l valued stationary Gaussian random process characterized filter, (.)* denotes the complex conjugation,  is the set kl, by its variance and power density spectrum (PDS) as of utilized pilots. 2 1 (())f fsh i As H(,) kpp l is zero mean, no correlation h (fN )0 exp{ } (2) i 2 2 2 (i ) 2 d (i ) withT(,) k l , the cross-correlation function can d pp k kpp, l l be expressed as where fish () is the Doppler shift of the i-th path. The Doppler Spread is given by f( i ) 2 ( i ) . E{ H ( k , l ) Hˆ * ( k , l )} (7) sp d k kpp, l l p p The received symbol can be written as The auto-correlation function k k, l l can be R()()()() k T k  H k  N k (3) p p p p expressed as: where R(k) is the discrete received symbol in frequency ˆ * E{ H ( kp , l p ) H ( k p , l p )} (8) domain, T(k) is the transmitted symbol, H(k) is the kp k p, l p l p channel response and N(k) is the additive white Gaussian According to (4), the autocorrelation function can be noise. decomposed as 2 III. INTERPOLATION ALGORITHMS FOR CHANNEL (9) kkllpppp,,, kkll pppp kkll pppp ESTIMATION ES{}kl,

Based on the known pilots, the channel where kp and lp donates the pilot index in the frequency ˆ and time domain, respectively, ES{| |} is the average response H(,) kpp l of the pilots can be calculated by (4) kl, [9]. As channel response of the pilots is known, channel energy of the transmitted symbols, and 2 is the variance response of the rest sub-carriers can be derived from of the noise. The tap coefficients of Wiener filter is given 1 interpolation algorithm. by k,, l k l , where kl, is the cross-correlation R(,)(,) k l N k l 1 ˆ p p p p matrix of the sub-carriers and pilots and is auto- H(,)(,) kp l p  H k p l p  (4) T(,)(,) kp l p T k p l p correlation inverse matrix of pilots. As large amount of computation is required for the two-dimensional Wiener where k p and l p donate the pilot index in the frequency filter, two cascade one-dimensional Wiener filters can be and time domain, respectively. There are three used to achieve the compromise of performance and

complexity. The 1-D Wiener filter interpolation formula where Dl and Dk are the distance of samples in time and at frequency direction is given by frequency direction, respectively. fTsp s and f are the Hˆ ()() k k Hˆ (10) l l p normalized channel bandwidths. As shown in Fig. 2, the l l pilot distance in time direction equals to 3 samples which 1 l()()()k l k l k (11) allows a maximum Doppler spread of around 6 Hz on the robust B according to the DRM standard. In frequency where Hˆ is the channel response of the pilots at the p direction, the spacing is 6 samples, which allows a frequency direction for lth symbol and wkl ()is the maximum delay of 1.8ms. In channel 5 the delay spread wiener filter coefficients at the kth sub-carrier for lth is defined as 4ms which means that the Nyquist theorem symbol. is not fulfilled. With a first interpolation in time domain the distance for interpolation in frequency domain can be C. Windowed DFT reduced to 2 samples and a delay spread of 5.3ms can be Windowed DFT is only used for interpolation in the tolerated. Fig. 3 shows the transmission frame structure frequency direction. Firstly, the receiver symbols in the after the interpolation in the time domain. frequency domain are transformed to time domain The channel estimation algorithm for DRM system can according to IDFT. Then insert 0 to the symbols in the be expressed: time domain. After transforming back to the frequency Firstly, the channel impulse response of the pilots can domain, the interpolation is completed. In order to bring be calculated by (4). The linear and wiener filter down signal sidelobes and spectrum spread, it is interpolation are used in the time and frequency domain necessary to be windowed prior to the Inverse Discrete respectively to complete the whole interpolation process. Fourier Transform (IDFT) [13]-[15]. Generally, the Discrete time-frequency cross-correlation function can Gaussian window is utilized: be divided into the cross-correlation function in the time

1 k 1 and frequency domain, respectively. ()e k 2 1 2 k w() ke e 01kKe (12) (14) k kp, l l p k k p l l p K: the number of gain pilots. Set to 1.6. The cross-correlation function in time and frequency Carriers (Frequency domain) domain can be divided into two models. One model sets S

y the filter delay filter as the channel delay spread . The m b o l s delay power spectrum is: ( T i m

e 1 filter

d o m a

i () 2 (15) n filter filter ) 0 others

:Pilot :Carrier need to estimate The cross-correlation function in frequency domain Fig. 2. The transmission frame after the interpolation can be expressed as:

