Research On The Distribution Characteristics Of GSVD And Its Applications In MIMO Precoding

Generalized singular value decomposition(GSVD)is a generalization of singular value decomposition(SVD),which can diagonalize two matrices simultaneously.As the wide use of SVD in the field of multiple input multiple output(MIMO)precoding,GSVD has also been widely used in the design of MIMO precoding schemes.The GSVD-based MIMO precoding schemes have two advantages:The efficient construction methods for GSVD enable the GSVD-based MIMO precoding schemes to have low complexity and high efficiency;On the other hand,since GSVD can diagonalize two channel matrices simultaneously,the GSVD-based MIMO precoding schemes can transform the complicated MIMO broadcasting channel into parallel single input single output(SISO)broadcasting channels,thus,the receiver can decode the signal in each SISO channel independently,which decreases the complexity of signal processing in MIMO broadcasting systems.Therefore,the design and performance analysis of GSVD-based MIMO precoding schemes is one of the hot research topics.This dissertation focuses on the two-user MIMO downlink scenario.The design and performance analysis of GSVD-based MIMO precoding schemes in this scenario are investigated.The main work is as follows.1)The distribution characteristics of GSVD for arbitrary dimension complex Gaussian matricesFirst,tke distribution characteristics,including the joint probability density function,marginal distribution function and limiting distribution function,of generalized singular values for arbitrary dimension complex Gaussian matrices are characterized.Next,the distribution characteristics of right generalized singular matrix for complex Gaussian matrices are studied,and the expectation of the sum of the squared singular values of this right generalized singular matrix is also figured out.At last,the effect of the non-identically distributed condition on the distribution characteristics of generalized singular values is investigated,and the sufficient and necessary conditions of the generalization of GSVD to more than two matrices are ananlyzed.The main contribution of this work is to establish a relationship between the distribution characteristics of GSVD and the well known Wishart matrix for arbitrary matrix dimensions,which makes it possible to characterize the distribution characteristics of the generalized singular values and right generalized singular matrix for arbitrary dimension complex Gaussian matrices.Moreober,this work also lays the theoretic foundation for performance analysis of GSVD-based MIMO precoding schemes.2)The GSVD-based MIMO precoding schemes without the security constraintFirst,focusing on the MIMO downlink with two users and no security constraint,a GSVD-based MIMO precoding scheme is proposed by combing the Non-orthogonal multiple access(NOMA)with GSVD.Different from the existing MIMO precoding schemes in the considered scenario,the proposed GSVD-NOMA precoding scheme first transforms the complex MIMO broadcasting channel,by utilizing GSVD,into parallel SISO broadcasting channels,then,applies NOMA to the SISO broadcasting channels,which increases the channel utilization efficiency and user fairness.Next,the performance of the proposed GSVD-NOMA precoding scheme are analyzed.The ergodic rate and limiting normalized information rate of users are characterized.Moreover,the performance of GSVD-NOMA and OMA is theoretically compared,and it is also proved that in the high signal to noise ratio(SNR)region,GSVD-NOMA always outperforms the OMA.Finally,computer simulations are provided to show that GSVD-NOMA can outperform QR-NOMA and OMA no matter the performance metric is user fairness or user sum rate,and GSVD-NOMA can approach DPC performance upper bound when the number of transmit antennas is large.3)The GSVD-based MIMO precoding schemes with the security constraintFor the two-user MIMO downlink with the security constraint,the concepts of common message and private message are introduced to design a new GSVD-based MIMO precoding scheme,which aims to fully utilize each channel.The existing GSVD-based MIMO precoding schemes in the considered scenario try to transmit private messages in the decomposed SISO broadcasting channels where the two users have similar channel gains,which makes the information rates on these SISO channels are extremely small.However,the proposed GSVD-based MIMO precoding scheme in this dissertation,tries to transmit common messages in those SISO channels where the two users have similar channel gains,which increases the information rates significantly.Next,the performance of the proposed GSVD-based MIMO precoding scheme is analyzed,and the ergodic rates of the common message and private message are also characterized.Finally,the performance of the proposed GSVD-based MIMO precoding scheme and OMA scheme is theoretically compare,and it is proved that in the high SNR region,the proposed GSVD-based MIMO precoding scheme outperforms the OMA.