Presentation Date: April 16, 2009. LRA Detection. 林忠良. Harmoko H. R. 魏學文. Prof. S-W Wei. Outline. System Model Conventional Detection Schemes Lattice Reduction (LR) LR Aided Linear Detection Simulation Results Conclusions. System Model.
System model of a MIMO system with M transmit and Nreceived antennas
where H=[h1,…,hM], representing a flat-fading channel
Since ML requires computing distances to every codeword to find the closest one, it has exponential complexity in transmission rate.
Take form of , where A is some matrix
Q(.) is a slicer
Zero forcing detector
Minimum mean square estimator (MMSE) detector
The transmitted vector can be estimated by
where is the extended channel matrix and is the extended received vector
к(H) = σmax/σmin ≥1
where σmax = largest singular value
σmin= smallest singular value
Definition 1 (Lenstra Lenstra Lovasz reduced ):
A basis with QR decomposition is LLL reduced with parameter , if
for all 1 ≤ l < k ≤ M … (1)
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.
OUTPUT: a basis which is LLL-reduced with parameter δ, T satisfying
Block diagram of conventional ZF detector
Block diagram of LR-ZF detector with shift & scale operation included at Receiver
*LRA: Lattice Reduction Aided
Transformed into contiguous integer and also include origin
Describe the same transmitted signal
shift & scale
Using the extended model, LR-MMSE detector can be expressed as
 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.
 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.