Elsevier

Physical Communication

Volume 29, August 2018, Pages 86-94
Physical Communication

Full length article
An improved channel estimation method using doubly reduced matching pursuit over fractional delay multipath channel

https://doi.org/10.1016/j.phycom.2018.04.020Get rights and content

Abstract

Owing to the inherent sparse channel feature in multi-carrier modulation systems, compressed sensing (CS)-based techniques have been used for channel estimation with less pilot subcarriers for orthogonal frequency division multiplexing (OFDM) systems. Because of a sparse multipath channel’s characteristic of fractional delay, the channel measurement matrix that is generated by conventional time-domain sampling approaches cannot perfectly recover the channel impulse response (CIR), especially in the case of two adjacent paths that both have with non-negligible power. In this study, a fractional delay multipath channel model is used to simulate the wireless multipath channel. In addition, a time-domain oversampling based doubly reduced matching pursuit (DRMP) algorithm at the receiver is proposed to improve the estimation accuracy while reducing the computational complexity. Simulation results show that the proposed method can improve both the bit error rate (BER) performance and estimation time compared to conventional methods in an environment with fractional delay.

Introduction

In recent years, compressed sensing (CS) has attracted much attention as a novel technique for recovering a sparse signal from a small set of measurements. CS is a creative approach to acquire, process, and recover sparse signals [1], and it has emerged as a very competitive alternative to traditional information processing operations such as sampling, sensing, compression, and estimation. A typical application of CS is channel estimation. In various wireless channels, such as ultra-wideband (UWB), underwater acoustic (UWA), or millimeter wave (mmWave) channels, delay spread is far larger than the number of significant paths, and the channel impulse response (CIR) is approximately sparse [[2], [3], [4]]. Recent developments have shown that CS-based methods can achieve more accurate pilot-assisted channel estimation with less pilot subcarriers [[5], [6], [7]]. [[8], [9]] used the basis pursuit (BP) algorithm based on l1-norm minimization for sparse channel estimation in underwater acoustic communication. [[10], [11], [12]] used matching pursuit (MP) and orthogonal matching pursuit (OMP) based on greedy iteration for channel estimation in an orthogonal frequency division multiplexing (OFDM) communication system. On the other hand, in recent years, many optimization methods for sparse channel estimation have focused on the pilot’s structure [[13], [14], [15], [16]]. However, there is an underlying assumption that the receiver is perfectly synchronous without considering the interference of fractional delay in [[10], [11], [12], [13], [14], [15], [16]]. In other words, signal sampling at receivers is exactly synchronous with the same symbol rate with transmitters. Actually, this assumption does not always hold. With fractional delay, the path energy will leak to all other taps, and the discrete-time CIR becomes non-strictly sparse in the classical sense [17]. Therefore, conventional CS-based channel estimators cannot perform well, and they may even fail completely over fractional delay channels. To resolve this problem, [[18], [19], [20]] introduced a time-domain oversampling approach that is helpful for realizing additional multipath diversity. This method can improve the channel estimation accuracy in the time-domain instead of the frequency-domain because the number of parameters to be estimated is at most equal to the size of the guard interval [21]. Recently, CS-based channel estimation methods have been applied the time-domain [22]. In [22], a time-domain oversampling scheme was proposed to achieve multipath diversity over Rayleigh fading channels. Though the problem originating from fractional delay is suppressed effectively in [[18], [19], [20], [22]], time-domain oversampling at the transmitter and receiver results in extra transmission bandwidth and power. [23] executes virtual oversampling in the receiving side with a low-complexity algorithm called modified orthogonal matching pursuit (MOMP), but this scheme is only applicable to the channel model proposed in [24], in which the channel delay changes slowly compared to the channel gain.

In this paper, we mainly use a channel model of Bad Urban 12 (BU12) in COST207 [25] with fractional delay in which the delay time is shorter than the normal sampling period of the receiver. To flexibly detect the fractional delay, a time-domain oversampling method at the receiver without increasing any transmission bandwidth is proposed. However, time-domain oversampling almost certainly results in higher computational cost, and this is disadvantageous for its application. Reduced matching pursuit (RMP) is a new algorithm proposed for efficient CS signal reconstruction [26]. RMP is advantageous in terms of both accuracy and algorithm complexity compared to conventional algorithms [26]. In this study, we use RMP for channel estimation in the OFDM system. Furthermore, we propose an improved RMP algorithm called doubly reduced matching pursuit (DRMP) to further reduce the computational cost without losing the advantages of RMP.

The main contributions of this paper are summarized as follows:

(1) The RMP algorithm achieves higher reconstruction accuracy with significantly low computational complexity compared to existing greedy recovery algorithms, and it is applied for channel estimation in the OFDM system in this study. Furthermore, owing to the special structure of the measurement matrix in the OFDM communication system, this study proposes a DRMP algorithm that can further reduce the computational cost of RMP without sacrificing the advantages of RMP.

(2) To demonstrate the advantages of the method proposed in this study, a metric called BER time product (BTP), similar to that used in [26], is newly proposed to measure the tradeoff between the channel estimation time and the error.

