A Study Of Oblique Projection And Its Application In Blind Channel Estimation

Oblique projection is a kind of mathematical tool founded in the 1930s. Compared to the great popularity using of orthogonal projection, oblique projection seems to be paid little attentions. As new concepts and system model such as structured noise are proposed, the limitation of orthogonal projection becomes obvious and people are paying more and more attentions to the using of oblique projection.Integrate and systematical analysis about oblique projection theory is proposed in this thesis including how to construct an oblique projection operator, what its properties are on geometric, algebraic and signal processing, if it's stable and robut in the case of noise existed and how to computer it and so on. The point about the oblique projection is that it's actually a weighted least square solution and it performs well in the case of low noise ratio and interferences existed.Blind channel estimation is a hot and quite important subject to high spectrum efficiency transmission. In the second part of this paper, we firstly establish the mathematics model of some kinds of classical channels such as SISO, SIMO, MIMO and OFDM which are critical to master all channel estimation algorithm. It's proved all of them are related to FIR channel model.Provided that oversampling in space domain ( ? ?0) and FIR channel model as well as the same structure between outputs and inputs, oblique projection can be used to do the blind channel estimation. Toeplitze structure in channel and Hankel structure in datas are essential. Combining algorithm with system design is an attractive idea in getting good channel estimator since reasonable model and signal processing method result in good estimator.Finally, the case of block precoded ST-OFDM (MIMO-OFDM) system which oblique projection is used to do the blind channel estimation is explained in detail. It is proved that the outer product of the channel matrix and the input symbol matrix can be obtained by oblique projection. The ambiguity is resolved too. Simulation results show that the oblique projection blind channel algorithm in this system can provide competitive channel estimation performance with fewer symbol numbers compared to subspace-based blind channel estimator, which makes it is competent for estimating slowly time-varing multipath channels in the future and completes blind channel estimation algorithm using oblique projection from SIMO to MIMO.