A Physical Interpretation of Beamforming, BLAST and SVD Algorithms Ada Poon, Bob Brodersen

Physical Interpretation? Under “certain” channel conditions, in a wireless system with N users, a base-station with M = N + K receive antennas can separate the N transmitted signals as well as achieve K + 1 degrees of diversity for each transmitted signal. (Jack Winters et al, 1994)

Physical Interpretation SU M = 3 N = 2 users K = 1 Array Processing SU BS

Physical Interpretation SU M = 3 N = 2 K = 1 Array Processing SU BS

Physical Interpretation … means the radiation patterns at the transmitter and receiver resulting from the array processing algorithms SU M = 3 N = 2 K = 1 Array Processing SU BS

Beamforming & Antenna Diversity Beamforming focuses the energy from the antenna Enables a high gain steerable antenna Increases SNR Diversity provides redundancy Enabled by spatial interleaving of signals Decreases the fluctuations in SNR

Line-of-sight Channel Array Processing where i is the mean angle of arrival from user i to base-station.

Single-user, Single-receive Antenna where A is the path gain( or loss) and  is the path delay. Narrowband baseband equivalent: where .

Single-user, Multiple-receive Antennas d where  is the mean angle of arrival and . Vector form: where a() is the normalized array response vector.

Multiple-user, Multiple-receive Antennas Array Processing Summing over all the users, the received signal vector is

Continued … Matrix form:

Beamforming Beamforming solution: Example: In N users, a base-station with M = N + K receive antennas can separate the N transmitted signals as well as achieve K + 1 degrees of diversity for each transmitted signal Example:

Beamforming: Radiation Pattern Array Processing

Beamforming: Radiation Pattern Array Processing

Multi-transmit, Multi-receive Antennas Array Processing

Multi-transmit, Multi-receive Antennas Array Processing Array Processing

Adding Reflector Array Processing Array Processing

Adding Reflector Vector form: Array Processing Array Processing Vector form: where ar() and at() is the normalized array response vector at the receiver and the transmitter , respectively.

More Reflectors 1st path 2nd path Array Processing Array Processing 3rd path Summing over all the multipaths, the received signal vector is

Continued … Matrix form: Multipath is not enemy but friend for capacity enhancement

Example

Radiation Pattern: Beamforming 1st path, a1 = 1 Array Processing Array Processing 2nd path, a2 = 0.6

Radiation Pattern: Beamforming 1st path, a1 = 1 Array Processing Array Processing 2nd path, a2 = 0.6

QR Decomposition (BLAST) QR decomposition of H:

Continued … Therefore, Successive Decoding and Cancellation:

Radiation Pattern: QR Decomposition 1st path, a1 = 1 Array Processing Array Processing 2nd path, a2 = 0.6

Radiation Pattern: QR Decomposition 1st path, a1 = 1 Array Processing Array Processing 2nd path, a2 = 0.6

Singular Value Decomposition (SVD) Singular value decomposition of H: MIMO technology !!!

Radiation Pattern: SVD 1st path, a1 = 1 Array Processing Array Processing 2nd path, a2 = 0.6 Multipath is not enemy but friend for capacity enhancement

Radiation Pattern: SVD 1st path, a1 = 1 Array Processing Array Processing 2nd path, a2 = 0.6 Multipath is not enemy but friend for capacity enhancement

Summary Beamforming at receiver BLAST (layered space-time coding) 1 transmit antenna and M receive antennas BLAST (layered space-time coding) N transmit and M receive antennas Beamforming and diversity gain at receiver SVD (Singular value decomposition) Beamforming and diversity gain at both receiver and transmitter