Techniques James s Chen Advisor : Andy Wu Graduate Institute of - PowerPoint PPT Presentation

Introduction to Hybrid Beamforming Techniques James s Chen Advisor : Andy Wu Graduate Institute of Electronics Engineering National Taiwan University Taipei, Taiwan Mar. 31, 2015

Outline Introduction of Precoding Why Hybrid beamforming? Problem Formulation Existing Hybrid Beamforming Technique Summary 2 ACCESS

Introduction of Precoding MIMO System Precoding mitigates channel interference SVD is the optimal method but require higher bandwidth Transmit Receive . . . . . . . . Beamforming Beamforming Precoding Equivalence . . . . . . . . (Precoder) (Combiner) . . . . . . . . Channel Transmit Receive Transmit Receive Transmit Receive Antennas Antennas Antennas Antennas Antennas Antennas Reduce the interference among antennas SVD:H=U Σ V H RX Precoder Channel Decoder Noise σ 1 H σ 1 v 1 H = σ 2 H u 1 u 2 u 3 v 2 V H U H y x V U σ 4 σ 3 H v 3 V H Σ U Feedback link SVD H ( from RX) 3 ACCESS

Why Hybrid beamforming?(1/2) In mmWave scenario, the pathloss is extremely high[3] 30 GHz shows additional about 20 dB loss compared to 3 GHz. High pathloss can be compensated by:  Large antenna array to increase the array gain  Beamforming via precoding Channel is rank deficient Maximum supportable streams are less then the number of Tx antennas BS MS 4 ACCESS

Why Hybrid beamforming?(2/2) Traditional Beamforming is done at BB Requiring one RF chain per transmitting antenna A RF chain consists of a mixer, PA/LNA and DAC/ADC Hybrid Beamforming relies on RF precoding to reduce the number of RF chains[2] Two-staged transmitting (F RF, F BB ) structure 5 ACCESS

Problem Formulation(1/3) Step 1: The optimal solution of the precoding matrix, F opt ,is given by:  F V opt 1 V1 is eigenvectors corresponding to N s largest eigenvalues of H V1 can be acquired from performing SVD on H Step 2: We further realize F opt by hybrid precoder (F RF, F BB ) arg min   Tx Precoding for Hybrid Beamformer ( , ) F F F F F AoD BB RF opt RF BB , F F F CSI RF BB Spatially Sparse Precoding Acquisition SL- SVD V H 1 F F Number of RF chains BB RF can be reduced RF-Chain RF-Chain Baseband Precoder Baseband Equalizer RF Beamformer RF-Chain RF-Chain MIMO Channel …… …… …… …… …… …… …… H RF-Chain RF-Chain …… RF-Chain RF-Chain W F W F RF BB BB RF 6 ACCESS

Problem Formulation(2/3) Step 1: Get the optimal F OPT L The channel matrix H[3]: N N         * MS BS BS MS ( ) ( ) H a a U V  l MS l BS l L  l 1 𝐶𝑇 ) is the AOD of active path : a BS ( ɵ 𝑚   2 2   BS   BS sin( ) ( 1 ) sin( ) j d j N d   l BS l   BS T ( ) [ 1 , ,..., ] a e e BS l F opt =V 1 can be formed by linear combinations of a BS (ɵ l ) Tx Precoding for Hybrid Beamformer AoD ( θ CSI BS BS a ) Spatially Sparse Precoding Acquisition BS 1 SL- SVD V H 1 F F BB RF ( θ BS a ) BS 2 RF-Chain RF-Chain ( θ BS a ) Baseband Precoder Baseband Equalizer BS 3 RF Beamformer RF-Chain RF-Chain MIMO   1 Channel …… …… …… …… …… …… ……    2  BS j d sin( ) MS H 3   e   RF-Chain RF-Chain    ……   RF-Chain RF-Chain  2 W   F W BS F ( 1 ) sin( )  j N d  RF BB BB BS  3 RF   e 7 ACCESS

Problem Formulation(3/3) Step 2: Separate F opt into(F BB ,F RF ) arg min Tx Precoding for Hybrid Beamformer   ( , ) F F F F F AoD BB RF opt RF BB CSI , F F F Spatially Sparse Precoding Acquisition SL- SVD RF BB V H 1 F F BB RF Due to spatial sparsity, this is RF-Chain RF-Chain Baseband Precoder Baseband Equalizer RF Beamformer RF-Chain RF-Chain equivalent to solve an MIMO Channel …… …… …… …… …… …… …… H RF-Chain optimization problem RF-Chain …… RF-Chain RF-Chain F W W F RF BB BB RF 1      F BB F RF T T T T BS BS BS BS Acan [ a ( ) , a ( ) , a ( ) ,..., a ( ) ]  BS 1 BS 2 BS 1 BS L L N t Choose best Nrf columns to form F RF , ~ and then Find F BB       L N N L N t N A C F C ( θ BS V C s a ) s t B BB BS 1 1 can S ( θ BS a ) BS 2 ( θ BS a ) BS 3   1    2  BS sin( ) j d  3 Nt: Number of Tx antennas   e M  Nrf: Number of RF chains   Ns: Number of Tx data streams F RF  L: Number of Active Path S    2   BS ( 1 ) sin( )  j N d  F BB BS  3   e 8 ACCESS

