# Singular Value Decomposition Channel Estimation in STBC MIMO-OFDM System
## 1 Introduction
The blind channel estimation method can transmit more data symbols in a certain time interval. However, blind channel estimation is a very complex method. The semi-blind channel estimation method has a good tradeoff between bandwidth utilization and computational complexity [15; 16]. The semi-blind channel estimation is the combination of pilot-based and blind channel estimation methods. Semi-blind schemes are computationally simpler than blind channel estimation methods, at the cost of only requiring a few pilot symbols. Channel estimation in the MIMO-OFDM system is more complex than that in the OFDM system due to the interference between transmit and receive antennas. Many studies are also focused on channel estimation in MIMO-OFDM systems. A fast blind subspace channel estimation method for STBC-OFDM systems based on the circular property of the channel matrix was proposed in [17]. This method has fast convergence property than conventional blind subspace channel estimation methods. However, it cannot estimate the strong frequency-selectivity and fast fading channels. A sparse Bayesian learning (SBL)-based channel estimation scheme was proposed in an STBC MIMO-OFDM wireless system [18]. The pilot-based SBL technique obtains successive updates of the approximately sparse MIMO channel based on an expectation maximization formulation for estimation of the SBL channel hyper parameters. The data aided SBL scheme utilizes the maximum likelihood symbol detection to further improve the system performance. Although this method has better performance, the complexity is further improved. An optimal pilot pattern selection using the cat swarm optimization algorithm is applied in [19]. It improves the accuracy of channel estimation. During channel estimation, the pilots are optimally selected using the cat swarm optimization algorithm with the fitness of delay and phase, which reduces the mutual coherence and communication complexity. Under the condition of 20 or 100 users, the proposed method has the best bit error rate (BER) performance in static Rayleigh channels. However, it has poor performance in the fast fading channel. A joint maximum likelihood and MMSEestimation based signal detection is proposed for the combination system of radio over fiber link and MIMO-OFDM wireless channel [20]. It can automatically determine which kind of estimation method can be used according to the channel signal-to-noise ratio (SNR) condition. The advantages of this method are that it has low system complexity and improves the nonlinear effect of radio over fiber link. A robust semi-blind receiver combined with the Tucker-2 model was proposed in [21]. The proposed receiver has high spectral efficiency and can be used in multi-user massive MIMO systems. The BER performance decreases dramatically with the increase of SNR. However, this method cannot adapt to the fast fading environment. In this paper, an orthogonal pilot sequence is designed to suppress the interference of pilot symbols from other transmit antennas. The multiple antennas channel estimation problem can be transformed into the single antenna channel estimation problem, which reduces the complexity of the channel estimation. This paper also focuses on the analysis of the STBC and MMSE channel estimation method to improve the system performance. To further reduce the calculation complexity, the singular value decomposition (SVD) is used to decompose the channel autocorrelation matrix. This paper uses different constellation modulation modes such as quadrature phase shift keying (QPSK), 16-quadrature amplitude modulation (16 QAM), and 64 QAM. Different channel environments such as China DTV Test 1 st (CDT1), CDT6, CDT8, Brazil A, and Brazil B are used to test the performance of the STBC MIMO-OFDM system. Simulation results verify that the SVD method combined with STBC has better BER performance than conventional LS and threshold channel estimation methods in the multipath channel environment. The rest of this paper is organized as follows.