# Singular Value Decomposition Channel Estimation in STBC MIMO-OFDM System
## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-out (MIMO) technologies have been widely used in wireless communication systems [1; 2]. The OFDM technology improves the spectrum utilization efficiency. Moreover, inter-symbol interference (ISI) can be avoided by adding the cyclic prefix (CP), which is inserted in the front of the OFDM symbol. The OFDM technology can flexibly select suitable subcarriers for transmission, so the spectrum resource allocation is more flexible. The MIMO technique with multiple antennas at both transmitter and receiver can increase system capacity and link reliability in the multipath propagation environment [3; 4]. Hence, the combination of MIMO and OFDM technologies could improve the system performance. By using specially designed channel codes at the transmitter and channel decoding at the receiver in MIMO-OFDM systems, space-time block coding (STBC) can provide diversity transmission gains and combat channel fading effectively. Hence, STBC is widely used in MIMO-OFDM systems [5]. Space-time block decoding (STBD) requires accurate channel state information (CSI). Due to the effect of additive white Gaussian noise (AWGN) and interference between antennas, CSI cannot be easily obtained in STBC MIMO-OFDM systems. Hence, channel estimation is a key technology to improve the STBC MIMO-OFDM system performance. There have been many studies on channel estimation in single antenna OFDM systems. Pilot-based channel estimation methods are widely used in communication systems. Pilot-based channel estimation method estimates the channel by inserting the known pilot sequences into the transmitted OFDM symbols [6; 7]. Pilot symbols are inserted in various patterns, such as block-type, comb-type, and scatter-type to adapt to different channel environments. The comb-type and scatter-type pilots are more adapt to the fast fading channel and block-type pilot is more adapt to the slow fading channel [8]. The least square (LS) channel estimation method is very simple and has low complexity [9]. However, the performance of the LS channel estimation method is poor because it is heavily affected by noise. The threshold channel estimation method filters out AWGN in channel coefficients by setting an appropriate threshold. However, the choice of the threshold has great impact on system performance. It is very difficult to select the appropriate threshold to filter out the noise as much as possible. A linear filtering LS (LFLS) channel estimation method was proposed in [10]. It can keep the energy of the main paths and remove the effect of AWGN. However, the disadvantage of the LFLS method is that the suppression factor of linear filter changes with the change of the channel environment. A novel channel estimation method based on the time-domain threshold was proposed in [11]. The threshold value was determined by obtaining a standard deviation of estimation noise through the wavelet decomposition of the frequency-domain estimated channel coefficients. This method obtained an appropriate threshold through the wavelet decomposition to filter out the AWGN. However, it cannot be directly applied to multiple antennas systems. An iterative scatter-based channel estimation method for the OFDM/offset quadrature amplitude modulation (OQAM), which reduces the real and imaginary interferences at the receiver to improve the channel estimation, was proposed in [12]. In OFDM/OQAM systems, the orthogonal condition of the subcarriers is guaranteed from the complex domain to the real domain. OFDM/OQAM also does not use any CP, which improves the spectral efficiency and accuracy of channel estimation. Inserting pilot sequences into the transmitted data would reduce the spectral efficiency. To solve this problem, the blind channel estimation method is proposed for OFDM systems [13; 14]. The blind channel estimation method does not require inserting pilots at the transmitter. The relevance of input data and output data can be used to estimate the channel.