Existing Hybrid Beamforming Technique (I) (1/2) [3] Use Orthogonal Matching Pursuit(OMP) to calculate (F BB ,F RF ) Perform Nrf iterations of correlation to find F RF Perform pseudo-inverse to fine F BB ~       N L L N N t N F C A C V C t s s BB 1 can Nt: Number of Tx antennas F RF Nrf: Number of RF chains L: Number of Active Path Ns: Number of Tx data streams F BB 9 ACCESS

Existing Hybrid Beamforming Technique (I) (2/2) Hybrid precoding shows near optimal spatial efficiency while compared with traditional baseband precoding Spatial efficiency: the data rate that can be transmitted over a given bandwidth (units: bit/s/Hz)  Formula:    1 * * * * * log (| |) R I R W W HF F F F H W W 2 N BB RF RF BB BB RF RF BB N s n s [3] 10 ACCESS

Problem 1: Impractical Candidate Matrix Impossible to get all AOD’s information 1      BS T BS T BS T BS T 1 [ a ( ) , a ( ) , a ( ) ,..., a ( ) ] Acan  BS 1 BS 2 BS L 1 BS L N t Require large bandwidth to return all AOD’s information from Rx Need a candidate matrix without the information of All AOD ~      ( θ BS  L N N L BS a ) N t N F C A C V C s t s BS 1 BB 1 can ( θ BS a ) BS 2 ( θ BS a ) BS 3   1    2  MS BS Nt: Number of Tx antennas sin( ) j d  3 F RF   e Nrf: Number of RF chains    L: Number of Active Path  Ns: Number of Tx data streams    2   BS j ( N 1 ) d sin( )   3 BS  F BB   e 11 ACCESS

Problem 2: High Complexity Optimization Algorithm Long computation time for finding (F BB ,F RF ) OMP need Nrf iterations Need an faster algorithm with less iterations Pseudo-inverse is not suitable for HW implementation Computational complexity: 𝑃(𝑜 3 ) Need an algorithm without pseudo-inverse ~       L N N L N t N F C A C V C t s s BB 1 can Nt: Number of Tx antennas F RF Nrf: Number of RF chains L: Number of Active Path Ns: Number of Tx data streams F BB 12 ACCESS

Existing Hybrid Beamforming Technique (II) (1/3) For problem 1, a DFT codebook is used Predefined set: Consist of orthogonal column vectors  Don’t require all AOD’s information  Possibly find all Nrf columns using only 1 iteration Equally space 360 degree with Nt angles to form a full rank matrix  Hence Acan has Nt columns ~     N t N   N t N A C N t N V C t s F C s can 1 BB ( θ BS B a ) BS 1 S ( θ BS a ) BS 2 ( θ BS a ) BS 3   1    2 M F RF  BS sin( ) j d  3   e  Nt: Number of Tx antennas S    Nrf: Number of RF chains    Acan: DFT codebook 2 Ns: Number of Tx data streams   BS ( 1 ) sin( )  j N d  F BB BS  3   e 13 ACCESS

Existing Hybrid Beamforming Technique (II) (2/3) For problem 2, OBMP with DFT codebook is used instead of OMP with Acan1 ~     N N   N N V C A C N N t s t t F C t s 1 can Constraints: Acan must be orthogonal BB Using 1 iteration to find (F BB ,F RF ) No pseudo-inverse F RF F BB Algorithm : Othogonality-Based Matching Pursuit Require : F opt 1: F = F OPT res 2: Ψ = A * F can res  * 3: k = {n | n is the largest N index of ( ) } , RF l l (k) 4: F = A RF can * 5: F = F F BB RF opt F BB 6: F = N BB s F -F F opt RF BB 7: return F , F RF BB 14 ACCESS

Existing Hybrid Beamforming Technique (II) (3/3) OBMP’s computation time for finding (F BB ,F RF ) is less then that of OMP by 89.6% when Nrf equals 8 89.6% 15 ACCESS

Summary Advantage of hybrid beamforming Reduce the number of RF chains but remain near optimal performance Design goal of hybrid beamforming arg min   ( , ) F F F F F BB RF opt RF BB , F F F RF BB Method for finding (F BB ,F RF ) OMP[3] OBMP Number of iteration Nrf 1 Complexity High Low Constraints None Orthogonal Acan 16 ACCESS