Carriers (Frequency domain) sin(filter (k k p ) F s ) kk . (16) S p y

m filter()k k p F s b o l s where F is sampling rate. Set Doppler spectrum in the

( s T i m e

filter design as the power spectral density: d o m a i n ) 1 ffD D, filter Sf() 2 fD, filter (17) fDD, filter :Pilot :Interpolation in time domain :Carrier need to estimate 0 others Fig. 3. The transmission frame structure after the interpolation So the cross-correlation function in time domain is:

IV. THE CHANNEL ESTIMATION ALGORITHM FOR DRM sin(2fD, filter ( l l p ) T s ) . (18) llp 2f ( l l ) T If 2-D channel estimation can be separated for each D, filter p s dimension, the distance of pilots in time and frequency where T 1 . domain are chosen accurately to fulfill the Nyquist s Fs sampling theorem [16]: The other model is that the power spectrum of the delay spread obeys negative exponential distribution and 11 f T D and f D (13) cross-correlation function in frequency domain is: sp s l22 k

1 line of the cross-correlation function matrix of the nth (19) kkp 1 2 91 1j 2 ( k kp ) filter / T s group. According to (9), w13,14 w 15,16 w 194,195 . n The classical Doppler spectrum can be expressed a s: Where wxy, is the xth and yth line of the wiener filter 11 coefficients of the nth group. Finally, the number of ffmax 2 wiener filter coefficients is 25*13<<207*104. The Pf() fmax 1 (ff ) (20) max computations and the hardware resources are greatly 0 others reduced. So the cross-correlation function in time domain is: TABLE I: PILOT NUMBERS FOR EACH MODE IN FREQUENCY DOMAIN J(2 f ( l l ) T ) (21) AFTER INTERPOLATION l lp 0, D filter p s Robust Mode Spectrum occupancy: 3 where Ts is the length of the OFDM symbol. A 58 Before channel estimation, frequency offset and timing delay are compensated, and equation (16) is used as B 104 cross-correlation function in frequency domain [17]. The C 70 number of the carriers in the frequency domain is 207 D 89 when the bandwidth is 10Hz on the Robust B. After the interpolation in the time domain, the number of pilots in TABLE II: CARRIER NUMBERS FOR EACH MODE frequency domain is 104. To estimate the channel Robust Mode Spectrum occupancy: 3 response of the residual carriers, in accordance with (11), Kmin -114 the number of Wiener filter coefficient is 207*104. Either A the computations or the occupied hardware resources are Kmax 114 too large [18]. Kmin -103 B This paper proposes one improved coefficient Kmax 103 algorithm. i1,,, i 2 i 207 : the sub-carrier indices in Kmin -69 C frequency domain. PPP1,,, 2 104 : the pilot indices in the Kmax 69 frequency direction after linear interpolation. Firstly, the Kmin -44 D pilots are divided into 91 groups: Kmax 44 The 1th group： PPP,,, . 1 2 13 TABLE III: THE NUMBERS OF ADDITIONS OF THE CONVENTIONAL AND The 2th group： PPP2,,, 3 14 . PROPOSED METHODS The 3th group： PPP,,, . 3 4 15 Conventional Robust Mode Proposed method ⋮ method The 90th group： PPPP,,,, . A 2×58+2×57 2×9+2×8 91 92 93 103 The 91th group： PPPP,,,, . B 2×104+2×103 2×13+2×12 92 93 94 104 C 2×70+2×69 2×13+2×12 The wiener filter coefficients of i1,,,, i 2 i 3 i 14 are derived from the pilots of the 1th group. D 2×89+2×88 2×13+2×12

The wiener filter coefficients of ii15, 16 are derived TABLE IV: THE NUMBERS OF MULTIPLICATIONS OF THE from the pilots of the 2th group. CONVENTIONAL AND PROPOSED METHODS The wiener filter coefficients of ii, are derived Conventional 17 18 Robust Mode Proposed method from the pilots of the 3th group. method ⋮ A 4×58 4×9 B 4×104 4×13 The wiener filter coefficients of ii190, 191 are derived from the pilots of the 89th group. C 4×70 4×13 D 4×89 4×13 The wiener filter coefficients of ii192, 193are derived from the pilots of the 90th group. Table I and Table II are pilot numbers after The wiener filter coefficients of i194,,, i 195 i 207 are derived from the pilots of the 91th group. interpolation in the frequency domain and carrier As the pilots in the frequency domain after the numbers for each mode at spectrum occupancy 3, interpolation are obedient to uniform distribution respectively. From Table III and Table IV, we can see that compared to the conventional method, the additions 1 2 91 , where n is the auto- k kp k k p k k p kkp and multiplications of the proposed method are reduced correlation function matrix of the nth group. about 85% in mode A, about 88% in mode B, about 82% 1 2 91 n in mode C and about 86% in mode D. 13,14 15,16 194,195 . Where xy, is the xth and yth

V. SIMULATION RESULTS algorithm can only be used in the frequency domain, and the spectral leakage can’t be avoided. Based on the In this paper, the channel bandwidth is 10Hz and the Robust B mode is selected. The useful part of OFDM MMSE criterion, the performance of the wiener filter is symbol Tu: 21.33ms, guard interval Tg : 5.33ms, sub- superior to other algorithms. As shown in Fig. 6, under condition of the same BER, carrier spacing: 4678. The DRM channel model 3 and 5 the performance of the proposed algorithm is about 0.2dB is chosen. Set a Bit Error Rate (BER) threshold to smaller than the traditional algorithm. Simulation results 3 10 used to compare the different methods. Linear-wiener show that the proposed algorithm can fulfill the linear-linear, linear-DFT, wiener-DFT, and wiener- requirements of the DRM system. wiener are on behalf of linear, windowed DFT and Channel 3 0 wiener filter interpolation in the time and frequency 10 direction, respectively. the proposed algorithm linear-wiener -1 As shown in Fig. 4, from the BER curves of linear- 10 wiener and wiener-wiener, we can see that before the

-2 BER threshold is reached, there is a minor interval 10 between the two curves. When BER exceeds the threshold, the performance of wiener-wiener is 2 ~ 3dB -3 10 higher than the linear-wiener. BER

Channel 3 0 -4 10 10 linear-wiener

-1 wiener-wiener Reference 4 -5 10 10

-2 10 -6 10 0 5 10 15 20 25

-3 SNR/dB 10 Fig. 6. BER versus SNR for linear-wiener and the proposed method

BER -4 10

-5 10 VI. CONCLUSIONS

-6 A larger number of the filter coefficients occupy a lot 10 of memory, and consume a large number of multipliers to

-7 10 implement the filter. The proposed algorithm in this paper 0 5 10 15 20 25 is mainly based on two aspects. Firstly, based on the SNR/dB Fig. 4. BER versus SNR for wiener-wiener and linear-wiener method transmission channel characteristics of DRM, the auto- correlation function of pilots and the cross-correlation Channel 3 0 function between pilots and data positions are only 10 related to the distance between pilots and data. Secondly,

-1 10 the distribution of DRM pilots is uniformly distributed after linear interpolation, so the auto-correlation functions -2 10 of the pilots in every group are equal. Theoretically, further reduction of computation -3 10 complexity can be achieved with the increase of the

BER -4 number of groups. However, the fundamental principles 10 of Wiener Filter are based on MMSE, and the accuracy of

-5 10 channel estimation will reduce if the number of groups linear-linear linear-DFT Reference 5 increases further. The proposed algorithm is used to -6 10 linear-wiener reduce the number of the coefficients. The simulation wiener-DFT Reference 15 results show that the performance of proposed algorithm -7 wiener-wiener Reference 4 10 0 5 10 15 20 25 can fulfill the requirements of the DRM system. SNR/dB Fig. 5. BER versus SNR for different methods ACKNOWLEDGMENT As shown in Fig. 5, even at a relatively high SNR, the The authors would like to thank the reviewers for their BER of the linear-linear and linear-DFT can’t reach the detailed reviews and constructive comments, which have threshold. From the comparison of the BER cures helped improve the quality of this paper. This work was between wiener-wiener and wiener-DFT, we can see that, supported by Science Research Fund of the State performance of wiener-wiener is 1 ~ 2dB higher than the Administration of Radio Film and Television in China wiener-DFT with the same BER. Windowed DFT under Grant No. GDT1221.