The remainder of this paper is organized as follows. Section 2 introduces the system model. In Section 3, we discuss the proposed channel estimation method using DRMP algorithm with oversampling. Section 4 presents the numerical results, and finally, Section 5 presents the conclusions of this study.

Notation: We represent matrices and vectors with bold upper and lower case letters, respectively. Superscript T denotes the transpose. h˜ and hˆ denote the observed signal and estimated signal of h, respectively. g˜ and gˆ denote the observed signal and estimated signal of g, respectively.

Section snippets

System model

Fig. 1 shows a system block diagram for an OFDM communication system with a fractional delay channel model, in which it contains the proposed channel estimation method using DRMP algorithm with oversampling.

The payload u contains K subcarriers. These K subcarriers comprise M pilot subcarriers and K-M data subcarriers. u is defined as u=[u0u1uK1]T,where uCm+i=pm,fori=0dCm+i,for0<i<C,where pm is the mth pilot symbol and dk, the k th data symbol. C=round(KM) denotes the number of data

Impulse response estimation using compressed sensing

To suppress the impact of the fractional delay in the transmission path, we use a time-domain oversampling method only at the receiver and therefore the transmission power remains unchanged.

The parameter X is defined as the number of multiples of oversampling. Thus, the oversized sampling FFT matrix and reordering matrix are given by FX=exp(j2πknXN)0kXN10nXN1,and QX=0K2,K2IK20XNK,K20XNK,K2IK20K2,K2,

Then, the received signal vector v in the frequency domain can

Numerical results

In this section, to demonstrate the performance of the proposed estimation scheme, a simulation platform was developed using MATLAB for OFDM systems. The proposed method was evaluated in terms of BER performance, normalized mean square error (NMSE) performance and CPU running time. In addition, the most common tradeoff for different channel estimation methods is between the estimation accuracy and the computational complexity. We propose BTP as a metric to clarify the tradeoff between accuracy

Conclusion

This study performs channel estimation for a BU12 channel with fractional delay. To detect the fractional delay, the receiver uses a time-domain oversampling scheme. Because signal oversampling is only done at the receiver, this system can avoid an increase in extra bandwidth during transmission. The BER performance shows that a system with signal oversampling at the receiver has better performance compared to a system with a normal sampling rate. Therefore, signal oversampling at the receiver

Acknowledgments

The authors would like to thank editor and anonymous reviewers for their valuable comments to improve the quality of this paper. This work was supported in part by the Central State-Owned Capital Management and Budget Project under Grant 2013-470, in part by the National Nature Science Foundation of China under Grant 61771191, in part by the Fundamental Research Funds for the Central Universities under Grant1053214004, in part by the Natural Science Foundation of Hunan Province under Grant

Ziji Ma received the B.E. degree in electronics engineering and the M.S. degree in electronics science and technology from Hunan University, Changsha, China, in 2001 and 2007, respectively. He received the Ph.D. in information systems from Nara Institute of Science and Technology, Japan, in 2012.

From 2012 to 2013, he was an assistant professor at Nara Institute of Science and Technology. From 2013, he moved to the school of electrical and information engineering of Hunan University, Changsha,

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  • Ziji Ma received the B.E. degree in electronics engineering and the M.S. degree in electronics science and technology from Hunan University, Changsha, China, in 2001 and 2007, respectively. He received the Ph.D. in information systems from Nara Institute of Science and Technology, Japan, in 2012.

    From 2012 to 2013, he was an assistant professor at Nara Institute of Science and Technology. From 2013, he moved to the school of electrical and information engineering of Hunan University, Changsha, China. His major research interests include digital signal processing, wireless communication and sensor technology. He is a member of IEEE and IEICE, also an associate editor of IEICE Trans. on Fund. E-mail: [email protected]

    Qiang Peng received the B.E. degree in electronics engineering from Hunan Institute of Engineering, Xiangtan, China, in 2012. He is currently pursuing his M.S. degree in electronics science and technology in School of Electrical and Information Engineering, Hunan University, Changsha, China. His main research interest includes wireless communications. E-mail: [email protected]

    Hongli Liu received the B.E. and M.S. degrees in electrical engineering and the Ph.D. degree in control theory and engineering from Hunan University, Changsha, China, in 1985, 1988 and 2000, respectively. In 2000, he joined the Department of Electronics and Information Engineering, Hunan University. Now, he is a professor and the dean of the same department. His research interests include wireless communication theory and its applications in wireless sensor networks and cognitive radio. E-mail: [email protected]

    Zhi Yan received the B.E. degree in mechanical engineering and automation and the Ph.D. degree in communications and information systems from Beijing University of Posts and Telecommunications, Beijing, China, in 2007 and 2012, respectively. From 2012 to 2014, he was a Researcher with the Network Technology Research Center, China Unicom Research Institute. He is currently an Assistant Professor with the School of Electrical and Information Engineering, Hunan University, Changsha, China. His current research interests are in cognitive radio, cooperative communication, and cellular network traffic analysis and modeling. E-mail: [email protected]

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