Semi-blind Channel Estimation for MIMO-OFDM Systems Based on Received Signal Reconstruction

Abstract

Blind channel estimation for MIMO-OFDM systems was discussed, and a subspace based blind channel estimation algorithm by re-constructing the received signal and its simplified one were proposed. The algorithm changed the channel matrix of the transfer function into a block Toeplitz high matrix exploiting OFDM cyclic prefix, and the channel estimation characteristic equation was obtained with the orthogonality between the signal subspace and the noise subspace of the reconstructed signal. In order to eliminate the influence of virtual carriers, the singular value decomposition of the equivalent transmit signal was imported. The simplified algorithm exploited a QR decomposition and Gram-Schmidt orthogonalization process aiming at reducing the complexity of obtaining the noise subspace. Simulation results illustrate the performance of the proposed algorithm via numerical experiments compared with the other one, and it’s insensitive to overestimates of the true channel order. Introduction Channel estimation the pre-condition of coherent detection in MIMO-OFDM systems. Traditional method is to insert pilot in the transmitting data [1]. In order to improve frequency spectrum efficiency, blind channel estimation has become hot topic in recent years [2]~[7]. Among those blind algorithm, subspace based algorithm receives great attention because of its better accuracy performance [8]. An OFDM subspace algorithm exploiting CP is proposed in [9]. Although with a good accuracy performance, it is not applicable to systems with existence of virtual sub-carriers. Traditional OFDM subspace based algorithm is expanded to MIMO-OFDM systems in [10] with slow convergence rate. The paper pays attention to fast semi-blind channel estimation in MIMO-OFDM systems with existence of virtual sub-carriers. Learnt from [9], a semi-blind algorithm based on received signal reconstruction and its simplified one are proposed. Some notations are illustrated as follows: T ( ) ⋅ , ( ) ⋅ and H ( ) ⋅ are transposition, conjugate and conjugate transpose respectively. N I is N N × unit matrix. [ ] E ⋅ is statistical average. [1: ] k x is the front k elements in x . [:, ] k X and [ ,:] k X are the k -th column and k -th row of X . [ : , : ] i j m n X is the sub-matrix of X from row i to j and column m to n . ( ) span X and ( ) rank X are the column space of matrix X and its rank respectively. ( ) vec X is vectorization of matrix X . 2 || || ⋅ is 2 l norm. ⊗ is Kronecker product. Define exp( 2 / ) N w j N p � . 2 (0, ) σ CN is complex Gaussian distribution. MIMO-OFDM System Model Assume that the number of transmitting and receiving antennas in MIMO-OFDM system are t N and r N respectively with r t N N ≥ . There are N sub-carriers with D data sub-carriers and ( ) N D − virtual sub-carriers. The indices of data sub-carriers are denoted by 0 k to 0 1 k D + − . CP and OFDM length are P and Q N P = + International Conference on Automation, Mechanical Control and Computational Engineering (AMCCE 2015) © 2015. The authors Published by Atlantis Press 1890 respectively. Data to be transmitted is T 1 2 ( , ) [ ( , ), ( , ),..., ( , )] t N n k x n k x n k x n k = x , where ( , ) i x n k is the data on the k -th sub-carrier of antenna i in n -th OFDM symbol. Accordingly, the total n -th data to be modulated can be denoted by T T T T 0 0 0 [ ( , ) , ( , 1) ,..., ( , 1) ] n n k n k n k D = + + − x x x x . n s is the modulated data after insertion of CP. Define T 1 2 ( , ) [ ( , ), ( , ),..., ( , )] t N n k s n k s n k s n k = s , where ( , ) i s n k the k -th data after IFFT on antenna i . We have T T T T T T [ ( , ) ,..., ( , 1) , ( ,0) , ( ,1) ,..., ( , 1) ] n n N P n N n n n N = − − − s s s s s s . Define: