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The transmit subspace for MIMO systems

Subspace of signal is convenional concept and very useful for applying to communication theory. In MIMO, the transmit beams can be created based on this concept, that can be predicted channel fading matrix. Here, the paper considers good subspace for transmitter can form for these beams. Moreover, the author using simulation to show higher capacity given by these beams than conventional method of creating transmit beam. | The transmit subspace for MIMO systems Nghiên cứu khoa học công nghệ THE TRANSMIT SUBSPACE FOR MIMO SYSTEMS TRAN HOAI TRUNG Abtract: Subspace of signal is convenional concept and very useful for applying to communication theory. In MIMO, the transmit beams can be created based on this concept, that can be predicted channel fading matrix. Here, the paper considers good subspace for transmitter can form for these beams. Moreover, the author using simulation to show higher capacity given by these beams than conventional method of creating transmit beam. Keywords: Wireless communication, MIMO system, Transmit subspace 1. PROBLEM The subspace method, obtained from the covariance of the channel matrix, represents the productive transmit dimensions and the power allocation at the receiver. Simulations of the productive dimensions are used to investigate the invariance of these dimensions at the transmitter. 2. THE SUBSPACE OF A SIGNAL When a signal can be expressed in terms of its phase and time parameters [1]: L x(t ) a i e j ( 2 fi t i ) (1) i 1 The correlation of this function at times of t and t k is defined as [1]: rxx (k ) E x(t ) x(t k ) ai2 e j 2 fi k (2) The correlation matrix for K times of observation is expressed as: rxx [0] rxx [ 1] . rxx [( ( K 1)] r [1] rxx [0] . rxx [ ( K 2)] (3) R xx xx . . . . rxx [ K 1] rxx [ K 2] . rxx [0] It can be rewritten to emphasise the influence of subspace: R xx SPS H , (4) where S is defined as: S s1 s2 . s L in which s i , i 1 L that is defined as: s i [1 e j 2 f . e j 2 ( K 1) f ] (5) and P diag[a12 , a 22 ,., a L2 ] . Therefore, the subspace of a signal consists of linear combinations of all vectors s i , i 1 L of S . R xx can be then rewritten so as to emphasize the influence of the SVD (Singular Value Decomposition) is defined as: R xx UΣ V H ,where U, V are .