REFERENCES [12] X. Chen and X. Li, “Performance Analysis of Wiener Filtering Channel Estimation in LTE,” Electronic Test, vol. 4, pp. 17-21, [1] Digital Radio Mondiale (DRM)-System Specification, ETSI Apr. 2010. Standard ES 201 980 V3.1.1-2009. [13] K. Yun, H. Zhang, W. Lu, and Q. Wu, “Kalman filter and FFT- [2] X. Yang, Y. Gu, and J. Zhang, “Low-complexity decision based channel estimation algorithm in OFDM system,” feedback channel estimation approach for high mobility OFDM,” Electronic Measurement Technology, vol. 30, pp. 156-159, Nov. in Proc. 8th International Conference on Wireless 2007. Communications, Networking and Mobile Computing, Shanghai, [14] R. Wen, “Optimization of DFT Interpolation,” Journal of Yichun China, 2012, pp. 1-4. University, vol. 34, no. 4, pp. 10-12, Apr. 2012. [3] J. Nuckelt, M. Schack, and T. Kurner, “Performance evaluation [15] R. Guo, “A DFT based channel estimation method for downlink of wiener filter designs for channel estimation in vehicular of LTE system,” Journal of Beijing Union University (Natural environments,” in Proc. IEEE Vehicular Technology Conference, Sciences), vol. 25, no. 2, pp. 20-23, Jun. 2011. San Francisco, 2011, pp. 1-5. [16] M. Henkel, C. Schilling, and W. Schroer, “Comparison of [4] P. Krishna, T. Kumar, and K. Rao, “Pilot based LMMSE channel channel estimation methods for pilot aided OFDM systems,” in estimation for Multi-User MIMO- OFDM systems with power Proc. IEEE 65th Vehicular Technology Conference, Dublin, 2007, delay profile,” in Proc. IEEE Asia Pacific Conference on Circuits pp. 1435-1439. and Systems, Ishigaki, Japan, 2014, pp. 487-490. [17] X. Tong and T. Luo, Principles and Applications of OFDM [5] Y. Ma, K. Liu, J. Duan, and Y. Song, “Research and Mobile Communication Technology, The People's Posts and implementation of channel estimation of digital radio receiver Telecommunications Press, 2003, ch. 5, pp. 127-129. based on OFDM,” in Proc. International Conference on Neural [18] M. Liu, M. Crussiere, and J. Helard, “A Novel data-aided channel Networks and Signal Processing, Nanjing, China, 2008, pp. 104- estimation with reduced complexity for TDS-OFDM systems,” 108. IEEE Trans. Broadcasting, vol. 58, no. 2, pp. 247-260, June 2012. [6] Y. Liang, S. Zhang, P. Gu, and L Wu, “On the design of MLC- LDPC-OFDM in DRM MF and HF channels,” in Proc. Sixth Ming Yan received his B.S. in International Conference on Wireless Communications and communication engineering from the Nanjing Signal Processing, Hefei, China, 2014, pp. 1-6. University of Posts and Telecommunications [7] C. Qi, G. Yue, L. Wu, and A. Nallanathan, “Pilot design for (NJUPT) in 2002 and his M.S. in signal and sparse channel estimation in OFDM-based cognitive radio information processing from the systems,” IEEE Trans. on Vehicular Technology, vol. 63, no. 2, Communication University of China (CUC) in pp. 982-987, Feb. 2014. 2006. He received his Ph.D. in communication [8] K. Kwon, S. Kim, J. Hwang, and J. Paik, “Performance and information system from CUC in 2012. In evaluation of synchronization method for reducing the overall January 2012, Dr. Yan Ming joined the synchronization time in digital radio mondiale receivers,” KSII GxSOC Research Institute at CUC as a Research Assistant. Transactions on Internet and Information Systems, vol. 7, no. 8, pp. 1860-1875, Aug. 2013. Cheng Yan received his B.S. degree from the [9] S. Hu, “Pilots-based OFDM channel estimation schemes research School of Electronic Information and Control and application,” M.S. thesis, Beijing University of Posts and Engineering at Shandong Polytechnic Telecommunications, Beijing, China, 2008. University Jinan in 2011 and his M.S. in signal [10] L. Zhang, “Study of channel estimation based on pilot in OFDM and information processing from the Communication University of China (CUC) in communication system,” M.S. thesis, Jilin University, Jilin, 2014. He is currently pursuing a Ph.D. degree China, 2009. [11] C. Liu and L. Qian, “Implementation of OFDM channel at Beijing University of Posts and estimation based on two-dimension Wiener filtering,” Telecommunications. His research interests Information Technology, vol. 32, pp. 27-30, May 2008. include signal processing, mobile multimedia and wireless communication.