研究生： 指導教授： Student ： Advisor ： LRA Detection 魏學文 林忠良 Harmoko H. R. Prof. S-W Wei Presentation Date: April 16, 2009

Outline System Model Conventional Detection Schemes Lattice Reduction (LR) LR Aided Linear Detection Simulation Results Conclusions /04/16

System Model 2009/04/16 3 where H=[h 1,…,h M ], representing a flat-fading channel System model of a MIMO system with M transmit and N received antennas  The received signal vector y can be represented as

Conventional Detection Schemes Maximum likelihood (ML) detector Since ML requires computing distances to every codeword to find the closest one, it has exponential complexity in transmission rate. Linear detector Take form of, where A is some matrix Q(.) is a slicer Zero forcing detector  A = H + where (.) + is pseudoinverse operation Problem: ZF performance suffer dramatically due to noise enhancement if H is near singular /04/16

Minimum mean square estimator (MMSE) detector  A = ( H H H + σ n 2 I ) -1 H H The transmitted vector can be estimated by where is the extended channel matrix and is the extended received vector 5 Conventional Detection Schemes 2009/04/16 and

Lattice Reduction A complex lattice is the set of points If we can find a unimodular transformation matrix T that contains only integer entries and the determinants is det(T)=±1, then will generates the same lattice as the lattice generated by The aim of lattice reduction is to transform a given basis H into a new basis with vectors of shortest length or, equivalently, into a basis consisting of roughly orthogonal basis vectors /04/16

Lattice Reduction To describe the impact of this transformation, we introduce the condition number : к( H ) = σ max /σ min ≥1 where σ max = largest singular value σ min = smallest singular value Usually, is much better conditioned than H, therefore leads to less noise (interference) enhancement for linear detection, this is the reason why LR can help the detector to achieve better performance. Lenstra-Lestra Lovasz (LLL) reduction algorithm can help us finding the transformation matrix T /04/16

LLL Algorithm 8 With the help of QR decomposition, the basis matrix H becomes H =QR, where Q is unitary and R is upper triangular Each vector h k is represented by The basis vector h k is nearly orthogonal to subspace spanned by h 1, …, h k-1, if the entries R 1,k, …,R k-1,k are small compared to R k,k 2009/04/16

LLL Algorithm 9 Definition 1 (Lenstra Lenstra Lovasz reduced ): A basis with QR decomposition is LLL reduced with parameter, if for all 1 ≤ l < k ≤ M … (1) and for all 1 ≤ l < k ≤ M. … (2) The parameter δ (1/2 < δ < 1) trade off the quality of the lattice reduction for large δ, and a faster termination for small δ. and 2009/04/16

LLL Algorithm 10 OUTPUT: a basis which is LLL-reduced with parameter δ, T satisfying 2009/04/16

LRA Linear Detection 11 Block diagram of conventional ZF detectorBlock diagram of LR-ZF detector with shift & scale operation included at Receiver *LRA: Lattice Reduction Aided 2009/04/16

LRA Linear Detection 12 Transformed into contiguous integer and also include origin  Shift and scale operation: Example:  The received signal vector is expressed as 2009/04/16

LRA Linear Detection 13  Lattice reduction aided zero forcing (LR-ZF): shift & scale  The received signal vector can be rewritten as Describe the same transmitted signal 2009/04/16

LRA Linear Detection 14  Lattice reduction aided MMSE (LR-MMSE): Using the extended model, LR-MMSE detector can be expressed as 2009/04/16

Simulation Results /04/16

Conclusions Various MIMO detection methods that make use of lattice reduction algorithm are discussed. It is also shown that LRA detection perform much better than other conventional linear detector /04/16

References 17 [1]D. Wubben, R. Bohnke, V. Kuhn, and K. D. Kammeyer, “ Near- maximum-likelihood detection of MIMO systems using MMSE- based lattice reduction, ” in Proc. 39th Annu. IEEE Int. Conf. Commun. (ICC 2004), Paris, France, June 2004, vol. 2, pp [2]H. Vetter, V. Ponnampalam, M. Sandell, and P. A. Hoeher, "Fixed Complexity LLL Algorithm," Signal Processing, IEEE Transactions on, no. 4, vol. 57, pp , April, /04/16

References 2016/2/20 18 THANK YOU