1. Sphere Decoding Algorithm for MIMO Detection Arslan Zulfiqar

2. Motivation  Future mobile applications include  Mobile TV  High Speed Internet  Future wireless systems need to provide  High Data Rate  High Quality of Service (QoS)  Key challenges  Hostile propagation environment  Bandwidth is a limited resource  How do we meet these challenges?  Multiple-Input multiple-output (MIMO) systems

3. Motivation contd.  How can MIMO help?  Spatial Multiplexing  Diversity  MIMO has been proposed in modern wireless standards  IEEE 802.11n  IEEE 802.16e (WiMax)  3GPP LTE  Tradeoff: Increased complexity of the decoder!

4. Problem Formulation  Simple model of a communication system: Channel TX vector RX vector Estimate Channel MIMO Decoding M complex symbols to be transmitted M transmit antennas N receive antennas M decoded symbols How do we do this?

5. Problem Formulation contd.  First, convert the problem involving complex quantities to one that involves real quantities dimensions scale by 2.  Optimal ML solution= Model Dimensions

6. ML solution  How do we compute ?  Brute force search  Search over all  Smart search: Sphere decoding algorithm  This algorithm finds a subset of that lie in a sphere around

7. Experiment  64-QAM constellation  QAM alphabet set = ={-7,-5,-3,-1,1,3,5,7}  4x6 MIMO system  SNR considered:  15dB,18dB,20dB  Inputs to MIMO decoder:  received vector  channel matrix

8. Experiment: Brute Force Search  ML equation:  Total number of possibilities for ~16 minutes!

9. Experiment: Sphere Decoding Algorithm  ML equation:  Proposed by Fincke and Pohst  Pick a radius such that, d

10. Experiment: Sphere Decoding Algorithm

12. Optimizations  Parallel tree traversal  Look ahead transformation  Schnorr-Euchner modification