A New Approach to Beamformer Design for Massive MIMO Systems Based on k-regularity Gilwon Lee Dept. of Electrical Engineering KAIST Joint work with Juho Park, Youngchul Sung and Junyeong Seo GLOBECOM 2012 Workshop LTE-B4G, Dec. 3, 2012

Massive MIMO Systems Massive MIMO is an emerging technology, which scales up MIMO by an order of magnitude. Antenna arrays with a few hundred elements. Massive MIMO Rate↑ Transmission reliability↑ Energy efficiency↑

Practical Issues on Massive MIMO Antenna elements: cheap. But, the multiple RF chains associated with multiple antennas are costly in terms of size, power and hardware. The number of RF chains is restricted in massive MIMO systems.

System Model Single user massive MIMO BS MS Assumptions (1) (2) (3) RF chain RF chain Assumptions (1) The size of antenna array at the MS is limited (2) (3) due to hardware constraint.

The Conventional Method: Antenna Selection At transmitter RF chain RF chain RF chain Antenna selection: M RF chains select M different antennas out of the NT available transmit antennas. Hardware Complexity↓

The Conventional Method: Antenna Selection At transmitter RF chain RF chain Antenna Selection RF chain However, the performance of antenna selection should be far interior to that of a method using all of transmit antennas. Especially, the gap of performance will be increasing as NT increases.

The Proposed Scheme: k-regular Beamformer At transmitter RF chain RF chain Antenna Selection RF chain k-regular beamformer RF chain

The Proposed Scheme: k-regular Beamformer Specifically RF chain k-regular beamformer k-regular beamformer: Each of the M data streams is multiplied by k complex gains and assigned to k out of the available NT transmit antennas and signals assigned to the same transmit antenna will be added to be transmitted.

The Proposed Scheme: k-regular Beamformer For example, Each column of V has k=2 nonzero elements. ⇒ k-regularity or k-sparse constraint But, how to design the matrix V?

Problem Formulation Data k-regular streams beamformer Channel k-regularity Problem) k-regular constraint power constraint Assumptions M independent data stream transmission with equal power for each stream There is no power amp in k-regular beamformer

Observations In combinatorial approach, (brute search) Impossible to implement should be required to find optimum V Need an algorithm to reduce complexity!

Observations Without k-regular constraint, the optimal transmit beamforming matrix V is given by where (SVD) is i-th column of The matrix is called eigen beamforming matrix Based on this fact, we can propose a method to design k-regular beamformer.

The Maximum Correlation Method A simple way to design k-regular BF matrix: to approximate the eigen beamforming matrix of H under k-regular constraint Maximum correlation method (MCM) ⇒ Pick k largest absolute values in v and let other values be zeroes. After then, normalize it Very simple, Systematic ⇒ Possible to analyze Heuristic ⇒ Performance loss

The Relaxed Problem Original Problem -norm relaxation of k-regular constraint ⇒ where How can we solve the relaxed problem?

Iterative Shrinkage Thresholding Algorithm For a convex function ⇔ < Iterative Shrinkage Thresholding Algorithm (ISTA) > Shrinkage operator Gradient method where Here,

Iterative Shrinkage Thresholding Algorithm ⇔ If we directly apply ISTA to our problem

Iterative Shrinkage Thresholding Algorithm ⇔ If we directly apply ISTA to our problem without the power constraint, Shrinkage operator for i-th column vector where

Projected ISTA (PISTA) With the power constraint, Projected ISTA (PISTA) Metric projection of vector i-th column onto B

Projected ISTA (PISTA) The Projected ISTA for k-regular Beamformer Design 0. (Initialization) Generate randomly 1. (PISTA) Update 2. (Stop criterion) If 3. (Hard-thresholding) For update, update, 4. (Power adjusting) For

Simulation Results Antenna selection scheme: Parameters:

Simulation Results k-regular beamformer scheme: Parameters: 200% gain Antenna Selection gain 200%

Simulation Results k-regular beamformer scheme with varying k Parameters: eigen BF gain Antenna Selection gain with small k

Simulation Results Distribution of antennas over numbers of connections Parameters: 89% 69% 44% 28% A large portion of antennas are not connected to signals for small k

Simulation Results

Conclusion Proposed k-regular beamformer architecture Proposed PISTA and MCM to design k-regular beamforming Enable system designers to choose optimal trade-off their hardware constraint and required rate performance showed that the proposed k-regular BF significantly improves the rate gain over simple antenna selection