时变频率选择性MIMO信道估计：一种一阶统计量方法
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*This work was supported by NSFC (No. 60496310, 60272046), NSF of Jiang-Su Province (BK2002051) and the Grant of PhD Programmes in High Education Institutes of MOE (No. 20020286014).
Luxi Yang Jun Tao (DSP Division, Wireless Department, Southeast University, Nanjing 210096) Abstract: The technology of Multiple Input and Multiple Output (MIMO) is a breakthrough in the field of mobile communication. In this paper, we address the problem of MIMO time-variant channel estimation and propose a method based on the first-order statistics of received measurements. In the proposed method, periodic sequences with different periods are superimposed on the information-bearing symbols corresponding to different transmit antennas. And in this way, coefficients of different sub-channels can be separated for estimation. Simulations are given to verify effectiveness of the method. Besides, as an attempt to solve the problem of high peak-to-average symbol power ratio due to the superimposed sequences, a thorough analysis is given and optimal sequence in the sense of minimizing peak-to-average symbol power ration is designed. Keyword: MIMO channel, channel estimation, peak-to-average symbol power ratio 1. INTRODUCTION It has been recently shown that the Multi-Input and Multi-Output (MIMO) communication system leads to a significant increase in the system spectral efficiency. Accurate channel information at the receiver is critical to achieve optimum receiver performance. More recently, many channel estimation algorithms for MIMO systems have been developed. In wireless communication environments, multipath is a major impairment, it can bring about inter-symbol interferences, and leads to frequency-selective fading channels. Mobile communication channels are also characterized by fast fading or time dispersion especially when strong Doppler shifts are present. So MIMO channel estimation in frequency-selective and time-varying case is necessary. Channel estimation with training sequence or pilot symbol is popular due to its practicability. We can, for example, present a linear least squares (LLS) approach by construct optimal training sequences for MIMO communication system [1]. In recent years. there are also many literatures on pilot methods among which a first-order statistical method with periodically superimposed pilot is especially attractive since usually very low computational complexity is needed and the superimposed pilot didn’t decrease communications throughput [2], [3], [4], [5]. However, among all these discussions for first-order methods of channel estimation, only Single-Input Single-Output (SISO) systems was considered, few ever deal with MIMO system, especially time-varying MIMO channel estimation. In fact, issue of estimation for complex exponential basis expansion time-varying channel model in a Single-Input Multi-Output (SIMO) wireless communication system has been addressed by [3]. Here we aim to generalize this basic idea to channel estimation of a MIMO system. The main difficulty for MIMO systems different from the SISO or SIMO systems is that each receiving signal is the weighted mixture of different transmit signals from different sub-channels, and we need to know how to separate the coefficients estimation of different sub-channels.
___________________________________________________________________________ http://www.paper.edu.cn
MIMO Channel Estimation in Time-Varying Frequency-Selective Fading Case: A First Order Statistical Method
中国科技论文在线 _________________________________________________________________wk.baidu.com_________ http://www.paper.edu.cn
In this paper, we propose a superimposed periodic pilot scheme for time-variant channel estimation of a MIMO system [6]. Periodic sequences with different periods are superimposed on the information-bearing symbols corresponding to different transmit antennas. And in this way, coefficients of different sub-channels can be separated for estimation. As a premise, the time-varying channel is assumed to follow a complex exponential basis expansion model. Estimation of such channel can be achieved only with a simple first-order statistics, and especially, mean-value uncertainty of additional noise is ignorable as is different from traditional method. Also, there is no loss of information rate except for a controllable increase in transmission power. Besides, as an attempt to solve the problem of high peak-to-average symbol power ratio due to the superimposed sequences, a thorough analysis is given and optimal sequence in the sense of minimizing peak-to-average symbol power ration is designed. At last, numerical simulations demonstrate the effectiveness of this proposed method. 2. MIMO CHANNEL ESTIMATION WITH SUPERIMPOSED PERIODIC PILOTS First, we give a brief description of SIMO system as described in [3]. Here, one transmit antenna and N receive antennas are employed. Let {b( n)} denote the scalar input to the SIMO time-variant channel with discrete-time impulse response h(n; l ) (0 ≤ l ≤ L) , which is a N dimension column vector. With complex exponential basis expansion channel model
