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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.

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lra detection

Presentation Date: April 16, 2009

LRA Detection


Harmoko H. R.


Prof. S-W Wei

  • System Model
  • Conventional Detection Schemes
  • Lattice Reduction (LR)
  • LR Aided Linear Detection
  • Simulation Results
  • Conclusions
system model
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

conventional detection schemes
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.
conventional detection schemes1
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


lattice reduction
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.
lattice reduction1
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.
lll algorithm
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)


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.


lll algorithm1
LLL Algorithm

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

lra linear detection
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

lra linear detection1
LRA Linear Detection
  • The received signal vector is expressed as
  • Shift and scale operation:


Transformed into contiguous integer and also include origin

lra linear detection2
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

lra linear detection3
LRA Linear Detection
  • Lattice reduction aided MMSE (LR-MMSE):

Using the extended model, LR-MMSE detector can be expressed as

  • 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.

[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.