LRA Detection

1. Presentation Date: April 16, 2009 LRA Detection 林忠良 Harmoko H. R. 魏學文 Prof. S-W Wei

2. Outline • System Model • Conventional Detection Schemes • Lattice Reduction (LR) • LR Aided Linear Detection • Simulation Results • Conclusions

3. System Model System model of a MIMO system with M transmit and Nreceived antennas • The received signal vector y can be represented as where H=[h1,…,hM], representing a flat-fading channel

4. 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.

5. Conventional Detection Schemes Minimum mean square estimator (MMSE) detector • A = ( HHH + σn2I )-1HH The transmitted vector can be estimated by where is the extended channel matrix and is the extended received vector and

6. Lattice Reduction • A complex lattice is the set of points • If we can find a unimodulartransformation 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.

7. Lattice Reduction • To describe the impact of this transformation, we introduce the condition number : к(H) = σmax/σmin ≥1 where σmax = largest singular value σmin= 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.

8. LLL Algorithm 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

9. LLL Algorithm OUTPUT: a basis which is LLL-reduced with parameter δ, T satisfying

10. LRA Linear Detection Block diagram of conventional ZF detector Block diagram of LR-ZF detector with shift & scale operation included at Receiver *LRA: Lattice Reduction Aided

11. LRA Linear Detection • The received signal vector is expressed as • Shift and scale operation: Example: Transformed into contiguous integer and also include origin

12. LRA Linear Detection • The received signal vector can be rewritten as Describe the same transmitted signal • Lattice reduction aided zero forcing (LR-ZF): shift & scale

13. LRA Linear Detection • Lattice reduction aided MMSE (LR-MMSE): Using the extended model, LR-MMSE detector can be expressed as

14. Simulation Results

15. 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.

16. References [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. 798-802. [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. 1634-1637, April, 2009.

17. References THANK YOU