Luxi Yang Jun Tao (DSP Division, Wireless Department, Southeast University, Nanjing 210096) Abstract: The technology of Multiple Input and Multiple Output (MIMO) is a breakthrough in the field of mobile communication. In this paper, we address the problem of MIMO time-variant channel estimation and propose a method based on the first-order statistics of received measurements. In the proposed method, periodic sequences with different periods are superimposed on the information-bearing symbols corresponding to different transmit antennas. And in this way, coefficients of different sub-channels can be separated for estimation. Simulations are given to verify effectiveness of the method. Besides, as an attempt to solve the problem of high peak-to-average symbol power ratio due to the superimposed sequences, a thorough analysis is given and optimal sequence in the sense of minimizing peak-to-average symbol power ration is designed. Keyword: MIMO channel, channel estimation, peak-to-average symbol power ratio 1. INTRODUCTION It has been recently shown that the Multi-Input and Multi-Output (MIMO) communication system leads to a significant increase in the system spectral efficiency. Accurate channel information at the receiver is critical to achieve optimum receiver performance. More recently, many channel estimation algorithms for MIMO systems have been developed. In wireless communication environments, multipath is a major impairment, it can bring about inter-symbol interferences, and leads to frequency-selective fading channels. Mobile communication channels are also characterized by fast fading or time dispersion especially when strong Doppler shifts are present. So MIMO channel estimation in frequency-selective and time-varying case is necessary. Channel estimation with training sequence or pilot symbol is popular due to its practicability. We can, for example, present a linear least squares (LLS) approach by construct optimal training sequences for MIMO communication system [1]. In recent years. there are also many literatures on pilot methods among which a first-order statistical method with periodically superimposed pilot is especially attractive since usually very low computational complexity is needed and the superimposed pilot didn’t decrease communications throughput [2], [3], [4], [5]. However, among all these discussions for first-order methods of channel estimation, only Single-Input Single-Output (SISO) systems was considered, few ever deal with MIMO system, especially time-varying MIMO channel estimation. In fact, issue of estimation for complex exponential basis expansion time-varying channel model in a Single-Input Multi-Output (SIMO) wireless communication system has been addressed by [3]. Here we aim to generalize this basic idea to channel estimation of a MIMO system. The main difficulty for MIMO systems different from the SISO or SIMO systems is that each receiving signal is the weighted mixture of different transmit signals from different sub-channels, and we need to know how to separate the coefficients estimation of different sub-channels.
___________________________________________________________________________ http://www.paper.edu.cn
MIMO Channel Estimation in Time-Varying Frequency-Selective Fading Case: A First Order Statistical Method
中国科技论文在线 _________________________________________________________________wk.baidu.com_________ http://www.paper.edu.cn
In this paper, we propose a superimposed periodic pilot scheme for time-variant channel estimation of a MIMO system [6]. Periodic sequences with different periods are superimposed on the information-bearing symbols corresponding to different transmit antennas. And in this way, coefficients of different sub-channels can be separated for estimation. As a premise, the time-varying channel is assumed to follow a complex exponential basis expansion model. Estimation of such channel can be achieved only with a simple first-order statistics, and especially, mean-value uncertainty of additional noise is ignorable as is different from traditional method. Also, there is no loss of information rate except for a controllable increase in transmission power. Besides, as an attempt to solve the problem of high peak-to-average symbol power ratio due to the superimposed sequences, a thorough analysis is given and optimal sequence in the sense of minimizing peak-to-average symbol power ration is designed. At last, numerical simulations demonstrate the effectiveness of this proposed method. 2. MIMO CHANNEL ESTIMATION WITH SUPERIMPOSED PERIODIC PILOTS First, we give a brief description of SIMO system as described in [3]. Here, one transmit antenna and N receive antennas are employed. Let {b( n)} denote the scalar input to the SIMO time-variant channel with discrete-time impulse response h(n; l ) (0 ≤ l ≤ L) , which is a N dimension column vector. With complex exponential basis expansion channel model