computer simulation in Section V and finally conclusions = Cr diag[Cr (0), Cr (1),..., Cr ( N P − 1)] are drawn in Section VI. T T T II. SIGNAL MODEL
Sun Songlin
School of Information and Communication Engineering Beijing University of Posts & Telecomms Beijing, China slsun@
Jing xiaojun
School of Information and Communication Engineering Beijing University of Posts & Telecomms Beijing, China jxiaojun@
h = [h1 ,..., hNt ]
MIMO-OFDM system with Nt transmit antennas and Nr receive antennas is considered. At each transmit (receive) antenna, the conventional OFDM modulator (demodulator) is used. OFDM is considered to employ N carriers for the transmission of Na parallel data symbols. Nv indicates the number of virtual carriers located at the edges of the OFDM spectrum. After inserting virtual carriers, the OFDM block becomes: u = [u0 , u1 ,..., u Nu , 0,..., 0, u− Nu ,..., u−2 , u−1 ] A cyclic prefix (CP) of length ν is inserted in the starting part of each frame. To avoid inter block interference, we assume that ν﹥L-1, where L is the maximum length of all channels. After removing the cyclic prefix at the receive antenna, we obtain the L×1 vector, which can be written as (1).
Abstract—A novel channel estimation scheme called LS_Tik is proposed in this paper. In Multiple-Input and Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system, virtual carriers are usually placed at the edges of the signal spectrum to keep the useful band isolation from interfering signals that occupy neighboring frequency bands. For a conventional LS channel estimation, it is observed that a linear increase in virtual carriers (VCs) contributes to an exponential increase of the condition number of the inverse matrix which will cause inverse problem. In this paper, the modified LS method uses Tikhonov regularization to deal with the inverse problem. And later we also derived the method of calculating the optimal regularization parameter. Simulation results show that the proposed algorithm outperforms the conventional LS algorithm using phase-shifted pilot. Keywords-MIMO-OFDM; carriers; Channel estimatioformation and Communication Engineering Beijing University of Posts & Telecomms Beijing,China huanghai@ filter, virtual carriers are used [4]. When introducing virtual carriers, the performance of the conventional LS channel estimation is significantly degraded due to dispersive distortion [5]. [6] analyses the effects of virtual carriers on channel estimation without suggesting an improvement strategy. [7] investigates the effect of virtual carriers on channel estimation and addresses the large performance degradation due to the poorly-conditioned matrix issue in the inverse problem. ML channel estimation method is proposed. The limitation is that the computational complexity is too high for calculating the channel second order statistics. Attempting to avoid the effect of the inverse problem on channel estimation, in [8], iterative DFT-based channel estimation method has been proposed. The phase-shifted pilot is used and the channel frequency responses (CFR) of the pilot position which falls into the VCs is calculated through the processing in the time domain. However, in order to make the MSE of the CFR as small as possible, we need to repeat the iteration procedure for several times. The optimum pilot design is proposed in [9] and [10], which is designed as non-equally powered and non-equally spaced in order to avoid inverse problem. However, the performance of optimum pilot designs will be affected by both channel length and the number of VCs and thus will have to compromise on the overall system performance. In this paper, we use generic equispaced and equipowered orthogonal pilot designs for implementation purposes. The DFT matrix at the pilot location may become poorly-conditioned because of the VCs. Thus, to solve the inverse problem, a modified LS channel estimation algorithm is proposed. The rest of this paper is organized as follows: Section II presents the system model of MIMO-OFDM systems with virtual carriers. The LS channel estimation and the MSE analysis is presented in section III. Next, in Section IV we analysis the modified LS channel estimation. We demonstrate the performance of the new techniques by
A Novel Channel Estimation Scheme for MIMO-OFDM Systems with Virtual Subcarriers