Study On Lattice Theory Based MIMO Detection Techniques

By transmitting multiple data streams in parallel through wireless channels with rich multipath,Multi-Input Multi-Output(MIMO)spatial multiplexing technique can significantly improve the spectrum efficiency without requiring additional bandwidth or transmit power,and therefore becomes one of the enabling technologies for future wireless communication systems to achieve high-speed data transmission.Low-complexity highperformance signal detection technology at the receiver side is the key to MIMO system implementation.By constructing unimodular coefficient matrices using the Lattice Reduction(LR)technique from the lattice theory and transforming the actual channel matrices into equivalent ones with better orthogonality,low-complexity linear and successive interference cancelation(SIC)detection schemes can achieve the same diversity gain as the optimal Maximum-Likelihood(ML)detection.The recently proposed IntegerForcing(IF)receiving technique further reveals that under the same detection architecture,some potential performance gain can be brought about by relaxing the constraint on the coefficient matrices to full-rank integer matrices.Focusing on this class of detection techniques,researches are carried out in this thesis to construct coefficient matrix extraction algorithms that have reasonable computational complexities and at the same time,ensure optimal or near-optimal detection performances.The main results achieved are as follows.Firstly,based on the algebraic and geometric interpretations of the dual of complex lattices,the relationships between the coefficient matrix optimization problems and the dual lattice of the channel matrix are achieved for uncoded MIMO systems as follows:When linear detection is employed,the optimal coefficient matrix can be obtained by exactly solving the Successive Minima Problem(SMP)of the dual lattice of the channel matrix,and by performing Complex Minkowski(CMinkowski)reduction under the unimodular matrix constraint.However,when SIC detection is employed,the coefficient matrix obtained by performing Complex Korkine-Zolotareff(CKZ)reduction to the dual lattice of the channel matrix is the optimal under either the full-rank integer or the unimodular constraint.Secondly,by decomposing SMP of a real-valued lattice into a series of subspace avoiding problems(SAPs),and by decomposing SMP of a complex-valued lattice into a series of SAPs of its isomorphic real-valued lattice,two practical algorithms solving SMP exactly for both real-and complex-valued lattices,Algorithm SMPR and Algorithm SMPC,are constructed for the first time in literature.An improved sphere-decoding(SD)algorithm based on the Schnorr-Euchner(SE)enumeration strategy is used to solve SAP in all iterations of both algorithms,and moreover,the initial search radius and the initial search positions of SD in subsequent iterations are optimized by exploiting the intermediate results of SD in the previous rounds.While ensuring the optimal linear detection performance,the computational complexities of the two algorithms can be even lower than the suboptimal Minkowski reduction algorithm.Thirdly,an efficient CKZ reduction algorithm for complex lattices,Algorithm CKZRED,is developed,and a blockwise modification is made to CKZ reduction and a ComplexBlock-KZ(CBKZ)reduction algorithm,Algorithm CBKZ-RED,is constructed by restricting each reduction operation within a local reduction block.Both algorithms adopt as building blocks Algorithm Csvp,a complex-domain SD algorithm based on an on-demand two-dimensional complex-plane SE enumeration,as well as Subroutine CTransform,which expands new bases by unimodular matrix transforming.Algorithm CKZ-RED employs Algorithm Partial-CLLL,a partial Complex Lenstra-Lenstra-Lov?asz(CLLL)reduction,as the preprocessor in each iteration,while Algorithm CBKZ-RED performs sorted Gram-Schmidt Orthogonalization(GSO)and size reduction in succession before all iteration for preprocessing.Algorithm CKZ-RED can achieve significant computational complexity reduction compared with the KZ reduction algorithm while ensuring the optimal SIC detection performance.On the other hand,Algorithm CBKZ-RED,whose computational complexity is about two orders of magnitude lower than Algorithm CKZRED,and even lower than CLLL reduction who has polynomial complexity,can ensure close-to-optimal performance.Fourthly,an efficient CMinkowski reduction for complex lattices,Algorithm CMINRED,is constructed for the first time,and in addition,a relaxation is proposed to CMinkowski reduction and a CMinkowski-Relax reduction algorithm,Algorithm CMIN-RELAX,which restricts the search of basis vectors within sub-lattices,is also developed.In each iterations of both algorithms,Algorithm Partial-CLLL-M,another partial CLLL reduction algorithm,is employed for preprocessing,Algorithm CMin-Search,a complex-domain SD algorithm developed on the basis of Algorithm Csvp,is employed for basis vectors search,and Subroutine CTransform is again employed for basis expansion.Algorithm CMIN-RED can achieve near-optimal linear detection performance while largely reduce the computational complexity compared with the Minkowski reduction algorithm.On top of this,Algorithm CMIN-RELAX can further bring significant computational complexity reduction while cause almost no performance loss.All the above algorithms except Algorithm SMPR work on complex lattices,and thus allow the receiver to perform detection directly to the complex-valued baseband system model.As a result,these algorithms can not only save the computational cost while guaranteeing the optimal or near-optimal detection performance,but also bring more freedom to the design of the signal modulation constellation.