Citation
Liu, ChihHao (2013) Transceiver Designs and Analysis for LTI, LTV and Broadcast Channels  New Matrix Decompositions and Majorization Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2VFFSZ70. https://resolver.caltech.edu/CaltechTHESIS:05282013115316389
Abstract
Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multipleinput multipleoutput (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrixvector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the pointtopoint MIMO transceiver design problems.
In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear timevarying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmitreceive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.
The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semiunitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.
In the second part of the thesis, we focus on MIMO transceiver design for slowly timevarying MIMO channels with zeroforcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly timevarying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the timevarying channels is not exploited. Based on the GTD, we develop spacetime GTD (STGTD) for the decomposition of linear timevarying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed STGTD, we develop spacetime geometric mean decomposition (STGMD) DFE transceivers under the zeroforcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each spacetime (ST) block (which consists of several coherence blocks), and the average per STblock BER in the moderate high SNR region. Moreover, the STGMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each STblock. In general, the newly proposed transceivers perform better than the GGMDbased systems since the superimposed temporal precoder is able to exploit the temporal diversity of timevarying channels. For practical applications, a novel STGTD based system which does not require channel prediction but shares the same asymptotic BER performance with the STGMD DFE transceiver is also proposed.
The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (minpower) with a total bitrate constraint and perstream BER constraints. The second problem is the rate maximization problem (maxrate) with a total transmit power constraint and perstream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the minpower and maxrate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.
Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFTFBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFTFBT such that the SINR at the receiver is maximized. Also, a novel pilotaided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasistationary multipath Rayleigh fading channels. Using the concept of a difference coarray, the new technique can construct M^2 copilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  MIMO, Transceiver, GTD, DFE 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Electrical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  21 May 2013 
Record Number:  CaltechTHESIS:05282013115316389 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:05282013115316389 
DOI:  10.7907/2VFFSZ70 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7758 
Collection:  CaltechTHESIS 
Deposited By:  ChihHao Liu 
Deposited On:  29 May 2013 20:36 
Last Modified:  04 Oct 2019 00:01 
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