Iterative LMMSE detection techniques in single- and multi-carrier communication systems

Abstract

Over the past two decades, wireless communication systems have experienced phenomenal growth. Tremendous research effort has been devoted, and many important developments have been made. The following emerging techniques may particularly have a significant impact on the future development of wireless communications: Ÿ turbo and low-density parity-check (LDPC) coding, Ÿ multi-input and multi-output (MIMO), Ÿ iterative multi-user detection (MUD), Ÿ multi-carrier transmission, and Ÿ single-carrier transmission with frequency domain equalization (FDE). Inspired by the success of turbo codes, the so-called turbo principle has been employed in joint signal detection and decoding to suppress various interferences such as intersymbol interference (ISI), multi-user interference (MUI), and cross antenna interference (CAI), which are the main impediments to reliable communications. The optimal signal detection is realized based on the maximum a posterior (MAP) principle, which usually involves prohibitive complexity. To overcome this problem, sub-optimal linear detection based on the linear minimum mean-square error (LMMSE) principle has been widely studied to achieve a good tradeoff between performance and complexity. This method was originally developed for MUD in code-division multipleaccess (CDMA) systems. It has been later applied to many other problems, e.g., equalization in ISI channels. The existing results related to iterative LMMSE detection principles are mostly aimed at specific applications, and so there is lack of a unified framework. Moreover, high complexity is still an issue for many existing LMMSE algorithms. The primary objectives of this thesis are to establish a unified framework of iterative LMMSE detection and to investigate computationally efficient solutions in various communication systems. The unified framework of iterative LMMSE detection is established based on a general coded linear system model that can characterize coded single-carrier, multi-carrier, MIMO, and multiple access systems. We will show that the key problem lies in properly handling extrinsic information exchange between two processors: one for binary codes and one for channel effects. The first processor involves the standard a posteriori probability (APP) decoding and we borrow existing research results in this thesis. The second processor, which is the focus of this thesis, is based on the LMMSE principle. We derive a generic LMMSE detector in a very concise matrix form based on the general linear system model and establish a connection between the LMMSE detector for a binary system and the LMMSE estimator for the Gaussian companion of the binary system, which provides the basis for efficient implementation of the LMMSE detector in various communication systems. We first consider systems with sparse system transfer matrices. A typical example is a system with a band-limited ISI channel matrix. Two approaches are discussed: the first one is a recursive extending window approach based on Cholesky factorization, which is more computationally efficient but without performance compromise compared with existing sliding window approaches. The second approach is based on factor graph techniques. We derived a vector form factor graph representation for ISI channels to which the recently proposed Gaussian message passing (GMP) techniques can be applied in order to efficiently realize the LMMSE detector. Compared with the existing approaches, this approach is very suited for parallel processing due to its intrinsic parallel architecture based on which a hybrid schedule can be flexibly adjusted according to the available hardware resources and system delay tolerance. For systems with non-sparse transfer matrices, both Cholesky factorization and graph approaches encounter high complexity problem. A typical example is a system with long ISI channel memory. We develop a solution in this case by transforming the system transfer matrix into a circulant matrix using the cyclic prefixing (CP) technique. This is motivated by orthogonal frequency-division multiplexing (OFDM) and FDE techniques. We will show that an LMMSE detector for a system with a circulant transfer matrix can be efficiently realized using the fast Fourier transform (FFT) technique. In this thesis, particularly, we combine the conventional single-carrier interleave-division multiple-access (IDMA) with the CP technique and apply the general framework to it. The recently proposed OFDM-IDMA scheme can be also regarded as the application of the general framework to multi-carrier IDMA. We show that the LMMSE detection (i.e., MUD) in the above schemes can be efficiently realized with complexity independent of the length of channel memory and the number of users, and their performance can be analyzed using an SNR-variance evolution technique. We also give a comprehensive comparison of OFDM-IDMA, OFDM-CDMA and OFDMA (for orthogonal frequency-division multiple-access), and demonstrate the advantages of OFDM-IDMA. Although the CP technique can greatly reduce the detection complexity for systems with dense transfer matrices, the overhead due to CP results in both power and spectral efficiency loss. We develop a solution to the problem of power efficiency loss based on a zero padding (ZP) technique. We particularly apply the ZP technique to both singleand multi-carrier IDMA schemes. We also compare the ZP-based schemes with the CPbased schemes, and demonstrate the potential advantages of the former in convergence speed and power efficiency. ZP also requires the use of guard intervals as CP. Therefore, both ZP and CP suffer from the same problem of spectral efficiency loss. This loss can be considerable in the case of rapid time-varying ISI channels with long memory (such as underwater wireless channels). We solve this problem by removing the guard intervals and demonstrate that, even without them, transmitted signals can still be efficiently detected by the circulant matrix-based LMMSE detectors using a block segmentation technique and a proposed ZP reconstruction technique to handle the interference between consecutive blocks. In summary, this thesis presents a generic LMMSE detector that can be applied to a wide range of wireless communication systems. Efficient computation techniques to implement the LMMSE detector are developed. Transmission schemes such as single and multi-carrier CP/ZP techniques, which can greatly facilitate the implementation of the LMMSE detector, are also investigated. We believe that the results of this thesis will be useful for the development of future wireless communication systems.