Blind channel estimation using redundant precoding: new algorithms, analysis, and theory

Digital signal processing (DSP) techniques have played an important role in channel equalization and estimation in communication systems. While channel equalization and estimation are usually done by pilot-assisted methods in most systems, algorithms for blind channel estimation have also been largely studied due to high bandwidth efficiency. However, up to date, most blind methods possess disadvantages such as slow convergence speed, high complexity, poor performance, etc., compared to pilot-assisted methods. These drawbacks have made many consider blind methods as inapplicable in modern communication systems which feature fast-varying channels. In this thesis, we consider the blind channel estimation problem in block transmission systems with linear redundant precoding (LRP) which have been widely adopted in modern communication systems in recent years. The main contribution of this thesis is to considerably reduce the amount of received data required for blind estimation and suggest blind methods which are applicable even in fast-varying environments (e.g., in wireless channels). New algorithms are proposed, performance analysis derived, and theoretical issues studied. The first part of the thesis focuses on new algorithms for blind channel estimation and blind block synchronization in LRP systems. Two major types of linear redundant precoding, namely zero-padding (ZP) and cyclic prefixing (CP), are considered in this thesis. We first propose a generalized, subspace-based algorithm for blind channel estimation in ZP systems of which two previously reported algorithms are special cases. The generalization uses an integer parameter called repetition index which represents the number of repeated uses of each received block. The number of received blocks required for subspace-based blind estimation is roughly inversely proportional to the repetition index. By choosing a larger repetition index, the amount of received data can be significantly reduced. The concept of repetition index is also applied in blind channel estimation in CP systems, which are more widely used than ZP systems in many current communication standards such as orthogonal frequency division multiplexing (OFDM) systems. The use of repetition index in CP systems is much less obvious and conceptually more complicated than in ZP systems. By choosing a repetition index larger than unity, the number of received blocks needed for blind estimation is significantly reduced compared to all previously reported methods. Theoretically, the proposed method can perform blind estimation using only three received blocks in absence of noise. In practice, the number of received blocks needed to yield a satisfactory bit error rate performance is usually on the order of half the block size. The proposed algorithm can be directly applied in OFDM systems without any modification of transmitter structure. A semiblind algorithm for channel estimation in OFDM systems is also proposed based on the extension of the blind algorithm. Another important problem, namely the blind block synchronization, is also studied. Most existing blind estimation methods in LRP systems assume the block boundaries of the received streams are perfectly known to the receiver, but this assumption is usually not true in practice since no extra known samples are transmitted. Two algorithms for blind block synchronization are proposed for ZP and CP systems, respectively. In particular, the block synchronization problem in CP systems is a broader version of the timing synchronization problem in the OFDM systems. The proposed algorithms exploit the concept of repetition index and both theoretical and simulation results suggest their advantages over all previously reported algorithms, especially when the amount of received data is limited. The second part of the thesis deals with theoretical issues related to blind channel estimation. Performance analysis of the generalized blindchannel estimation algorithm in ZP systems is first given and shows that the system performance in terms of channel estimation mean square error (MSE) is very close to the Cramer-Rao bound (CRB), even when only two received blocks are available. Another important theoretical problem, namely the signal richness preservation problem, is also studied. Signal richness is an essential property for input signals in subspace-based blind channel estimation algorithms studied in this thesis. This property, however, may be altered by a linear precoder. Necessary and sufficient conditions for a linear precoder to preserve signal richness are explored. Several relevant interesting mathematical problems are also studied.